Individuals differ widely in their contribution to the spread of infection within and across populations. Three key epidemiological host traits affect infectious disease spread: susceptibility (propensity to acquire infection), infectivity (propensity to transmit infection to others) and recoverability (propensity to recover quickly). Interventions aiming to reduce disease spread may target improvement in any one of these traits, but the necessary statistical methods for obtaining risk estimates are lacking. In this paper we introduce a novel software tool called SIRE , which allows for the first time simultaneous estimation of the genetic effect of a single nucleotide polymorphism (SNP), as well as non-genetic influences on these three unobservable host traits. SIRE implements a flexible Bayesian algorithm which accommodates a wide range of disease surveillance data comprising any combination of recorded individual infection and/or recovery times, or disease diagnostic test results. Different genetic and non-genetic regulations and data scenarios  were simulated to validate SIRE and to assess their impact on the precision, accuracy and bias of parameter estimates. This analysis revealed that with few exceptions, SIRE provides unbiased, accurate parameter estimates associated with all three host traits. For most scenarios, SNP effects associated with recoverability can be estimated with highest precision, followed by susceptibility. For infectivity, many epidemics with few individuals give substantially more statistical power to identify SNP effects than the reverse. Importantly, precise estimates of SNP and other effects could be obtained even in the case of incomplete, censored and relatively infrequent measurements of individuals’ infection or survival status, albeit requiring more individuals to yield equivalent precision. SIRE represents a new tool for analysing a wide range of experimental and field disease data with the aim of discovering and validating SNPs and other factors controlling infectious disease transmission. i.e. the relative risk to become infected when exposed to infectious individuals or material, (ii) “infectivity”, i.e. the propensity to transmit infection to others when infected, and/or by (iii) improving “recoverability”, i.e. the propensity to recover. However, to date it is impossible to assess how these three key epidemiological traits controlling disease transmission in a population are regulated by specific genes or interventions, as the necessary statistical methods for estimating genetic and non-genetic effects from available disease surveillance data don’t exist.Effective approaches to reduce the spread of infectious disease transmission in populations are urgently needed. Reduction in disease spread is most effectively achieved by reducing, separately or in combination, individual (i) “susceptibility”, This paper introduces a novel statistical method that can estimate, for the first time, genetic and non-genetic effects for host susceptibility, infectivity and recoverability simultaneously from a wide range of realistic disease surveillance data. The method has been incorporated into a user-friendly, freely available software tool called SIRE. SIRE can be applied to a range of experimental and field data and will help to move disease control significantly forward by simultaneously targeting multiple host traits affecting infectious disease spread. In the era of rapid expansion in the human population resulting in increasing demands on food security, effective solutions that reduce the spread of infectious diseases not only in humans, but also in plants and livestock, are urgently needed. Failure of stringent biosecurity measures ,2 and emThe advent of genome wide high density single-nucleotide polymorphism (SNP) chip panels has already led to a remarkable range of discoveries regarding the genetic regulation and biology of diseases and translation towards innovative therapeutics . In agrie.g.[susceptibility, the relative risk of an uninfected individual to become infected when exposed to a typical infectious individual or infectious material excreted from such an individual, infectivity, the propensity of an individual, once infected, to transmit infection to a typical (average) susceptible individual, and recoverability, the propensity of an individual, once infected, to recover or die) [Epidemiological models are widely used to identify risk factors for disease spread in populations. Indeed, modelling disease transmission in genetically heterogeneous populations is well established see e.g.,12). Par. Pare.g. or die) ,14. As d or die) . However or die) , remarka or die) ,19. In p or die) –22. Thise.g. infected or not) may not only depend on its own susceptibility and recoverability genes, but also on the infectiousness of other individuals in the same contact group, i.e. their infectivity and recoverability genes [In many conventional genome-wide association studies (GWAS) , target ty genes . This coThe motivation behind this paper is to introduce new statistical and computational methods that utilise information derived from observation of epidemics and trait interdependence to estimate, for the first time, genetic and other systematic effects for all three underlying epidemiological host traits. This requires combining statistical, epidemiological and genetic modelling principles. Analysis of incomplete epidemic data to draw inferences on epidemiological parameters is well established ,26. Howeet al. [i.e. they are determined by a large number of genes, each with small effect). This approach, however, does not incorporate genetic variation in recoverability, and does not estimate SNP effects. An alternative approach, based on the assumption that susceptibility and infectivity are controlled by two single bi-allelic genetic loci [i.e. discarding potentially useful information from the infection and recovery times themselves). It also failed to incorporate variation in recoverability, and relied on a number of simplifying assumptions which were found to produce biased estimates under certain circumstances. A variant of this approach [i.e. SNPs affecting more than one epidemic trait. This seems unrealistic, since, for example, SNPs that control within host pathogen replication may also lower the risk that infection can establish, i.e. reduce susceptibility, and simultaneously reduce pathogen shedding and hence infectivity, and speed up recovery.Alternative approaches have focused on disentangling susceptibility from infectivity effects. For example, Anacleto et al.  developetic loci ,32, usedapproach , which aapproach –33 is the.g. sex, breed or vaccination status) on host susceptibility, infectivity and recoverability from temporal epidemic data. This approach can be applied to a wide range of epidemic data, collected at the level of individuals, and accounts for different types of uncertainty in a statistically consistent way (e.g. censoring of data or imperfect diagnostic tests), and permits the incorporation of prior knowledge. We validate SIRE for a variety of simulated epidemic scenarios, comprising not only the ideal case in which infection and recovery / death times of each individual are known exactly, but also under more realistic scenarios in which epidemics are only partially observed.In this study we present a software tool called SIRE  that implements a novel Bayesian inference approach to simultaneously estimate the effects of a single SNP (importantly capturing any pleiotropy), together with that of other fixed effects .e.g. by the unintentional spread of infected material, or the introduction of an infected individual from elsewhere). For simplicity it is assumed that throughout the observation period groups are closed, i.e. no births, migrations, or transmission of disease between groups. This assumption generally holds for experimental studies and also for most common field situations, where a movement ban is imposed after disease notification [In the context of disease transmission experiments in plants or livestock, epidemics are initiated by means of artificially infecting a proportion of “seeder” individuals which go on to transmit their infection to susceptible individuals sharing the same contact group. In field data contact groups may consist of animal herds, or any group of individuals sharing the same environment such as a pasture, pen, cage or pond, and infection is assumed to invade the group by some external, usually unknown, means (fication .j (i.e. the probability per unit time of becoming infected) is given by λj(t) = βI(t), which is the product of an average transmission rate β and I(t), the number of infected individuals at time t. To incorporate individual-based variation in host susceptibility and infectivity, this simple expression for λj(t) is replaced by an individual force of infection , fi characterises the corresponding quantity for individual i’s infectivity, and the sum in Eq . The term Gz in Eq . Whilst variation in Gz may be small for a well-controlled challenge experiment, this may not be the case in real field data. Gz is assumed to be a normally distributed random effect with standard deviation σG. The exponential dependencies in Eq . This mean recovery time is expressed asrm describes the fractional deviation from this for individual m. This approach is taken to allow the recovery probability distribution to adopt a more biologically realistic profile compared with the exponential distribution often assumed  are decomposed into the following contributionsFollowing standard quantitative genetics theory , the indAA, AB and BB. The SNP contribution to the traits for individual j depends on j’s genotype in the following way:The model assumes that a specific locus defined by a SNP  plays an important contribution to the trait values . Assuming a diploid genomic architecture with biallelic SNP implies three SNP genotypes: ag, af and ar capture the relative differences in trait values between AA and BB individuals, and are subsequently referred to as the “SNP effects” for susceptibility, infectivity and recoverability, respectively . The scaled dominance factors Δg, Δf and Δr characterise the trait deviations between the heterozygote AB individuals and the homozygote mean  [The parameters ue of 0) .X and fixed effect vectors bg, bf and br in Eq . Following convention, an additional fixed effect is added to account for trait mean, which is explicitly chosen to ensure the population averages of g, f and r are zero .The design matrix br in Eq  allow foε =  accounts for all other contributions to the traits . We assume that for each individual the three trait residuals are drawn from a single multivariate normal distribution with zero mean and 3×3 covariance matrix Σ. Including these correlations is important because it allows for the possibility that, for example, more susceptible individuals may also, on average, be more infectious and recover at a slower rate . Note that in this study, which focuses on the estimation of SNP effects, there is no explicit distinction between random genetic and environmental effects, although the model could be extended to incorporate estimation of these polygenic effects. It is thus assumed that individuals are randomly distributed across the groups with respect to the genetic effects on the epidemiological traits not captured by the model. Also note that Eq . We denote the complete set of infection and recovery event times for all individuals as ξ over the observed duration of the epidemics [y will be problem dependant. For example, in some instances recovery or removal (e.g. due to death) times will be precisely known but infection times completely unknown. In other instances infection and recovery times will both be unknown, but results from disease diagnostic tests provide information regarding disease status at particular points in time. The framework presented in this paper is flexible to these various possibilities.Based on the description above, the model contains the following set of parameters: θ =  on the parameters θ is expressed in terms of the force of infections λj in Eq . Here the notation j∈z indicates that j goes over all those individuals j in contact group z, and e∈Ez indicates that e goes over all events Ez. The force of infection λj is calculated immediately prior to individual j becoming infected. The gamma distributed probability density function FΓ for recovery events gives the probability an individual is infected for duration δtm given a mean duration wm and shape parameter