Recent results showed that certain DEAD box protein RNA helicases, DDX3 and DDX1, play an important role in the HIV infection cycle by facilitating the export of long, singly spliced or unspliced HIV RNAs from the nucleus via the CRM1-Rev pathway. Close examination of an extensive microarray expression profiling dataset obtained from cells latently infected with HIV induced to undergo lytic viral replication indicated that additional DEAD box proteins, beyond DDX3 and DDX1, exhibit differential expression during lytic HIV replication, and in latently infected cells prior to induction into active replication. This finding provides additional evidence that the involvement of DEAD box proteins and other RNA-binding proteins may play roles in active HIV replication and in the control of viral latency. Agents targeting these functions may offer new approaches to antiretroviral therapy and the therapeutic manipulation of HIV latency. The DEAD box proteins, a family of RNA helicases containing the conserved amino acid motif Asp-Glu-Ala-Asp (D-E-A-D in the single letter amino acid code), play an essential role in many aspects of cellular RNA metabolism (reviewed in ,2), inclIn a directed analysis of a large data set, which describes global changes in cellular gene patterns before and after a latently infected cell line was induced into active viral replication , we founYedavalli et al.  identifiOur work on large scale expression profiling in HIV actively and latently infected cells has been guided by the hypothesis that there is one set of cellular conditions which is ideal for normal cellular growth and homeostasis, that there is another set of conditions which may be better suited to supporting viral replication, and that HIV has evolved ways of altering the host cell so as to better support viral replication. An interesting corollary of the hypothesis is that targeting the products of the differentially expressed genes may inhibit viral replication by making the host cell environment less hospitable to viral replication (reviewed in ,13). Sev, the data were subjected to statistical analyses using univariate parametric and multivariate permutation analyses, based on the one sample random variance t-statistic, where significance was based on P < 0.001 and the proportion of false discoveries was limited to 0.10 with a 90% confidence level. 1740 genes showed differential gene expression at a minimum of one timepoint during lytic replication. Hierarchical clustering analyses were performed using mAdb clustering tools, as well as Treeview . Since the data was obtained from latently infected cell lines, there may be some concern that infected primary cells may behave in a somewhat different fashion. However, the advantages of using latently infected cell lines are significant: Activation into active replication is reasonably synchronous and includes essentially all the cells, so that the signal from the cells supporting active replication is not diluted by the signal from uninfected cells or cells with virus at different stages of viral replication. Also, the signal comes only from infected cell and not from cells responding to effects from the exposure to very large numbers of defective viral particles that are in high multiplicity of infection inocula.In our study, we compared RNA samples obtained from HIV latently infected cell lines prior to induction of active replication by the integrated HIV-1 provirus and following such induction with phorbol myristyl acetate (PMA). We profiled ACH-2 cells treated with PMA side by side with similarly treated HIV-1 naïve parental A3.01 cells to assess differential cellular gene expression patterns associated with HIV lytic replication. The dataset was generated from samples obtained from three independent biological replicate experiments and at least two microarray hybridizations were done for each time point from each biological replicate (for a minimum of 6 microarrays per time point). A detailed description of the cell culture, induction, RNA isolation, and microarray labeling and hybridization methods are contained in reference . Followi[DDX10, a DEAD box protein with expression in many tissues having tumorigenic activity when fused to the nucleoporin NUP98 [DDX21, a DEAD-box protein originally identified as a nucleolar protein thought to be involved in ribosomal RNA metabolism[DDX23, a DEAD box protein first identified in U5 SnRNPs with significant homology to the yeast Prp28p splicing factor[DDX52, a human DEAD box protein identified through its homologies to a yeast gene [Figure . We founin NUP98 ,23, DDX2etabolism, DDX23, ng factor, and DDXast gene .EIF4G1 [NCBP1 (CBP80) [SMARCA2 and SMARCA5 [Other genes encoding proteins with RNA splicing/binding and RNA transport activity were also up regulated during this period, including the methylated mRNA cap binding proteins EIF4G1  and NCBP (CBP80) , which f SMARCA5 ,30. Anot SMARCA5 , indicatOur findings that several DEAD box protein genes are upregulated during HIV replication lend support to the published finding that two cellular DEAD-box proteins, including one (DDX3) that was identified in a broad-based screen for differentially expressed genes , may be In our recent publication , we showCellular genes may be differentially expressed during viral replication for many different reasons. Differential expression of cellular genes may conceivably occur because of viral actions on the host cell designed to optimize the cell for viral replication, because of cellular responses to infection aimed at inhibiting viral infection, or may be fundamentally unrelated to key aspects of viral replication. However, the findings that several DEAD box protein genes are differentially expressed during HIV replication, together with the recently published observations that two DEAD box genes, DDX3 and DDX1, exhibit differential expression during HIV replication and have important functions in HIV replication lend additional credence to the hypothesis that a careful, large scale study of differentially expressed cellular genes can provide insights into host cell factors involved in viral replication and pathogenesis. Future studies may reveal additional human co-factors for HIV replication. These cellular co-factors many represent important new therapeutic targets.The authors declare that there are no competing interests.VK designed and performed the experimental work and the data analysis. SZ directed and coordinated the study and participated in the data analysis. VK and SZ wrote the manuscript.


Bacterial signal transduction mechanism referred to as a "two component regulatory systems" contributes to the overall adaptability of the bacteria by regulating the gene expression. Osmoregulation is one of the well-studied two component regulatory systems comprising of the sensor, EnvZ and the cognate response regulator, OmpR, which together control the expression of OmpC and OmpF porins in response to the osmolyte concentration.Escherichia coli was constructed by integrating the enzyme rate equations using E-CELL system. Using the substance reactor logic of the E-CELL system, a total of 28 reactions were defined from the injection of osmolyte till the regulated expression of porins by employing the experimental kinetic constants as reported in literature. In the case of low osmolarity, steady state production of OmpF and repression of OmpC was significant. In this model we show that the steady state – production of OmpF is dramatically reduced in the high osmolarity medium. The rate of OmpC production increased after sucrose addition, which is comparable with literature results. The relative porin production seems to be unaltered with changes in cell volume changes, ATP, EnvZ and OmpR at low and high osmolarity conditions. But the reach of saturation was rapid at high and low osmolarity with altered levels of the above components.A quantitative model of the osmoregulatory switch operative in ompF and ompC regulatory regions. The preliminary simulation experiment indicates that both reaching steady state expression and saturation is delayed in the case of OmpC compared to OmpF. Experimental analysis will help improve the model. The model captures the basic features of the generally accepted view of EnvZ-OmpR signaling and is a reasonable starting point for building sophisticated models and explaining quantitative features of the system.The E-CELL system allows us to perform virtual experiments on the bacterial osmoregulation model. This model does not take into account interaction with other networks in the cell. It suggests that the regulation of OmpF and OmpC is a direct consequence of the level of OmpRP in the cell and is dependent on the way in which OmpRP interacts with  Among prokaryotes, a remarkable number of cellular functions are controlled by two component regulatory systems . DedicatTwo component systems interact with each other and also with other regulatory systems mediating specific