Shigella spp. was reported to be the third commonest bacterial agent responsible for childhood diarrhoea. Currently, isolation of the bacterium and confirmation of the disease by microbiological and biochemical methods remain as the "gold standard". This study aimed to detect the prevalence of four Shigella virulence genes present concurrently, in randomly selected Malaysian strains via a rapid multiplex PCR (mPCR) assay.In Malaysia, set1A, set1B, ial and ipaH) in Shigella spp. One hundred and ten Malaysian strains (1997–2000) isolated from patients from various government hospitals were used. Reproducibility and sensitivity of the assay were also evaluated. Applicability of the mPCR in clinical settings was tested with spiked faeces following preincubation in brain heart infusion (BHI) broth.A mPCR assay was designed for the simultaneous detection of chromosomal- and plasmid-encoded virulence genes  of shigellae per reaction mixture in spiked faeces following preincubation.The The mPCR system is reproducible, sensitive and is able to identify pathogenic strains of shigellae irrespective of the locality of the virulence genes. It can be easily performed with a high throughput to give a presumptive identification of the causal pathogen. Shigella, namely S. flexneri, S. dysenteriae, S. sonnei and S. boydii have caused and continue to be responsible for mortality and/or morbidity in high risk populations such as children under five years of age, senior citizens, toddlers in day-care centres, patients in custodial institutions, homosexual men and, war- and famine-engulfed people. Yearly episodes of shigellosis globally have been estimated to be 164.7 million and of these, 163.2 million were in developing countries and the remaining in industrialized nations. The mortality rate was approximately 0.7% [Shigella spp. was the third most common bacteria isolated. S. flexneri and S. dysenteriae type 1 infections are usually characterized by frequent passage of small amounts of stool and mucus or blood. At times, watery stool followed by typical dysenteric stool maybe present with S. dysenteriae type 1 infection. S. sonnei and S. boydii infections are less severe with watery faeces but little mucus or blood.Members of the genus Shigellosis is usually a self-limiting infection, however when it subsides, the intestinal ulcers heal with scar tissue formation. Uncomplicated recovery is usual and the organisms rarely cause other types of infections. Adversely, in 3 to 50% of cases, depending on the virulence of the strain, the nutritional and immune status of the host, the initial infection maybe followed by neurological complications or kidney failure. Serious complications do occur at greatest frequencies in malnourished infants, toddlers, older adults and immunocompromised individuals .inv plasmid borne by the organism. They are often multifactorial and coordinately regulated, and the genes tend to be clustered in the genome. Previously reported PCR-based detection methods concentrated mainly on the ipaH gene alone [ipaH and ial genes in two separate PCR assays [ial is found on the large inv plasmid which is prone to loss or deletions, this gene-based detection may give false negative results. ipaH, on the other hand, is present on both the Shigella chromosome and on a large plasmid and hence, it is a more stable gene to detect. However, the sole presence of ipaH is not an absolute indicator of virulence as loss or deletion of the plasmid renders the bacterium noninvasive and therefore, avirulent. set1A and set1B are chromosomal genes encoding Shigella enterotoxin 1 (ShET1), which cause the watery phase of diarrhoea in shigellosis [ial and ipaH are responsible for directing epithelial cell penetration by the bacterium and for the modification of host response to infection, respectively [Virulence genes responsible for the pathogenesis of shigellosis may be located in the chromosome or on the ne alone ,6 or on R assays ,8. As iagellosis ,10. ial ectively -13.set1A, set1B, ial and ipaH) in Shigella spp. and to determine the prevalence of these virulence genes in a random selection of Malaysian Shigella strains.Here, we describe the application of a multiplex PCR (mPCR) design for simultaneous detection of four virulence genes (Shigella strains of S. flexneri (n = 84), S. sonnei (n = 15), S. dysenteriae (n = 10) and S. boydii (n = 1) were used in this study. These strains were isolated from patients with diarrhoea in Peninsular Malaysia from 1997–2000, and were provided by the Institute for Medical Research (IMR), Malaysia. Serotyping of the strains (Shigella antisera from Mast Diagnostics, UK) was carried out by the Bacteriological Unit, IMR. All the strains were checked on Salmonella-Shigella (SS) agar before being transferred to Luria Bertani (LB) agar plate, incubated overnight at 37°C for subsequent screening of virulence-associated genes. All strains were stored at -20°C in LB broth containing 15% glycerol.A total of 110 2, 130 μM of each deoxynucleotide (dNTP), 0.5 μM of each primer, 1 U of Taq DNA polymerase (Promega, USA) and 2 μl of DNA template. Amplifications were carried out using a Robocycler Gradient 40 Temperature Cycler (Strategene Cloning Systems, USA). The cycling conditions were an initial denaturation at 95°C for 5 min, template denaturation at 95°C for 50 s, annealing at 55°C for 1.5 min, and extension at 72°C for 2 min for a total of 30 cycles, with a final extension at 72°C for 7 min.Boiled suspension of bacterial cells was used as DNA template. Previously described primers, obtained from Integrated DNA Techs, USA, for detection of the four virulence genes were applied to the template ,14,15 (T2 (2 to 4 μM), Taq DNA polymerase (0.6 to 4 U) and dNTPs (100–150 μM) and buffer strength (1.4X to 2.4X) were tested. The simultaneous gene amplifications were performed in a reaction volume of 25 μl consisting of 1.8X PCR buffer B (Promega, USA), 4 mM MgCl2, 130 μM of each dNTP, 0.3 μM of each ShET1B primer, Shig1 and Shig2 primers, 0.5 μM of each ShET1A and ial primers, 1 U of Taq DNA polymerase (Promega, USA) and 2 μl of DNA template. All the reaction mixtures were overlaid with 20 μl of sterile mineral oil. Amplifications were similarly carried out as above.Based on the results of individual priming, an mPCR was designed. Various parameters such as concentrations of primers (0.5–0.8 μM), MgClS. flexneri 2a) was chosen as a positive control for PCR assays. A negative control using sterile distilled water as template was included in every PCR assay. The DNA fragments were separated in 2% agarose gel.After initial screening, strain TH13/00 , S. Paratyphi C, S. Typhimurium, S. Enteritidis, S. Typhi (ATCC 7251), Listeria monocytogenes, Pseudomonas aeruginosa, Klebsiella pneumoniae, Citrobacter freundii, Escherichia coli O157:H7 and E. coli O78:H11.The specificity of the mPCR assay was tested with 12 other non-S. flexneri 2a was harvested and serially diluted 10-fold with BHI. Then, 250 μl of each dilution of cell culture was mixed with 250 μl of the broth-faecal suspension and 500 μl of BHI in a new eppendorf tube. The tubes were vortexed and preincubated at 37°C for 4 h without shaking. Simultaneously, 100 μl of each diluted culture was plated on LB agar (Oxoid Ltd., UK) to determine the number of viable bacteria in each dilution. After preincubation, mPCR assay was performed on the boiled lysates of each diluted culture. A pure culture of S. flexneri 2a (TH13/00) and an unspiked faecal sample served as positive and negative controls.. The test was repeated with a spiked faecal sample of another healthy individual, and the average detection limit was reported.This was based on a modification of that described by Chiu and Ou . ApproxiSS agar plates and incubated overnight at 37°C. mPCR assay was performed on the boiled lysate of the broth-faecal suspension after preincubation. A pure culture of strain TH13/00 and a Shigella-spiked faecal sample served as a positive control, whilst a PCR reaction mixture without bacterial DNA template and an unspiked faecal sample from a healthy individual acted as a negative control.0.2 g of each faecal sample from 10 patients suffering from diarrhoea in a local tertiary University Hospital was suspended in 1 ml of BHI and diluted 10-fold. A volume of 250 μl of broth-faecal suspension was inoculated into 5 ml of BHI and preincubated at 37°C for 4 h without shaking. Concurrently, 100 μl of the suspension was plated onto MacConkey and 2 (3 mM), dNTP (400 μM each) and primers (1 μM each) were used as recommended, unspecific bands were present together with intense primer-dimers. In order to reduce the background noise and primer-dimers, concentrations of 0.5 μM of each primer and 200 μM of each dNTP were used. Further optimizations of MgCl2 concentrations (2 to 4 μM) and dNTP (100,130 and 150 μM each) gave intense amplicons with a clean background in each monoplex amplification  and set1B (ShET1B) were reduced to 0.3 μM each and the primers for both set1A (ShET1A) and ial  genes were maintained at 0.5 μM each. Following optimization of the concentrations of Taq DNA polymerase (0.6 to 4U/25 μL), buffer strength (1.4 X to 2.4 X), dNTPs (140 to 220 μM) and annealing temperatures (49 to 59°C) (at a constant MgCl2 concentration of 4 mM), a more uniform amplification of all the genes with no background noise was obtained  is to increase the amount of primers of the gene at same time with a decrease of the amount of primers for all the loci that can be amplified, especially those with strong amplifications. Hence, the concentrations of primers for both Shigella spp. tested showed the presence of ipaH  belonged to S. flexneri 2a serotype. Among the predominant strains of Shigella flexneri in Malaysia, ial was found in serotypes 4a, 6, 3a, 2a, 1a and 3c. All the four genes were present only in S. flexneri 2a and 3a.All the 110 strains of aH Table . Conversset1A, set1B, ial and ipaH genes assayed in the mPCR was 100%. None of the non-Shigella strains tested gave any amplification (data not shown).Reproducibility for the detection ofS. flexneri 2a. All the four virulence-associated genes were detected until 10-3 dilutions (data not shown). This was equivalent to 2.45 × 105 lysate