k. The time dependent total rate of infection events Λz in contact group z immediately prior to event time te is given bys in group z at that time.The functional dependence of λj in Eq  and meanwm in Eq , which t r in Eq . The propidemics , m goes An important point to mention is that Eq  is calcuy being considered. To account for the prior assumption that residuals ε in Eq (G in Eq (π(θ) can be decomposed into-ε,G includes all parameters with the exception of ε and G andThe state of knowledge prior to data  ε in Eq  are multT is a three dimensional vector giving the residual contributions to the susceptibility, infectivity and recoverability of j. Σ is a 3×3 covariance matrix . Finally, the product z in Eq  is largely uninformative but does place upper and lower bounds on many of the key parameters to stop them straying into biologically unrealistic values (details are given in The default prior for θSamples for θ and ξ from the posterior are generated by means of an adaptive Markov Chain Monte Carlo (MCMC) schemes which implements optimised random walk Metropolis-Hastings updates for most parameters and posterior-based proposals  to aid ftheITEAM.github.io/SIRE.html  or the GitHub repository github.com/theITEAM/SIRE. An easy to use point and click interface allows for data tables to be imported in a variety of formats and graphical outputs are dynamically displayed as inference is performed. The core of SIRE utilises efficient C++ code and allows for running MCMC chains on multiple CPU cores. The manual for SIRE theITEAM.github.io/manual.pdf gives a detailed description of how the software is used and how results are interpreted.SIRE is a desktop application that implements the Bayesian algorithm outlined above. It is freely available to download from SIRE takes as input any combination of information about infection times, recovery times, disease status measurements, disease diagnostic test results, genotypes of SNPs or any other fixed effects :This represents the best case scenario for inferring parameter values. For example, appearance of symptoms or visual or behavioural signs may indicate the onset of infection, and recovery/removal times are given by the time of death.Often “recovery” in compartmental SIR models represents the death and removal of individuals. Consequently DS2 is pertinent to cases in which the only measurable quantity is the time at which individuals die. For example, disease challenge experiments in aquaculture routinely record time of death rather than infection times, which are usually difficult to measure .Whilst less common than DS2, in some instances data provides information regarding when individuals become infected but not when they recover. For example in human epidemics, patients may go to the doctor when they become ill, but no records will be kept on when they recover.DS4 represents the most common scenario for monitoring infectious disease spread in livestock or plant populations, where each individual is periodically checked to establish its disease status. Under DS4 the point at which epidemics start is usually unknown, as well as the infection and recovery times of individuals themselves. However the diagnostic test results place constraints on these quantities. For example, if an individual is found to be uninfected at one sampling time and infected at the next sampling time this means that infection must have occurred at some point in the intervening period .e.g. animal welfare), even though epidemics have not completely died out.This data scenario relates to situations in which epidemics are not observed over their entire time period. For example a disease transmission experiment being carried out may be terminated early, due to cost or other factors (In this section we apply SIRE to simulated datasets in order to 1) test the extent to which the inferred posterior parameter distributions agree with their true values, and 2) investigate how the precision, accuracy and bias of inferred model parameters depends on the type of data available.Initially the focus of results will be on DS1  and later in section 3.5 consideration is given to DS2-5.We first demonstrate the performance of SIRE assuming complete information of individuals’ infection and recovery times, for a representative but complex set of parameters with regards to the genetic and non-genetic regulation of the three epidemiological host traits. Subsequently we investigate how these results change under different parameter and data scenarios.Ngroup different contact groups, with each group containing Gsize individuals. The SNP under investigation was assumed to be in Hardy-Weinberg equilibrium [A allele frequency of p = 0.3. For the effect sizes we used the values ag = 0.4, af = 0.3, ar = -0.4, representing a relatively large pleiotropic effect . The choice of Δg = 0.4, Δf = 0.1, Δr = -0.3 for the scaled dominance factors represents partial, but not strong, dominance of either the A or B allele. For simplicity we included only a single fixed effect, e.g. sex, of arbitrary moderate size bg0 = 0.2, bf0 = 0.3, br0 = -0.2 with individuals in the population randomly selected to be male or female. The residual variances were chosen to be Σgg = Σff = Σrr = 1, corresponding to a large variation in traits between individuals . In line with the direction of the SNP effects, the covariances were chosen to be Σgf = 0.3, Σgr = -0.4 and Σfr = -0.2, representing a potential scenario in which individuals that are more susceptible are also more infectious and recover at a slower rate and vice-versa). To accommodate variation in epidemic speed across groups, we set the standard deviation in the normally distributed group effects to σG = 0.5. Finally, the average transmission rate was chosen to be β = 0.3/Gsize  and an average recovery rate γ = 0.1 with shape parameter k = 5 (corresponding to the infection duration being relatively highly peaked around a mean of 10 time units).Individuals were randomly assigned into ilibrium  with an Ngroup = 1 with Gsize = 50 individuals is shown in AB and BB individuals remain uninfected at the end of the epidemic. The absence of AA individuals partly stems from natural stochasticity in the system, but also partly from the fact that ag = 0.4 is positive, i.e. AA individuals are more susceptible to disease and so on average less likely to remain uninfected. Consequently we can link the genetic composition in the final state of the epidemic to the expected value for ag . Over and above information from the final state, however, there is much to be gained from also accounting for the infection and recovery event times themselves. The Bayesian approach adopted in this paper utilises all this information to extract the best available parameter estimates.Simulated epidemic data was generated by means of a Doob-Gillespie algorithm  modifiedNgroup = 20 contact groups, each containing Gsize = 50 individuals. The infection and recovery event times from this simulation were then used as input data into SIRE (scenarios in which infection and recovery times are not known precisely are discussed later in section 3.5).The information content from a single epidemic is generally insufficient to estimate the large number of parameters in the model. Therefore we next simulated a more realistic dataset (using the same parameter set as above) made up of 1000 individuals split into k is wide, it is clearly able to discount the possibility of an exponential recovery duration (i.e. k = 1), which has a very low posterior probability, over a more peaked distribution (i.e. k>1).The recovery rate γ has the greatest precision , followed by the transmission rate β. Whilst the distribution for the shape parameter ar is highly peaked around its true value of -0.4  and secondly the recovery processes is gamma distributed which has a smaller standard deviation than the more dispersed Poisson process governing infection. The infectivity SNP effect af in does lie within the 95% posterior credible interval (which goes from -0.35 to 2.1) means that no certain association with infectivity can be made in this particular example. The estimated recovery SNP effect  of -0.4 . ImportaCompared to the SNP effects themselves, precision of the scaled dominance parameters is relatively poor, and actually reduces as the size of the SNP effects goes down, which makes sense in the limit of zero SNP effect size, because here no information about dominance is available. Estimating them accurately, therefore, either requires very large SNP effects or substantially more data.Since SNP effects are also a type of fixed effect, the same comments as above also apply for other fixed effects.–Interestingly, it was possible to obtain relatively good estimates for elements in the residual covariance matrix. Again, the familiar pattern is observed whereby quantities related to recoverability are more precisely estimated than those related to susceptibility, with infectivity the least precise. Finally, the variance of the group effect could be estimated with similar precision as that for susceptibility .x-axis. Plots in which most crosses lie near to the diagonal line imply that inference is able to accurately capture the true parameter values. f for which prediction accuracy was only 34%, prediction accuracies for all other parameters ranged from 69–99%. In line with the discussion above, parameters associated with recoverability have generally higher predication accuracies than those associated with susceptibility, which are again higher than those for infectivity.The previous section showed an illustrative example for a particular parameter set. Here we assess what happens when different parameters in the model are altered. This was achieved by means of taking the following “base” set of parameters others) . Fig 4 sy-intercept and slope values are shown in y-intercept and a slope of one indicate absence of bias. Whilst the majority of observed y-intercepts tended to be very small, the slope for some of the parameters is markedly less than one (most notably for Δf). The reason for this is as follows. When Bayesian analysis reveals insufficient information regarding a parameter, its distribution follows that of the prior . Therefore, the slopes of less than one in Bias indicates systematic differences between the true parameter values and those inferred from the data. Bias was measured by fitting regression lines through the posterior means in e.g. the average SDs in R0 is large such that most individuals become infected. Cases in which only a fraction of individuals become infected lead to a reduction in this optimum, but this reduction is typically small under most realistic scenarios.From the point of view of this paper, the probability distributions which are of greatest interest are the SNP effects. Noting the sizes of the error bars across e.g. group size, number of individuals per group and allele frequency, and then go on to consider how observations of the system influence what can be learned.Consequently, the remainder of this paper focuses on investigating how SNP effect estimates are affected by contact group structure and the nature of the measured data using this base set of parameters. We focus first on outlining the behaviour with respect to key design features, Gsize within each contact group (here Ngroup = 10 contact groups are assumed). The SD in ag reduces as the number of individuals in each contact group Gsize increases , as illustrated by that black dashed line in Gsize×Ngroup = 100 individuals are needed to make associations for recovery SNP effects . A very different state of affairs, however, is observed in af poorly estimated, but also its precision does not markedly improve even when the number of individuals in each contact group Gsize is substantially increased.The crosses in ncreases . ImportaGsize and fixing the number of contact groups Ngroup, we now fix Gsize = 10 and vary Ngroup. Results for this are shown in ag and ar, but crucially we find the SD in the infectivity SNP effect af now also scales with the familiar line of slope -½. The reason for this behaviour lies in the fact that infectivity is an indirect genetic effect, i.e. an individual’s infectivity SNP affects the disease phenotype of group members rather than its own disease phenotype [A alleles consistently experience epidemics which are faster than those with fewer A alleles, this provides evidence that the A allele confers greater infectivity than the B allele . Because information about the infectivity SNP effect comes from epidemic-wide behaviour, it