This commentary takes up Pearl's welcome challenge to clearly articulate the scientific value of principal stratification estimands that we and colleagues have investigated, in the area of randomized placebo-controlled preventive vaccine efficacy trials, especially trials of HIV vaccines. After briefly arguing that certain principal stratification estimands for studying vaccine effects on post-infection outcomes are of genuine scientific interest, the bulk of our commentary argues that the “causal effect predictiveness” (CEP) principal stratification estimand for evaluating immune biomarkers as surrogate endpoints is not of ultimate scientific interest, because it evaluates surrogacy restricted to the setting of a particular vaccine efficacy trial, but is nevertheless useful for guiding the selection of primary immune biomarker endpoints in Phase I/II vaccine trials and for facilitating assessment of transportability/bridging surrogacy.
principal stratification; causal inference; vaccine trial
Participants in longitudinal studies on the effects of drug treatment and criminal justice system interventions are at high risk for institutionalization (e.g., spending time in an environment where their freedom to use drugs, commit crimes, or engage in risky behavior may be circumscribed). Methods used for estimating treatment effects in the presence of institutionalization during follow-up can be highly sensitive to assumptions that are unlikely to be met in applications and thus likely to yield misleading inferences. In this paper, we consider the use of principal stratification to control for institutionalization at follow-up. Principal stratification has been suggested for similar problems where outcomes are unobservable for samples of study participants because of dropout, death, or other forms of censoring. The method identifies principal strata within which causal effects are well defined and potentially estimable. We extend the method of principal stratification to model institutionalization at follow-up and estimate the effect of residential substance abuse treatment versus outpatient services in a large scale study of adolescent substance abuse treatment programs. Additionally, we discuss practical issues in applying the principal stratification model to data. We show via simulation studies that the model can only recover true effects provided the data meet strenuous demands and that there must be caution taken when implementing principal stratification as a technique to control for post-treatment confounders such as institutionalization.
Principal Stratification; Post-Treatment Confounder; Institutionalization; Causal Inference
Pearl (2011) asked for the causal inference community to clarify the role of the principal stratification framework in the analysis of causal effects. Here, I argue that the notion of principal stratification has shed light on problems of non-compliance, censoring-by-death, and the analysis of post-infection outcomes; that it may be of use in considering problems of surrogacy but further development is needed; that it is of some use in assessing “direct effects”; but that it is not the appropriate tool for assessing “mediation.” There is nothing within the principal stratification framework that corresponds to a measure of an “indirect” or “mediated” effect.
causal inference; mediation; non-compliance; potential outcomes; principal stratification; surrogates
Pearl’s article provides a useful springboard for discussing further the benefits and drawbacks of principal stratification and the associated discomfort with attributing effects to post-treatment variables. The basic insights of the approach are important: pay close attention to modification of treatment effects by variables not observable before treatment decisions are made, and be careful in attributing effects to variables when counterfactuals are ill-defined. These insights have often been taken too far in many areas of application of the approach, including instrumental variables, censoring by death, and surrogate outcomes. A novel finding is that the usual principal stratification estimand in the setting of censoring by death is by itself of little practical value in estimating intervention effects.
principal stratification; causal inference
Association studies using unrelated individuals have become the most popular design for mapping complex traits. One of the major challenges of association mapping is avoiding spurious association due to population stratification. Principal component analysis (PCA) on genome-wide marker genotypes is one of the most popular population stratification control methods. It implicitly assumes that the markers are in linkage equilibrium, a condition that is rarely satisfied and that we plan to relax.
We carefully examined the impact of linkage disequilibrium (LD) on PCA, and proposed a simple modification of the standard PCA to automatically adjust for the correlations among markers.
We demonstrated that LD patterns in genome-wide association datasets can distort the techniques for stratification control, showing ‘subpopulations’ reflecting localized LD phenomena rather than plausible population structure. We showed that the proposed method effectively removes the artifactual effect of LD patterns, and successfully recovers underlying population structure that is not apparent from standard PCA.
PCA is highly influenced by sets of SNPs with high LD, obscuring the true population substructure. Our shrinkage PCA applies to all available markers, regardless of the LD patterns. The proposed method is easier to implement than most existing LD adjusted PCA methods.