gene expression or cellular locomotion. Such complexes should be analysed quantitatively. Although quantitative data on cellular processes other than metabolism are still relatively sparse, scientists have modeled some systems with considerable success . For exaTwo-component regulatory systems  are widely used signaling machinery of bacterial adaptive responses. The system constitutes of sensor kinases and response regulators that can be phosphorylated and dephosphorylated by sensor kinases  Figure .4) is transferred to a specific Histidine (His) residue in the protein. The transmitter domain possesses a kinase activity that enables it to transfer the phosphate group to the receiver-regulator, when the environmental signal is detected [4) from the transmitter domain. The second domain is the regulator that in response to phosphorylation can bind to specific DNA sequences near specific promoters to activate gene expression. These two domains are linked together by a flexible linker [The first component sensor-transmitter that spans the cytoplasmic membrane has two domains a sensory domain and a transmitter domain. The two domains are anchored in the cytoplasmic membrane by two membrane-spanning regions. The transmitter domain is capable of autophosphorylation utilizing ATP. During this reaction a phosphate group (POdetected . The rece linker .Escherichia coli, playing an important role in regulating the cellular response to different solute concentrations in their environment [Osmoregulation is one of the well-studied two component regulatory systems operative in ironment . Among sironment . Both thironment . EnvZ thironment ,12. EnvZironment ,14.ompC and ompF promoters [ompF and ompC in Escherichia coli [i.e., a high osmolarity form and a low osmolarity form) regulated by the osmotic signal and modulates the ratio of the kinase to phosphatase activity of EnvZ [ompF gene triggering OmpF expression. In case of high osmolyte concentration the kinase activity of EnvZ is triggered resulting in the binding of the phosphorylated regulator to the low affinity promoters of ompC gene favouring OmpC expression [The sensor kinase is triggered by the osmolyte concentration of the environment and controls the production of phosphorylated regulator OmpR. This leads to the expression of outer membrane proteins OmpC or OmpF . Phosphoromoters ,17. OmpRromoters  and reguhia coli . The osmhia coli . First,  of EnvZ ,22. Undepression .ompC and ompF genes. As the number of phosphorylated OmpR protein molecules increases, two events occur: OmpR binds not only to the high affinity binding sites upstream of the ompF promoter but also to the one low affinity-binding site. Binding to this low affinity site results in repression of ompF gene expression. So OmpF porin protein production is stopped. When OmpR binds to the three low affinity sites upstream of the OmpC promoters ompC gene expression is stimulated, more OmpC porin protein is made and appears in the outer membrane of the cell [In the high osmolarity state, EnvZ actively undergoes autophosphorylation at histidine residue-243 in the C-terminal kinase domain, and then efficiently transfers its phosphoryl group to the N-terminal receiver domain of OmpR at aspartate residue-55 through EnvZOmpR complex formation . Upon phthe cell . The sumi.e., high phosphatase activity) towards OmpR. Such osmotic modulation of the kinase/phosphatase activity of EnvZ results in the relative amounts of the phosphorylated form of OmpR in cells varying in response to the medium osmolarity. When the medium osmolarity is low, the relative amount of the phosphorylated form of OmpR in cells is relatively small. In this particular situation, the ompF gene is first triggered, because the ompF promoter has relatively high-affinity OmpR-binding sites [ompC gene with low affinity OmpRP binding sites [In the low osmolarity state Figure , howeverng sites . As the ng sites .In summary, the relative amount of phosphorylated OmpR protein in the cell determines whether OmpF or OmpC is the predominantly expressed outer membrane porin. The relative amount of phosphorylated OmpR is determined by the perception of osmotic pressure by EnvZ .Escherichia coli cells are grown in normal nutrient medium. The first event of start of simulation is the activation of phosphatase activity of EnvZ followed by autophosphorylation of EnvZp by ATP dissociation. Later EnvZpp-OmpR complex formation occurs . OmpF synthesis seen to be triggered at the start of simulation. The entire trend of OmpF synthesis, gradual increase, steady state (at 50 seconds after the start of simulation with about a constant increase of 10 molecules for every 10 seconds) and final saturation  are represented graphically. Figure . A similEscherichia coli cells are grown in nutrient broth with 20% additional concentration of sucrose  [For high osmolarity conditions, the model generated incorporates the concentration of sucrose with the assumption that ivalent) . With thompF promoters and ompC promoters. OmpC molecules start accumulating. In the course of time there is complete dissociation of EnvZkOmpR complex, thereby both sensor and response protein are brought back to the pool  and saturation reaches by 100 seconds. OmpF repression shows steady state increase of 6 molecules for every 10 seconds and finally at saturation takes up a constant value by 90 seconds  in silicos Figure  but stils Figure . Here 10Escherichia coli is associated with osmotic change [-15 Litres was incorporated into the simulation model at low and high osmolarity conditions. In both cases the decrease in volume did not affect the relative porin production. Although the reach of saturation was rapid, the levels of porin and their relative ratios were found to be maintained with the same trend. This agrees with the data by Wood [Escherichia coli K-12. The simulation model presented is at the first phase of physiological and structural responses triggered by osmotic shift where there is decreased cytoplasmic streaming. Our simulation time also corresponds with the time period of this first phase of the responses in the above literature. Table Shrinkage of c change . The eff by Wood  with regEscherichia coli cells [To address the issue whether ATP levels has any effect over relative porin levels, simulation run was done at high and low levels of ATP. ATP level of 3 and 5 mM has been reported in exponentially growing li cells ,36. Simuli cells . This doEscherichia coli in the absence of sensor, EnvZ has been studied [in vitro, EnvZ is required for the maximal OmpC production and for efficient induction of OmpC at high osmolarity. This is established in the in silico model. Also the lack of EnvZ in the simulation did not affect the OmpF at low osmolyte condition and incomplete OmpF repression could be noticed after osmolyte shift as reported by in vitro studies. The relative levels of porins without EnvZ is cross verified with the data reported by Frost et al. [Regulation of OmpC and OmpF expression in  studied . We havet et al. , over stWithin the context of the EnvZ/OmpR two component system, the mathematical model predicts the OmpF/OmpC transcription to be insensitive to variations in the level of EnvZ and OmpR. By increasing levels of EnvZ upto 10 fold (1000 molecules), the relative porin ratio was found to be constant during simulation, evidently agreeing with the robust nature of the switch as per the mathematical model .in silico model the OmpC/OmpF transcription was found to be independent of the OmpR levels upto 10-fold increase (20000 molecules). In either case both at high and low osmolarity, porins levels were found to be insensitive to elevated or decrease levels of response regulator, OmpR corresponding to the results of mathematical model . The simulation models are constructed with three fundamental object classes, Substance, Reactor and System. Substances represent state variables, Reactors represent operations on the state variables, and Systems represent logical and/or physical compartments containing other objects. The distributed package of version employed for carrying out simulation has 18 different classes of standard Reactors, such as for Michaelis-Menten formula and generalized chemical equilibrium . In the in vivo condition considering Escherichia coli cells grown in mid-log phase. Accordingly the levels of OmpR and EnvZ are reported to be 3500 and 100 molecules in cell respectively. OmpR and EnvZ levels were almost the same from cells grown in L-broth medium or in a high osmolarity medium (NB (Nutrient Broth) +20% sucrose) [-15 liters [The present model is built on the assumption of the sucrose) . The rat5 liters . At low 5 liters Table 1)in vivo c5 liters . The lis5 liters . As the KVS was responsible for data collection and analysis. SK conceived of the study, and participated in its design and analysis. Two referees and an advisor of the journal helped to bring this information into the biological context.