is expected to scale linearly with the number of contact groups Ngroup . Lastly, ar is largely independent of Gsize. This is because recovery is solely an individual-based process, and so happens independently of others sharing the same contact group .Finally, we investigate the case in which we fix the total number of individuals to A allele frequency p = 0.3 in the population. p, which in turn changes the Hardy-Weinberg equilibrium frequencies for the three genotypes. We find that the SD curves are symmetric around a minimum of p = 0.5 and remain remarkably flat over a large region, . They oup paper .This section shows results from the various data scenarios introduce in section 2.4, in which the infection and recovery times of all individuals are not known precisely:ag and af relate to the infection process, naïvely it might be expected that because infection times are unknown then nothing can be inferred about these SNP effects. This section, however, clearly demonstrates this not to be the case. The reason lies in the fact that whilst infection times are latent variables, the distribution from which they are sampled is informed by the available recovery data through the likelihood in Eq . The number of individuals per group needed to identify an association for a susceptibility SNP effect of ag = 0.4 is now Gsize = 80 . However the SD for the recovery SNP effect ar is much larger, meaning that little can be inferred regarding SNP-based differences in recoverability. This is because under DS3 the only indirect information regarding recovery times comes from the very early stages of each epidemic . This explains why SDs for recovery SNP effects decrease at a rate of -½  as the number of contact groups Ngroup increases . We see that statistical power only marginally reduces even when disease diagnostic checking is performed on a similar timescale as the epidemics as a whole. This result is perhaps surprising and reflects the fact that most information comes from general patterns of behaviour rather than specific timings of events. One reason is because infection times are so open to stochastic variation  and so the knowledge that a particular individual gets infected at a particular time holds very little value. It is only when one considers collections of individuals and sees patterns that inferences can be made .Because knowledge of precise timings is not vital it means that insights obtained using perfect data (DS1), as explored in sections 3.1–3.4 , remaini.e. only the initial and final states of the epidemic are observed). Unfortunately it was found to be difficult to probe this regime using SIRE due to mixing problems arising in the MCMC algorithm [The limit on the right hand side of lgorithm  (principThe results here emphasise the fact that even relatively infrequent disease status checks provide useful data from which accurate inferences regarding SNP effects can be drawn.tend (subsequent to which no further data is available). We find that very little information is lost when restricting tend to around the average recovery time 〈tR〉. This is largely because most individuals recover before 〈tR〉 as a consequence of a small number of individuals having very low recoverability . Given that 〈tR〉 is usually substantially less than the total epidemic time, from a practical point of view terminating disease transmission experiments prior to the end of the epidemic when no new infections occur, (and perhaps performing further replicates) may be beneficial. However, the effectiveness of this approach would depend on a large assumed variation in recoverability in the population, which a priori may be unknown.In tstart after the start of the epidemic up until its termination. This scenario may apply to field outbreaks, where sampling occurs only after notification of the outbreak. Here again we see a reduction in statistical power with increasing tstart, but this reduction is not substantial until around the average infection time. This result is surprising, but it turns out that whilst none of the events before tstart are actually measured , the disease status of all the individuals at tstart can be accurately inferred  and this encapsulates almost the same amount of information as when the event times are precisely known.It should be noted that the data scenarios DS1-5 considered are not comprehensive. Any combination of infection time, recovery time, disease status data and diagnostic test results can be used as inputs into SIRE. Furthermore SIRE accounts for additional uncertainties in cases in which data is missing on some individuals and where diagnostic tests are imperfect.The availability of dense genome-wide SNP panels has revolutionized human medicine and has paved the way for genetic disease control in agriculture. With declining genotyping costs, discovery of new disease susceptibility loci has increased exponentially over recent years, and evidence for their effective utilization in personalized medicine and livestock and plant breeding programmes continues to emerge –56. HoweIn this paper we developed a Bayesian methodology to allow for simultaneous estimation of SNP effects for host susceptibility, recoverability and infectivity from temporal epidemic data. As well as considering uncertainty in the model parameters themselves, our methods do not require infection or recovery times to be known; these are treated as latent variables that represent the underlying dynamics of the system. Whilst computationally demanding, this approach offers for the first time the possibility to estimate and disentangle different host genetic effects underlying disease transmission from experimental or field data without making simplifying assumptions that can lead to biased or spurious results.The methodology was validated with data from simulated epidemics, which were also used to assess how different parameter values and data scenarios representing different recording schemes in field or experimental studies may affect the estimates of SNP effects and other parameters influencing transmission dynamics. The sophisticated Bayesian algorithm outlined in this paper has been implemented into a user-friendly software tool called SIRE, which allows computationally efficient analyses to be performed by anyone with relevant epidemiological data  yields SNP effects with high precision, given sufficient data. Lastly, precise estimates of SNP effects could still be obtained with censored epidemic data.Our results indicate that it is possible to obtain simultaneous unbiased estimates of SNP effects for all three epidemiological host traits, in addition to that of other fixed or random effects influencing disease transmission, from temporal epidemic data. Across simulated data scenarios we found that recoverability SNP effects are generally (with few exceptions) easiest to identify, followed by susceptibility and then infectivity SNP effects. In the latter case a large number of contact groups with few individuals provide much more information than the reverse. Simulations of different data scenarios representing optimal (perfect and complete data) and practically feasible recording schemes produced the following relevant insights: firstly, even when only recovery (or death) times of individuals are known inference of SNP effects is still possible, albeit requiring around four times as many individuals to gain equivalent precision as for perfect data. Secondly, only knowing infection times marginally reduces statistical power to detect SNP effects for susceptibility and infectivity, but recovery SNP effects become difficult to detect. Thirdly, when data consists of periodic measurements of individuals’ disease status it was found that even relatively infrequent measurements (i.e. pleiotropy), but with different allele substitution effects and different modes of dominance. Furthermore, we assumed that the traits are also influenced by other fixed effects, have large residual variance (introducing much noise into the system) and are correlated, and that environmental group effects influence the within-group transmission dynamics. This choice represents an extremely challenging system in which to estimate SNP effects and in practice most real world examples are likely to be considerably less challenging as simpler structures and reduced variation/better control of variation will improve the quality of the parameter estimates.For model validation, we chose a complex inter-dependence structure for the model parameters by assuming that the SNP under consideration is associated with all three epidemiological host traits  of SNP effect estimates, and group size or number of groups . For the.g. for mastitis, bovine Tuberculosis, and other infectious diseases [We chose a dataset comprising of 1000 individuals partly because of computational efficiency but also because generating datasets of this size seems feasible for transmission experiments in plants and most domestic livestock species, in particular aquaculture species ,59,60. Hdiseases –63 alreadiseases ,65, the i.e. regulated by many genes each with small effect, and hence that SNPs with large effect on disease phenotypes are the exception rather than the norm [e.g. pathogen entry, replication or shedding affecting susceptibility, recoverability or infectivity, respectively, may be higher [It is widely recognised that disease traits are for the most part polygenic, the norm ,62. Thise higher . Therefoe higher . Hence, e higher ,68. In ce higher ,48,69. TThe approach developed in this study and integrated into SIRE complement and succeed previous studies that aimed to develop statistical methods for estimating genetic effects for the different host epidemiological traits ,29–31,33e.g. surviving infectious challenge are less likely to become infected (i.e. less susceptible), or more prone to surviving infection (e.g. due to better recoverability), and also less prone to transmitting infection, once infected (i.e. less infective). From an epidemiological perspective, SNPs with favourable pleiotropic effects on all three host epidemiological traits are highly desirable for preventing or mitigating disease spread [Many disease challenge experiments and field studies have identified SNPs with moderate to large effects on measurable disease resistance phenotypes ,55,70. He spread . In contFurthermore, although this paper focused on estimating SNP effects, SIRE could also immediately be applied to estimating breed, age, sex, treatment or vaccination effects, or any other factor that may affect disease spread, even if genetic information is absent.A allele frequency p across groups, a follow up paper [af, without the need for large numbers of epidemic contact groups .One of the potential practical limitations for accurately estimating infectivity SNP effects is that they require a large number of epidemic groups. Previous work has shown that experimental designs can have a significant impact on the precision and accuracy with which model parameters can be estimated . In parup paper  will shoA tool such as SIRE that can accurately estimate the effects of single SNPs on hitherto inaccessible epidemiological traits presents an important first step towards creating a statistically consistent scheme for performing GWAS on epidemiological traits using potentially incomplete data. GWAS, however, typically contains additional features beyond the scope of the simple single SNP analysis presented here. In particular, the current software focuses on one SNP at a time for estimating genetic effects for susceptibility, infectivity and recovery, but ignores the contributions of other genes on these traits. In the current model design these are incorporated into the residual effects. This simplifying assumption may have little impact for appropriately designed transmission experiments, but may lead to biased estimates of SNP effects if genetically similar individuals are not randomly distributed across groups Click here for additional data file.S2 Appendix(PDF)Click here for additional data file.S3 Appendix(PDF)Click here for additional data file.S4 Appendix(PDF)Click here for additional data file.S5 Appendix(PDF)Click here for additional data file.S6 Appendix(PDF)Click here for additional data file.S7 Appendix(PDF)Click here for additional data file.S8 Appendix(PDF)Click here for additional data file.S9 Appendix(PDF)Click here for additional data file.S10 Appendix(PDF)Click here for additional data file.S11 AppendixInformation for users of the software tool.(PDF)Click here for additional data file.