PCA; Loadings; GWAS
Genome-Wide Association Studies are powerful tools to detect genetic variants associated with diseases. Their results have, however, been questioned, in part because of the bias induced by population stratification. This is a consequence of systematic differences in allele frequencies due to the difference in sample ancestries that can lead to both false positive or false negative findings. Many strategies are available to account for stratification but their performances differ, for instance according to the type of population structure, the disease susceptibility locus minor allele frequency, the degree of sampling imbalanced, or the sample size. We focus on the type of population structure and propose a comparison of the most commonly used methods to deal with stratification that are the Genomic Control, Principal Component based methods such as implemented in Eigenstrat, adjusted Regressions and Meta-Analyses strategies. Our assessment of the methods is based on a large simulation study, involving several scenarios corresponding to many types of population structures. We focused on both false positive rate and power to determine which methods perform the best. Our analysis showed that if there is no population structure, none of the tests led to a bias nor decreased the power except for the Meta-Analyses. When the population is stratified, adjusted Logistic Regressions and Eigenstrat are the best solutions to account for stratification even though only the Logistic Regressions are able to constantly maintain correct false positive rates. This study provides more details about these methods. Their advantages and limitations in different stratification scenarios are highlighted in order to propose practical guidelines to account for population stratification in Genome-Wide Association Studies.
In vaccine trials, the vaccination of one person might prevent the infection of another; a distinction can be drawn between the ways such a protective effect might arise. Consider a setting with 2 persons per household in which one of the 2 is vaccinated. Vaccinating the first person may protect the second person by preventing the first from being infected and passing the infection on to the second. Alternatively, vaccinating the first person may protect the second by rendering the infection less contagious even if the first is infected. This latter mechanism is sometimes referred to as an “infectiousness effect” of the vaccine. Crude estimators for the infectiousness effect will be subject to selection bias due to stratification on a postvaccination event, namely the infection status of the first person. We use theory concerning causal inference under interference along with a principal-stratification framework to show that, although the crude estimator is biased, it is, under plausible assumptions, conservative for what one might define as a causal infectiousness effect. This applies to bias from selection due to the persons in the comparison, and also to selection due to pathogen virulence. We illustrate our results with an example from the literature.
Genetic ancestry is known to impact outcomes of genotype-phenotype studies that are designed to identify risk for common diseases in human populations. Failure to control for population stratification due to genetic ancestry can significantly confound results of disease association studies. Moreover, ancestry is a critical factor in assessing lifetime risk of disease, and can play an important role in optimizing treatment. As modern medicine moves towards using personal genetic information for clinical applications, it is important to determine genetic ancestry in an accurate, cost-effective and efficient manner. Self-identified race is a common method used to track and control for population stratification; however, social constructs of race are not necessarily informative for genetic applications. The use of ancestry informative markers (AIMs) is a more accurate method for determining genetic ancestry for the purposes of population stratification.
Here we introduce a novel panel of 36 microsatellite (MSAT) AIMs that determines continental admixture proportions. This panel, which we have named Continental Ancestry Informative Markers or CoAIMs, consists of MSAT AIMs that were chosen based upon their measure of genetic variance (Fst), allele frequencies and their suitability for efficient genotyping. Genotype analysis using CoAIMs along with a Bayesian clustering method (STRUCTURE) is able to discern continental origins including Europe/Middle East (Caucasians), East Asia, Africa, Native America, and Oceania. In addition to determining continental ancestry for individuals without significant admixture, we applied CoAIMs to ascertain admixture proportions of individuals of self declared race.
CoAIMs can be used to efficiently and effectively determine continental admixture proportions in a sample set. The CoAIMs panel is a valuable resource for genetic researchers performing case-control genetic association studies, as it can control for the confounding effects of population stratification. The MSAT-based approach used here has potential for broad applicability as a cost effective tool toward determining admixture proportions.
Using multiple historical trials with surrogate and true endpoints, we consider various models to predict the effect of treatment on a true endpoint in a target trial in which only a surrogate endpoint is observed. This predicted result is computed using (1) a prediction model (mixture, linear, or principal stratification) estimated from historical trials and the surrogate endpoint of the target trial and (2) a random extrapolation error estimated from successively leaving out each trial among the historical trials. The method applies to either binary outcomes or survival to a particular time that is computed from censored survival data. We compute a 95% confidence interval for the predicted result and validate its coverage using simulation. To summarize the additional uncertainty from using a predicted instead of true result for the estimated treatment effect, we compute its multiplier of standard error. Software is available for download.
Randomized trials; Reproducibility; Principal stratification
To explore classification rules based on data mining methodologies which are to be used in defining strata in stratified sampling of healthcare providers with improved sampling efficiency.