or a minimum of 490 cfu of shigellae per 25 -μLmPCR reaction.The mPCR assay was tested on 10-fold dilutions of an overnight culture of 4 colony-forming units (cfu) shigellae ml-1 or approximately 100 cfu per reaction mixture . When the faecal suspension was diluted and preincubated in BHI for 4 h, the mPCR assay was successful in detecting the presence of the four virulence genes at an average concentration of 5.0 × 10ure Fig.  lane 8.Shigella virulence genes on faecal samples was tested on ten diarrhoeal patients. No mPCR product was detected although both the positive controls had amplifications. By conventional culture method, there was no growth of Shigella on the LB, MacConkey and SS agar plates.A preliminary study on the efficacy of the mPCR assay in the direct detection of the aforementioned Shigella by monoplex PCRs [Shigella detection, on the other hand, are scarce. Although the optimization of mPCR is more tedious and difficult to achieve than monoplexes, the ease of screening a large number of specimens, once the system is optimized, far outweighs the initial problems. The present mPCR system encompasses the presence of virulence genes found in the Shigella chromosome and on the large inv plasmid. Hence, it can determine if the pathogenesis of a particular strain is attributable to its chromosome or the plasmid, or if the strain is still invasive or otherwise, in a single reaction.Numerous studies had been performed to detect virulence genes in lex PCRs ,17,18. Set al. [Taq DNA polymerases and found that they displayed different specificity in PCR.Initially, the monoplex PCRs were carried out following reaction conditions as proposed by a previous report . Howeveret al.  had compPreferential amplification of one target sequence over another is a known phenomenon in mPCRs and it is usually overcome by increasing the amount of primers for the weaker amplification simultaneously with a decrease of primer concentrations for the stronger amplification. Buffer concentration may also affect mPCR amplifications despite it being seldom considered during monoplex optimization works . Upon adial and ipaH in strains of enteroinvasive Escherichia coli (EIEC) [Although other studies have demonstrated the presence of i (EIEC) ,13,21, wet al. [et al. [Shigella strains. Their studies showed that both set1A and set1B were present exclusively in S. flexneri 2a. The complete correlation between the presence of both set1A and set1B showed that both genes are indeed found in tandem in the Shigella genome. In this study, almost all the Shigella strains positive for the presence of set1A and set1B (41/45 strains) belonged to S. flexneri 2a, thus confirming previous works that both genes are highly conserved in this particular serotype [Our study supported the observations of Noriega et al.  and Varg [et al.  in localserotype .ial and ipaH were independent of the four different species of Shigella tested. Though both ial and ipaH are responsible for invasion-related processes and are found on the inv plasmid, the ial gene cluster resides near a region of the plasmid, which is a hot spot for spontaneous deletions [ial (45/110 strains) than ipaH (110/110 strains) in the Malaysian Shigella strains. Since invasiveness is a prerequisite for virulence in shigellae and since most of these virulence genes are located on the large plasmid, these strains would have possessed the plasmid when first isolated from patients. Due to storage/subculturing, the plasmid might have been lost together with the virulence-associated genes. By virtue of multiple copies being present on both the chromosome and the inv plasmid [ipaH seemed to be less compromised by plasmid loss and/or deletions. As the sole presence of ipaH is not indicative of the invasive phenotype, our mPCR design, which incorporated three other virulence genes, could determine the invasiveness of Shigella strains in epidemiological studies.Both the prevalence of eletions . This pr plasmid , ipaH seet al. [4 cfu shigellae ml-1 by amplifying the IS 630 sequences in shigella spp.. Yavzori et al. [4 cfu shigellae per gram of faeces with the use of virF primers. Although it has been reported that ingestion as low as 100 shigellae resulted in clinical disease [4 viable organisms. Thus, the average detection limit of mPCR described in this study (5.0 × 104 cfu/ml) is within the common infectious dose for shigellae.Dilution of the faecal sample with BHI was performed to lower the levels of PCR inhibitors such as bilirubin, bile salts and heme in the faeces . An addiet al.  detectedi et al.  reported disease , the higResults from the preliminary clinical screening were promising. Nevertheless, the consideration of other diarrhoeal pathogens being present in the clinical samples cannot be negated. More patient samples are warranted to thoroughly vet the robustness and applicability of the developed mPCR in clinical environments.Shigella spp., unlike the multiplex reactions based on specific rfc genes developed by Houng et al. [set1A or set1B may be omitted from the multiplex system as both genes are shown to exist tandemly. rfc primers of different Shigella origins maybe incorporated to enable the discrimination of Shigella spp. as well as the identification of virulent strains in one assay.One limitation of the present mPCR system is its inability to differentiate g et al. . For futial and ipaH genes.We conclude that the mPCR system is able to identify pathogenic strains of shigellae irrespective of the locality of the virulence genes. The described assay is reproducible, sensitive, can be easily performed and is able to give a presumptive identification of the causal pathogen, which could be confirmed by culture techniques using selective media. An added advantage would be that EIEC, which gives a similar illness, might also be detected by this method, as EIEC also harbours The author(s) declare that they have no competing interests.SLLH carried out the experiments, data analysis and wrote the manuscript. RMY provided the bacterial strains. SDP contributed to the writing of the manuscript. TKL conceived and co-designed the study, provided input for writing and supervision of the study. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:


Suction drains are routinely used after modified radical mastectomy and are an important factor contributing to increased hospital stay as the patients are often discharged only after their removal. Amongst various factors that influence the amount of postoperative drainage, the negative suction pressure applied to the drain has been reported to be of great significance. While a high negative suction pressure is expected to drain the collection and reduce the dead space promptly, it may also prevent the leaking lymphatics from closing and lead to increased drainage from the wound. Against this background a prospective randomized clinical study was conducted to compare the amount and duration of drainage between a half negative suction and full vacuum suction drainage in patients following modified radical mastectomy. The associated postoperative morbidity was also compared between the two groups.85 FNAC (fine needle aspiration cytology) proven cases of locally advanced breast cancer were randomized.  in to 50 patients with full vacuum suction (pressure = 700 g/m2) and 35 cases in to half vacuum suction drainage (pressure = 350 g/m2) groups. The two groups were comparable in respect of age, weight, and technique of operation and extent of axillary dissection. Surgery was performed by the same surgical team comprising of five surgeons (two senior and three resident surgeons) using a standardized technique with electrocautery. External compression dressing was provided over the axilla for first 48 hrs and following that patients were encouraged to do active and passive shoulder exercises. The outcomes measured were postoperative morbidity and the length of hospital stay.Statistical methods used: Descriptive studies were performed with SPSS version 10 and group characteristics were compared using student t-test.Half vacuum suction drains were removed earlier than the full suction vacuum suction drains. There was no significant difference in the incidence of seroma formation in the two groups and there was a significant reduction in the total hospital stay in patients with half vacuum suction drainage systems as compared to the full suction drainage group (p < 0.001) without any added morbidity.Half negative suction drains provide an effective compromise between no suction and full or high suction drainage after modified radical mastectomy by reducing the hospital stay and the post operative morbidity including post operative seromas. This on drain . The amoThe study also compared the drain volume, average hospital stay and postoperative morbidity between full vacuum and half vacuum suction groups.The study was conducted in one surgical unit of a tertiary care center over a period of two years.85, FNAC (fine needle aspiration cytology) proven cases of locally advanced breast cancer were randomized  into full vacuum suction (pressure = 700 g/m2) group – (A) and 35 cases into half vacuum suction (pressure = 350 g/m2) group – (B). The two groups were comparable in respect of age, weight and type of operation i.e. modified radical mastectomy (MRM). Following complete routine and metastatic work up, all patients received three cycles of Neoadjuvant chemotherapy (NACT) using CAF regime (Cyclophosphamide, Adriamycin, 5-Fluorouracil) and underwent Patey's modified radical mastectomy after three weeks of the last cycle. Surgery was performed by the same surgical team comprising of five surgeons (two senior and three resident surgeons) using a standardized technique with electro cautery. Axillary dissection was done up to level- III in all the cases. The boundaries of axillary dissection were defined by superior limit as the posterolateral border of the Pectoralis major muscle and axillary vein, medial limit being clavipectoral fascia or Hallstead's ligament, lateral limit as the anterior border of lattismus dorsi and the inferior limit being the angular vein joining the thoracodorsal vein. The long thoracic and thoracodorsal nerves were