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1.  A Bayesian Approach to Surrogacy Assessment Using Principal Stratification in Clinical Trials 
Biometrics  2009;66(2):523-531.
A surrogate marker (S) is a variable that can be measured earlier and often easier than the true endpoint (T) in a clinical trial. Most previous research has been devoted to developing surrogacy measures to quantify how well S can replace T or examining the use of S in predicting the effect of a treatment (Z). However, the research often requires one to fit models for the distribution of T given S and Z. It is well known that such models do not have causal interpretations because the models condition on a post-randomization variable S. In this paper, we directly model the relationship among T, S and Z using a potential outcomes framework introduced by Frangakis and Rubin (2002). We propose a Bayesian estimation method to evaluate the causal probabilities associated with the cross-classification of the potential outcomes of S and T when S and T are both binary. We use a log-linear model to directly model the association between the potential outcomes of S and T through the odds ratios. The quantities derived from this approach always have causal interpretations. However, this causal model is not identifiable from the data without additional assumptions. To reduce the non-identifiability problem and increase the precision of statistical inferences, we assume monotonicity and incorporate prior belief that is plausible in the surrogate context by using prior distributions. We also explore the relationship among the surrogacy measures based on traditional models and this counterfactual model. The method is applied to the data from a glaucoma treatment study.
PMCID: PMC3365598  PMID: 19673864
Bayesian Estimation; Counterfactual Model; Randomized Trial; Surrogate Marker
2.  Accommodating Missingness When Assessing Surrogacy Via Principal Stratification 
Clinical trials (London, England)  2013;10(3):363-377.
When an outcome of interest in a clinical trial is late-occurring or difficult to obtain, surrogate markers can extract information about the effect of the treatment on the outcome of interest. Understanding associations between the causal effect of treatment on the outcome and the causal effect of treatment on the surrogate is critical to understanding the value of a surrogate from a clinical perspective.
Traditional regression approaches to determine the proportion of the treatment effect explained by surrogate markers suffer from several shortcomings: they can be unstable, and can lie outside of the 0–1 range. Further, they do not account for the fact that surrogate measures are obtained post-randomization, and thus the surrogate-outcome relationship may be subject to unmeasured confounding. Methods to avoid these problem are of key importance.
Frangakis C, Rubin DM. Principal stratification in causal inference. Biometrics 2002; 58:21–9 suggested assessing the causal effect of treatment within pre-randomization “principal strata” defined by the counterfactual joint distribution of the surrogate marker under the different treatment arms, with the proportion of the overall outcome causal effect attributable to subjects for whom the treatment affects the proposed surrogate as the key measure of interest. Li Y, Taylor JMG, Elliott MR. Bayesian approach to surrogacy assessment using principal stratification in clinical trials. Biometrics 2010; 66:523–31 developed this “principal surrogacy” approach for dichotomous markers and outcomes, utilizing Bayesian methods that accommodated non-identifiability in the model parameters. Because the surrogate marker is typically observed early, outcome data is often missing. Here we extend Li, Taylor, and Elliott to accommodate missing data in the observable final outcome under ignorable and non-ignorable settings. We also allow for the possibility that missingness has a counterfactual component, a feature that previous literature has not addressed.
We apply the proposed methods to a trial of glaucoma control comparing surgery versus medication, where intraocular pressure (IOP) control at 12 months is a surrogate for IOP control at 96 months. We also conduct a series of simulations to consider the impacts of non-ignorability, as well as sensitivity to priors and the ability of the Decision Information Criterion to choose the correct model when parameters are not fully identified.
Because model parameters cannot be fully identified from data, informative priors can introduce non-trivial bias in moderate sample size settings, while more non-informative priors can yield wide credible intervals.
Assessing the linkage between causal effects of treatment on a surrogate marker and causal effects of a treatment on an outcome is important to understanding the value of a marker. These causal effects are not fully identifiable: hence we explore the sensitivity and identifiability aspects of these models and show that relatively weak assumptions can still yield meaningful results.
PMCID: PMC4096330  PMID: 23553326
Causal Inference; Surrogate Marker; Bayesian Analysis; dentifiability; Non-response; Counterfactual
3.  Estimating Causal Effects in Trials Involving Multi-Treatment Arms Subject to Non-compliance: A Bayesian framework 
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).