We performed k-means clustering to group providers with similar characteristics, then, constructed decision trees on cluster labels to generate stratification rules. We assessed the variance explained by the stratification proposed in this study and by conventional stratification to evaluate the performance of the sampling design. We constructed a study database from health insurance claims data and providers' profile data made available to this study by the Health Insurance Review and Assessment Service of South Korea, and population data from Statistics Korea. From our database, we used the data for single specialty clinics or hospitals in two specialties, general surgery and ophthalmology, for the year 2011 in this study.
Data mining resulted in five strata in general surgery with two stratification variables, the number of inpatients per specialist and population density of provider location, and five strata in ophthalmology with two stratification variables, the number of inpatients per specialist and number of beds. The percentages of variance in annual changes in the productivity of specialists explained by the stratification in general surgery and ophthalmology were 22% and 8%, respectively, whereas conventional stratification by the type of provider location and number of beds explained 2% and 0.2% of variance, respectively.
This study demonstrated that data mining methods can be used in designing efficient stratified sampling with variables readily available to the insurer and government; it offers an alternative to the existing stratification method that is widely used in healthcare provider surveys in South Korea.
Sampling Studies; Decision Trees; Data Mining
We examine the practicality of propensity score methods for estimating causal treatment effects conditional on intermediate posttreatment outcomes (principal effects) in the context of randomized experiments. In particular, we focus on the sensitivity of principal causal effect estimates to violation of principal ignorability, which is the primary assumption that underlies the use of propensity score methods to estimate principal effects. Under principal ignorability, principal strata membership is conditionally independent of the potential outcome under control given the pre-treatment covariates; i.e., there are no differences in the potential outcomes under control across principal strata given the observed pretreatment covariates. Under this assumption, principal scores modeling principal strata membership can be estimated based solely on the observed covariates and used to predict strata membership and estimate principal effects. While this assumption underlies the use of propensity scores in this setting, sensitivity to violations of it has not been studied rigorously. In this paper, we explicitly define principal ignorability using the outcome model (although we do not actually use this outcome model in estimating principal scores) and systematically examine how deviations from the assumption affect estimates, including how the strength of association between principal stratum membership and covariates modifies the performance. We find that when principal ignorability is violated, very strong covariate predictors of stratum membership are needed to yield accurate estimates of principal effects.
randomized experiments; intermediate outcomes; principal ignorability; principal scores; principal stratification; propensity scores
The use of accepted prostate cancer risk stratification groups based on prostate-specific antigen, T stage and Gleason score assists in therapeutic treatment decision-making, clinical trial design and outcome reporting. The utility of integrating novel prognostic factors into an updated risk stratification schema is an area of current debate. The purpose of this work is to critically review the available literature on novel pre-treatment prognostic factors and alternative prostate cancer risk stratification schema to assess the feasibility and need for changes to existing risk stratification systems.
A systematic literature search was conducted to identify original research publications and review articles on prognostic factors and risk stratification in prostate cancer. Search terms included risk stratification, risk assessment, prostate cancer or neoplasms, and prognostic factors. Abstracted information was assessed to draw conclusions regarding the potential utility of changes to existing risk stratification schema.
The critical review identified three specific clinically relevant potential changes to the most commonly used three-group risk stratification system: (1) the creation of a very-low risk category; (2) the splitting of intermediate-risk into a low- and high-intermediate risk groups; and (3) the clarification of the interface between intermediate- and high-risk disease. Novel pathological factors regarding high-grade cancer, subtypes of Gleason score 7 and percentage biopsy cores positive were also identified as potentially important risk-stratification factors.
Multiple studies of prognostic factors have been performed to create currently utilized prostate cancer risk stratification systems. We propose potential changes to existing systems.