Recognizing that family data provide unique advantage of identifying rare risk variants in genetic association studies, many cohorts with related samples have gone through whole genome sequencing in large initiatives such as the NHLBI Trans-Omics for Precision Medicine (TOPMed) program. Analyzing rare variants poses challenges for binary traits in that some genotype categories may have few or no observed events, causing bias and inflation in commonly used methods. Several methods have recently been proposed to better handle rare variants while accounting for family relationship, but their performances have not been thoroughly evaluated together. Here we compare several existing approaches including SAIGE but not limited to related samples using simulations based on the Framingham Heart Study samples and genotype data from Illumina HumanExome BeadChip where rare variants are the majority. We found that logistic regression with likelihood ratio test applied to related samples was the only approach that did not have inflated type I error rates in both single variant test (SVT) and gene-based tests, followed by Firth logistic regression that had inflation in its direction insensitive gene-based test at prevalence 0.01 only, applied to either related or unrelated samples, though theoretically logistic regression and Firth logistic regression do not account for relatedness in samples. SAIGE had inflation in SVT at prevalence 0.1 or lower and the inflation was eliminated with a minor allele count filter of 5. As for power, there was no approach that outperformed others consistently among all single variant tests and gene-based tests. Family data provide a distinct advantage of detecting rare risk genetic variants associated with human traits. One of the possible reasons for lack of reproducibility in population-based genetic studies of rare variants is heterogeneity, that is, multiple causal rare variants are underlying the disease. Using family samples can increase the presence of the disease predisposing alleles thus has a better chance to detect the association than using unrelated samples.1, RAREMETALWORKER2, EPACTS3, FREGAT4  and seqMeta (https://cran.r-project.org/web/packages/seqMeta/index.html). These software packages use either a relationship coefficient matrix based on pedigree information or a genetic/genomic relationship matrix (GRM) estimated from genotype data to account for relatedness. Those that use a GRM  can additionally account for population stratification.With continuous traits, linear mixed effects model (LME) is the commonly used method for association analyses with related samples implemented in popular software packages such as GCTAFor binary traits, the field is more complex possibly due to the need to deal with computational and separation issues caused by low frequencies in some genotype category and/or event outcome. The aforementioned packages either handle an unrelated subset only, which results in power loss, or use LME and treat binary traits as continuous for fast computing speed, which however produces uninterpretable effect estimate.5. For binary outcomes, RVFam fits a generalized linear mixed effects model (GLMM). Unlike LME, there is no close form solution to the maximum likelihood of GLMM, therefore binary trait association analyses using RVFam/GLMM take more time than using LME.We have developed RVFam that provides tools for analyzing three types of traits: continuous, binary and survival measured in family samples6. However, such score statistic can be inflated when applied to rare variants. Recently Zhou et al.7 proposed Scalable and Accurate Implementation of Generalized mixed model (SAIGE) that uses the saddle point approximation to calibrate the distribution of score test statistics to better handle extremely unbalanced data. It reduces computational and memory cost by utilizing strategies such as the average information restricted maximum likelihood algorithm and replacing the spectral decomposition with the preconditioned conjugate gradient method to solve linear systems and avoid the need of inversing GRM.Additional tools for binary outcomes have emerged in recent years that tried to address the computational and separation issues caused by low frequencies in some genotype category and/or event outcome. GMMAT  fits GLMM with a GRM and derives a score statistic for association analyses which is faster than the maximum likelihood method9 was proposed to resolve the separation issue by adding a penalty for sparsity on the likelihood of a logistic regression. It has been shown that Firth logistic regression maintained a valid type I error when applied to rare variants analyses in unrelated samples10. Note Firth logistic regression does not account for relatedness and population structure. However, population structure can be controlled by adjusting for principal components of variance-standardized relationship matrix estimated using genome-wide data in association testing as is also the practice of other methods which we compared in this study. Here we are interested in examining its performance on both unrelated and family samples.Firth logistic regression11), rare-variant transmission disequilibrium test (RV-TDT12), rare-variant generalized disequilibrium test (RV-GDT13), and a rare-variant association test for affected sibships14. The family based methods use within family information to control for population stratification and can be used for association analyses of binary phenotypes measured on families. However these family-based methods may be less powerful compared to population based methods when the latter are able to control for population stratification through covariate adjustment. In this study, we focus on the population based methods.In this paper, we perform extensive simulation studies to compare RVFam, GMMAT, seqMeta, EPACTS-q.emmax (LME treating binary traits as continuous), logistic regression with likelihood ratio test (LRT), Firth logistic regressions and SAIGE. These approaches are population based as opposed to family based methods such as family based association tests  is an R package/wrapper for rare variants analysis with family data that can be applied to continuous, binary or survival traits5. For binary traits, RVFam uses GLMM with a logistic link by calling the glmer function in lme4 R package. Users can choose a gene-based test from either a collapsing burden test15, a Madsen and Browning’s burden test16 or a sum of squares (SSQ) test17 in addition to single variant test (SVT). RVFam reports p-values from LRT except for the SSQ test that is a chi-square test. When a convergence issue occurs in estimating the variance–covariance matrices of the random effects in the glmer function call , RVFam catches warning messages returned from lme4 and provides a remark. Even though the warning messages do not necessarily imply incorrect glmer fitting, the resulting regression coefficients may not be reliable.RVFam (https://github.com/lin-lab/GMMAT) is an R package that uses a logistic mixed model with a GRM to account for population substructure and relatedness in genetic association studies of binary traits6. GMMAT also has a component for analyzing continuous traits. Gene-based tests including burden tests and sequence kernel association test18 (SKAT) are available in addition to SVT. GMMAT is the component for binary traits in GENESIS  R package available on the Analysis Commons, a cloud-based computing platform, for National Heart, Lung, and Blood Institute’s TOPMed project.GMMAT , is a software implemented for efficiently controlling for unbalanced case–control ratios, sample relatedness and population stratification for genome-wide association study (GWAS) of large sample sizes. SAIGE uses saddle point approximation to control for case–control imbalance in a logistic mixed effects model and reports score test results7. Advanced optimization techniques are used in SAIGE and their efficiency is seen in its applications to UK Biobank data of 408,961 white British samples. Burden test and SKAT are also available in SAIGE.SAIGE,  is an R package that can be used for individual study analysis and meta-analysis, and it can be applied to continuous, binary and survival traits using unrelated samples, with exception of continuous traits that can be applied to family data using LME. For binary outcomes, seqMeta uses logistic regression. Burden tests and SKAT are implemented in addition to SVT.seqMeta (9. The approach is implemented in logistf R package (https://cran.r-project.org/web/packages/logistf). We created a function for gene-based tests and SVT using Firth logistic regression implemented in logistf R package based on RVFam’s binary traits component. Theoretically both GLM and Firth logistic regression (denoted Firth test) are only applicable to unrelated samples as they do not account for relatedness.Logistic regression with LRT is carried out using the glm  function in R and is denoted as GLM. Based on RVFam’s binary traits component framework, we implemented a function for SVT and gene-based tests using GLM. Firth logistic regression is proposed to correct asymptotic bias of maximum likelihood estimates and to provide a solution to separation by using a penalized likelihood function3 . Treating binary traits as continuous was seen in some GWAS literatures using popular software that implement LME21. Here we used q.emmax option in EPACTS and treated binary outcomes as continuous.EMMAX (efficient mixed-model association eXpedited), is a component for analyzing continuous traits using LME in EPACTSWe conducted two simulation studies to evaluate the performance of aforementioned methods in terms of type I error rate and statistical power for testing genetic association.22 and simulated phenotypes of 3380 Framingham Heart Study (FHS) Offspring Cohort participants with exome chip data in 1147 pedigrees containing participants from three generation recruitments25. The exome chip data consists