PMCID: PMC3104736  PMID: 21637737
Causal Inference; Complier Average Causal Effect; Multi-arm Trials; Non-compliance; Principal Compliance; Principal Stratification
4.  Is blood pressure reduction a valid surrogate endpoint for stroke prevention? an analysis incorporating a systematic review of randomised controlled trials, a by-trial weighted errors-in-variables regression, the surrogate threshold effect (STE) and the biomarker-surrogacy (BioSurrogate) evaluation schema (BSES) 
Blood pressure is considered to be a leading example of a valid surrogate endpoint. The aims of this study were to (i) formally evaluate systolic and diastolic blood pressure reduction as a surrogate endpoint for stroke prevention and (ii) determine what blood pressure reduction would predict a stroke benefit.
We identified randomised trials of at least six months duration comparing any pharmacologic anti-hypertensive treatment to placebo or no treatment, and reporting baseline blood pressure, on-trial blood pressure, and fatal and non-fatal stroke. Trials with fewer than five strokes in at least one arm were excluded. Errors-in-variables weighted least squares regression modelled the reduction in stroke as a function of systolic blood pressure reduction and diastolic blood pressure reduction respectively. The lower 95% prediction band was used to determine the minimum systolic blood pressure and diastolic blood pressure difference, the surrogate threshold effect (STE), below which there would be no predicted stroke benefit. The STE was used to generate the surrogate threshold effect proportion (STEP), a surrogacy metric, which with the R-squared trial-level association was used to evaluate blood pressure as a surrogate endpoint for stroke using the Biomarker-Surrogacy Evaluation Schema (BSES3).
In 18 qualifying trials representing all pharmacologic drug classes of antihypertensives, assuming a reliability coefficient of 0.9, the surrogate threshold effect for a stroke benefit was 7.1 mmHg for systolic blood pressure and 2.4 mmHg for diastolic blood pressure. The trial-level association was 0.41 and 0.64 and the STEP was 66% and 78% for systolic and diastolic blood pressure respectively. The STE and STEP were more robust to measurement error in the independent variable than R-squared trial-level associations. Using the BSES3, assuming a reliability coefficient of 0.9, systolic blood pressure was a B + grade and diastolic blood pressure was an A grade surrogate endpoint for stroke prevention. In comparison, using the same stroke data sets, no STEs could be estimated for cardiovascular (CV) mortality or all-cause mortality reduction, although the STE for CV mortality approached 25 mmHg for systolic blood pressure.
In this report we provide the first surrogate threshold effect (STE) values for systolic and diastolic blood pressure. We suggest the STEs have face and content validity, evidenced by the inclusivity of trial populations, subject populations and pharmacologic intervention populations in their calculation. We propose that the STE and STEP metrics offer another method of evaluating the evidence supporting surrogate endpoints. We demonstrate how surrogacy evaluations are strengthened if formally evaluated within specific-context evaluation frameworks using the Biomarker- Surrogate Evaluation Schema (BSES3), and we discuss the implications of our evaluation of blood pressure on other biomarkers and patient-reported instruments in relation to surrogacy metrics and trial design.
PMCID: PMC3388460  PMID: 22409774
Blood pressure; Stroke; Surrogate Endpoint; Biomarker
5.  Links between analysis of surrogate endpoints and endogeneity 
Statistics in medicine  2010;29(28):2869-2879.
There has been substantive interest in the assessment of surrogate endpoints in medical research. These are measures which could potentially replace “true” endpoints in clinical trials and lead to studies that require less follow-up. Recent research in the area has focused on assessments using causal inference frameworks. Beginning with a simple model for associating the surrogate and true endpoints in the population, we approach the problem as one of endogenous covariates. An instrumental variables estimator and general two-stage algorithm is proposed. Existing surrogacy frameworks are then evaluated in the context of the model. In addition, we define an extended relative effect estimator as well as a sensitivity analysis for assessing what we term the treatment instrumentality assumption. A numerical example is used to illustrate the methodology.
PMCID: PMC2997195  PMID: 20803482
Clinical Trial; Counterfactual; Nonlinear response; Prentice Criterion; Structural equations model
6.  A Trivariate Continual Reassessment Method for Phase I/II Trials of Toxicity, Efficacy, and Surrogate Efficacy 
Statistics in medicine  2012;31(29):3885-3895.