Prostate cancer is a very complex disease, and the decision-making process requires the clinician to balance clinical benefits, life expectancy, comorbidities, and potential treatment related side effects. Accurate prediction of clinical outcomes may help in the difficult process of making decisions related to prostate cancer. In this review, we discuss attributes of predictive tools and systematically review those available for prostate cancer. Types of tools include probability formulas, look-up and propensity scoring tables, risk-class stratification prediction tools, classification and regression tree analysis, nomograms, and artificial neural networks. Criteria to evaluate tools include discrimination, calibration, generalizability, level of complexity, decision analysis, and ability to account for competing risks and conditional probabilities. We describe the available predictive tools and their features, focusing on nomograms. While some tools are well-calibrated, few have been externally validated or directly compared to other tools. In addition, the clinical consequences of applying predictive tools need thorough assessment. Nevertheless, predictive tools can facilitate medical decision-making by showing patients tailored predictions of their outcomes with various alternatives. Additionally, accurate tools may improve clinical trial design.
prostate cancer; nomogram; prediction; recurrence; diagnosis; decision analysis
Artificial insemination and genetic selection are major factors contributing to population stratification in dairy cattle. In this study, we analyzed the effect of sample stratification and the effect of stratification correction on results of a dairy genome-wide association study (GWAS). Three methods for stratification correction were used: the efficient mixed-model association expedited (EMMAX) method accounting for correlation among all individuals, a generalized least squares (GLS) method based on half-sib intraclass correlation, and a principal component analysis (PCA) approach.
Historical pedigree data revealed that the 1,654 contemporary cows in the GWAS were all related when traced through approximately 10–15 generations of ancestors. Genome and phenotype stratifications had a striking overlap with the half-sib structure. A large elite half-sib family of cows contributed to the detection of favorable alleles that had low frequencies in the general population and high frequencies in the elite cows and contributed to the detection of X chromosome effects. All three methods for stratification correction reduced the number of significant effects. EMMAX method had the most severe reduction in the number of significant effects, and the PCA method using 20 principal components and GLS had similar significance levels. Removal of the elite cows from the analysis without using stratification correction removed many effects that were also removed by the three methods for stratification correction, indicating that stratification correction could have removed some true effects due to the elite cows. SNP effects with good consensus between different methods and effect size distributions from USDA’s Holstein genomic evaluation included the DGAT1-NIBP region of BTA14 for production traits, a SNP 45kb upstream from PIGY on BTA6 and two SNPs in NIBP on BTA14 for protein percentage. However, most of these consensus effects had similar frequencies in the elite and average cows.
Genetic selection and extensive use of artificial insemination contributed to overlapped genome, pedigree and phenotype stratifications. The presence of an elite cluster of cows was related to the detection of rare favorable alleles that had high frequencies in the elite cluster and low frequencies in the remaining cows. Methods for stratification correction could have removed some true effects associated with genetic selection.
Population stratification leads to a predictable phenomenon—a reduction in the number of heterozygotes compared to that calculated assuming Hardy-Weinberg Equilibrium (HWE). We show that population stratification results in another phenomenon—an excess in the proportion of spouse-pairs with the same genotypes at all ancestrally informative markers, resulting in ancestrally related positive assortative mating. We use principal components analysis to show that there is evidence of population stratification within the Framingham Heart Study, and show that the first principal component correlates with a North-South European cline. We then show that the first principal component is highly correlated between spouses (r=0.58, p=0.0013), demonstrating that there is ancestrally related positive assortative mating among the Framingham Caucasian population. We also show that the single nucleotide polymorphisms loading most heavily on the first principal component show an excess of homozygotes within the spouses, consistent with similar ancestry-related assortative mating in the previous generation. This nonrandom mating likely affects genetic structure seen more generally in the North American population of European descent today, and decreases the rate of decay of linkage disequilibrium for ancestrally informative markers.
population stratification; non-random mating; Hardy-Weinberg equilibrium
The effects of vaccine on postinfection outcomes, such as disease, death, and secondary transmission to others, are important scientific and public health aspects of prophylactic vaccination. As a result, evaluation of many vaccine effects condition on being infected. Conditioning on an event that occurs posttreatment (in our case, infection subsequent to assignment to vaccine or control) can result in selection bias. Moreover, because the set of individuals who would become infected if vaccinated is likely not identical to the set of those who would become infected if given control, comparisons that condition on infection do not have a causal interpretation. In this article we consider identifiability and estimation of causal vaccine effects on binary postinfection outcomes. Using the principal stratification framework, we define a postinfection causal vaccine efficacy estimand in individuals who would be infected regardless of treatment assignment. The estimand is shown to be not identifiable under the standard assumptions of the stable unit treatment value, monotonicity, and independence of treatment assignment. Thus selection models are proposed that identify the causal estimand. Closed-form maximum likelihood estimators (MLEs) are then derived under these models, including those assuming maximum possible levels of positive and negative selection bias. These results show the relations between the MLE of the causal estimand and two commonly used estimators for vaccine effects on postinfection outcomes. For example, the usual intent-to-treat estimator is shown to be an upper bound on the postinfection causal vaccine effect provided that the magnitude of protection against infection is not too large. The methods are used to evaluate postinfection vaccine effects in a clinical trial of a rotavirus vaccine candidate and in a field study of a pertussis vaccine. Our results show that pertussis vaccination has a significant causal effect in reducing disease severity.