identified, dissected and preserved. Two silicone tube drains 12Fr)  were inserted in all the patients. All resected specimens were examined and the lymph nodes dissected, counted and assessed histo-pathologically for metastases. No patient received intra-operative blood transfusion. Both the drains were connected to a single 600 ml suction bottle (Romovac -Romson). In-group A (n = 50), drainage was performed using complete vacuum negative suction (700 g/m2) and in-group B (n = 35) with half vacuum suction drainage (350 g/m2). The pressure was also measured by attaching a manometer to the exit opening of the drainage bottle. The two groups were comparable with respect to age, weight (body mass index), type of operation indicating the success of randomization 1.Technique: Use of elctrocautery has been reported to be associated with increased incidence of seroma formation as compared to cold knife. It has also been reported that tissue ligation around the axillary vein rather than mere transection with knife or diathermy may reduce the amount of postoperative discharge, the technique was followed in the presented study [2. ed study .Drains themselves encourage drainage by stimulating tissue reactions or by suction [3  suction Early shoulder exercises have been implicated but were not observed to be a factor in the present study [4.nt study ,11 Althont study ,11.The negative suction applied may prevent the lymphatics from closing leading to continuous leakage and discharge [5 ischarge .Extent of axillary dissection. More seromas were seen when more lymph nodes were dissected from the axilla. The higher lymph node yield may well be an indirect measure of more extensive dissection performed. [6.rformed. . The draIt is an accepted fact that negative suction prevents seroma collection and helps in the adherence of the walls of the axilla thus reducing the dead space and allowing the lymphatics to close. High negative suction pressure generated by the drain can maintain lymph drainage by a negative pressure gradient . It is aReducing the negative suction pressure applied to the drain  along with external compression dressings applied for first 48 hours can significantly reduce drainage from the axilla following modified radical mastectomy without increasing the incidence of seroma formation as was observed in this randomized prospective clinical study. The hospital stay was reduced considerably compared to a matched group with full suction drain (p < 0.001). Half suction drain following axillary dissection in patients with carcinoma breast may thus be recommended as an effective approach to reducing the hospital stay and the cost of treatment without adding to the morbidity.The author(s) declare that they have no competing interests.CM was the surgeon in charge of the project and prepared the study design. VS was the first surgical assistant and did the data processing and statistical analysis. JP, the second surgical assistant assisted in the preparation of the manuscript. SS the Director of ICMR and AB the research officer, Tumor Biology Lab ICMR were responsible for the histopathological analysis and contributed to the preparation of the manuscript.The pre-publication history for this paper can be accessed here:


This contrast is typically used to distinguish the exposure's indirect effect, through the specified intermediate variables, from its direct effect, transmitted via pathways that do not involve the specified intermediates.Epidemiologic research is often devoted to etiologic investigation, and so techniques that may facilitate mechanistic inferences are attractive. Some of these techniques rely on rigid and/or unrealistic assumptions, making the biologic inferences tenuous. The methodology investigated here is We apply a causal framework based on latent potential response types to describe the limitations inherent in effect decomposition analysis. For simplicity, we assume three measured binary variables with monotonic effects and randomized exposure, and use difference contrasts as measures of causal effect. Previous authors showed that confounding between intermediate and the outcome threatens the validity of the decomposition strategy, even if exposure is randomized. We define exchangeability conditions for absence of confounding of causal effects of exposure and intermediate, and generate two example populations in which the no-confounding conditions are satisfied. In one population we impose an additional prohibition against unit-level interaction (synergism). We evaluate the performance of the decomposition strategy against true values of the causal effects, as defined by the proportions of latent potential response types in the two populations.We demonstrate that even when there is no confounding, partition of the total effect into direct and indirect effects is not reliably valid. Decomposition is valid only with the additional restriction that the population contain no units in which exposure and intermediate interact to cause the outcome. This restriction implies homogeneity of causal effects across strata of the intermediate.Reliable effect decomposition requires not only absence of confounding, but also absence of unit-level interaction and use of linear contrasts as measures of causal effect. Epidemiologists should be wary of etiologic inference based on adjusting for intermediates, especially when using ratio effect measures or when absence of interacting potential response types cannot be confidently asserted. A large portion of epidemiologic research is devoted to etiologic investigation, and so techniques that may facilitate mechanistic inferences are sought by researchers and are applied frequently in their work. Unfortunately, some of these techniques have been found to provide far more ambiguous evidence on which to base mechanistic conclusions than was first believed. For example, analysis of patterns of joint effects has been proposed as a means of identifying causal structure , but simThe list of such untenable overgeneralizations in epidemiologic practice is surely large and varied, and has led to any number of false conclusions and misunderstandings. We describe here one particular epidemiologic technique that is applied frequently in practice, and yet is invalid in all but a surprisingly narrow range of circumstances. It is a remarkable example in that the analytic strategy is exceedingly common, and yet is described infrequently in epidemiologic texts or methodologic articles. The few textbook citations that do exist provide no formal justification, and therefore there is little guidance available from within the sources in our field to guide users and warn them of important limitations of this approach. This situation motivates the present article, in which we will show that although widely applied, this analytic approach is almost never justifiable on the basis of reasonable assumptions about the data.indirect effect, through the specified intermediate variables, from its direct effect, transmitted via pathways that do not involve the specified intermediate variables. If control of hypothetical causal intermediates greatly attenuates an exposure's estimated effect, it is generally inferred that the exposure's effect is mediated primarily through pathways involving these quantities; a small degree of attenuation is interpreted as evidence that other pathways predominate. These mechanistic inferences then inform policy recommendations concerning the utility of potential interventions. Although this effect decomposition approach is quite common in the epidemiologic literature, its general validity has not been adequately investigated.The methodologic approach of interest in this article is the decomposition of effects purportedly accomplished by contrasting two adjusted effect estimates for the exposure of interest: an estimate adjusted for potential confounders, and an estimate adjusted for the same set of potential confounders plus one or more additional variables hypothesized to be causal intermediates, i.e., to lie on pathway(s) through which the exposure exerts its effect. This contrast is then typically used to distinguish the exposure's This analytic strategy for effect decomposition in epidemiologic research is recommended by Susser , pp. 121, pp. 184U/RRA, or the percent excess risk explained by the variables adjusted for:  "." The degree to which a given mechanism...explains the relationship of interest is given by the comparison of adjusted (A) and unadjusted (U) measures of association (e.g., a relative risk, RR). This comparison can be made using the ratio of the unadjusted RRs, RRCalculations similar to this "% Excess Risk Explained" are the most common framework for describing the effect decomposition analysis in epidemiologic research.For example, a study by Heck and Pamuk investigated the relation between education and postmenopausal breast cancer incidence using data from the National Health and Nutrition Examination Survey I Epidemiologic Follow-up Study. ProportIn a seminal article on the topic, Robins & Greenland employedOur critique would appear to contradict standard practice in the social sciences, in which decomposition analysis is also commonly applied,18. We sFor clarity, we limit our exposition to the simplest possible decomposition problem, which is the structure that includes three measured binary variables and sample size sufficiently large to justify the assumption of zero sampling error (see endnote 1). The three variables are designated as X, Y and Z. The causal relationships between these nodes are described by the directed acyclic graph (DAG) in Figuru at node Z is denoted by Zux where index u identifies the individual unit and index x specifies the X value factually or counterfactually experienced by that unit. Given the deterministic model at the individual unit level, there are four possible patterns of response Zux to input x that unit u can exhibit, and these have received various appellations in the literature, such as "doomed" for Zux= 1 regardless of x, "causal" for Zux= x, "preventive" for Zux= 1-x, and "immune" for Zux = 0 regardless of x[The potential response variable for unit less of x. These fu is denoted by Yuxz, where u