Recently, many Bayesian methods have been developed for dose-finding when simultaneously modeling both toxicity and efficacy outcomes in a blended phase I/II fashion. A further challenge arises when all the true efficacy data cannot be obtained quickly after the treatment, so that surrogate markers are instead used (e.g, in cancer trials). We propose a framework to jointly model the probabilities of toxicity, efficacy and surrogate efficacy given a particular dose. Our trivariate binary model is specified as a composition of two bivariate binary submodels. In particular, we extend the bCRM approach [1], as well as utilize the Gumbel copula of Thall and Cook [2]. The resulting trivariate algorithm utilizes all the available data at any given time point, and can flexibly stop the trial early for either toxicity or efficacy. Our simulation studies demonstrate our proposed method can successfully improve dosage targeting efficiency and guard against excess toxicity over a variety of true model settings and degrees of surrogacy.
PMCID: PMC3532950  PMID: 22807126
Bayesian adaptive methods; Continual reassessment method (CRM); Maximum tolerated dose (MTD); Phase I/II clinical trial; Surrogate efficacy; Toxicity
7.  Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes 
Biostatistics (Oxford, England)  2010;11(2):353-372.
Most investigations in the social and health sciences aim to understand the directional or causal relationship between a treatment or risk factor and outcome. Given the multitude of pathways through which the treatment or risk factor may affect the outcome, there is also an interest in decomposing the effect of a treatment of risk factor into “direct” and “mediated” effects. For example, child's socioeconomic status (risk factor) may have a direct effect on the risk of death (outcome) and an effect that may be mediated through the adulthood socioeconomic status (mediator). Building on the potential outcome framework for causal inference, we develop a Bayesian approach for estimating direct and mediated effects in the context of a dichotomous mediator and dichotomous outcome, which is challenging as many parameters cannot be fully identified. We first define principal strata corresponding to the joint distribution of the observed and counterfactual values of the mediator, and define associate, dissociative, and mediated effects as functions of the differences in the mean outcome under differing treatment assignments within the principal strata. We then develop the likelihood properties and calculate nonparametric bounds of these causal effects assuming randomized treatment assignment. Because likelihood theory is not well developed for nonidentifiable parameters, we consider a Bayesian approach that allows the direct and mediated effects to be expressed in terms of the posterior distribution of the population parameters of interest. This range can be reduced by making further assumptions about the parameters that can be encoded in prior distribution assumptions. We perform sensitivity analyses by using several prior distributions that make weaker assumptions than monotonicity or the exclusion restriction. We consider an application that explores the mediating effects of adult poverty on the relationship between childhood poverty and risk of death.
PMCID: PMC2830580  PMID: 20101045
Direct effect; Mediated effect; Monotonicity; Mortality; Poverty
8.  Surrogate endpoints for overall survival in digestive oncology trials: which candidates? A questionnaires survey among clinicians and methodologists 
BMC Cancer  2010;10:277.
Overall survival (OS) is the gold standard for the demonstration of a clinical benefit in cancer trials. Replacement of OS by a surrogate endpoint allows to reduce trial duration. To date, few surrogate endpoints have been validated in digestive oncology. The aim of this study was to draw up an ordered list of potential surrogate endpoints for OS in digestive cancer trials, by way of a survey among clinicians and methodologists. Secondary objective was to obtain their opinion on surrogacy and quality of life (QoL).
In 2007 and 2008, self administered sequential questionnaires were sent to a panel of French clinicians and methodologists involved in the conduct of cancer clinical trials. In the first questionnaire, panellists were asked to choose the most important characteristics defining a surrogate among six proposals, to give advantages and drawbacks of the surrogates, and to answer questions about their validation and use. Then they had to suggest potential surrogate endpoints for OS in each of the following tumour sites: oesophagus, stomach, liver, pancreas, biliary tract, lymphoma, colon, rectum, and anus. They finally gave their opinion on QoL as surrogate endpoint. In the second questionnaire, they had to classify the previously proposed candidate surrogates from the most (position #1) to the least relevant in their opinion.
Frequency at which the endpoints were chosen as first, second or third most relevant surrogates was calculated and served as final ranking.
Response rate was 30% (24/80) in the first round and 20% (16/80) in the second one. Participants highlighted key points concerning surrogacy. In particular, they reminded that a surrogate endpoint is expected to predict clinical benefit in a well-defined therapeutic situation. Half of them thought it was not relevant to study QoL as surrogate for OS.