Causal inference; Infectious disease; Maximum likelihood; Principal stratification; Sensitivity analysis
Principal stratification has recently become a popular tool to address certain causal inference questions, particularly in dealing with post-randomization factors in randomized trials. Here, we analyze the conceptual basis for this framework and invite response to clarify the value of principal stratification in estimating causal effects of interest.
causal inference; principal stratification; surrogate endpoints; direct effect; mediation
The framework of principal stratification provides a way to think about treatment effects conditional on post-randomization variables, such as level of compliance. In particular, the complier average causal effect (CACE)–the effect of the treatment for those individuals who would comply with their treatment assignment under either treatment condition–is often of substantive interest. However, estimation of the CACE is not always straightforward, with a variety of estimation procedures and underlying assumptions, but little advice to help researchers select between methods. In this paper we discuss and examine two methods that rely on very different assumptions to estimate the CACE: a maximum likelihood (“joint”) method that assumes the “exclusion restriction,” and a propensity score based method that relies on “principal ignorability.” We detail the assumptions underlying each approach, and assess each method’s sensitivity to both its own assumptions and those of the other method using both simulated data and a motivating example. We find that the exclusion restriction based joint approach appears somewhat less sensitive to its assumptions, and that the performance of both methods is significantly improved when there are strong predictors of compliance. Interestingly, we also find that each method performs particularly well when the assumptions of the other approach are violated. These results highlight the importance of carefully selecting an estimation procedure whose assumptions are likely to be satisfied in practice and of having strong predictors of principal stratum membership.
Complier average causal effect; Intermediate outcomes; Noncompliance; Principal stratification; Propensity scores
When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.
Bayesian estimation; Counterfactual model; Identifiability; Multiple trials; Principal stratification; Surrogate marker
Population stratification can cause spurious associations in population–based association studies. Several statistical methods have been proposed to reduce the impact of population stratification on population–based association studies. We simulated a set of stratified populations based on the real haplotype data from the HapMap ENCODE project, and compared the relative power, type I error rates, accuracy and positive prediction value of four prevailing population–based association study methods: traditional case-control tests, structured association (SA), genomic control (GC) and principal components analysis (PCA) under various population stratification levels. Additionally, we evaluated the effects of sample sizes and frequencies of disease susceptible allele on the performance of the four analytical methods in the presence of population stratification. We found that the performance of PCA was very stable under various scenarios. Our comparison results suggest that SA and PCA have comparable performance, if sufficient ancestral informative markers are used in SA analysis. GC appeared to be strongly conservative in significantly stratified populations. It may be better to apply GC in the stratified populations with low stratification level. Our study intends to provide a practical guideline for researchers to select proper study methods and make appropriate inference of the results in population-based association studies.
If a vaccine does not protect individuals completely against infection, it could still reduce infectiousness of infected vaccinated individuals to others. Typically, vaccine efficacy for infectiousness is estimated based on contrasts between the transmission risk to susceptible individuals from infected vaccinated individuals compared with that from infected unvaccinated individuals. Such estimates are problematic, however, because they are subject to selection bias and do not have a causal interpretation. Here, we develop causal estimands for vaccine efficacy for infectiousness for four different scenarios of populations of transmission units of size two. These causal estimands incorporate both principal stratification, based on the joint potential infection outcomes under vaccine and control, and interference between individuals within transmission units. In the most general scenario, both individuals can be exposed to infection outside the transmission unit and both can be assigned either vaccine or control. The three other scenarios are special cases of the general scenario where only one individual is exposed outside the transmission unit or can be assigned vaccine. The causal estimands for vaccine efficacy for infectiousness are well defined only within certain principal strata and, in general, are identifiable only with strong unverifiable assumptions. Nonetheless, the observed data do provide some information, and we derive large sample bounds on the causal vaccine efficacy for infectiousness estimands. An example of the type of data observed in a study to estimate vaccine efficacy for infectiousness is analyzed in the causal inference framework we developed.
causal inference; principal stratification; interference; infectious disease; vaccine
In the treatment of lung cancer, an accurate estimation of patient clinical outcome is essential for choosing an appropriate course of therapy. It is important to develop a prognostic stratification model which combines clinical, pathological and demographic factors for individualized clinical decision making.