identifies the individual unit and indices x and z specify the X and Z inputs to that unit. Conditional on the individual unit and conditional on the z input, there are four possible patterns of response Yuxz to input x: Yuxz = 1 regardless of x, Yuxz = x, Yuxz= 1-x, and Yuxz = 0 regardless of x. Therefore, each unit can be fully characterized by one of the 4 × 4 × 4 = 64 possible values of three indices, {ijk}, where index i specifies the Zux response, index j specifies the Yux0 response, and index k specifies the Yux1 response. As an illustration, {123} refers to a unit in which Z will equal 1 regardless of the value taken by X. Under this naturally occurring outcome for Z, Y will equal 1-x. However, if Z were to be manipulated by external intervention to equal 0, then Y would equal x.At the endogenous node Y, the counterfactual or potential response variable for unit ijk to be the proportion of type {ijk} in the total population. Furthermore, because X is exogenous, the potential response types occur in these same proportions inboth X = 0 and X = 1 subpopulations. The set of all 64 qijk proportions determines the causal behavior of the population in the context of the three observed variables (X, Y, Z) and potential confounding of the causal effects between them. The values of the 64 qijk proportions, however, are not identified from the 8 observed proportions in the study population: Pr(Y = y, X = x, Z = z); x = 0,1; y = 0,1; z = 0,1.In this way, the 64 possible potential response types for individual units in the population are symbolized by {ijk}; i = 1,...,4; j = 1,...,4; k = 1,...,4. We define qu and for z = 0,1 and x = 0,1:We make a further simplifying assumption of (strong) monotonicity for the remainder of this paper (see endnote 2). This assumption states that there are no individuals who exhibit preventive effects at either endogenous node. That is, for all units u0 ≤ Zu1Zu0z ≤ Yu1zYux0 ≤ Yux1YSince the binary values can be arbitrarily coded, the monotonicity of effects can be in any direction . This assumption reduces the number of potential response types in the population from 64 to 18, and may be reasonable on substantive grounds. For example, consider X to be assignment to cholesterol lowering drug cholestyramine versus placebo in the Lipid Research Clinics (LRC) Primary Prevention Trial, Z = 1 tThe total average causal effect (ACE) of the treatment X in the population is the proportion of all individuals in the population who would experience outcome Y if they were treated, but not if they were untreated, without regard to Z. Given the monotonicity assumption, this effect is the sum of 8 of the 18 potential response type proportions in the population:[X→Y] = average causal effectACE= Pr(Y = 1|SET[X = 1]) - Pr(Y = 1|SET[X = 0])122 + q241 + q222 + q421 + q422 + q221 + q142 + q242)=  direct effect (ACDE) of the treatment X in the population is the proportion of individuals who would experience outcome Y if they were treated, but not if they were untreated, if Z were forced (SET) to have a specific value z (thus blocking any indirect effects). In general, there is no reason for this effect to take the same value if Z were forced (SET) to 0 as it would take if Z were forced (SET) to 1, and so for binary Z in our DAG there are two distinct average causal direct effects. Given the monotonicity assumption, these effects are the sums of 6 of the 18 potential response type proportions in the population:[X→Y] | SET[Z = 0] = average causal direct effect for Z forced (SET) to 0ACDE= Pr(Y = 1|SET[X = 1,Z = 0]) - Pr(Y = 1|SET[X = 0,Z = 0])122 + q222 + q422 + q121 + q221 + q421)=  to 1ACDE= Pr(Y = 1|SET[X = 1,Z = 1]) - Pr(Y = 1|SET[X = 0,Z = 1])122 + q222 + q422 + q142 + q242 + q442)=  by external intervention, then Y = Z = 0, regardless of X. Alternatively, if Z were to be forced to occur (i.e. SET to Z = 1) by external intervention, then Y = Z = 1. For potential response types {242} and {221}, however, the common-sense meaning of an indirect effect may also apply, depending on the specific intervention applied to Z. Specifically, if the external intervention on the intermediate is SET[Z = 0], then potential response type {242} is an indirect type, whereas if the external intervention on the intermediate is SET[Z = 1], then potential response type {221} is an indirect type  of the treatment X on the intermediate covariate Z, which is the proportion of individuals who would experience intermediate Z if they were treated, but not if they were untreated. Given the monotonicity assumption, this effect is the sum of 6 of the 18 potential response type proportions in the population:[X→Z] = average causal effect of X on ZACE= Pr(Z = 1|SET[X = 1]) - Pr(Z = 1|SET[X = 0])211 + q241 + q222 + q244 + q221 + q242)=  to 1, but not if Z were forced (SET) to 0, conditional on X = x. In general, there is no reason for this effect to take the same value in the X = 0 subpopulation as it does in the X = 1 subpopulation, and so for binary X in our DAG there may be two distinct effects of Z on Y given strata of X. Given the monotonicity assumption, these effects are the sums of 6 of the 18 potential response type proportions in the population:[Z→Y] | X = 0 = Average causal effect of Z on Y in the X = 0 stratumACE= Pr(Y = 1|SET[Z = 1], X = 0) - Pr(Y = 1|SET[Z = 0], X = 0)141+ q241 + q441 + q121 + q221 + q421)=  - Pr(Y = 1|SET[Z = 0], X = 1)141 + q241 + q441 + q142 + q242 + q442)=  to 1, but not if Z were forced (SET) to 0, over the entire population. As this is not a stratum-specific quantity, there is only a single value, although this depends on the marginal distribution of X in the population [[Recall that because X is randomized, the potential response type distributionsare independent of X, meaning that the proportions over the total population are the same within the X = 1 and X = 0 subpopulations. We can define ACEulation [, eq 3.19[Z→Y] = Pr(Y = 1|SET[Z = 1]) - Pr(Y = 1|SET[Z = 0])ACE= Pr(Y = 1, X = 1|SET[Z = 1]) - Pr(Y = 1, X = 1|SET[Z = 0]) + Pr(Y = 1, X = 0|SET[Z = 1]) - Pr(Y = 1, X = 0|SET[Z = 0])Given that X is not affected by Z in the specified DAG, this can be re-written as:(Pr(Y = 1|X = 1,SET[Z = 1]) - Pr(Y = 1|X = 1,SET[Z = 0]) )Pr(X = 1) +(Pr(Y = 1|X = 0,SET[Z = 1]) - Pr(Y = 1|X = 0,SET[Z = 0]) )Pr(X = 0)[Z→Y] | X = 1 + Pr(X = 0) ACE[Z→Y] | X = 0 = Pr(X = 1) ACE[Z→Y] | X = x terms are each comprised of the sums of 6 of the 18 potential response type proportions in the population, 3 of which are common across the two strata of X and 3 of which are unique to one or the other stratum, so that ACE[Z→Y] involves a weighted sum of 9 of the 18 potential response type proportions, with weights dependent upon the marginal distribution of X.As shown above, the ACExz as the risk (proportion) of Y = 1 among those with X = x and Z = z, i.e., Pr(Y = 1|X = x, Z = z). With binary variables, exogeneity of X and the monotonicity assumption, these observable quantities are related to the latent response type proportions as follows:The causal effects defined above are counterfactual, in that they involve hypothetical manipulation of the treatment or intermediate or both. The realized data are the risks that arise in the form of observed proportions in the population. We define Rxz are used to compute the associational estimates of effect (see endnote 3), as follows:The observed risk values R[X→Y] = R1• - R0• is the associational estimate of the total average causal effect of X on Y on the additive scale, where Rx• indicates the risk under X = x collapsed over levels of Z, i.e., Rx• = Pr(Z = 0|X = x)Rx0 + Pr(Z = 1|X = x)Rx1. Because X is assumed to be randomized and therefore Pr(Z = z|X = x) = Pr(Z = z), RD[X→Y] equals the causal RD Pr - Pr(Y = 1|SET[X = 0,Z = z]).The direct risk difference DRD[X→Z] = Pr(Z = 1|X = 1) - Pr(Z = 1|X = 0) is the associational estimate on the additive scale of the effect of X on Z. Because X is assumed to be randomized, however, this associational estimate equals the analogous causal quantity Pr(Z = 1|SET[X = 1]) - Pr(Z = 1|SET[X = 0]).RD[Z→Y] | X = x = Rx1 - Rx0 is the associational estimate on the additive scale of the effect of Z on Y within stratum X = x. Because randomization of X does not imply that the effect of Z on Y is unconfounded, it may be a biased estimate of the analogous causal quantity, i.e., RD[Z→Y] | X = x is not necessarily equal to Pr(Y = 1|SET[Z = 1], X = x) - Pr(Y = 1|SET[Z = 0], X = x)RD[Z→Y] = Pr(X = 1)RD[Z→Y] | X = 1 + Pr(X = 0)RD[Z→Y] | X = 0 is the associational estimate on the additive scale of the effect of Z on Y standardized to the distribution of X.sRDThe associational estimate for the indirect effect is generally computed by one of two methods:[X→Y] | Z = z from RD[X→Y], or1) by subtracting DRD[X→Z] by sRD[Z→Y]2) by multiplying RD[X→Y] | Z = z from RD[X→Y] is also recommended in the social sciences methodology literature. For example, Stolzenberg writes: "Once the total and direct effects are calculated, indirect effects may be computed merely by subtracting the direct effect of an antecedent variable from its total effect. This subtraction procedure is applicable both to linear additive models ... and to nonlinear / nonadditive models." [[The first of these methods is the one more commonly applied in epidemiologic research, as represented for example by the expression for "Excess Risk Explained" in Szklo & Nieto. Subtracodels." [ p. 483].odels." [, and thiodels." [].