DFS, in the neoadjuvant settings or early stages, and PFS, in the non operable or metastatic settings, were ranked first, with a frequency of more than 69% in 20 out of 22 settings. PFS was proposed in association with QoL in metastatic primary liver and stomach cancers (both 81%). This composite endpoint was ranked second in metastatic oesophageal (69%), colorectal (56%) and anal (56%) cancers, whereas QoL alone was also suggested in most metastatic situations.
Other endpoints frequently suggested were R0 resection in the neoadjuvant settings (oesophagus (69%), stomach (56%), pancreas (75%) and biliary tract (63%)) and response. An unexpected endpoint was metastatic PFS in non operable oesophageal (31%) and pancreatic (44%) cancers. Quality and results of surgical procedures like sphincter preservation were also cited as eligible surrogate endpoints in rectal (19%) and anal (50% in case of localized disease) cancers. Except for alpha-FP kinetic in hepatocellular carcinoma (13%) and CA19-9 decline (6%) in pancreas, few endpoints based on biological or tumour markers were proposed.
The overall results should help prioritise the endpoints to be statistically evaluated as surrogate for OS, so that trialists and clinicians can rely on endpoints that ensure relevant clinical benefit to the patient.
PMCID: PMC2904280  PMID: 20537166
The annals of applied statistics  2008;2(1):386-407.
Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics 58 (2002) 21–29] and adapted by Gilbert and Hudgens (2006), we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.
PMCID: PMC2601643  PMID: 19079758
Clinical trial; discrete failure time model; missing data; potential outcomes; principal stratification; surrogate marker
10.  Commentary on “Principal Stratification — a Goal or a Tool?” by Judea Pearl 
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.
PMCID: PMC3204668  PMID: 22049267
principal stratification; causal inference; vaccine trial
11.  Using latent outcome trajectory classes in causal inference* 
Statistics and its interface  2009;2(4):403-412.
In longitudinal studies, outcome trajectories can provide important information about substantively and clinically meaningful underlying subpopulations who may also respond differently to treatments or interventions. Growth mixture analysis is an efficient way of identifying heterogeneous trajectory classes. However, given its exploratory nature, it is unclear how involvement of latent classes should be handled in the analysis when estimating causal treatment effects. In this paper, we propose a 2-step approach, where formulation of trajectory strata and identification of causal effects are separated. In Step 1, we stratify individuals in one of the assignment conditions (reference condition) into trajectory strata on the basis of growth mixture analysis. In Step 2, we estimate treatment effects for different trajectory strata, treating the stratum membership as partly known (known for individuals assigned to the reference condition and missing for the rest). The results can be interpreted as how subpopulations that differ in terms of outcome prognosis under one treatment condition would change their prognosis differently when exposed to another treatment condition. Causal effect estimation in Step 2 is consistent with that in the principal stratification approach (Frangakis and Rubin, 2002) in the sense that clarified identifying assumptions can be employed and therefore systematic sensitivity analyses are possible. Longitudinal development of attention deficit among children from the Johns Hopkins School Intervention Trial (Ialongo et al., 1999) will be presented as an example.
PMCID: PMC2863041  PMID: 20445809
Causal inference; Latent trajectory class; Longitudinal outcome prognosis; Growth mixture modeling; Principal stratification; Reference stratification
12.  Gestational surrogacy: Viewpoint of Iranian infertile women 
Surrogacy is a popular form of assisted reproductive technology of which only gestational form is approved by most of the religious scholars in Iran. Little evidence exists about the Iranian infertile women's viewpoint regarding gestational surrogacy.
To assess the viewpoint of Iranian infertile women toward gestational surrogacy.
This descriptive study was conducted at the infertility clinic of Tabriz University of Medical Sciences, Iran.
The study sample consisted of 238 infertile women who were selected using the eligible sampling method. Data were collected by using a researcher developed questionnaire that included 25 items based on a five-point Likert scale.
Data analysis was conducted by SPSS statistical software using descriptive statistics.
Viewpoint of 214 women (89.9%) was positive. 36 (15.1%) women considered gestational surrogacy against their religious beliefs; 170 women (71.4%) did not assume the commissioning couple as owners of the baby; 160 women (67.2%) said that children who were born through surrogacy would better not know about it; and 174 women (73.1%) believed that children born through surrogacy will face mental problems.
Iranian infertile women have positive viewpoint regarding the surrogacy. However, to increase the acceptability of surrogacy among infertile women, further efforts are needed.