of 85% rare variants defined as variants with minor allele frequency (MAF) less than 0.01. Among the 3,380 samples, a subset of 1,868 unrelated samples were identified. We first simulated a QTL and its linked continuous trait using the FHS sample with SOLAR26. The QTL (MAF 0.05) explained 2% of the trait variance (genotypic mean decided by sqrt(0.02/(2 × 0.05 × 0.95)) under an additive model) and the polygenic variance proportion was set to be 25%. With prevalence , genotype relative risk (GRR = 1.5) and the QTL allele frequency, we computed the probabilities of being affected per genotype under an additive model and used them as quantiles to dichotomize simulated continuous traits per genotype group to obtain our binary outcomes. To evaluate type I error rates, 100 replicates of phenotype data were generated and tested for association with all exome chip variants independent of the QTL. For power simulation, as RVFam has a survival component, we simulated a survival trait and took the event variable as our binary trait, so we could evaluate both survival (not included in the present study) and binary components. The survival trait was simulated to follow a Weibull distribution with shape parameter 1 (constant failure rate over time) and scale parameter that incorporated normally distributed random effects and effects of the five selected independent (r2 < 0.0063) QTL with various MAF from the ABO gene that contained 36 variants (4 monomorphisms) in the exome chip data. The MAF, r2 and assigned effect information of the five QTL  are given in Supplementary Table In the first simulation study, we used the real genotypes of 246,670 Single Nucleotide Polymorphisms (SNPs) captured on the Illumina HumanExome BeadChipvg) at 0.25 and 0.5, prevalence (k) at 0.01, 0.05, 0.1 and 0.2, and MAF (p) at 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1 and 0.3, 64 scenarios in total and 10,000 replicates for each scenario. Thus, each vg has 32 scenarios (4 k’s and 8 p’s), each k has 16 scenarios (2 vg’s and 8 p’s) and each p has 8 scenarios (2 vg’s and 4 k’s). Type I error rates were evaluated at significance levels of, 0.05, 0.001 and 5E−6. An inflated type I error rate was claimed when a type I error rate estimate was greater than significance level inferred by a one-sided proportion test.In the second simulation study, we were interested in evaluating the type I error rates of SVT using simulated genotypes and phenotypes based on the same FHS samples. We simulated dichotomized traits similarly as in the first study with two differences: (i) polygenic variance was additionally set to 50%, (ii) a SNP independent of the QTL was simulated to have MAF of 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1 and 0.3, and was tested to estimate type I error rates. That is, we have polygenic variance  estimates were presented in the legend of each QQ plot. Dash line represents the genome-wide significance level for SVT, points above this line represent false positives. SeqMeta, GMMAT and q.emmax identified many false positives at prevalence 0.01, 0.05 and 0.1. SAIGE identified several rare variant (MAC < 3) false signals at prevalence 0.01 with very small p-values that were replaced by 1E-45 for better presentation. At prevalence 0.05, GLM, RVFam, Firth test and SAIGE identified one false positive each. No false positive was detected at prevalence 0.2. Firth (unrelated) test did not identify any false positive. The results agreed with Table As the majority of the exome chip data are rare variants, we applied two minor allele account (MAC) filters to exclude rare variants with MAC not greater than 5 and 10 to see whether this could eliminate the inflated type I error rates in SVT. Table 28 may need to be applied to correct for inflation observed in Firth tests, which may result in a lower power for variants with p-values at the tail of the distribution. As rare variants are the dominant majority in exome chip data, one may apply the correction to rare variants only. When either MAC filter was applied, unlike other approaches that had fluctuating λ estimates at different prevalences, GLM had stable λ estimates very close to 1.We further computed λ in SVT of all replicates at each prevalence for each approach and then made average λ versus prevalence plots Fig. . When noTable th column) and results of replicates without convergence remark (5th column). The convergence issues occurred to rare variants exm792721 and exm792698 and that led to very biased beta estimates. Excluding results with convergence issues, the biases were reduced (5th column). First of all, Firth test applied to related samples consistently had the best precision . For exm792698 , GMMAT gave the closest estimate, followed by seqMeta, Firth tests, GLM and RVFam. For exm792721 , Firth tests gave the closest estimate, followed by GMMAT, seqMeta, GLM and RVFam. While for the other three QTL, RVFam’s were closest to the true beta values, followed by GLM, Firth tests, seqMeta, GMMAT and SAIGE. Estimates from GMMAT and SAIGE were quite similar. Without excluding results with convergence issues, estimates from RVFam and GLM were also similar.Figure We also compared computing efficiency for approaches applied to related samples using a Linux Centos 6.6 cluster with a 2 ten-core 2.6 GHz Intel Xeon E5-2660v3 processor and 256 Gigabytes memory. We used a replicate of simulated data with prevalence 0.2 used in assessing type I error rates in the first simulation study and analyzed chromosome 1 only for SVT and gene-based tests with MAF threshold of 0.05. With a single thread, GLM, Firth test, SAIGE, GMMAT and RVFam took 9.13, 21.15, 15.6, 18.12, and 52.1 minutes.Even though GLM outperformed other methods in maintaining correct type I error rates and computation efficiency, its biased effect estimate in rare variants can lead to biased results in the popular fixed effect meta-analysis. As Firth test was proposed to correct bias, we sought to replace GLM with Firth test in SVT for variants with some MAC threshold. We first computed mean of the effect estimate and its standard deviation of GLM and Firth test applied to related samples with MAC thresholds of 5 and 10 (Supplementary Table 1), unlike the first simulation study where inflation increased when prevalence decreased in most approaches (except for Firth tests that had no inflation), no such trend was observed in all methods. No inflation was seen at MAF 0.0001 in all methods. RVFam and GLM had the same number of scenarios with inflation and did not have inflation at MAF ≤ 0.001, Firth test applied to unrelated samples did not have inflation at MAF ≤ 0.005. Firth test applied to unrelated samples, q.emmax and SAIGE had the least scenarios with inflation, while RVFam and GLM had the most scenarios with inflation (23/64).Table 2), the observation of inflation increased when prevalence decreased was seen in GMMAT, seqMeta and Firth test applied to unrelated samples. RVFam, GLM, both Firth tests and SAIGE had better control on type I error rates compared to GMMAT, seqMeta and q.emmax. RVFam and GLM again had the same number of scenarios with inflation.At significance level 0.001 Table , α2, the3), GLM was the only approach that had no scenario with inflation. In general, more scenarios with inflation were identified when prevalence decreased (as observed in the first simulation study). The observation contradicted results in Table 1). Again, RVFam, both Firth tests and SAIGE had better control on type I error rates compared to GMMAT, seqMeta and q.emmax.At significance level 5E−6  that are not necessarily due to incorrect fitting. However, Fig. The second simulation study demonstrates that for SVT at Bonferroni correction threshold, GLM did not identify any false positives and thus had 0 scenario with inflation, followed by Firth test applied to related samples (1 scenario with inflation), Firth test applied to unrelated samples and RVFam (each with 2 scenarios with inflation) and then SAIGE (4 scenarios with inflation).Based on our simulation results, we recommend a hybrid strategy that uses GLM for gene-based tests and variants with MAC.d > 2 and Firth test otherwise in SVT for rare variant association analyses of binary outcomes with unrelated samples or family data. This strategy provided correct type I error rates, least biased effect estimation, good power and computation efficiency without necessity of filtering out variants. Even though theoretically GLM and Firth test do not account for relatedness in samples, our simulation results showed that they outperformed other approaches like RVFam, GMMAT and SAIGE that account for relatedness in controlling type I error rates when applied to related samples. We think this may be due to (i) the use of LRT, (ii) the fact that the familial correlation of complex binary outcomes is weaker than continuous traits’, and (iii) an appropriate genome-wide significance is used. In the case of population stratification, one can adjust for genetic principal components in association testing.Our study evaluates the statistical performance of approaches applied to binary trait GWAS with family data using exome chip data from the FHS. We believe our results can be generalized to similar datasets. However there are limitations. First, we considered only population based methods that do not adjust for ascertainments, so they may be subject to ascertainment bias if the families were collected from proband(s) instead of randomly sampled, e.g. in cohort studies where sample collection does not depend on the disease status of other family members. Second, there are scenarios that were not considered in the study, e.g. rarer diseases . So we could not assess e.g. whether GLM still have correct type I error rates for rarer diseases that can be considered for much larger sample sizes. In addition, it’s also likely that SAIGE and the hybrid strategy will need a larger MAC/MAC.d filter to avoid false positives.Supplementary Information.