[X→Y] | Z = 0 = DRD[X→Y] | Z = 1). The usual regression-based approach for the second method involves the regression of Z on X, followed by the regression of Y on both X and Z, and finally the multiplication of the coefficient estimate for X in the first model by the coefficient estimate for Z in the second model. This conditional estimation of the Z→Y effect in the second model is analogous to taking a weighted average over stratum-specific values as we have done for sRD[Z→Y]. Any presumed equivalence of the two approaches shown above by virtue of a homogeneity assumption for the stratum-specific estimates would often be unwarranted, as even under monotonicity it would generally require the additional restrictions that q142 = q242 = q442 = q121 = q221 = q421 = 0 (see endnote 4).There will generally be two distinct estimates by the first method above, depending the level chosen for Z. This is a necessary consequence of the manipulative definition of the controlled direct effect, since it involves deactivation of the indirect pathway by preventing variation in Z, and so if Z is to be fixed to a unique value, this value must be specified. In the second method shown above, however, only the two components of the indirect pathway are involved, and so no explicit fixing of Z is specified. This leads to a single estimate of the direct effect, and so the two methods can only be consistent with one another when there is homogeneity of the ACDE over strata of Z  to take the value 0 rather than the actually occurring value 1.The second set of counterfactual parameters are the risks of outcome Y among those with X = x and Z = 0 that would have been observed had Z been forced (SET) to take the value 1 rather than the actually occurring value 0.It is now possible to specify exchangeability conditions that are sufficient to guarantee that there is no confounding, meaning that associational measures and causal effects are equivalent. The fou11|SET[Z = 0] = R10R01|SET[Z = 0] = R00R10|SET[Z = 1] = R11R00|SET[Z = 1] = R01R[X→Y] | Z = 0 is unconfounded, whereas the latter two sets of exchangeability conditions imply that DRD [X→Y] | Z = 1 is unconfounded. Under the general scenario in which stratum-specific direct effects may differ, all four conditions are needed to guarantee that there is no confounding in either stratum of Z for any arbitrary choice of effect contrast that may be constructed from the four component risks.These conditions assert that the risk that is observed among those with X = x and Z = 0 is the same risk that would have been observed among those with X = x and Z = 1 had Z been forced (SET) from 1 to 0, and that the risk that is observed among those with X = x and Z = 1 is the same risk that would have been observed among those with X = x and Z = 0 had Z been forced (SET) from 0 to 1. The first two sets of exchangeability conditions imply that DRD[X→Y] | SET[Z = 0] and ACDE[X→Y] | SET[Z = 1]. Under the monotonicity assumption, this requires that 6 of the 18 types, namely {142}, {242}, {442}, {121}, {221}, and {421} be absent from the population. For example, potential response type {242} refers to a unit in which Z will equal x. When X = Z = 1, outcome Y will occur (Y = 1), and when X = Z = 0, outcome Y will not occur (Y = 0), leading to a unit-level casual effect of X on Y equal to (1-0) = 1. However, if Z were to be manipulated by external intervention (SET) to equal 0, then the unit-level effect of X on Y becomes (0- 0) = 0. That is to say, there is no direct effect at this controlled level of Z. In contrast, if Z were to be manipulated by external intervention (SET) to equal 1, the unit-level effect of X on Y remains (1-0) = 1. The direct causal effects of X on Y are heterogeneous for these 6 omitted potential response types because there is unit-level interaction; the value obtained by Y depends not only on the value taken by X, but also on the level to which Z is held by external manipulation. Homogeneity of the stratum-specific direct effects ACDE[X→Y] | SET[Z = 0] and ACDE[X→Y] | SET[Z = 1] also corresponds to absence of effect measure modification on the additive scale.We now impose an additional restriction which, as we will see in Section 6, is necessary for the general validity of the decomposition strategy described above. This restriction is that for no individual in the population may there exist both a causal effect of X on Y and a causal effect of Z on Y. For this condition to hold in general, it must be the case that Z does not modify the effect of X for any unit. This restriction, which can be characterized as the absence of unit-level synergism or interaction, implies homogeneity of the stratum specific direct effects ACDE[X→Y] = q241. The total effect is indeed decomposable into the sum of direct and indirect effects under this restriction, and in the absence of confounding may be estimated without bias. The decomposition is valid because the ACE[X→Y] reduces to the sum of only 4 proportions (i.e., q122, q222, q422, and q241), since 4 of the previous 8 are restricted to be 0 (i.e., q221,q421, q142 and q242). The average causal direct effects (ACDE) of X on Y are the sums of 3 potential response type proportions (rather than 6), which are identical in the two strata: ACDE[X→Y] | SET[Z = 0] = ACDE[X→Y] | SET[Z = 1] = (q122 + q222 + q422). Likewise, ACE[X→Z] is the sum of four proportions, ACE[Z→Y] = ACE[Z→Y] | SET[X = 0] = ACE[Z→Y] | SET[X = 1] is the sum of three proportions, and the observed risks RXZ are similarly restricted by deleting the prohibited interacting potential response types from the quotients shown above  of the treatment X in the population as the proportion of all individuals who would experience outcome Y if they were treated, but not if they were untreated, by virtue of the effect that X has on Z and then the effect that Z has on Y. In this mechanism, therefore, external intervention to hold Z fixed will prevent X from having the effect on Y, regardless of the specific value to which Z is SET. Given the restrictions, the average causal indirect effect is merely a single potential response type proportion in the population: ACIEijk as shown in Table XZ of R11 = 0.9170, R01 = 0.5377, R10 = 0.6101 and R00 = 0.2307. These observed risk values then determine the various associational estimates of effect. The total effect RD[X→Y] = (0.8763- 0.3117) = 0.5646. The observed stratum-specific risk differences DRD[X→Y] | Z = 0 = DRD[X→Y] | Z = 1 = (R1z - R0z) = 0.3793. Likewise the observed risk difference and stratum-specific risk differences for the effect of Z on Y are also homogeneous, sRD[Z→Y] = RD[Z→Y] | X = 0 = RD[Z→Y] | X = 1 = 0.3070. The observed effect of X on Z, RD[X→Z] = 0.6036.Consider data arising from a population of unit-level potential response type proportions q11|SET[Z = 0] = 0.6101; R01|SET[Z = 0] = 0.2307; R10|SET[Z = 1] = 0.9170; and R00|SET[Z = 1] = 0.5377. The absence of confounding is implied by the following set of equalities, the first two of which imply an absence of confounding of DRD[X→Y] | Z = 0 and the latter two of which imply an absence of confounding of DRD[X→Y] | Z = 1:Furthermore, the data in this example are constructed such that there is no confounding of the relation between Z and Y. To verify this property, we use the proportions in Table 11|SET[Z = 0] = R10 = 0.6101R01|SET[Z = 0] = R00 = 0.2307R10|SET[Z = 1] = R11 = 0.9170R00|SET[Z = 1] = R01 = 0.5377R[X→Y] = (q241) = 0.1853. As described above, there are two common approaches for estimating the associational measure of the indirect effect. The first is to subtract DRD[X→Y] | Z = z from RD[X→Y], which in this case yields (0.5646- 0.3793) = 0.1853. The second is to multiply RD[X→Z] by sRD[Z→Y], which yields (0.6036 × 0.3070) = 0.1853. The estimation of direct and indirect effects and their decomposition from total effects is valid, as will always be the case with this set of assumptions. The justification for this assertion is trivial: this set of assumptions is sufficient to guarantee that the true total ACE is the sum of three ACDE type proportions and one ACIE type proportion, whereas in general, without these restrictions, the ACDE is not constrained to be a subset of the total ACE. We have demonstrated a valid and unbiased estimation of the portion of a total effect that is transmitted through a specified intermediate when there is both absence of confounding and absence of unit-level interaction. We next relax this second constraint in order to demonstrate that the decomposition analysis can then fail.In this example, which was constructed to have no confounding and in which potential response types corresponding to unit-level synergism have been eliminated, the associational estimates of the total and direct effects are unbiased. That is, the true total average causal effect equals the observed risk difference (0.5646) and the homogeneous average causal direct effects equal the stratum-specific risk differences (0.3793). It only remains to show that the indirect estimate is valid and that the total effect is decomposable. The true average causal indirect effect in the table is the single potential response type proportion, ACIE142 = q242 = q121 = q221 = q421 = q442 = 0. Therefore we have, under the monotonicity restriction alone, 18 potential response types in the population. Consider data arising from a population of unit-level potential response type proportions qijk as shown in Table XZ of R11 = 0.9580, R01 = 0.3910, R10 = 0.4180 and R00 = 0.3170. These observed risk values then determine the various associational estimates of effect. The associational estimate of the total ACE is RD[X→Y] = (0.8166- 0.3470) = 0.4696. The observed stratum-specific risk differences are no longer constrained to be homogeneous: DRD[X→Y] | Z = 0 = (R10 - R00) = 0.1010 and DRD[X→Y] | Z = 1 = (R11 - R01) = 0.5670. The observed stratum-specific risk differences for the effect of Z on Y similarly need not be homogeneous: RD[Z→Y] | X = 0 = 0.0740 and RD[Z→Y] | X = 1 = 0.5400. sRD[Z→Y] will now depend on the observed marginal distribution of X. If values were assigned with equal probability, then sRD[Z→Y] = (0.5 × 0.0740) + (0.5 × 0.5400) = 0.3070. The observed effect of X on Z, RD[X→Z], equals 0.3327.Now we relax one assumption, the prohibition of unit-level interaction, which was operationalized in Section 5 by requiring that q11|SET[Z = 0] = 0.4180; R01|SET[Z = 0] = 0.3170; R10|SET[Z = 1] = 0.9580; and R00|SET[Z = 1] = 0.3910. The absence of confounding is implied by the following set of equalities, the first two of which imply an absence of confounding of DRD[X→Y] | Z = 0and the latter two of which imply an absence of confounding of DRD[X→Y] | Z = 1 :To verify that, as in the previous example, the data in this example are unconfounded, the proportions in Table 11|SET[Z = 0] = R10 = 0.4180R01|SET[Z = 0] = R00 = 0.3170R10|SET[Z = 1] = R11 = 0.9580R00|SET[Z = 1] = R01 = 0.3910R[X→Y] = ACE[X→Y] = 0.4696. Furthermore, because we have established that there is no confounding, the