PMCID: PMC3276948  PMID: 22346081
Assisted reproductive technology; infertility; surrogacy
13.  Evaluating Candidate Principal Surrogate Endpoints 
Biometrics  2008;64(4):1146-1154.
Frangakis and Rubin (2002, Biometrics 58, 21–29) proposed a new definition of a surrogate endpoint (a “principal” surrogate) based on causal effects. We introduce an estimand for evaluating a principal surrogate, the causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. Although the CEP surface is not identifiable due to missing potential outcomes, it can be identified by incorporating a baseline covariate(s) that predicts the biomarker. Given case–cohort sampling of such a baseline predictor and the biomarker in a large blinded randomized clinical trial, we develop an estimated likelihood method for estimating the CEP surface. This estimation assesses the “surrogate value” of the biomarker for reliably predicting clinical treatment effects for the same or similar setting as the trial. A CEP surface plot provides a way to compare the surrogate value of multiple biomarkers. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection.
PMCID: PMC2726718  PMID: 18363776
Case cohort; Causal inference; Clinical trial; HIV vaccine; Postrandomization selection bias; Structural model; Prentice criteria; Principal stratification
14.  Best Practicable Aggregation of Species: a step forward for species surrogacy in environmental assessment and monitoring 
Ecology and Evolution  2013;3(11):3780-3793.
The available taxonomic expertise and knowledge of species is still inadequate to cope with the urgent need for cost-effective methods to quantifying community response to natural and anthropogenic drivers of change. So far, the mainstream approach to overcome these impediments has focused on using higher taxa as surrogates for species. However, the use of such taxonomic surrogates often limits inferences about the causality of community patterns, which in turn is essential for effective environmental management strategies. Here, we propose an alternative approach to species surrogacy, the “Best Practicable Aggregation of Species” (BestAgg), in which surrogates exulate from fixed taxonomic schemes. The approach uses null models from random aggregations of species to minimizing the number of surrogates without causing significant losses of information on community patterns. Surrogate types are then selected in order to maximize ecological information. We applied the approach to real case studies on natural and human-driven gradients from marine benthic communities. Outcomes from BestAgg were also compared with those obtained using classic taxonomic surrogates. Results showed that BestAgg surrogates are effective in detecting community changes. In contrast to classic taxonomic surrogates, BestAgg surrogates allow retaining significantly higher information on species-level community patterns than what is expected to occur by chance and a potential time saving during sample processing up to 25% higher. Our findings showed that BestAgg surrogates from a pilot study could be used successfully in similar environmental investigations in the same area, or for subsequent long-term monitoring programs. BestAgg is virtually applicable to any environmental context, allowing exploiting multiple surrogacy schemes beyond stagnant perspectives strictly relying on taxonomic relatedness among species. This prerogative is crucial to extend the concept of species surrogacy to ecological traits of species, thus leading to ecologically meaningful surrogates that, while cost effective in reflecting community patterns, may also contribute to unveil underlying processes. A specific R code for BestAgg is provided.
PMCID: PMC3810874  PMID: 24198939
Environmental impacts; higher taxon approach; modeling; multivariate analysis; natural variations; randomizations; species surrogates; taxonomic relatedness; taxonomic sufficiency.
15.  Principal Stratification in Causal Inference 
Biometrics  2002;58(1):21-29.
Many scientific problems require that treatment comparisons be adjusted for posttreatment variables, but the estimands underlying standard methods are not causal effects. To address this deficiency, we propose a general framework for comparing treatments adjusting for posttreatment variables that yields principal effects based on principal stratification. Principal stratification with respect to a posttreatment variable is a cross-classification of subjects defined by the joint potential values of that posttreatment variable under each of the treatments being compared. Principal effects are causal effects within a principal stratum. The key property of principal strata is that they are not affected by treatment assignment and therefore can be used just as any pretreatment covariate, such as age category. As a result, the central property of our principal effects is that they are always causal effects and do not suffer from the complications of standard posttreatment-adjusted estimands. We discuss briefly that such principal causal effects are the link between three recent applications with adjustment for posttreatment variables: (i) treatment noncompliance, (ii) missing outcomes (dropout) following treatment noncompliance, and (iii) censoring by death. We then attack the problem of surrogate or biomarker endpoints, where we show, using principal causal effects, that all current definitions of surrogacy, even when perfectly true, do not generally have the desired interpretation as causal effects of treatment on outcome. We go on to formulate estimands based on principal stratification and principal causal effects and show their superiority.