Ncases/Ncontrols = 59,674/316,078) and BP , we find positive genetic correlations of migraine with diastolic BP  and systolic BP , but not pulse pressure . Cross-trait meta-analysis reveals 14 shared loci (P ≤ 5 × 10−08), nine of which replicate (P < 0.05) in the UK Biobank. Five shared loci  are reinforced in gene-level analysis and highlight potential mechanisms involving vascular development, endothelial function and calcium homeostasis. Mendelian randomization reveals stronger instrumental estimates of DBP  on migraine than SBP  and a corresponding opposite effect for PP . These findings support a critical role of DBP in migraine susceptibility and shared biology underlying BP and migraine.Blood pressure (BP) was inconsistently associated with migraine and the mechanisms of BP-lowering medications in migraine prophylaxis are unknown. Leveraging large-scale summary statistics for migraine ( The association between blood pressure (BP) and migraine is poorly understood. Here, the authors explore this relationship using summary-level GWAS data for BP and migraine. Cross-trait meta-analysis reveals shared loci between BP and migraine, while Mendelian randomization suggests that diastolic BP specifically plays a key role in migraine susceptibility. The link between migraine and the vascular system has been substantiated by an array of physiologic and epidemiologic evidence, including migraine comorbidities with other vascular conditions including stroke, coronary artery disease (CAD)2. Recently, additional evidence for vascular involvement in migraine has emerged from genome-wide association studies (GWAS)3. Approximately, 40% (13 of 38) of the genome-wide significant GWAS loci for migraine map near genes with known or suspected vascular functions, including vascular development, endothelial structure, and smooth muscle function. Loci mapping to the END1/PHACTR1, LRP1, and FHL5 genes in particular are shared by migraine and CAD or cervical artery dissection5.Migraine is a chronic intermittent neurological disorder affecting up to 14.7% people worldwide and ranks as the second leading cause of disability, responsible for 5.6% of all years lived with disability6. In contrast to highly consistent associations of increased BP with increased susceptibility to vascular disease, associations of BP with migraine are not consistent7. For example, some studies have found associations between elevated systolic BP (SBP) or diastolic BP (DBP) and lower prevalence of migraine8, whereas some have found inverse associations only for SBP10. One study suggested that migraine was associated with higher DBP but lower SBP11. Still other reports focused on pulse pressure (PP), defined as the difference between SBP and DBP, consistently showed an inverse relationship between PP and migraine11. The relationship is further complicated by longitudinal studies suggesting that migraine may increase the risk of incident hypertension13, whereas BP has been found to be inversely related to onset of headache and migraine14. Regardless, BP-lowering medications notably provide prophylactic benefit for many migraineurs, and the choice of antihypertensive appears to be related to comorbidities, cost, availability, or side effect profile rather than the specific mechanism of BP-lowering16.Blood pressure (BP) has been associated not only with vascular disease but also with migraine17 and local genetic correlation18 between BP measures  and migraine. Additional genetic methods using GWAS summary statistics, including cross-trait meta-analysis19 and transcriptome-wide association study (TWAS)20, may be used to identify specific shared genetic components and pathophysiology between BP and migraine. Finally, instrumental genetic analysis, i.e. Mendelian randomization (MR), may suggest causality and directionality of effects of BP on migraine, or the reverse, i.e. migraine influences on BP21. Therefore, in the current study, we leverage large-scale genetic summary-level data and the preceding genetic methods to gain insight into mechanistic links between BP and migraine.Recently developed but widely accepted genetic methods leveraging only GWAS summary statistics may be used to estimate globalOur analysis identifies positive overall genetic correlations of migraine with DBP and SBP, but not PP, and evidence of local genetic overlap with BP at certain previously identified migraine loci after accounting for multiple testing. Cross-trait meta-analysis reveals shared loci between BP and migraine, some of which are also reinforced in gene-level analysis highlighting potential shared biological mechanisms. In addition, MR shows stronger instrumental estimates of DBP on migraine than SBP. Our results suggest a critical role of DBP in migraine susceptibility and shared biological mechanisms between BP and migraine.rg = 0.11, Wald test P = 3.56 × 10−06) and SBP , but not PP  using linkage disequilibrium (LD) score regression (LDSC)  and MO , whereas SBP was only marginally correlated with MA . Findings for genetic covariance analyzer (GNOVA), which included SNPs with lower minor allele frequency (MAF) than LDSC, were similar with rg of 0.12 , 0.07 , and 0.00  for DBP, SBP, and PP, respectively  between migraine and DBP, and the strongest negative genetic correlation observed at chr19  between migraine and PP  using heritability estimation from summary statistics (ρ-HESS) . The genetic correlation between migraine and SBP was negative in the chromosome 7 region despite being positive across the whole genome  and 7 , which were also significantly correlated for the other BP measures. Results were consistent for these regions with the alternative pairwise traits analysis of GWAS (GWAS-PW) approach  or between lipids and CAD (rg ~ 0.25)22, they nevertheless indicate potential shared genetic etiologies, especially at certain chromosomes or regions, and are therefore worthy of additional investigation into potential mechanisms using cross-trait analysis and expression-trait analysis.Taken together, although the overall genetic correlations between BP traits and migraine were relatively modest compared to more closely related phenotypes, e.g. among psychiatric disorders (PCPASSOC ≤ 5 × 10−08) and suggestive trait-specific significance (PGWAS ≤ 1 × 10−05) for migraine and at least one BP measurement  package. Thirty-three independent loci reached genome-wide significance for combined statistics . Rs62155750 was a significant expression quantitative trait locus (eQTL) for its nearby gene ADRA2B  but not broadly defined headache (P = 0.55 based on SHet statistic) in the replication dataset (Supplementary Table rs1048483 (at chr17p13.3) that was associated with both SBP (PCPASSOC = 9.29 × 10−27 based on SHet statistic) and PP  receptors24. Lead SNP rs6438857  implicating ITGB5 was the only locus that was shared between migraine and all the three BP measurements. ITGB5 encodes a beta subunit of integrin , which is a member of integrin family of heterodimeric transmembrane cell surface receptors and has a role in vascular permeability induced by vascular endothelial growth factor (VEGF) in the systemic circulation25. COL4A1 at chr13q34 was shared between migraine and DBP  as well as PP . COL4A1 encodes a type IV collagen alpha protein, and COL4A1 mutations may present with small vessel disease and stroke, both of which also have migraine as a clinical feature27. TGFB1 at chr19q13.2  was shared between migraine and PP alone and encodes a transforming growth factor-beta 1 protein (TGF-β1) family member.Among the candidate migraine loci, lead SNP PHACTR1, LRP1, and FHL5, were shared between both migraine subtypes and BP while locus rs4141663 implicating ITGB5 was genome-wide significant in cross-trait meta-analysis between MO and BP measurements, but not MA  and BP showed that previous reported migraine loci, including ITGB5, SMG6, ADRA2B, ANKDD1B, and KIAA0040). ITGB5, SMG6, and ADRA2B are described above. Data on ANKDD1B and KIAA0040 were limited, but ANKDD1B was previously suggested to have a shared role between migraine and major depressive disorder (MDD)28. Other gene-level genetic overlap between migraine and BP included genes  that were related to regulation of calcium homeostasis and reactive oxygen species (ROS)30. TWAS genes with independent effects shared by subtypes of migraine and BP were consistent with findings for overall migraine at ITGB5, while identifying additional associations at HMOX2 for MA and BP, and HVCN1 and MANBA for MO and BP  and 1.05  per 10 mmHg increment of DBP and SBP, and 1.09  per 10 mmHg decrement of PP (Table P = 1.01 × 10−10) and PP , but not DBP . All heterogeneity P-values were non-significant (PHEIDI > 0.01) indicating at worst only subtle heterogeneity among retained instruments. In conditional analysis to distinguish effects mediated by DBP from those mediated by SBP, there was an increase in the instrumental association of high DBP on migraine with conditioning on SBP , while an opposite effect of high SBP on migraine with conditioning on DBP . The diverging instrumental effects of DBP and SBP on migraine were also supported by restricting analysis to SNP instruments that were non-significant (P > 0.05) for one measure but highly significant (P < 1 × 10−5) for the other , whereas no significant association was observed for MA after controlling for multiple testing (Table PMR-Steiger < 0.05). Taken together, the instrumental analyses suggest a potential causal role of elevated DBP on migraine susceptibility, whereas conditional on DBP, SBP may be causally protective. These relationships are also reflected in a potential inverse causal relationship between PP and migraine.Finally, we used bi-directional MR instrumental analysis to develop evidence for causality in the relationship between BP and migraine. Genetically instrumented elevated DBP and SBP, and decreased PP were associated with increased risk of having migraine with odds ratios (OR) of 1.20 31. Instrumental associations at these SNPs were directionally consistent with the preceding findings but none was significant alone or in combination , nor was any SNP strongly associated with migraine alone   for one BP trait but non-significant for the other (P > 0.05), SBP was inferred to have stronger effects than DBP on CAD and LAS, for which the effect of DBP was protective as observed in the conditional analysis , dopamine (DA), noradrenalin (NE), substance P, and calcitonin gene-related peptide (CGRP), have all been identified as contributing causally to migraine35, as well as potential therapeutic targets37, and all are related with the α2-adrenergic receptor regulation38. Therefore, our results support the role of α2-adrenergic receptor in migraine mechanisms.Meanwhile, 9 replicating SNPs from