An important challenge for transcript counting methods such as Serial Analysis of Gene Expression (SAGE), "Digital Northern" or Massively Parallel Signature Sequencing (MPSS), is to carry out statistical analyses that account for the within-class variability, i.e., variability due to the intrinsic biological differences among sampled individuals of the same class, and not only variability due to technical sampling error.We introduce a Bayesian model that accounts for the within-class variability by means of mixture distribution. We show that the previously available approaches of aggregation in pools ("pseudo-libraries") and the Beta-Binomial model, are particular cases of the mixture model. We illustrate our method with a brain tumor vs. normal comparison using SAGE data from public databases. We show examples of tags regarded as differentially expressed with high significance if the within-class variability is ignored, but clearly not so significant if one accounts for it.Using available information about biological replicates, one can transform a list of candidate transcripts showing differential expression to a more reliable one. Our method is freely available, under GPL/GNU copyleft, through a user friendly web-based on-line tool or as R language scripts at supplemental web-site. A much more usual approach is to assign an index  that measures the confidence/significance of the hypothesis and let the biologists themselves to establish a cutoff of what they call significant.An important challenge in Serial Analysis of Gene Expression (SAGE)  analysisThis necessity arises because counting sequenced SAGE tags is a process prone to random and systematic errors that affect gene expression abundance estimates. Systematic errors may come from various sources such as GC content bias , sequencIf an Expressed Sequence Tag (EST) library is non-normalized, its counting data, also known as "Digital-Northern", reflects the abundance of genes. Likewise, the Massively Parallel Signature Sequencing (MPSS)  techniquNowadays, the variability in SAGE abundance data is modeled only as due to sampling from sequencing, since almost all statistical procedures are performed after aggregation of observations from various libraries of the same class, creating a "pseudo-library". See -11 for gHere we propose a Bayesian model of mixtures to account for within-class variability as a generalization of the Beta-Binomial model . We alsoi-th library is often modeled as a Bernoulli Process and a fixed unknown tag abundance πi is implicitly assumed. The pdf of the random variable of interest, "expression abundance" π ∈ [0;1] among all n libraries is unknown, thus each library could be regarded as being created by a realization of π. These features lead naturally to mixture models [The counting process from automatic sequencing of one single e models ,14:f(·) is the unknown pdf of the abundance among same-class libraries parameterized by a vector θ, X = (x1,..., xn) is the vector of counts in all n libraries of same class, M = (m1,..., mn) is the vector of library sizes and L is the likelihood of each i-th observation.where: π = θ and zero over every other π ≠ θ, or a Dirac's Delta function. Using f(·) as a Dirac's Delta function constrained to [0;1], turn Eq.1 into the familiar and commonly used binomial distribution (see derivation in the Methods section).The common procedure of merging all observations from libraries of the same class, constructing a "pseudo-library" before statistical inference, is recognized as a particular case of this mixture model: just assume that all libraries have strictly the same abundance, with no biological variability. Mathematically, this is a function with infinite probability density over one single abundance value f(·) as a Beta in Eq.1, yields the so-called Beta-Binomial model (see derivation in the Methods section).We believe that Dirac's Delta is a naive description of real-life SAGE libraries. The Beta distribution is an alternative with non-zero within-class variance to account for intuitively expected biological differences among them. Using θ that describes the random variable π of some fixed gene G, we must decide if there is a difference between A and B classes . We propose to consider genes as being differentially expressed based on non-superposition of the predictive Beta pdfs of both A and B classes. By "predictive" we mean that we use the a posteriori mode in the Beta pdfs. The "non-superposition" intuitive feature is mathematically written as the Bayes Error Rate E [Given the parameter vector r Rate E :f(·) is the Beta pdf and "hat" over the parameters indicate the values that lead to an a posteriori pdf maximum. The a posteriori distribution is obtained as usual from Bayesian Statistical Theory (a priori pdf choice and detailed derivation are in the Methods section).where E. For adepts of the Frequentist Statistics, this evidence measure could resemble a typeI and typeII errors sum, however it is just an illustrative analogy.Intuitively, if the pdfs are "far apart", the gene probably has reproducible differential expression between classes. In this case, rarely could one misclassify class A as B and vice-versa. Figure E value. This cutoff should be guided by external and independent confirmatory assays. To avoid crude decision boundaries, one could rank their significance results but there is no way to avoid some arbitrariness in any kind of statistical test.As in any significance test method, the experimenter must define what is a high significance P-value ≤ 0.01 in a t-like-test, hoping that this could control the error at this level. However, due to technical difficulties such as lack of sensitivity of posterior confirmatory methods or high absolute expression  necessity, this apparent statistically sound results could be not useful in a pragmatic sense. That is why we prefer to rank the differential expression results and allow researchers to establish a cutoff compatible with their subsequent application for the selected genes, rather than split them based in assumption-derived error-rate cutoffs. People familiar with the Frequentist Statistics framework could miss multiple testing considerations, typeI/typeII error studies, and so on. However, in the Bayesian framework, several of these concerns are meaningless since we work with parameters space and not with sample space. The bayesians avoid statements about "data that could be observed but was not" and work only with available information , extracting all possible information from data effectively observed.In the classical Frequentist Statistics framework, it is common to call a result as significant if it presents a For those genes classified as differentially expressed, one should aggregate intuitive information adding "error-bars" to expression ratios. Recently we have developed a method to add credibility intervals to gene expression ratio , which cTo show the model is usefulness, we applied it to a tumor vs. normal two-classes comparison problem. We chose a subset of brain tumor SAGE data from The Cancer Genome Anatomy Project's SAGE Genie public database web-site . The SAGWe used all 4 available libraries in SAGE Genie until Jan/2004 from astrocytoma grade III tumors and almost all  normal brain libraries (see Methods section for details about libraries).0, i.e., there is no evidence of differential behavior between tumor and normal classes; (ii) when our method agreed with others rejecting H0, i.e., there is evidence of differential expression; and (iii) when our method showed evidence in favor but other evidence measures showed evidence against the H0. Case (iii) is the main motivation of our method since it reveals situations that researchers may call a gene differentially expressed and, in fact, it could be not so significant if biological replicates are taken into account. The other evidence measures used were: the Audic-Claverie bayesian evidence [P-value, and the classical χ2 P-value, all obtained using the IDEG6 web-interface [We want to stress 3 typical and important cases: (i) when our measure agreed with other evidence measures accepting null hypothesis Hevidence , the clanterface ,22 (see XT = (0, 2, 5, 8) and XN = (1, 1, 0, 0, 0, 7, 2). The Audic-Claverie, Fisher and χ2 methods yield P-values of 0.06, 0.44, 0.41, respectively, indicating low evidence against H0 for all mystical significance level cutoffs ≤ 0.01, ≤ 0.05 or ≤ 0.1. The Bayes Error Rate evidence is E = 0.61, an intuitively unacceptable superposition level between the normal and tumoral predictive Beta pdfs, showing that there is no separable behavior between classes. Figure A case (i) prototype is the TTTCAATAGA tag with XT = (7, 11, 18, 10) and XN = (7, 1, 2, 1, 2, 0, 3). All P-values are 0.00 (zero), significant at any cutoff level. Our evidence is E = 0.03, showing safely that this gene behaves differentially between normal brain and astrocytoma grade III patients. Figure A case (ii) prototype is the AAAAGAAACT tag with XT = (7, 239, 244, 123) and XN = (54, 27, 33, 21, 40, 196, 28). All P-values are 0.00 (zero), indicating significant difference between classes. On the other hand, our evidence E = 0.73 indicates high superposition between tumor and normal classes. Figure A case (iii) prototype is the TTGGAGATCT tag with P-values < 0.01 from all other methods, and they are the main concern of our method since they may lead to waste of resources in clinical validation efforts of genes that, by SAGE itself, could be left behind in favor of other promising genes. All tag results are available as additional file and graphics for all tags are at the supplemental web-site [There are several other obvious case (iii) examples, such as tag TACAGTATGT in Figure web-site .0 rejection, but considering "pseudo-libraries" leads to H0 acceptance. This seems to be inconsistent since one expects that, once H0 is accepted in a simplified model, it should also be accepted in the complete model. In fact, we do not observe such a situation, except by tags with P-values or Bayes Error Rate very close to arbitrarily defined cutoff values. We believe that these occurrences are just "edge effect" manifestations.One could think about a case (iv) when considering within-class variability leads one to Ht-test approximation [In order to assure that we are dealing with a fundamental question in SAGE analysis, we show more insights analyzing the method's robustness using the same data but excluding "small" libraries. Also, we draw some parallels between our proposed method and the only available published solution for dealing with within-class variability, a ximation .We used our method with all available libraries but some of them are smaller than 50,000 tags  for all P-values of the no differential expression null hypothesis. Using the conceptually different Bayesian P-value implemented at SAGE Genie [E = 0.00 meaning no superposition between the two classes pdfs. All these results indicate strong significance in differential expression of these tags.To prove that the incoherence of using "pseudo-libraries" methods is not a prerogative of tags showing small fold-changes, we analyzed another three very illustrative examples: ATGGCAACAG, GGATGTGAAA, and GTATGGGCCC; which are case (iii) tags. These tags present high fold changes: 7.59, 8.15 and 25.80 fold-change respectively, augmented in pooled tumor libraries. Using the well-known Fisher Exact test, GE