PMCID: PMC4137767  PMID: 11890317
Biomarker; Causal inference; Censoring by death; Missing data; Posttreatment variable; Principal stratification; Quality of life; Rubin causal model; Surrogate
16.  Handling Missing Data in Randomized Experiments with Noncompliance 
Treatment noncompliance and missing outcomes at posttreatment assessments are common problems in field experiments in naturalistic settings. Although the two complications often occur simultaneously, statistical methods that address both complications have not been routinely considered in data analysis practice in the prevention research field. This paper shows that identification and estimation of causal treatment effects considering both noncompliance and missing outcomes can be relatively easily conducted under various missing data assumptions. We review a few assumptions on missing data in the presence of noncompliance, including the latent ignorability proposed by Frangakis and Rubin (Biometrika 86:365–379, 1999), and show how these assumptions can be used in the parametric complier average causal effect (CACE) estimation framework. As an easy way of sensitivity analysis, we propose the use of alternative missing data assumptions, which will provide a range of causal effect estimates. In this way, we are less likely to settle with a possibly biased causal effect estimate based on a single assumption. We demonstrate how alternative missing data assumptions affect identification of causal effects, focusing on the CACE. The data from the Johns Hopkins School Intervention Study (Ialongo et al., Am J Community Psychol 27:599–642, 1999) will be used as an example.
PMCID: PMC2912956  PMID: 20379779
Causal inference; Complier average causal effect; Latent ignorability; Missing at random; Missing data; Noncompliance
17.  Attitudes of Iranian infertile couples toward surrogacy 
Surrogacy arrangements are multifaceted in nature, involving multiple controversial aspects and engaging ethical, moral, psychological and social issues. Successful treatment in reproductive medicine is strongly based on the mutual agreement of both partners, especially in Iran where men often make the final decision for health-related problems of this nature. AIM: The aim of the following study is to assess the attitudes of Iranian infertile couples toward surrogacy.
This descriptive study was conducted at the infertility clinic of Hamadan university of medical sciences, Iran.
The study sample consisted of 150 infertile couples selected using a systematic randomized method. Data collection was based on responses to a questionnaire consisting of 22 questions.
P <0.05 were considered to be statistically significant.
While 33.3% of men and 43.3% of women surveyed insisted on not using surrogacy, the overall attitudes toward surrogacy were positive (53.3% of women and 54.6% of men surveyed).
Although, there was not a significant difference between the overall positive attitudes of infertile women and men toward surrogacy, the general attitude toward using this method is not strongly positive. Therefore, further efforts are required to increase the acceptability of surrogacy among infertile couples.
PMCID: PMC4018798  PMID: 24829531
Attitude; infertility; surrogacy
18.  Tumor Response and Progression-Free Survival as Potential Surrogate Endpoints for Overall Survival in Extensive-Stage Small Cell Lung Cancer (ES-SCLC): Findings Based on North Central Cancer Treatment Group (NCCTG) Trials 
Cancer  2010;117(6):1262-1271.
We investigated the putative surrogate endpoints (PSEs) of best response (BR), complete response (CR), confirmed response (CoR), and progression-free survival (PFS) for associations with Overall Survival (OS), and as possible surrogate endpoints for OS.
Individual patient (pt) data from 870 untreated ES-SCLC pts participating in 6 single-arm (274 pts) and 3 randomized trials (596 pts) were pooled. Patient-level associations between PSEs and OS were assessed by Cox models using landmark analyses. Trial-level surrogacy of PSEs assessed by the association of treatment effects on OS and individual PSEs. Trial-level surrogacy measures included: R2 from weighted least squares regression model (WLS R2), Spearman's correlation coefficient, and R2 from bivariate survival model (Copula R2).
Median OS and PFS were 9.6 (95% CI: 9.1-10.0) and 5.5 (95% CI: 5.2-5.9) months, respectively; BR, CR, and CoR rates were 44%, 22%, and 34%, respectively. Patient-level associations showed that PFS status at 4 months was a strong predictor of subsequent survival (HR=0.42 (95% CI: 0.35-0.51); concordance index=0.63; p<0.01), with 6-month PFS being the strongest (HR=0.41 (95% CI: 0.35-0.49); concordance index=0.66; p<0.01). At the trial-level, PFS showed the highest level of surrogacy for OS (WLS R2=0.79; Copula R2=0.80), explaining 79% of the variance in OS. Tumor response endpoints showed lower surrogacy levels (WLS R2≤0.48).