average causal direct effect of X on Y is identified by the observed associational measure of effect: ACDE[X→Y] | SET[Z = z] = DRD[X→Y] | Z = z. In this example, ACDE[X→Y] | SET[Z = 0] = DRD[X→Y] | Z = 0 = 0.1010 and ACDE[X→Y] | SET[Z = 1] = DRD[X→Y] | Z = 1 = 0.5670. However, in this scenario in which the only assumption we have relaxed is to allow the presence of unit-level synergism, the total average causal effect is no longer decomposable into direct and indirect effects. The average causal indirect effect no longer has single unambiguously true value. If the external manipulation contemplated is to SET[Z = 0], then ACIE[X→Y] = (q241 + q242) = (0.0100 + 0.1517) = 0.1617. On the other hand, if the external manipulation contemplated is to SET[Z = 1], then ACIE[X→Y] = (q241+ q221) = (0.0100 + 0.0200) = 0.0300.Because X is randomized, the average causal effect of X on Y is identified by the observed associational measure of effect: RD[X→Y] | Z = z from RD[X→Y], which in this case yields either (0.4696- 0.5670) = -0.0974 or (0.4696-0.1010) = 0.3686, depending on the stratum of Z, neither of which equals either of the corresponding true values of 0.0300 or 0.1617. The second approach is to multiply RD[X→Z] by sRD[Z→Y], which yields (0.3327 × 0.3070) = 0.1021, a value that equals neither of the corresponding true values of 0.0300 or 0.1617, nor is it the weighted average formed from any meaningful set of weights. In this scenario, the estimation of direct and indirect effects and their decomposition from total effects is not valid. It is immediately apparent that once unit-level interaction is permitted, there are potential response types that contribute to the ACDE but which do not contribute to the total ACE, making it incorrect to view the ACDE as a partition of the total ACE. Likewise, there are potential response types that contribute to the ACDE in one stratum of the intermediate, but which contribute to the ACIE in the alternate stratum, making it incorrect to view ACDE and ACIE as adding together to sum to a total effect. Therefore, for the decomposition methodology to be reliable, there must be both absence of confounding and absence of unit-level interaction. Because the absence of unit-level interaction would be difficult to assert with any confidence in a real-world application, the practical utility of decomposition as an analytic strategy is doubtful.As described above, there are two common approaches for estimating the associational measure of the indirect effect. The first is to subtract DRD[X→Y] / ACE[X→Z]) = (q241 / q211 + q241+ q222 + q244 + q221 + q242) = (0.1853 / 0.5646) = 32.8%. We note that a valid contrast between total and direct effects for ratio measures of effect was described by Joffe & Colditz[The demonstration above would appear to be somewhat gloomy as regards the potential for analytic epidemiology to identify biologic pathways through the contrast of variously specified statistical models. Indeed, the situation is even more grim than stated above, because even the optimistic scenario in Example 1 (Section 5) relies on the linear causal contrast estimator (i.e., the risk difference). Epidemiologic applications, such as those recommended by Szklo and Nieto [, pp. 184& Colditz, but thaEven if one steadfastly utilized the risk difference as the causal contrast and justified the no-confounding assumption, in order to reliably decompose the effect, one would still have to believe that there are no units in the population for whom Z and X both affect Y. Under the sharp null hypothesis for the exposure effect, this might be plausible. That is, if X has no effect on Y for any unit, then it follows that there are no units in the population for whom both X and Z have an effect on Y. However an average causal effect equal to the null does not imply this condition. If one were able to assert the no-confounding assumption, then observing that the association parameter is equal to the null would imply that the average causal effect is null, but no observation would imply the absence of unit-level interaction. The observation of heterogeneity would be sufficient to reject the assumption, but the observation of homogeneity would have no implications for this assumption. Nevertheless, as a practical matter, the incidental balancing out of unit-level causal effects leading to homogeneity might be considered unlikely, and therefore as a feasible approximation, the observation of risk difference homogeneity under a substantively defensible assertion of no-confounding might be taken as a setting in which effect decomposition can be attempted with a modicum of credence.Several previous authors working with latent potential response models have commented on the non-decomposibility of total effects into direct and indirect effects, most notably Robins, Robins controlled direct effect, which is to say, the proportion of individuals who would experience outcome Y if they were treated, but not if they were untreated, if Z were to be fixed to have a specific value z (thus blocking any indirect effects). Rather than impose through external intervention a uniform value of Z = z for all units, it is possible to define the average causal direct effect of X on Y that results from fixing Z to the value that would naturally occur under a specific single value of X, for example the unexposed level X = 0. This is referred to by Robins as the "pure direct effect"[We note that our specification of average causal direct effects in this manuscript corresponds to the t effect" and by Pt effect". It is nAlthough it allows for decomposition without the assumption of no unit-level interaction, the approach involving pure  direct and indirect effects has a substantial deficiency. The exchangeability conditions shown above (Section 4) characterize confounding in relation to hypothetical but defined manipulations of the target population. That is, X and Z are controlled to specific values. Because the pure  direct and indirect effects are defined based on intermediate Z being manipulated to an unobserved value that it would have taken under an exposure X value that may not have occurred, the exact nature of this intervention remains obscure. Because the hypothetical manipulation cannot be specified, the decomposed effects no longer have any possible relevance to a specific public health intervention or policy [, SectionFor example, if one were to estimate that the pure  indirect effect through intermediate Z equals 50% of the total effect, one could not infer that 50% of the outcomes attributable to the exposure could be prevented by blocking Z from occurring. Controlled direct effects can be used to make statements such as "The effect that postmenopausal hormone therapy would have on breast cancer risk if we were to persuade every woman to receive a screening mammography is ...." No similarly practical statement could be made for a pure  direct effect, however, which would correspond to something like "The effect that postmenopausal hormone therapy would have on breast cancer risk if every woman were to engage in the screening mammography behavior that she would have exhibited under the absence of treatment is ...." This latter statement obviously has no clear public health policy implications, since it requires a policy of fixing the intermediate to different values, some of which are unobserved .In summary, the ubiquitous strategy of adjusting for one or more putative causal intermediates in order to estimate the portion of the effect that it mediated by this pathway, in epidemiology and in other fields, lacks a reliable foundation. There are highly constrained sets of assumptions which allow this strategy to be valid, but it is often difficult to know when, if ever, these assumptions are approximately satisfied. Previous critiques have focused on confounding between the intermediate and the outcome, but we show that even when there is no confounding, the total causal effect of treatment is not generally decomposable into direct and indirect effects. Valid estimation of the direct or indirect effects, or of the proportion of the total effect that is due to an intermediate variable, requires not only the assumption of no confounding, but also the assumed absence of unit-level synergism, the latter of which may be particularly difficult to assert in a real-world analysis. Furthermore, even under these conditions, the decomposition is only valid for the difference contrast as the measure of causal effect, not for ratio measures of effect such as risk ratios, rate ratios, hazard ratios or odds ratios. In circumstances when it is possible to estimate (controlled) average causal direct effects, these should not generally be interpreted as portions of the total average causal effect, nor should they generally be used to make any statement about the proportion of the effect that is attributable to the measured intermediate variable.ACE average causal effectACDE average causal (controlled) direct effectACIE average causal (controlled) indirect effectCHD coronary heart diseaseDAG directed acyclic graphDRD direct risk differenceLRC Lipid Research ClinicsRD risk differenceRR relative risk or risk ratiosRD standardized risk differenceSUTVA stable-unit-treatment-value assumptionThe authors declare that they have no competing interests.1. Because of the assumption of zero sampling error "proportions" (in the observed sample) and "probabilities" (in the source population)are interchangeable.strong is intended to distinguish it from a weaker stochastic monotonicity assumption that may be defined:2. The characterization of this monotonicity assumption as 0 = 1) ≤ Pr(Z1 = 1)Pr(Z0z = 1) ≤ Pr(Y1z = 1); z = 0,1Pr(Yx0 = 1) ≤ Pr(Yx1 = 1); x = 0,1Pr = (q121 + q221 + q421), but this incidental cancellation would be difficult to anticipate, whereas the absence of some potential outcomes types is a more plausible form of background knowledge that an investigator could bring to the analysis.4. Strictly, equivalence of the two approaches for specifying the indirect effect requires merely that (qJSK led the writing, but all three authors contributed heavily to editing and revision. RFM devised the notational system and the numeric examples.