Genie ,25 we obet al. [t-test P-values, and our method yields Bayes Error Rates of 0.38, 0.37, 0.43 respectively; indicating not so significant evidence in favor of the differentially expressed hypothesis. A closer look at the graphics of these tags induces one to believe that there is no reproducible differential expression because several observations of tumor and normal are superimposed .et al. [t-test approximation. Without knowing the true state of all tags, it is impossible to carry out a serious benchmark. Since the interpretation of evidence measures is very different, the performance could be subjected to an arbitrary cutoff selection for each method. Figure Since we show clearly that methods that use "pseudo-library" aggregation could be incoherent in some cases, a natural question is how our proposed method performs compared to the only published solution that accounts for within-class variability, the Baggerly et al. t-test apt-test approximation, considering E ≤ 0.1 and P-value ≤ 0.01. There are also some tags selected by t-test and ignored by ours. It is impossible to know which method perform better without the true unknown status of those tags. Looking at individual libraries results, constructed as depicted in Figure It is clear from this graphic that there are many more tags considered as differentially expressed using our method than the et al. [It is important to bear in mind that a difficulty is hidden in the Beta modeling imposed in the very first beginning. If Beta is not a good model for an unknown biological behavior, then some apparent inconsistency could appear in both Baggerly et al.  and our et al. . We beliet al. [t-like statistics, outlined a possible hypothesis test using the classical Frequentist Statistics framework and evoked some asymptotic results for t pdf justification.Until now, almost all statistical methods for SAGE data analysis tacitly ignore the within-class variability. To our knowledge, the firsts to formally address this issue was Baggerly et al.  who intrIn this work we presented the Bayesian alternative for this problem and defined a theoretical model that views Baggerly's Beta-Binomial approach or even the common Binomial approach as particular cases of mixture models. Other models are possible modifying the mixing distribution, such as Beta-Poisson , or usinWe show that there are cases in which approaches that ignore within-class variability will lead to high significance in differences between tumor and normal classes, but looking carefully at individual observations jointly, one should not attribute such high significance to them since abundance probability density functions have considerable superposition.In conclusion, we recommend that within-class variability must be taken into account in any statistical analysis of SAGE data if replicates are available. We suggest that biological replication should be considered in planning new SAGE experiments.π ∈ [0;1] of some gene G is indexed in a model family by means of a parameter vector θ. Therefore, following the usual Bayesian framework, the a posteriori pdf that describes the class is:To start generically, suppose that the probability density function (pdf) for the random variable of interest "expression abundance" X = (x1,..., xn) is the vector of counts in all n libraries of same class, M = (m1,..., mn) is the vector of total observations in all n libraries of same class, g(·) is the a priori pdf, and L is the likelihood of each i-th observation. Note that the product of all likelihood functions over all observations is the so-called Likelihood Function.where: posteriori expression anyway.The counting process from automatic sequencing is often modeled as a Binomial. Since the sample size and the stopping rule are not known in advance the model is not strictly Binomial. We do not need the combinatorial constant in the model, but we write it just because it is commonly used and will vanish in f(·) as a Dirac's Delta in Eq.1:Merging all observations from the same class libraries and constructing "pseudo-libraries", with the sum of their components, is the standard procedure to use replicates. Our general model is reduced to this  one if one uses 1{·} is the indicator function.where: Using Eq.4 in Eq.3 yield:θ) = 1, the non-informative uniform a priori distribution.where: g(θ ~ Beta(1 + Σxi, 1 + Σmi - Σxi), and the sum of observations is the mathematical translation of "pseudo-libraries" construction.The expert recognizes that f(·) as a Beta in Eq.1 we get the Beta-Binomial model as a particular case of general model:The only published solution that allows non-zero within-class variance in SAGE analysis is the Beta-Binomial model . Using fB(·) is the beta special function, and:where: θ = (θ1, θ2) as the mean and standard deviation (stdv) of a Beta random variable. We prefer this parameterization of Beta distributions instead of the common (α, β) one because: (i) it is much more intuitive to biologists to deal with mean and stdv than with abstract α and β, and (ii) as α, β > 0, the domain Θ = {(θ1, θ2): 0 ≤ θ1 ≤ 1, 0 ≤ θ22 <θ1 (1- θ1) ≤ 1/4} is bounded and much more amenable to perform the necessary numerical computations.Again, an expert recognizes Using Eq.6 in Eq.3 yield:g(θ1, θ2) is the priori pdf.where: a priori pdf. We use an uniform distribution over Θ. On the other hand, we know in advance that variance of this model cannot be smaller than the variance eventually obtained if we do not consider within-class variability. Even if the within-class variability is very small, it cannot be estimated as being smaller than the simple sampling error because they are inseparable, and sampling error is the lower limit [To complete a Bayesian model, it is necessary to choose the er limit . As an ia priori distributions. To match our desired features, it is sufficient to define an uniform over the Θ parameter space but constrained at a minimum stdv σ, obtained from the result of no within-class variance model:This kind of knowledge is naturally incorporated in Bayesian statistics by means of θ1, θ2): 0 ≤ θ1 ≤ 1, 0 ≤ θ22 <θ1 (1 - θ1) ≤ 1/4}.over domain Θ = {(θ ~ Beta(1 + Σxi, 1 + Σmi - Σxi), it is easy to obtain our lower stdv boundary from Beta variance:Since we showed (Eq.5) that the no within-class variance model is posteriori is completely defined.Therefore, using Eq.9 and Eq.10 in Eq.8, our E [We detect a tag as differentially expressed using the Bayes Error Rate E  in both where:f(·) is the Beta pdf, as in Eq.6 development. The "hat" over θ = (θ1, θ2) indicates values that leads Eq.8 to maximum. As usual, the maximization, subject to constrain Θ defined previously, is made upon logarithm of posteriori's core since it gives the same estimates as the posteriori itself:Note that Figure The method was implemented as R language ,28 scripOur method is computer-intensive mainly because some numeric maximization and integration are needed. We used efficient R built-in routines to perform such numerical tasks. Remember that maximization needed in Eq.12 is constrained, thus we used simply auxiliary re-parameterization to obtain linear constrains and used the constrOptim R routine. For numerical integration we used the 1-dimensional gaussian quadrature integrate R built-in function. Although numerical integration of Eq.9 should be performed in all [0;1] support, the relevant contribution for this integral is concentrated in a much smaller region. Integrating over the formal limits will cause serious numerical errors, and to avoid this problem we approximate our integration region to an interval delimited by 0.005 and 0.995 quantile of each Beta pdf since the relevant density lie in there.The credibility intervals ("error-bars") for the expression ratio of interesting tags were obtained as described in our recent work . We chosWe have also developed an easy-to-use web-based service that performs all calculations at our server and provides password-protected results. Although desirable, for the sake of automatic web hyperlink with SAGE Genie database, it is not necessary to explicitly identify the tags analyzed but rather any (custom) i.d. string. This could increase privacy or make our web-interface useful for "Digital-Northern", MPSS or any mathematically related problem of mixtures from binomial sampling. Figure The Table For our aims, it is sufficient to focus the analysis at the tag level. Thus, we process the tag counts and let the identification of tag's best gene match as a posterior question that could be carefully done only to really interesting tags. We choose not to process tags whose counts appear only in libraries of one class. It is important to note that all libraries are from bulk material, without cell-lines, and came from patients with similar disease description. The normal libraries came from different normal regions of the brain.We think that this data set is very illustrative since there are biological replicates in the tumor class allowing clear verification of within-class biological variability. On the other hand, taking only one kind of disease, astrocytoma grade III, instead of all brain tumors in the database, leads one to believe that the within-class variability is in fact due to biological diversity of the patients and not due to very distinct molecular profile of distinct brain tumors stored in SAGE Genie's database.in silico comparison is well-suited to demonstrate the necessity of dealing with within-class effect, although it is not our aim here to make a detailed or biological analysis of brain tumor data.Therefore, we believe that this χ2 proportion test and the bayesian Audic-Claverie's method. All these tests were performed using the easy-to-use web-interface IDEG6 [To bring some intuition about our differential expression evidence measure, we tabulated evidence measure obtained from the famous Fisher Exact Test, the classical Pearson's ce IDEG6 ,22.P-values" are conceptually very different from our evidence measure but are the most used evidence measures. Although numbers cannot be compared, the conclusions obtained from these methods should be since graphical representation of each library observation gives clear indication of incoherence of "pseudo-library" methods. The results of the significance measures for all tags are available as additional Excel© or OpenOffice© interactive files in which the user can set cutoffs for the significance measures, and explore the differences in conclusions.The "et al. [t-test approximation in a graphical way since it is impossible to judge them without the unknown true status of analyzed tags, given the too different interpretation of numeric values returned. In their Frequentist framework, the estimator pi = xi/mi is used for πi and a linear combination of these abundances is proposed as the correct way to combine results from different libraries:We carry out a qualitative comparison of our method with Baggerly et al. t-test apwi are the weights that yield an unbiased minimum variance estimator Vu for weighted proportion's variance and θ = (α, β) are the Beta pdf parameters. However, this unbiased variance could be unrealistically small when it becomes smaller than the sampling variability. We know that the variance of this model cannot be smaller than the variance eventually obtained if we do not consider within-class variability. Therefore, they propose the final ad hoc estimator:where V = max [Vu; Vpseudo-lib]     (14)where:V is not unrealistic small when Vu is unrealistic small. To fit all these parameters, they used the computationally practical Method of Moments. Once pA, pB, VA and VB are found for classes A and B, these authors test if the proportions are significantly different proposing the use of a tw statistics as following a Student's tdf pdf:The max(·) function assure that SAGE: Serial Analysis of Gene ExpressionMPSS: Massively Parallel Signature SequencingEST: Expressed Sequence Tagpdf: probability density functionGEO: Gene Expression OmnibusRV conceived and executed this work. HB helped with all biological issues. DFCP helped in differential expression detection methods and implemented the on-line web-based tool. CABP helped with Bayesian statistics and proposed the mixture ideas.Results for all evidence measures. This file allows the user to interactively define significance cutoffs for ranked tags. The ranks are based on evidence measures against "no differential expression" hypothesis, i.e., evidences closer to 0 (zero) denote higher confidence in differential expression and closer to 1 (one) denote no evidence of differential expression.Click here for file