PFS was strongly associated with OS at both the patient and trial-level. PFS also shows promise as a potential surrogate for OS, but further validation is needed using data from a larger number of randomized phase III trials.
PMCID: PMC3025267  PMID: 20960500
extensive-stage small cell lung cancer; surrogate endpoints; pooled analysis; progression-free survival; tumor response
19.  Sensitivity Analysis and Bounding of Causal Effects With Alternative Identifying Assumptions 
When identification of causal effects relies on untestable assumptions regarding nonidentified parameters, sensitivity of causal effect estimates is often questioned. For proper interpretation of causal effect estimates in this situation, deriving bounds on causal parameters or exploring the sensitivity of estimates to scientifically plausible alternative assumptions can be critical. In this paper, we propose a practical way of bounding and sensitivity analysis, where multiple identifying assumptions are combined to construct tighter common bounds. In particular, we focus on the use of competing identifying assumptions that impose different restrictions on the same non-identified parameter. Since these assumptions are connected through the same parameter, direct translation across them is possible. Based on this cross-translatability, various information in the data, carried by alternative assumptions, can be effectively combined to construct tighter bounds on causal effects. Flexibility of the suggested approach is demonstrated focusing on the estimation of the complier average causal effect (CACE) in a randomized job search intervention trial that suffers from noncompliance and subsequent missing outcomes.
PMCID: PMC3150587  PMID: 21822369
alternative assumptions; bounds; causal inference; missing data; noncompliance; principal stratification; sensitivity analysis
20.  Generalized Causal Mediation Analysis 
Biometrics  2011;67(3):1028-1038.
The goal of mediation analysis is to assess direct and indirect effects of a treatment or exposure on an outcome. More generally, we may be interested in the context of a causal model as characterized by a directed acyclic graph (DAG), where mediation via a specific path from exposure to outcome may involve an arbitrary number of links (or ‘stages’). Methods for estimating mediation (or pathway) effects are available for a continuous outcome and a continuous mediator related via a linear model, while for a categorical outcome or categorical mediator, methods are usually limited to two-stage mediation. We present a method applicable to multiple stages of mediation and mixed variable types using generalized linear models. We define pathway effects using a potential outcomes framework and present a general formula that provides the effect of exposure through any specified pathway. Some pathway effects are nonidentifiable and their estimation requires an assumption regarding the correlation between counterfactuals. We provide a sensitivity analysis to assess of the impact of this assumption. Confidence intervals for pathway effect estimates are obtained via a bootstrap method. The method is applied to a cohort study of dental caries in very low birth weight adolescents. A simulation study demonstrates low bias of pathway effect estimators and close-to-nominal coverage rates of confidence intervals. We also find low sensitivity to the counterfactual correlation in most scenarios.
PMCID: PMC3139764  PMID: 21306353
Copula; Generalized linear model; G-computation algorithm; Path analysis; Potential outcome; Sensitivity analysis
21.  Performance of propensity score calibration – a simulation study 
American journal of epidemiology  2007;165(10):1110-1118.
Confounding can be a major source of bias in non-experimental research. The authors recently introduced propensity score calibration (PSC), which combines propensity scores (PS) and regression calibration to address confounding by variables unobserved in the main study by using variables observed in a validation study. Here, the authors assess the performance of PSC using simulations in settings with and without violation of the key assumption of PSC: that the error-prone PS estimated in the main study is a surrogate for the gold-standard PS (i.e. contains no additional information on the outcome). The assumption can be assessed if data on the outcome are available in the validation study. If data are simulated allowing for surrogacy to be violated, results largely depend on the extent of violation. If surrogacy holds, PSC leads to bias reduction between 74 and 106 percent (>100 percent representing an overcorrection). If surrogacy is violated, PSC can lead to an increase in bias. Surrogacy is violated when the direction of confounding of the exposure-disease association caused by the unobserved variable(s) differs from that of the confounding due to observed variables. When surrogacy holds, PSC is a useful approach to adjust for unmeasured confounding using validation data.
PMCID: PMC1945235  PMID: 17395595
bias (epidemiology); cohort studies; confounding factors (epidemiology); epidemiologic methods; propensity score calibration; research design
22.  Emotional experiences in surrogate mothers: A qualitative study 
Background: Surrogacy is one of the new techniques of assisted reproduction technology in which a woman carries and bears a child for another woman. In Iran, many Shia clerics and jurists considered it permissible so there is no religious prohibition for it. In addition to the risk of physical complications for complete surrogate mothers, the possibility of psychological complications resulted from emotional attachment to a living creature in the surrogate mother as another injury requires counseling and assessment prior to acceptance by infertile couples and complete surrogate mothers.