It is unclear if thymus-derived glucocorticoids reach sufficient local concentrations to support normal thymus homeostasis, or if adrenal-derived glucocorticoids from the circulation are required. Modern approaches to this issue (transgenic mice that under or over express glucocorticoid receptor in the thymus) have yielded irreconcilably contradictory results, suggesting fundamental problems with one or more the transgenic mouse strains used. In the present study, a more direct approach was used, in which mice were adrenalectomized with or without restoration of circulating corticosterone using timed release pellets. Reversal of the increased number of thymocytes caused by adrenalectomy following restoration of physiological corticosterone concentrations would indicate that corticosterone is the major adrenal product involved in thymic homeostasis.A clear relationship was observed between systemic corticosterone concentration, thymus cell number, and percentage of apoptotic thymocytes. Physiological concentrations of corticosterone in adrenalectomized mice restored thymus cell number to normal values and revealed differential sensitivity of thymocyte subpopulations to physiological and stress-inducible corticosterone concentrations.This indicates that thymus-derived glucocorticoids are not sufficient to maintain normal levels of death by neglect in the thymus, but that apoptosis and possibly other mechanisms induced by physiological, non stress-induced levels of adrenal-derived corticosterone are responsible for keeping the total number of thymocytes within the normal range. Although it is clear that elevated concentrations of endogenous glucocorticoids can cause apoptosis in the thymus -3, the r+CD8+ non-mature thymocytes, is most susceptible to elevated concentrations of glucocorticoids [It has also been suggested that glucocorticoids play a role in homeostasis in the adult thymus by inducing death by neglect of thymocytes that are neither positively nor negatively selected. This idea has been based on the observation that the predominant cell type subjected to death by neglect, CD4rticoids . Recent rticoids ,12-14. FA small number of studies have been reported in which systemic glucocorticoid concentrations were reduced by adrenalectomy, leading to increased numbers of cells in the thymus -17. Howe+CD8+ cells, which are the predominant cell type subjected to death by neglect [-CD8+) would be increased, as these cells have been reported to be particularly sensitive to glucocorticoids [If physiological  concentrations of corticosterone are important in the induction of death by neglect of thymocytes, it would seem likely that any increase in cell number in the thymus of adrenalectomized mice would be explained mostly by an increase of CD4 neglect . In addirticoids . If phys+CD8- and CD4+CD8+ cells. The number of CD4-CD8+ and CD4-CD8- cells was also greater in adrenalectomized mice than in the naive control group, but the difference was not significant. This indicates that the number of CD4+CD8- and CD4+CD8+ cells is diminished to a greater extent than CD4-CD8+ and CD4-CD8- cells by normal, physiological concentrations of corticosterone. Results for adrenalectomized mice were comparable whether a placebo pellet was implanted or not, indicating that non-adrenal-derived stress mediators induced by pellet implantation did not affect cell number. Timed release corticosterone pellets were used to restore corticosterone in adrenalectomized mice, and 0.5 and 1.5 mg pellets had only minimal effects on any subpopulation 24 hours after implantation of pellets  concentrations of corticosterone. However, this was not supported by the results presented here. The results in Figure +CD8+ cells increase in number to a greater extent than CD4-CD8+ or CD4-CD8- cells in ADX mice, but CD4+CD8- cells increase in number proportionally more than all these other subpopulations in mice with sub-physiological concentrations of corticosterone (ADX groups).The results shown in Figure +CD8+ cells than the other subpopulations to stress-inducible concentrations of corticosterone (in mice with a 5 mg pellet). The greater sensitivity of CD4-CD8- cells than CD4-CD8+ and CD4+CD8- cells noted in Figure +CD8+ cells, which are the most abundant and were diminished to the greatest extent. No significant change in subpopulation percentages was caused by adrenalectomy with or without a placebo pellet. However, it should be noted that the results shown in Figure +CD8+ and CD4+CD8- cells increased to a greater extent than the number of CD4-CD8- or CD4-CD8+ cells. This did not result in a substantial change in percentages  account for over 90% of the total thymocyte population, and changes in this subpopulation were reflected in the denominator  of the equation that determines the percentage of cells in each population.The changes in subpopulation percentages  mice at certain times of the day  observe, because+CD8+ cells and the increased percentages of the other subpopulations. The results demonstrate that increasing concentrations of corticosterone affect CD4-CD8- and CD4+CD8+ similarly, but the slope for CD4+CD8+ cells is significantly greater (by the method of Zar as implemented by Prism software) than for CD4-CD8- cells, indicating slightly greater sensitivity to high concentrations of corticosterone. The effect of increasing concentrations of corticosterone on CD4+CD8- cells was significantly less than the effect on CD4+CD8+ cells with regard to the slopes of the respective lines. The slope for CD4-CD8+ cells was less than the slope for all other subpopulations, suggesting a lower sensitivity of these cells to corticosterone across the whole range of concentrations. However, the decrease for CD4+CD8- cells and CD4-CD8+ cells relative to naive control was essentially the same in mice treated with a 5 mg pellet, suggesting that the difference in sensitivity is minimal as the corticosterone concentration increases. Although non-linear models would likely have given better correlation coefficients than linear ones for some of these data, linear models facilitate comparison. In addition, the Runs Test was conducted for all linear regression analyses, and the non-linear component was not significant for any of these data.It is clear that thymic subpopulations differ in their sensitivity to high (stress-inducible) corticosterone concentrations. However, linear regression analysis Figure  indicateThere are several mechanisms by which corticosterone might act to alter the number of cells in each subpopulation in the thymus. Although induction of apoptosis is generally regarded to be the major mechanism -3,22, al+CD8+, as expected, with a substantial percentage in the CD4-CD8- category and lesser percentages of the mature single positive categories. The percentages of apoptosis in all populations increased in mice treated with a 5.0 mg corticosterone pellet, except CD4+CD8+ cells, for which the percentage decreased. This almost certainly reflects the fact that this subpopulation was depleted by 24 hours of elevated corticosterone concentrations  [Initially, changes in the percentage of apoptotic cells in the various subpopulations did not seem entirely consistent with the changes in the percentages of each subpopulation in the thymus  . However+CD8+ cells in the thymus [+ cells was decreased to a greater extent than for mature single positive cells at this time point  are apparently the immediate precursors for CD4e thymus . One repe thymus . Resultst Figure . This suy others ,26.+CD8+, CD4-CD8-, and CD4+CD8- cells, but not CD4-CD8+ cells [+CD8+, CD4-CD8+, and CD4-CD8- cells, but not in CD4+CD8- cells  of TCR signalling. It would be of interest to explore this with TCR transgenic mice.The relationship between the results reported here and results from studies on the interactions between glucocorticoids and self-antigen in positive selection is not clear. A recent study indicates that activation through the TCR down regulates SRG3, a protein that associates with the glucocorticoid receptor and increases sensitivity to glucocorticoids . This haOne study in which adrenalectomy has been used to evaluate the effects of glucocorticoids on cellular subpopulations in the thymus yielded different results than those reported here. In that study, there was no increase in total cell number in the thymus, and there were no changes in subpopulation percentages in adrenalectomized mice two weeks after adrenalectomy . The bas+CD8+ and CD4+CD8- cells are increased in number in ADX mice is consistent with the idea that death by neglect of CD4+CD8+ cells is mediated by corticosterone. The increase in CD4+CD8- cells could be explained by the failure of CD4+CD8+ cells to die before reaching maturity, as they would have done in the presence of corticosterone. The observation that CD4-CD8+ cells are not increased to the same extent as CD4+CD8- cells is exactly what would have been predicted if sub-physiological concentrations of corticosterone allow survival of cells that would normally die by neglect. Whereas maturation of CD4+CD8+ cells to CD4-CD8+ cells requires MCH class I-dependent signals, maturation to CD4+CD8- status can be MHC-independent and apparently occurs by default [+CD8- cells before dying by corticosterone-mediated apoptosis. However, sub-physiological concentrations of corticosterone apparently allow these non-selected cells to survive.The results presented here do not directly demonstrate the extent to which corticosterone contributes to death by neglect or the extent to which it contributes to the death of negatively selected thymocytes. The fact that both CD4 default . Thus, cFemale C57BL/6 × C3H F1 (B6C3F1) mice were used in this study. Normal, adrenalectomized (ADX), and sham adrenalectomized mice were purchased from Charles River Labs (Wilmington, MA). The mice were allowed to recover from shipping stress for at least two weeks before use in experiments, and surgery was performed approximately one week before shipping. Thus, mice were evaluated at least three weeks after surgery at an age of 8–12 weeks. Mice were maintained on a 12 hour light/dark cycle, with free access to lab chow and water, except that ADX mice were given water with 0.9% sodium chloride. Sentinel mice housed periodically in the same room as the mice used in this study were negative for common adventitious agents and pathogens of mice. Animal care and use was in accord with the regulation of LSU Health Sciences Center and the NIH Guide for Care and Use of Laboratory Animals. The animal facility in which the mice were maintained is approved by the American Association for Accreditation of Laboratory Animal Care.Timed-release corticosterone pellets and placebo pellets were purchased from Innovative Research of America (Sarasota, FL). The pellets are designed to yield constant blood levels of corticosterone for 3 weeks. Pellets were implanted subcutaneously in the scapular area of mice that were anesthetized with sodium pentobarbital (55 mg/kg) and inhalation of methoxyflurane, as described in a previous study . The inc2 inhalation and the thymus was removed for analysis. In one experiment mice were euthanized by decapitation, trunk blood was obtained and allowed to clot, and serum was isolated after centrifugation. The serum was used to determine corticosterone concentration, using a radioimmunoassay kit (Diagnostic Products Corporation, Los Angeles, CA) as described previously [7 per ml, and 50 μl was added to the wells of a 96-well V-bottom microplate. Antibodies diluted in 50 μl of FACS buffer  were added to appropriate wells. In each experiment in which multiple antibodies were used, controls included cells labeled with each antibody singly, cells labeled with each isotype control antibody singly, cells labeled with all isotype control antibodies together, and unlabeled cells. The following antibodies were used: anti-CD4 (GK1.5) labeled with phycoerythrin (PE), anti-CD8a labeled with Cychrome, and anti-CD3 labeled with fluorescein isothiocyanate (FITC). These antibodies and matching isotype controls were obtained from BD Pharmingen. Titration of the antibodies indicated that a 1:8 dilution of anti-CD4 and anti-CD8 and a 1:5 dilution of anti-CD3 were appropriate for this study. After labeling for 30 min at 4°C, the cells were washed, fixed with 1% paraformaldehyde (EM Sciences, Ft. Washington, PA), washed again, and resuspended in FACS buffer. Samples were diluted in Isoton II (0.4 ml) for analysis. Cells were analyzed using a FACScan flow cytometer (Becton-Dickinson). A gate was set using forward scatter and side scatter to exclude debris, erythrocytes, and clumps of cells. All cells within this gate were then analyzed for CD3, CD4, and CD8.In two experiments, mice were euthanized by COeviously ,31. The In some experiments, cells were labeled to detect DNA fragmentation instead of CD3. Cells were first labeled with anti-CD4 (phycoerythrin) and anti-CD8 (cychrome) as described above, then the cells were fixed with 4% paraformaldehyde . A terminal dUTP nick end labeling (TUNEL) kit from Boehringer-Mannheim (Indianapolis, IN) with fluorescein-labeled dUTP was used to label apoptotic cells. Flow cytometry was used to identify apoptotic cells by two criteria. Cells that were small (as indicated by forward scatter) and labeled with fluorescein (indicating DNA fragmentation) were regarded to be apoptotic.Values significantly different from the naive (untreated) control group were determined by analysis of variance (ANOVA) followed by Dunnett's post hoc test. Statistical analysis, linear regression, and non-linear regression analysis were performed using Prism 4.0 software (GraphPad, Inc., San Diego, CA). Comparison of slope or intercept of pairs of regression lines was done using the method of Zar  as impleThe authors contributed approximately equally to conceiving, designing, and conducting these experiments. S.B.P. wrote the manuscript, and E.L.P. revised it.