The appropriate evaluation of atrial electrical function is only possible by means of invasive electrophysiology techniques, which are expensive and therefore not suitable for widespread use. Mechanical atrial function is mainly determined from atrial volumes and volume-derived indices that are load-dependent, time-consuming and difficult to reproduce because they are observer-dependent.To assess the feasibility of tissue velocity echocardiography (TVE) to evaluate atrial electromechanical function in young, healthy volunteers.We studied 37 healthy individuals: 28 men and nine women with a mean age of 29 years (range 20–47). Standard two-dimensional (2-D) and Doppler echocardiograms with superimposed TVE images were performed. Standard echocardiographic images were digitized during three consecutive cardiac cycles in cine-loop format for off-line analysis. Several indices of regional atrial electrical and mechanical function were derived from both 2-D and TVE modalities.Some TVE-derived variables indirectly reflected the atrial electrical activation that follows the known activation process as revealed by invasive electrophysiology. Regionally, the atrium shows an upward movement of its walls at the region near the atrio-ventricular ring with a reduction of this movement towards the upper levels of the atrial walls. The atrial mechanical function as assessed by several TVE-derived indices was quite similar in all left atrium (LA) walls. However, all such indices were higher in the right (RA) than the LA. There were no correlations between the 2-D- and TVE-derived variables expressing atrial mechanical function. Values of measurement error and repeatability were good for atrial mechanical function, but only acceptable for atrial electrical function.TVE may provide a simple, easy to obtain, reproducible, repeatable and potentially clinically useful tool for quantifying atrial electromechanical function. The enlargement of left atrial (LA) diameter is associated with cardiovascular disease and is a risk factor for atrial fibrillation, stroke and death. -6 LA funWe studied 37 healthy individuals: 28 men and nine women with a mean age of 29 years (range 20–47). The individuals were recruited from among hospital employees, cardiovascular technicians and medical students. None showed symptoms of cardiovascular disorders or were receiving pharmacological cardiovascular agents. All had normal standard two-dimensional (2-D) and Doppler echocardiograms. All subjects were on sinus rhythm and none hade A-V or intra-ventricular conduction defects. The Ethical Committee at the Karolinska University Hospital, Huddinge, approved the study. All individuals received written information and gave informed consent.A standard 2-D and Doppler echocardiogram with superimposed TVE images was performed using a 3.5 MHz transducer with commercially available equipment (System FiVe™, GE Vingmed, Horton, Norway). Standard parasternal short- and long-axis views as well as apical 2-, 3- and 4-chamber views acquired at expiratory apnea with at least 90 frames per second were digitized during three consecutive cardiac cycles in cine-loop format for off-line analysis.All echocardiographic images were analyzed off-line using software (Echopac™ 6.3.4, GE Vingmed) for the calculation of standard 2-D and Doppler echocardiography as well as for the analysis of TVE variables.Measurements of the left ventricular (LV) function comprised septum and posterior wall thickness; LV end-systolic and diastolic dimensions; LV fractional shortening, and LV ejection fraction (LVEF) according to international standards. Measurempeak systolic velocity (PSV, in centimeters per second), measured at the peak velocity during the ejection period; peak velocity at early diastole (E'-wave, in centimeters per second), measured at the peak velocity at early diastole, and peak velocity at late diastole (A'-wave, in centimeters per second), measured at the peak velocity at late diastole. The atrio-ventricular myocardial wall displacement (A'-V' disp., in millimeters) in the long axis was obtained by automated temporal integration of the PSV of the basal segments during the ejection period.The RV and LV long axis functions were assessed from apical views. Six basal LV segments were identified as follows: the RV free wall; the LV postero-septal wall, and the LV lateral wall from the apical 4-chamber view; the LV inferior and anterior walls from the apical 2-chamber view, and the LV posterior wall from the apical 3-chamber view. A sample volume was positioned at the base of each ventricular wall excluding the A-V plane during the entire heart cycle to obtain a tissue velocity profile during three consecutive cardiac cycles. Both systolic and diastolic phases of the velocity profile were considered and the following parameters were analyzed  was defined as the time between the beginning of the P-wave on the monitor's ECG to the start of the A' wave on the TVE-curve profile. The PA-peak interval (P-Aa' peak) was the time between the beginning of the P-wave on the monitor's ECG to the peak of the A' wave on the TVE-curve profile. The A-wave duration (Aa'-dur.) was the time from the beginning to the end of the A'-wave on the TVE-curve profile. The total electromechanical activity (TEMA) was the time between the beginnings of the P-wave on the monitor ECG to the end of the A' wave on the TVE-curve profile.The different atrial walls were identified from the same apical views as follows: the right atrial wall (RA), the inter-atrial septum (IAS), and the left atrial lateral wall (LA-Lat) from the apical 4-chamber view; the left atrial inferior wall (LA-Inf) and the left atrial anterior wall (LA-Ant) from the apical 2-chamber view; and the left atrial posterior wall (LA-Post) from the apical 3-chamber view. Each atrial wall was studied at low and mid levels, placing a 2 mm sample volume at low atrial walls excluding the A-V plane during the entire cardiac cycle and at the mid portion of each atrial wall. The regional electromechanical function at each atrial wall was studied by the following time intervals , the atrial displacement occurring during atrial contraction (Aa' disp.) and the ratio of atrial displacement measured at atrial level to the total LV myocardial displacement measured at ventricular level (Aa' cont.)  and strain (Aa' S) were assessed in each low atrial wall using a sample volume of 12 mm.The regional mechanical function of each atrial wall was assessed by the P < 0.05 was considered statistically significant.Data are presented as means ± standard deviations (SD). Analysis of variance (ANOVA) with repeated measures was used to test statistical significance of the studied variables at different atrial and ventricular walls. When ANOVA showed statistically significant differences among atrial and ventricular walls, post hoc analysis with Bonferroni's test was performed to assess differences among those walls. Correlation coefficients were calculated to assess the relationship among several markers of atrial mechanical function. The inter- and intra-observer repeatability and measurement errors for variables reflecting the atrial electromechanical function were assessed by the coefficient of variation and by the British Standards Institution method, the value below which the difference between two measurements will lie with a probability of 0.95. All demographic features and measures of standard 2-D and pulsed-wave Doppler echocardiography data are shown in Table PA-start interval (P-Aa' start) was longer at low atrial levels in each atrial wall than at the mid atrial level and shorter at the RA than for all LA walls  was similar at low and mid atrial levels in almost all atrial walls with exceptions in the inferior and posterior LA walls. This interval was shorter for the IAS, inferior and posterior LA walls than for the lateral and anterior LA walls at mid and low levels  was shorter at the low atrial level than at the mid atrial level in each atrial wall, but not in the inferior and posterior LA walls. The total electromechanical activity (TEMA) was similar in all RA and LA atrial walls measured at low and mid levels, and no differences were found between any of the LA walls.Table lls Fig. . Some stels Fig. . The A-wThe peak velocity during atrial contraction (Aa' peak vel.) was higher at low than mid levels in each atrial wall, but no significant differences were found between any LA walls. This variable was higher in RA than in all LA walls. Similar results were found for the atrial displacement occurring during atrial contraction (Aa' disp.) and the ratio of atrial displacement measured at atrial level to the total LV myocardial displacement measured at ventricular level (Aa' cont.). The strain rate (Aa' SR) was higher in the RA than in all LA-walls, and lower in the IAS than in the lateral and posterior LA walls. The strain (Aa' S) was higher in the RA than in all LA-walls, and no differences were found between LA walls.Table Tables PA-start interval and the PA-peak interval, which mainly express atrial electrical function showed the largest inter- and intra-observer measurement errors and variability. However, the A-wave duration and the total electromechanical activity, which express a combination of the atrial electrical and mechanical functions, had better values of measurement error and repeatability. The same was true for all the TVE-derived variables that express regional and global atrial mechanical function.The inter- and intra-observer measurement error and repeatability, as expressed by the British Standards Institution guidelines and coefficients of variation are presented in Table The main new findings of this study of healthy young individuals are as follows. (1) Some TVE-derived variables indirectly reflect the atrial electrical activation that follows the known activation process as revealed by invasive electrophysiology. (2) The regional and global atrial mechanical function is explained by an upward movement of the atrial walls at the region near the A-V ring with a continuous reduction of this movement towards the upper levels of atrial walls. (3) The atrial mechanical function is quite similar in all LA walls; however, all indices of mechanical function were higher in the RA than in the LA. (4) There were no correlations between the 2-D- and TVE-derived variables expressing atrial mechanical function. (5) Values of measurement error and repeatability were good for atrial mechanical function, but only acceptable for electrical function.PA-start interval, began at the RA and followed through the IAS, to the inferior and posterior LA walls. This is the known normal electrical activation process, as obtained by invasive electrophysiology techniques.