cross-trait association analysis as well as 12 genes from TWAS of both migraine and BP suggested potential functions relevant to migraine. The five loci identified in both SNP and TWAS analysis revealed potential shared biological mechanisms in migraine and BP regulation involving vascular development and endothelial function, neurogenic inflammation, calcium homeostasis through proteins encoded by 39. This suggests that different mechanisms may underlie BP associations with migraine compared to CVD. Thus, observational associations of migraine with cardiovascular events likely do not involve BP-based etiology in a trivial way, a conclusion further supported by the larger MR effects of BP on cardiovascular events compared to the MR effects of BP on migraine. However, it is also possible that potential genetic heterogeneity in migraine or misclassification due to changes in migraine presentation over time may have attenuated the MR association between BP and migraine3.In contrast to the results for the genetic effects of DBP and PP on migraine, the genetic association between BP and cardiovascular events was driven by SBP, consistent with the results from observational studiesP < 1.00 × 10−5) but non-significant (P > 0.05) for the other. However, we acknowledge limitations. First, our conclusions are limited to a general susceptibility of migraine and its major subtypes MA and MO but may not extend to different migraine traits over time or forms of migraine that may not arise from the common, population-based genetic susceptibilities implicit in our datasets, e.g. familial forms of migraine. Second, although the instrumental analysis focused on genetic variation in targets of BP-lowering medications  was not significant, it may also have been underpowered. Based on the combined effects of SNPs in these genes on BP, we estimated there was only <50% power at nominal significance to detect such instrumental effects on migraine in our datasets40. Third, although our analysis points to tissues and genes relevant to migraine susceptibility and BP, more work is needed to identify individual cell types and more detailed molecular mechanisms with the goal of developing potential therapeutic strategies.This study comprehensively investigates the genetic-based association between migraine and BP. The main strengths of our study include large-scale genetic data , independent replication of migraine candidate loci from cross-trait meta-analysis, the use of multiple MR sensitivity analysis for outliers, horizontal pleiotropy, and reverse causation, and the use of exclusive SNP instruments for DBP or SBP that were significant for one trait  and ICBP 41. In the original GWASs, migraine and its two sub-forms (MA and MO) were defined by diagnostic criteria from the International Headache Society and the summary statistics were adjusted for age, sex, and principle components where applicable in each sub-cohort3, whereas BP summary statistics  were adjusted for age, age2, sex, and body mass index (BMI) in the parent study, and all sub-cohorts corrected for hypertension treatment (+15/10 mmHg in the presence of any hypertensive medication)41. All of the participants were of European descent with only a small fraction of overlapping samples  between migraine and BP traits. Analysis in the current study was restricted to SNPs, at most ~7 million, which were common to GWASs for migraine and the BP traits. To compare the instrumental effects of BP traits on migraine and two migraine cardiovascular comorbidities, coronary artery disease (CAD) and stroke, we used publicly available GWAS summary statistics from European descent individuals for CAD and stroke from CARDIoGRAM and MEGASTROKE, respectively43. To minimize the bias from overlapping samples when conducting the instrumental analyses of BP with CAD and stroke, we used BP GWAS summary statistics  from the UK Biobank, which is publicly available at http://www.nealelab.is/uk-biobank/44. All participants provided written informed consent to each of the sub-cohort of the consortium.We used the most recent GWAS summary-level data from International Headache Genetics Consortium (IHGC) for migraine (any migraine and two subtypes of migraine: migraine with aura [MA] and migraine without aura [MO]) and from the International Consortium of Blood Pressure-Genome Wide Association Studies (ICBP) and UK Biobank (UKB) for three BP traits 17 and the more recent genetic covariance analyzer (GNOVA)45. For LDSC, we used precomputed LD-scores derived from ~1.2 million common- and well-imputed SNPs in European populations as represented in the Hapmap3 reference panel excluding the HLA region17. With GNOVA, which is potentially more powerful than LDSC45, we estimated the genetic correlation across ~5 million well-imputed SNPs in the 1000 Genomes Project and partitioned the estimates among categories of SNPs defined by 11 functional categories46, quartiles of MAF, and regions implicated in transcription for seven broadly-defined tissue types45. Both LDSC and GNOVA controlled for potential overlapping samples between each pair of traits45.To evaluate genetic correlation between migraine and BP, we used conventional cross-trait linkage disequilibrium (LD) score regression (LDSC)18 and GWAS-PW47. Both methods are designed to identify small contiguous regions of the genome in which the genetic associations with two traits are locally concordant. However, they use different approaches. ρ-HESS quantifies the local genetic covariance (and correlation) and P-values (Pρ-HESS) between pairs of traits at local regions18, whereas GWAS-PW uses a Bayesian framework to estimate the posterior probability (PPA_3) that genetic associations with the two traits co-localize using priors that are learned from the data47. BP and migraine were considered to have genetic correlation at local region if Pρ-HESS was significant after correcting for multiple testing (Pρ-HESS < 0.05/1703) and PPA_3 from GWAS-PW was larger than 0.9.We estimated local genetic correlations between migraine and BP traits in 1703 pre-specified LD-independent segments with both ρ-HESS19 through the statistic SHet that implements a sample size-weighted, fixed effect meta-analysis of the association statistics from the individual traits while modeling genetic covariance from all sources. In these analyses, we used total sample size values directly from the summary statistics file for BP and an average effective sample size for migraine48. The cross-trait meta-analysis was not inflated by observing a mean ratio of (LDSC intercept-1)/(mean(χ2) − 1) at 0.05 49. With TWAS, we compared gene-based models of genetic effects on tissue-specific gene expression from GTEx v.7 for migraine and the BP measures from the GWAS summary statistics to estimate strength of association between concordant gene-based genetic influences on gene expression on migraine or BP. In total, we performed 48 TWASs for each trait, one tissue–trait pair at a time. The null hypothesis of TWAS is no expression–trait association (or genetic correlation between expression and a trait) conditional on the observed GWAS statistics at the locus. In practice, a permutation test based on 1000 resampling iterations was run for each TWAS gene to ensure that the TWAS false positive rate was well controlled49. We applied Bonferroni correction to identify significant expression-trait associations adjusted for multiple comparisons for all gene–tissue pairs tested for each trait , and then identified genes that had Bonferroni significant associations for both migraine and BP. We further tested for conditional relationships among the shared genes to identify an independent set of gene-based genetic models using an extension of TWAS that leverages previous methods for joint/conditional tests of SNPs using summary statistics20 (Supplementary Note 2).To identify genes whose expression pattern across tissues implicates etiology or biological mechanisms shared by migraine and the BP measures, we performed TWAS21. GSMR applies strict criteria to select independent SNP instruments and extends conventional MR by accounting for the sampling variance in the genetic effects on both exposure (bzx) and outcome (bzy) in estimating the instrumental effect. Further, as pleiotropy is an important potential confounder that could bias the estimates and possibly result in an inflated test-statistic in MR, we used heterogeneity criteria in HEIDI  in the GSMR package to exclude likely pleiotropic SNPs from the analysis. To evaluate separate effects of SBP and DBP on migraine, we performed conditional instrumental analysis using mtCOJO , also within GSMR, with a two-step procedure requiring only the GWAS summary statistics21. SNP effects on SBP (y) were adjusted for effects on DBP (x) (or vice-versa) (i.e. bxy obtained from GSMR) in step 1, and then the adjusted instruments were used to derive the conditional instrumental estimate in step 2. P-values were corrected for multiple testing using Bonferroni criteria. We conducted sensitivity analyses using conventional inverse-variance weighted (IVW) MR, weighted median, simple median, MR-egger (Egger regression), and MR-Steiger (Supplementary Note 3). As migraine is a binary variable, we interpreted the reverse causal estimates as the average change in BP per doubling (twofold increase) in the odds of migraine, which could be obtained by multiplying the reverse causal estimate by 0.693 (loge2)50.To examine evidence for potential causal relationships between migraine and BP, we conducted instrumental variable analysis using bi-directional MR implemented in generalized summary-data-based Mendelian randomization (GSMR)Further information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