A total of 234,412 patients diagnosed with adenocarcinomas or squamous cell carcinomas of the lung or bronchus between 1988 and 2006 were retrieved from the SEER database to construct a prognostic model. A model was developed by estimating a Cox proportional hazards model on 500 bootstrapped samples. Two models, one using stage alone and another comprehensive model using additional covariates, were constructed. The comprehensive model consistently outperformed the model using stage alone in prognostic stratification and on Harrell's C, Nagelkerke's R2, and Brier Scores in the whole patient population as well as in specific treatment modalities. Specifically, the comprehensive model generated different prognostic groups with distinct post-operative survival (log-rank P<0.001) within surgical stage IA and IB patients in Kaplan-Meier analyses. Two additional patient cohorts (n = 1,991) were used as an external validation, with the comprehensive model again outperforming the model using stage alone with regards to prognostic stratification and the three evaluated metrics.
These results demonstrate the feasibility of constructing a precise prognostic model combining multiple clinical, pathologic, and demographic factors. The comprehensive model significantly improves individualized prognosis upon AJCC tumor staging and is robust across a range of treatment modalities, the spectrum of patient risk, and in novel patient cohorts.
Many patients undergo non‐invasive testing for the detection of coronary artery disease before non‐cardiac surgery. This is despite the low predictive value of positive tests in this population and the lack of any evidence of benefit of coronary revascularisation before non‐cardiac surgical procedures. Further, this strategy often triggers a clinical cascade exposing the patient to progressively riskier testing and intervention and results in increased costs and unnecessary delays. On the other hand, administration of β blockers, and more recently statins, has been shown to reduce the occurrence of perioperative ischaemic events. Therefore, there is a need for a shift in emphasis from risk stratification by non‐invasive testing to risk modification by the application of interventions, which prevent perioperative ischaemia—principally, perioperative β adrenergic blockade and perhaps treatment with statins. Clinical risk stratification tools reliably identify patients at high risk of perioperative ischaemic events and can guide in the appropriate use of perioperative medical treatment.
perioperative risk, non‐cardiac surgery, preoperative evaluation, β adrenergic blockers
Data analysis for randomized trials including multi-treatment arms is often complicated by subjects who do not comply with their treatment assignment. We discuss here methods of estimating treatment efficacy for randomized trials involving multi-treatment arms subject to non-compliance. One treatment effect of interest in the presence of non-compliance is the complier average causal effect (CACE) (Angrist et al. 1996), which is defined as the treatment effect for subjects who would comply regardless of the assigned treatment. Following the idea of principal stratification (Frangakis & Rubin 2002), we define principal compliance (Little et al. 2009) in trials with three treatment arms, extend CACE and define causal estimands of interest in this setting. In addition, we discuss structural assumptions needed for estimation of causal effects and the identifiability problem inherent in this setting from both a Bayesian and a classical statistical perspective. We propose a likelihood-based framework that models potential outcomes in this setting and a Bayes procedure for statistical inference. We compare our method with a method of moments approach proposed by Cheng & Small (2006) using a hypothetical data set, and further illustrate our approach with an application to a behavioral intervention study (Janevic et al. 2003).
Causal Inference; Complier Average Causal Effect; Multi-arm Trials; Non-compliance; Principal Compliance; Principal Stratification
We propose a new general Bayesian latent class model for evaluation of the performance of multiple diagnostic tests in situations in which no gold standard test exists based on a computationally intensive approach. The modeling represents an interesting and suitable alternative to models with complex structures that involve the general case of several conditionally independent diagnostic tests, covariates, and strata with different disease prevalences. The technique of stratifying the population according to different disease prevalence rates does not add further marked complexity to the modeling, but it makes the model more flexible and interpretable. To illustrate the general model proposed, we evaluate the performance of six diagnostic screening tests for Chagas disease considering some epidemiological variables. Serology at the time of donation (negative, positive, inconclusive) was considered as a factor of stratification in the model. The general model with stratification of the population performed better in comparison with its concurrents without stratification. The group formed by the testing laboratory Biomanguinhos FIOCRUZ-kit (c-ELISA and rec-ELISA) is the best option in the confirmation process by presenting false-negative rate of 0.0002% from the serial scheme. We are 100% sure that the donor is healthy when these two tests have negative results and he is chagasic when they have positive results.