[PA-start interval between IAS and the inferior and posterior LA walls, indicating that the activation process could indistinctly occur through any of these walls, as demonstrated by the presence of preferential conduction pathways nearby the IAS, the posterior LA wall and the coronary sinus.[Atrial electrical activation, as assessed by the chniques.,37 In thry sinus.,34,37. Iry sinus.The relation between atrial anatomy and its mechanical function has been poorly studied. The present study showed that all atrial walls actively moved upwards from the region of the A-V ring at late diastole, with a reduction of this movement towards the upper parts, thus empting the atria and contributing towards the last part of filling of the LV. This longitudinal movement of the atrial walls is probably related to the longitudinal endocardial muscular fibers along the walls of the LA and RA. The more pronounced longitudinal movement in the RA may be explained in part by the larger pectinate muscles in the RA, but also by the lower pressures in the heart's right side. To what extent circumferential contraction of the atrial muscle fibers might contribute to atrial mechanical function is unknown. Anatomically, the large amount of circumferential muscle fibers present in the vestibules of the RA and LA,31,44 miNo correlations were found between 2-D- and TVE-derived variables of atrial mechanical function, as was also found in a previous study. AlthougPA-start interval and the PA-peak interval, had only fair measures of repeatability and measurement error. However, most of the TVE-derived variables expressing atrial mechanical function had good values of repeatability and measurement error. Assessing atrial mechanical function by measuring volumes is time-consuming and depends on age, gender, and body surface area[Some measures of atrial electrical function, for example the face area,19 In adface area,47 and aThe identification of an abnormal electrical activation process could be of interest in some patients with atrial fibrillation or other supra-ventricular tachy-arrhythmias, in whom the premature atrial contraction acting as a triggering factor could be aggravated by local delayed conduction (reviewed in,49). FurThe assessment of pure mechanical atrial function by means of atrial wall movements may give more concrete clues about the recovery process of atrial electromechanical function after conversion for atrial fibrillation and flutter and can give additional pathophysiological insights on the thromboembolic process that occur in some of those patients. TVE-deriSeveral studies have shown the independent prognostic value of atrial function measurements in subsets of patients.,11,12 TVThe results of the present study refer only to a group of young healthy individuals and the values for each of the studied variables are, therefore, only applicable to that population group. As discussed, the measures of atrial electrical function showed only fair values of repeatability and measurement error. There were two reasons: the image acquisition rate (less than 100 frames per second) means an implicit measurement error of 10 ms; it was also difficult to identify the beginning of the P-wave in the ECG from the monitor in the echocardiography machine. Improving temporal resolution by image acquisition at more than 200 frames per second, and improving and adjusting the ECG quality in the present equipment may help solve or decrease this problem. The velocities and displacements registered by atrial walls do not only represent the process of atrial contraction, but also the translational movement of the heart. Until now, no appropriate algorithms that correctly deal with this problem have been found. Presently, it is not possible by means of TVE to simultaneously record the electromechanical function of all atrial walls in one heartbeat. The development of three-dimensional TVE may help resolve this difficulty.TVE is a noninvasive bedside tool that requires further refinements to provide reproducible, repeatable and potentially clinically useful data on atrial electromechanical function in health and disease.


While many lessons have been learned from the spatial analysis of cancer, there are several caveats that apply to many, if not all such analyses. As "flies in the ointment", these can substantially detract from a spatial analysis, and if not accounted for, can lead to weakened and erroneous conclusions. This paper discusses several assumptions and limitations of spatial analysis, identifies problems of scientific inference, and concludes with potential solutions and future directions. But this quote from Ecclesiastes has a much wider scope than a few dead flies – it is the ointment itself that stinks, and the entire endeavor is thereby ruined. By analogy, there are several caveats that apply to many, if not all spatial analyses of cancer data. As "flies in the ointment", these caveats can substantially detract from a spatial analysis, and if not accounted or otherwise controlled for, can lead to weakened or erroneous conclusions. Several of these caveats have been identified in the papers in this collection; others have yet to be described. This paper brings them together in one location, where they are discussed under three broad headings.• Problems of inference;• Assumptions and limitations; and• Potential solutions and future directions.This section provides an overview of the scientific method as applied to spatial data, limitations inherent in the study of spatial systems, including those on inference, spatial methods and data, and finally, limitations imposed on spatial analyses of human health data by society and the context from which health data arise.The Classic Paradigm of Karl Popper. Popper [. Popper  posed anThe useful lessons from Popper are first, that hypotheses and theories emerge from patterns and relationships in a set of observations; second, that the validity of the hypotheses is evaluated by distilling falsifiable predictions from them; third, that experiments designed to test these falsifiable predictions result in new data collected specifically to evaluate the predictions (these are designed experiments); and fourth, in order to avoid a tautology predictions cannot be tested on the data that gave rise to them. It is important to realize that useful predictions are falsifiable ones. Popper's approach can never prove a theory or hypothesis to be true. Rather, a body of evidence is collected from a series of experiments designed to test specific predictions, thereby increasing confidence that the hypothesis on which the predictions are based is true. Popper thus saw science as advancing much in the way used by Sir Arthur Conan Doyle's fictitious character Sherlock Holmes: If the alternative explanations are disproven, then the remaining explanation, no matter how unlikely, must be true.Recognizing this, Platt , proposeSpatial systems typically are large, and the spatial phenomena of interest in public health  are often difficult to observe directly and/or change slowly through time. This makes it difficult, if not impossible, to conduct designed experiments, and in any event there are substantial ethical considerations with experimentation on human populations. The spatial health researcher must often work with encountered data that have been collected for some purpose other than her specific study. In some instances the data are sampled in a systematic way from a spatially distributed population. But in each of these instances spatial analysis plays a critical role in identifying spatial and temporal relationships in population-level data, giving rise to hypotheses that can then be evaluated on additional data to be collected from the same system or on data from analogous spatial systems .Under both Popper's and Platt's inference frameworks, study designs that attempt to confirm rather than reject hypotheses are not particularly useful. Repeating spatial studies to search for confirmation is less useful than undertaking analyses that are designed specifically to reject scientifically meaningful alternative hypotheses. But because it is so difficult to manipulate spatial systems, it can be difficult to design and undertake the critical analytical experiments that test falsifiable predictions.The spatial analyst's tool box includes techniques for quantifying spatial patterns, modeling risk surfaces, and assessing relationships between cancer outcomes and potential exposures. These techniques allow researchers to determine whether observed spatial patterns are statistically significant, to identify the locations of clusters, hotspots and cool spots, to construct maps showing excesses and deficits relative to a risk model, and to quantify association between two spatial variables . Although these techniques can be quantitatively powerful, the inferences that can be drawn from them have attendant limitations. We now consider three limitations on the inferences that can be reached from analyses (1) of spatial patterns, (2) of spatial associations, and (3) by using randomization (Monte Carlo)-based techniques.Pattern does not demonstrate causation. As noted by Waller and Jacquez [ Jacquez  tests fo Jacquez  that are Jacquez  employedAssociation is not causation. The spatial analyst has an increasingly diverse suite of tools for documenting and quantifying associations between the spatial patterns of two or more variables. These techniques include cross-correlograms and related measures [measures ,7., the measures ,9., bounmeasures , polygonmeasures , as wellmeasures  coincideRandomization limits inference to the data set. Many disease cluster techniques and approaches to spatial modeling employ randomization, either based on sampling algorithms from spatial models  or on distributional assumptions of randomization (e.g. the randomization hypothesis for Moran's I). Traditional statistics based on distribution theory (e.g. student's test, ANOVA etc) are able to make inferences regarding the "Universe" from which the population sample was drawn. Inferences for methods based on randomization, however, are limited only to the data set to which they were applied. This is one of the critical distinctions between methods based on distribution theory and "distribution free" techniques based on re-sampling a data set to construct empirical distributions [ibutions .All methods have attendant limitations, and this is true as well for techniques in the spatial analyst's toolbox. We now consider limitations imposed by spatial methods including the amount of knowledge required to use them, the selection and specification of spatial weights, and the subjectivity of the methods themselves.Amount of knowledge Different analysis approaches require different amounts of knowledge. A distinction often is made between exploratory analysis, models of data, and models of process. When working with spatial data, a corresponding distinction