South America is a major food producer in the world, but there is still a large potential to optimize production efficiency and the industries’ long-term sustainability through the incorporation of modern phenotyping technologies, advanced breeding schemes, and better management strategies.There is a great diversity of livestock production systems  in South America, which makes it more challenging to collect certain phenotypes and also requires accounting for genotype-by-environment interactions in genetic evaluation models.There is a lack of large-scale and well-structured breeding programs for the majority of livestock and aquaculture species, mainly due to the low investments in pedigree recording, genotyping, and high-throughput phenotyping in commercial and small holder farms.As phenotype and pedigree recording and genotyping are still challenging in South America, data sharing across breeding associations and research institutions is paramount, especially for building training populations for genomic selection.The world population is expected to reach 9.1 billion people by 2050  and the The success of selective breeding is highly dependent on the quality of the phenotypes recorded and their degree of representation of the biological and physiological mechanisms underlying the breeding goals of interest. Development of equipment and efficient measurement’ protocols , the availability of new “-omics” technologies , and new statistical and bioinformatic tools, have enabled the livestock and aquaculture industries to speed up the rates of genetic progress per unit of time.High-throughput phenotyping is a reality in livestock and aquaculture production systems in developed countries e.g., . HoweverBos taurus indicus) in tropical regions  and Taurine breeds or crosses in sub-tropical regions . The three main beef cattle producers in South America are Brazil, Argentina, and Uruguay. Beef cattle production is pasture-based, with certain regions also finishing animals in feedlots. Nellore (Zebu cattle) is the main beef breed raised in South America.South America is a major beef cattle producer, with approximately 25% of the worldwide cattle population . The catThe main current breeding goals, according to its relative importance on economic indexes, are: growth (particularly growth rate and cow maturity weight) and reproduction. New initiatives are evaluating the inclusion of feed efficiency and meat/carcass quality (ultrasound-based carcass measurements) as index components. In order to meet such goals, there are around 10 Nellore breeding programs currently established in Brazil, evaluating over 0.5 million cows per year . There aAs previously mentioned, improved feed efficiency is a key breeding goal. However, the cost and difficulty to quantify individual feed intake, especially in pasture-based systems, have limited the inclusion of this trait in breeding programs. Over the past decade, various research groups in South America have concentrated efforts on identifying the best indicator variables of feed efficiency, unveiling the genetic relationship with traits already evaluated, and investigating the feasibility of developing a training population for genomic selection . Recent www.intergado.com.br/intergado-efficiency/; https://growsafe.com/about/). For instance, data from experimental farms have been used to derive feed efficiency-related traits, such as RFI, feed conversion ratio, average daily gain, and dry-matter intake , which are widely used in Brazil . TesticuAnimal resilience and adaptation is paramount in South American livestock production systems. For instance, tick infestation causes large economic losses and welfare issues, especially in Taurine populations. Therefore, infrared thermo-imaging was investigated as a potential tool to quantify (count) the number of ticks in the body surface of Brangus cattle . HoweverZebu breeds are known for having lower meat quality (marbling and tenderness) compared to Taurine animals. However, there is enough genetic variability to enable selective breeding . As meatBetter assessments of carcass yield and meat quality traits are still needed. Another potential alternative could be through collaborations with commercial slaughterhouses. However, there is limited interest from the beef industry on sharing and using such data for breeding purposes. In this context, image analysis and visual computing could be promising tools to predict carcass yield in different ages. Sensors  can be applied for this purpose. MK can minimize imaging interferences due to the ambient light through deep mapping image technology . SubsequA common challenge associated with pasture-based production systems is the long period of food scarcity caused by the seasonal patterns of rainfall, and high temperature and humidity. In this context, genetic selection for improved animal resilience and adaptation in such environments is gaining importance . AnotherThere are several challenges for wider adoption of phenotyping tools in beef cattle, but at the same time, modern technologies are becoming more accessible and producers more interested in their adoption. For instance, https://olhododono.agr.br/; https://techagr.com/). This could be used to identify the selection candidates  more related to each DNA pool, assuming that all selection candidates are individually genotyped. Through this approach, phenotypes from commercial farms (or slaughter plants) could contribute to improve the performance of genomic evaluation for certain traits, as shown in The DNA pooling technique  is anothhttps://bv.fapesp.br/pt/auxilios/97280). This will substantially reduce genotyping costs.As there are limited financial resources and infrastructure for collecting phenotypes and individual genotyping in developing countries, the establishment of collaborations for data sharing is of utmost value. For instance, recent efforts in Brazil have been made to join existing genomic datasets for imputation purposes  was the main breeding goal, as the large majority of producers were paid only based on milk volume. Genetic improvement for additional traits was also achieved by importing semen from bulls  selected for additional traits including milk composition, conformation, health, and reproductive ability. In the past two decades, the breeding goals in South America have been refined to include other traits. Currently, the main trait categories are as follows: milk production and composition , udder health (based on somatic cell count), fertility and reproduction , workability , and conformation traits. For instance, the Brazilian Girolando and Gyr national breeding programs currently report breeding values for milking ease and temperament, 305-d milk yield and composition , age at first calving and conformation. Adaptation and environmental resilience are also key breeding goals in dairy species raised in the tropical regions. The main indicator traits are heat tolerance, survival, and resistance to endo- and ectoparasites. However, genetic selection for these traits is still incipient.Even though the breeding goals for dairy goats are similar to those described above, phenotypic selection for morphological traits was heavily weighted as there were no production or reproduction records and pedigree information. In Brazil, milk recording in dairy goats started only in 2005 . In addiThe dairy industry payment system is an important challenge for dairy improvement. For instance, mastitis  is a great welfare and economic issue in South America  as produSystems for monitoring individual feeding and drinking behavior have been recently tested in dairy cattle e.g., . The frewww.apcbrh.com.br) provides a well-organized infrastructure to coordinate data collection, including laboratory milk analysis and genetic evaluations.There are several challenges involving dairy production in South America. First, there is a lack of centralized institutions integrating on-farm data collection, laboratory analysis of milk samples, and technical assistance to producers. Second, similarly to other regions around the world, the low profit margin and unstable milk prices make it difficult for producers to commit to investments in data recording. In most large dairy operations, protein and fat are usually controlled at the bulk tank level and not individually per cow. Somatic cell score, as part of a management protocol, is generally evaluated once a month in most herds. The lack of adequate payment and incentive to producers with regards to milk composition does not incentivize phenotyping and selection for such traits. However, there are some cases of success regarding data collection and genetic evaluations. For instance, the Holstein Association of Paraná  and survival status from field conditions  will allow recording of tens of thousands of phenotypes per day . This wiThe majority of swine and poultry raised in commercial farms in South America are from genetic resources developed in other countries, especially in North America and Europe. For minor species , there are examples of ongoing breeding program initiatives and national technologies mainly related with automatic feeding intake (to quantify feed efficiency). According to Many international genetic companies have applied modern phenotyping tools to obtain information on heat stress and behavior in pigs. This information is used at nucleus herds to obtain complementary traits when calculating selection indexes. The success of this strategy is maximized by using genomic information from both nucleus and commercial animals. In addition to the species mentioned above, meat sheep and goats, and South American camelids  are also of considerable importance to livestock production in South America. This is especially found in Uruguay, Southern Brazil, and Argentina (largest meat sheep producer region in South America), small-holder farmers in the Northeast and Central regions of Brazil (meat sheep and goats), and in the Andes Mountain region in Bolivia and Peru . The main breeding goals in meat or dual-purpose (meat and wool) sheep include the following: wool (or fiber) weight and quality , body weight and growth rate , carcass , reproductive , and resilience  traits. Meat sheep production systems in South America usually have low adoption of technologies with reduced to no phenotype recording, with the exception of Uruguay, Argentina, and some isolated regions of Brazil. In Brazil, there is a large number of locally developed sheep  and meat goats (e.g. Moxoto) breeds. The meat goat breeding goals are similar to those described above for meat sheep, with exception of wool/fiber traits. Phenotypic and pedigree recording in small ruminants is still limited in South America, but there are some breeding program initiatives with recent success.South America is a major livestock and aquaculture producer in the world. However, production efficiency is still lower than what could be achieved. This is partially due to the reduced adoption of phenotyping technologies, advanced breeding schemes and efficient management strategies. Furthermore, there is a great diversity of production systems, which makes it more challenging to collect certain phenotypes and also requires accounting for GxE interactions in genetic evaluation models. More recently, governments and industries are investing more in research and extension activities and there are clearer breeding goals, but the organization of data collection schemes and data sharing still needs to be substantially improved. We expect that phenomics will play an important role in improving livestock and aquaculture production efficiency in South America over the next few decades, considering that the industry continues (or increases) investments in phenotyping, pedigree recording and genotyping.