Protein-protein interaction networks were used to analyze the functional evolution of duplicated genes in yeast. Pairs of paralogs can be grouped into 3 classes, which likely form part of a continuous scale of diversity. Studying the evolution of the function of duplicated genes usually implies an estimation of the extent of functional conservation/divergence between duplicates from comparison of actual sequences. This only reveals the possible molecular function of genes without taking into account their cellular function(s). We took into consideration this latter dimension of gene function to approach the functional evolution of duplicated genes by analyzing the protein-protein interaction network in which their products are involved. For this, we derived a functional classification of the proteins using PRODISTIN, a bioinformatics method allowing comparison of protein function. Our work focused on the duplicated yeast genes, remnants of an ancient whole-genome duplication.Starting from 4,143 interactions, we analyzed 41 duplicated protein pairs with the PRODISTIN method. We showed that duplicated pairs behaved differently in the classification with respect to their interactors. The different observed behaviors allowed us to propose a functional scale of conservation/divergence for the duplicated genes, based on interaction data. By comparing our results to the functional information carried by GO annotations and sequence comparisons, we showed that the interaction network analysis reveals functional subtleties, which are not discernible by other means. Finally, we interpreted our results in terms of evolutionary scenarios.Our analysis might provide a new way to analyse the functional evolution of duplicated genes and constitutes the first attempt of protein function evolutionary comparisons based on protein-protein interactions. Saccharomyces cerevisae genome, 40% that of Drosophila melanogaster, 50% that of Caenorhabditis elegans, and 38% of the human genome are composed of duplicated genes [de facto the study of ancient duplication events , event genome . EnlargiIn addition, sequence analysis generally only reveal the possible molecular  function(s) of proteins and even this only applies when domains of known function are identified in the sequences. As discussed previously , the funFunction comparison was one of our aims while developing PRODISTIN, a computational method that we recently proposed . This meS. cerevisiae, focusing on the 899 duplicated genes which represent remnants of an ancient whole-genome duplication (WGD) [Saccharomyces lineage, after the divergence from Kluyveromyces waltii, and was probably followed by a gene-loss event leading to the current S. cerevisiae genome [In the work presented here, we addressed the question of the cellular functional fate of duplicated genes in the yeast on (WGD) -8. This e genome .After applying the PRODISTIN method to the yeast interactome, we established and analyzed the functional classification of the duplicated yeast genes originating from the WGD. This analysis allowed us to compare the cellular function(s) of 41 paralog pairs for which enough interaction data was available. Three different behaviors of the pairs of paralogs in respect of the PRODISTIN classification were identified from this analysis, allowing us to establish a scale of functional divergence for the duplicated genes based on the protein-protein network analysis. This work validates the use of interaction data and the analysis of interaction networks as a new means of investigating evolutionary processes at the level of the cellular function.To obtain a first estimation of the functional conservation/divergence of the yeast duplicated genes, we analyzed available textual information relative to the actual functions of the 460 pairs of paralogs from the WGD. For this purpose, we used the Gene Ontology (GO) annotations. The Gene Ontology consortium  developsThe distributions of the calculated distance values are showed in Figure Second, the vast majority of the duplicated pairs do not differ significantly when Molecular Function terms are compared: 74.5% of the pairs have a zero distance based on annotations , but interestingly, the classes containing the duplicates were dedicated to the same biological process. This is reminiscent of a previous observation we made while studying in detail the rationale sustaining the PRODISTIN clustering : classesin vivo, they display different specificities in some cases. Swi5 specifically promotes transcription of the HO gene whereas Ace2 localizes to daughter cell nuclei after cytokinesis, regulates the expression of daughter-specific genes and delays the G1 progression in daughters [HO transcription [Finally, nine pairs of duplicated genes were found in different classes devoted to different biological processes. This is exemplified by the case of Ace2 and Swi5  between sequence conservation/divergence and evolution of cellular function. Because we have proposed here a three-level scale of possible functional divergence between paralog pairs, what can be said about the sequence-identity patterns shown by protein pairs within and between these three groups? To answer this question, 41 binary sequence comparison analyses were performed  and the results are displayed according to the classification behavior of the pair identified in the PRODISTIN analysis , allowing us to neglect the weight of such inferred annotations in our distance calculation.Gene annotations provided by the GO consortium  are the As far as the quality of interactions is concerned, two main problems result from erroneous  interactions and missing  interactions. Taking into account that the PRODISTIN method was largely statistically assessed for robustness against the presence of false interactions in our previous study , we can In the present analysis, we worked solely on pairs of paralogs that supposedly originated from the ancient WGD ,7. This S. cerevisiae. Initially proposed by Wolfe and Shields [An important issue for the interpretation of our results is the validity of the hypothesis of the existence of a WGD in  Shields , the WGD Shields -27. Very Shields . Among tOur study was driven by the idea that investigating the cellular rather than the molecular function of the duplicated genes might provide new information about the extent of their actual divergence and, consequently, might help us to envisage how their cellular function has evolved since the duplication event. Indeed, the first important outcome of our study, based on the comparison of annotations for duplicated pairs, is that although both the molecular and cellular functions of the majority of protein pairs have been conserved since the date of the WGD, cellular functions have evolved more rapidly than molecular functions. Although this finding could seem rather intuitive, it is, to the best of our knowledge, the first time that evidence has been proposed in its favor. Conservation of the same molecular function for two duplicated proteins while allowing the diversification of their cellular functions may represent a simple and economical way of introducing functional diversity and complexity in a controlled manner during evolution. This may be the result of a change in interaction partners and/or subcellular localization.The second important result of our study is that since the date of the ancient WGD, cellular functions have evolved at variable rates, since a scale of functional divergence can be detected. In this respect, we propose to interpret this functional scale of divergence in the light of different theoritical evolutionary scenarios for cellular function.First, the first level of the functional scale (behavior I) may contain duplicates which have been conserved as such, because keeping two copies may confer an evolutionary benefit on the cell  evolved functionally according to the duplication-degeneration-complementation (DDC) or subfunctionalization model proposed by Force et al. . This pret al. ) and/or et al. [Finally, the third level of the functional scale (behavior III) may correspond to duplicates that have evolved by neofunctionalization, as not only their interactors are different but they are also involved in different cellular processes (for instance, Swi5/Ace2). These genes may illustrate Ohno's theory  of the eet al.  strengthMost network analyses carried out up to now either emphasized the prediction of function for uncharacterized proteins ,30 or, iSaccharomyces cerevisiae, less than 10% of the gene pairs, remnants of the WGD, are amenable to such a detailed analysis. As our knowledge on interaction networks is increasing and as more interactions become available, we can expect to improve both the coverage of duplicated pairs of interactors and the relevance of the functional clusters found by the PRODISTIN method.A limitation of this type of analysis is the present knowledge of interaction networks. Even in a well-studied organism such as Finally, it should be emphasized that the study of evolutionary processes greatly benefits by being approached using different tools not only at the sequence level, as is usual, but also directly at the functional level. In the case of the study of the 41 paralog pairs reported here, functional conclusions inferred from the sequence level would have been incomplete and even erroneous in several instances.GOproxy , a tool i,j) = number of (Terms(i) ΔTerms(j))/ [number of (Terms(i) ∪ Terms(j)) + number of (Terms(i) ∩ Terms(j))],Dist(i and j denote two genes, Terms(i) and Terms(j) are the lists of their GO terms and Δ is the symmetrical difference between the two sets. This distance formula increases the weight of the shared GO terms by giving more weight to similarities than to differences. The GOToolBox website can be accessed at [in which, essed at .in vitro binding, far western, gel retardation and biochemical experiments).The protein-protein interaction dataset we investigated contains a total of 4,143 selected interactions involving 2,643 proteins. We updated our former dataset  with 1,2PRODISTIN, a computational method we recently proposed , was usePairwise sequence alignments were carried out on the set of 460 pairs of duplicated protein sequences using the Needleman-Wunsch  algorithm. The program used is available at . The choThe following additional data are available with the online version of this paper. Additional data file The expectation values for the distribution of functional distances based on the GO annotationsClick here for additional data fileDetails of the 123 PRODISTIN classes contained in the classification treeClick here for additional data file