can be made between Exploratory Spatial Data Analysis (ESDA), spatial data models, and spatial process models. Each of these (ESDA, models of data, and models of process) has different inferential/predictive abilities, and requires different amounts of data and knowledge of the spatial system itself. ESDA quantifies spatial pattern, models of data are used for interpolation and prediction, and models of process are used for prediction and the assessment of proposed perturbations to the spatial system. ESDA  aims to identify spatial patterns and to generate hypotheses that might explain those patterns. It requires relatively little knowledge of the system being studied. In fact, the objective of exploratory techniques is to explore and quantify relationships in order to increase the analyst's knowledge of the spatial system. Models of data  require data of sufficient quality to estimate model parameters, and that the researcher possesses sufficient knowledge to be able to identify dependent and independent variables, and their relevant parameters. However the forms of these models do not convey any information regarding causal relationships. Models of process require a detailed understanding of the mechanics of the system being studied, and incorporate this understanding directly into the model itself. Spatial compartmental models that incorporate population and disease processes such as birth, death, migration and risk have been applied to model infectious diseases [diseases ,15. Thisdiseases ). But toSpatial weights Each of the 3 types of approaches outlined above require the use and specification of spatial relationships among the objects  being studied. In ESDA these are referred to as spatial weights. In models of data these may be called kriging weights (in geostatistics), autoregressive parameters , or spatial filters (in Bayesian smoothing). In models of process spatial relationships are quantified to correspond to the underlying mechanics of the system, for example in an infection model, by how likely pairs of nearby susceptible and infectious individuals are to contact one another. As one moves from ESDA to models of process, the methods used for quantifying spatial relationships become increasingly meaningful in terms of the spatial system being studied.For ESDA spatial weights model the spatial disease pattern . The selection and specification of spatial weights in ESDA is undertaken in the most "knowledge poor" circumstance, yet is critical since these weights quantify the alternative hypothesis of the pattern recognition statistic. For area-based data, commonly used spatial weights include first and higher order adjacencies, and functions of common border length. Some techniques evaluate nearest-neighbor and adjacency relationships on the centroids of areas, an approach that disposes of highly relevant geographic information (such as common borders) readily obtainable from polygon geometry. More advanced and realistic techniques are now being developed that account, not only for geographic relationships, but also for co-information such as population size [ion size . But in Subjectivity Most researchers recognize that all analytical methods impose a model, of one type or another, on the data and are therefore subjective. For example, the product-moment correlation coefficient imposes a linear model and is thus sensitive to linear relationships in bivariate data. Similarly, all techniques for spatial pattern analysis and modeling are founded on assumptions and are sensitive to or descriptive of different aspects of spatial pattern. For example, reliance on a single cluster statistic can only reveal those disease patterns that are consistent with that test's alternative hypothesis . This has prompted some researchers to employ a battery of spatial pattern methods to better describe different aspects of the morphology of geographic patterns in cancer incidence [ncidence . While eThe spatial data used in many geographic studies of cancer have inherent limitations attributable to granularity, spatial and temporal mismatch, under-reporting, misdiagnosis, the use of location as an exposure surrogate, human mobility, location and attribute uncertainty, static representation, as well as topological errors that result in erroneous spatial weights.Granularity has to do with the spatial resolution of the data. For human health applications, death certificates are often georeferenced to location of place of residence at time of diagnosis or death. Point-based methods then use these coordinates directly. Area-based methods require the point locations to be aggregated to provide raw or adjusted rates within areas, and these areas might be census units, metropolitan statistical areas, counties, states and so forth. Because of the need to protect patient privacy, publicly available data are often aggregated to a sufficient extent to prevent the disclosure or reconstruction of patient identity. So, for example, point maps displaying patient place-of-residence typically cannot be disclosed by researchers and public health agencies. But due to the Modifiable Areal Unit Problem (MAUP) how these data are aggregated can dramatically impact analysis results, and incompatible geographies (e.g. census vs. ZIP Code) make tests for association problematic [blematic . The abiblematic . Unmixinblematic .Spatial and temporal mismatch Cancer data, information on covariates and on environmental exposures typically do not "match up" in space or in time. For example, Jacquez and Greiling [Greiling  analyzedLocation and attribute uncertainty Uncertainty in spatial health data occurs in two data components: the locations (e.g. coordinates of place of residence) and attributes . Also referred to as positional uncertainty, the impacts of location uncertainty on spatial pattern analysis and modeling have been well documented in the geographical and natural resource sciences [sciences ,22. In tsciences  evaluatesciences . NonetheLocation as an exposure surrogate Location uncertainty has different sources, one of which is human mobility. Attempts at describing such mobility that transcend the use of place-of-residence to represent location include daily activity spaces[ty spaces,26, and ty spaces-29. But Use of place-of-residence in spatial analyses of cancer, and calculating purely spatial weights from those locations, seems appropriate only when individuals have resided at that location for as long or longer than the latency period, and when potential causative exposures occur either in the household or in the surrounding neighborhood. For what cancers might causative exposures occur in the home? Lung cancers attributable to household radon are a good example, as well as cancers caused by combustion by-products from cooking and second-hand smoke. Cancers of childhood reasonably may use place-of-residence as an exposure surrogate since the latency period is short and children tend to stay near the home. For other cancers and at larger scales of aggregation, such as census and ZIP Code geography, human mobility, especially in commuter communities, poses a substantial challenge to spatial analysis of cancer, and the finding of a geographic cluster can thus be difficult to interpret when place of residence is used to represent locations of individuals. Recently, Meliker et al [er et al  used theUnder reporting and misdiagnosis: Uncertainty in the attributes  arises from under reporting and misdiagnosis. Under reporting is especially an issue when working with data that encompasses health districts with different recording and reporting practices. Because states maintain their own cancer registries, differences in reporting practices can pose a special problem for data sets that cross state boundaries. For most cancers, diagnostic accuracy decreases as one works with retrospective data when the physician's diagnostic arsenal was not as robust. In addition, classifications of disease change through time, as when the International Classification of Disease (ICD) code is updated. When either differences in reporting and diagnosis are present, once cannot preclude the possibility that observed spatial variation in cancer rates is attributable to these causes.Static view: GIS typically represent the world as "snapshots" in time and do not effectively represent temporal change [l change . The impl change . There tl change .Polygons, Topology and computational geometry: The spatial analysis of area-based data requires the calculation of statistics such as polygon contiguity, length of common boundaries, areas and centroids. Calculation of these statistics employs methods of computational geometry that assume the polygons are correctly represented in the Euclidean plane. These assumptions usually are that polygons are closed (e.g. Jordan curves), and are not folded or joined together at single points to form "bow ties". When these assumptions are not met, techniques such as polygon triangulation will either fail or yield incorrect results, and resulting statistics, including placement of area centroids and spatial weights, will be wrong. Despite the importance of this problem, most spatial analysis software does not check shapefiles  to determine whether the polygons are topologically well-conditioned. While this may seem an arcane problem, we have discovered in practice that a substantial proportion of the shapefiles shared among researchers for use in spatial analysis are flawed to a sufficient extent so that the resulting spatial weights are incorrect. One example is the primary care service area file  that has 60 of 6000 polygons self intersecting, a 1% error rate.Limitations on inference in cluster investigations. Many disease cluster investigations are initiated by reports from concerned citizens, and the attendant increase in the probability of false positives due to such preselection bias is well known [ll known ,44. Othell known , becausell known  have notll known , and clull known .Limitations arising from lack of communication with community stakeholders Within public health departments spatial analyses of cancer data are best undertaken by teams comprised of a community stakeholder (e.g. community end-user of the study results), a political decision maker whose constituency is the subject of analysis, a public health practitioner capable of putting in place an intervention should the results be positive, a spatial analyst with a detailed understanding of the spatial analytic methods, and a GIS specialist to manage data and undertake mapping tasks. Such a team effort is most likely to translate analytical results into community action [y action .Information democracy vs. protection of privacy Efforts such as the National Spatial Data Infrastructure project are leading to the advent of data portals designed specifically to facilitate sharing and dissemination of spatial information. The DataWeb  is a network of online data libraries created in a collaboration between the CDC and the US Census Bureau. The libraries consist of both microdata and aggregate data, and include census, economic, health, income and unemployment, population, labor, cancer, crime, transportation, family dynamics, vital statistics, and other georeferenced data. Information in DataWeb is accessed through DataFerret, an application that prepares data sets for the user to download. It allows users to select a databasket of variables and then recode those variables as needed. Users develop and customize data tables and download them to their desktop (download formats include ASCII, SAS, SPSS, and Excel/Access). is a web-based portal for one-stop access to maps, data and other geospatial services that simplifies access to geospatial data collected by government agencies and other organizations. Geodata.gov is accelerating development and implementation of the National Spatial Data Infrastructure (NSDI) and includes state, local and tribal governments along with the private sector and academia as data providers. Geodata.gov offers access to thousands of data bases in 17 categories.Launched on June 30th, 2003, the Geospatial One Stop program The promise of these and like efforts is an information democracy in which all citizens have ready access to information describing health, the environment, services, resources, the economy and other data, both for their immediate neighborhood as well as larger areas. While freedom of information is arguably one of the pillars of a democratic society, the need to protect individual privacy is a substantial countervailing consideration. There are other important ethical considerations with the sharing of spatial data of very high resolution. For example, satellite imagery is now publicly available at 1 m and sub 1 meter spatial resolution, and hyperspectral imagery at comparable resolution will soon be available. From such imagery it will be possible to identify and classify microhabitat for disease vectors , and eveEvery study is based on assumptions, and ideally these are made explicit when the results are reported. This section describes several assumptions and considerations typical of spatial analyses of cancer, including ability to infer causality, the ecologic fallacy, and the role of higher-order interactions. This section concludes with a discussion of the lack of utility of the word "cluster" as a spatial pattern descriptor.never sufficient to demonstrate causality. This is particularly true of cancers because of long latencies, the substantial difficulties posed by exposure reconstruction, and because of our lack of a full our understanding of the environmental bases of carcinogenesis. However, the exploration and modeling of spatial cancer patterns can disprove predictions based on causal hypotheses that are expressed in spatial terms. For example, hypothesized exposure mechanisms that involve proximity to point sources, or for which attributed risks vary geographically, can be evaluated systematically using spatial analytic approaches.Earlier we pointed out than an important limitation of spatial analyses of cancer data is that demonstration of significant geographic patterns and associations is Studies of geographic clusters and cancer data must include consideration of the potentially misleading aspects of ecologic studies. Even ZIP Codes and census tracts can be considered coarse spatial units for aggregating cancer cases and for estimating exposures, and exposure and health data often are not available at the same resolution. Exposure data often are reported at spatial levels, such as census tracts, that partition the geography in a manner inappropriate for the exposure process. Other spatial divisions may be better descriptors of environmental exposure, including, for example, watersheds, aquifers, local public water systems for water-borne substances, or "windsheds" for airborne substances. But because of privacy concerns for the patients and the limitations on existing environmental data, the data used often are simply the data that are available. Every data collection protocol has a design. Is it appropriate to use data for purposes other than for which they were collected? ZIP Code, census tract or place of residence at diagnosis is an inadequate descriptor of an individual's location during the development of cancer. For example, using the ZIP Code of residence assumes the patient lived within that ZIP Code area during the period of time required to develop cancer following exposure to an environmental compound that influenced cancer risk. Hence the degree of exposure to the potential risk factors over a multi-year period has been estimated for each study subject based on their place of residence, aggregated at the census tract level. This assumption is clearly tenuous given the mobility of human populations and the arbitrariness of the spatial partition for the environmental data .In the 1980's many epidemiologists considered ecologic studies likely to lead to erroneous conclusions, and that the most accurate findings arise from individual-level data. Since the late 1990's, however, the potential of adding "contextual variables" to multi-level analyses has provided a sound methodological mechanism for combining individual-level data with higher geographical contextual data. Nonetheless, issues regarding the definition of spatial partitions, patient privacy, and the appropriate use of data still pertain.Especially for complex relationships (such as those between environment, genetics and cancer), apparent bivariate associations may be driven by multivariate interactions that are not directly quantified by the two variables under scrutiny. For example, elevated air pollution may be associated with lower housing prices , which in turn attracts poorer households with higher smoking rates. In this instance, an observed bivariate correlation between air pollution and cancer would actually overestimate the degree of association between these two variables. But because of their complexity, higher order multivariate interactions are difficult to quantify in spatial cancer studies.The term "cluster" by and of itself is so generic as to be almost meaningless for describing spatial variation in cancers. What is a cluster? Is it an excess of cancer, and, if so, how much extra is considered an excess? Do we use likelihood statistics to find an excess, or should we use some other statistical framework? Are we looking globally to identify clusters anywhere in the study area, or do we define patterns locally, or relative to a putative source? These kinds of questions suggest that the declaration of a "cluster" is meaningless without a precise description of the statistical test being employed and the patterns to which the test it is sensitive. Because different clustering techniques are sensitive to different aspects of cluster morphology, analytic approaches that employ several pattern recognition methods can be more informative, especially in the ESDA phase of an analysis, with the caveat that the multiple tests will need to be accounted for should accurate estimates of P-values be required. Analyses that rely on just one kind of cluster test are incomplete in the sense that they will have power to detect only one type of cluster. Cancer morbidity and mortality evinces rich geographic variation, and it thus can make sense to employ a variety of techniques to more fully describe relevant aspects of spatial pattern.This last section discusses salient trends and methodological challenges in the changing landscape of the spatial analysis of cancer. It summarizes expected improvements in cancer data, exposure measures, and genetic information, and concludes with some anticipated methodological and technological challenges for the next decade.Recent trends in cancer registries are resulting in improved reporting and linking of spatially referenced data, although there is substantial variation in quality from state to state. There is a trend towards increased availability of aggregated cancer statistics over the World Wide Web. Not withstanding the inherent limitations of ZIP Code data, a good exemplar of improved availability is New York State, which is publishing online atlases of cancer incidence at ZIP Code level geography. A second example is the National Cancer Mortality Atlas published by the National Cancer Institute. New York State also makes available findings from spatial analyses of the cancer incidence data using the spatial scan statistic , and theEfforts cited earlier in this paper such as the CDC's dataweb and geospatial onestop are making georeferenced information on socioeconomic, census, environmental, remote sensing and other data readily available for downloading over the web. In remote sensing, the trend is towards higher spatial, spectral and temporal resolutions which together hold great promise for improving environmental risk assessment, habitat classification, and change detection . ModelinThe recent revolution in gene sequencing, bioinformatics and proteomics is making possible a detailed understanding of genetic predispositions as well as the cascade of genetic changes that cause normal cells to turn into cancer cells. Research currently underway at the NCI is seeking to elucidate gene-environment interactions and how these interactions can lead to cancer, but in general spatial analysis has contributed little to the study of gene-environment interactions. In fact, such studies would require population-level information on genetic profiles and biomarkers sufficient to calculate human genetic distances, and this kind of data are not yet available. Some research has conducted on European populations to explore relationships between genetic distances calculated from blood polymorphisms and differences in cancer mortality . But to As noted earlier, the static view of GIS makes it difficult to represent human mobility and temporal change in cancer, environmental and socioeconomic data. GIS typically are based on spatial data models that apply to static spatial systems such as those found in geology, forestry, and physical geography. However, this purely spatial data model inadequately characterizes the "what, where, when" needed to effectively analyze cancer data and health-environment relationships. GIS built on spatial, rather than space-time data structures, cannot deal readily with space-time georeferencing nor space-time queries , and insIn the near future we will need techniques and methods that take full advantage of the burgeoning data stream while maintaining the values and ethos of an open, democratic society. Information detailing place of death, genetic makeup, socioeconomic status, product use, and lifestyle indicators will be available at unprecedented spatial and temporal resolution. Using these data, substantial benefits to society are expected to accrue from the rapid identification of cancers and other health risks. Syndromic and health surveillance systems are now being deployed that could make it possible to rapidly identify local increases in cancer risk, and even relate them to spatial patterns and changes in environmental data thought linked to causative exposures. But the benefits of analyzing such high spatial and temporal resolution data must be balanced against the need to maintain individual privacy, while at the same time providing equitable information access to all strata of society. Certain aspects of this problem can be met by the development of appropriate analysis techniques. Coming up with these techniques and applying them in a responsible fashion is a substantial challenge that will require the cooperation of researchers, funding agency program managers, and legislators.The author is President of a commercial company (BioMedware) that develops software for the exploratory spatial and temporal analysis of health and environmental data.