Objective: The purpose of this study was to assess the emotional experiences of surrogate mothers.
Materials and Methods: This was a qualitative, phenomenological study. We selected eight complete surrogate mothers in Isfahan. We used convenient sampling method and in-depth interview to collect the information. The data analysis was fulfilled via Colaizzi’s seven-stage method. Reliability and validity study of the roots in the four-axis was done.
Results: The findings of these interviews were classified into two main themes and four sub themes: acquired experiences in pregnancy (feelings toward pregnancy, relationship with family, relatives and commissioning couple) and consequences of surrogacy (complications of pregnancy, religious and financial problems of surrogacy).
Conclusion: Surrogacy pregnancy should be considered as high-risk emotional experience because many of surrogate mothers may face negative experiences. Therefore, it is recommended that surrogates should receive professional counseling prior to, during and following pregnancy.
PMCID: PMC4126251  PMID: 25114669
Surrogate mothers; Emotion; Experiences; Qualitative study
23.  Disease-Free Survival as a Surrogate for Overall Survival in Adjuvant Trials of Gastric Cancer: A Meta-Analysis 
In investigations of the effectiveness of surgery and adjuvant chemotherapy for gastric cancers, overall survival (OS) is considered the gold standard endpoint. However, the disadvantage of using OS as the endpoint is that it requires an extended follow-up period. We sought to investigate whether disease-free survival (DFS) is a valid surrogate for OS in trials of adjuvant chemotherapy for gastric cancer.
The GASTRIC group initiated a meta-analysis of individual patient data collected in randomized clinical trials comparing adjuvant chemotherapy vs surgery alone for patients with curatively resected gastric cancer. Surrogacy of DFS was assessed through the correlation between the endpoints as well as through the correlation between the treatment effects on the endpoints. External validation of the prediction based on DFS was also evaluated.
Individual patient data from 14 randomized clinical trials that included a total of 3288 patients were analyzed. The rank correlation coefficient between DFS and OS was 0.974 (95% confidence interval [CI] = 0.971 to 0.976). The coefficient of determination between the treatment effects on DFS and on OS was as high as 0.964 (95% CI = 0.926 to 1.000), and the surrogate threshold effect based on adjusted regression analysis was 0.92. In external validation, the six hazard ratios for OS predicted according to DFS were in very good agreement with those actually observed for OS.
DFS is an acceptable surrogate for OS in trials of cytotoxic agents for gastric cancer in the adjuvant setting.
PMCID: PMC4202244  PMID: 24108812
24.  A unified procedure for meta-analytic evaluation of surrogate end points in randomized clinical trials 
Biostatistics (Oxford, England)  2012;13(4):609-624.
The meta-analytic approach to evaluating surrogate end points assesses the predictiveness of treatment effect on the surrogate toward treatment effect on the clinical end point based on multiple clinical trials. Definition and estimation of the correlation of treatment effects were developed in linear mixed models and later extended to binary or failure time outcomes on a case-by-case basis. In a general regression setting that covers nonnormal outcomes, we discuss in this paper several metrics that are useful in the meta-analytic evaluation of surrogacy. We propose a unified 3-step procedure to assess these metrics in settings with binary end points, time-to-event outcomes, or repeated measures. First, the joint distribution of estimated treatment effects is ascertained by an estimating equation approach; second, the restricted maximum likelihood method is used to estimate the means and the variance components of the random treatment effects; finally, confidence intervals are constructed by a parametric bootstrap procedure. The proposed method is evaluated by simulations and applications to 2 clinical trials.
PMCID: PMC3616754  PMID: 22394448
Causal inference; Meta-analysis; Surrogacy
25.  Statistical identifiability and the surrogate endpoint problem, with application to vaccine trials 
Biometrics  2010;66(4):1153-1161.
Given a randomized treatment Z, a clinical outcome Y, and a biomarker S measured some fixed time after Z is administered, we may be interested in addressing the surrogate endpoint problem by evaluating whether S can be used to reliably predict the effect of Z on Y. Several recent proposals for the statistical evaluation of surrogate value have been based on the framework of principal stratification. In this paper, we consider two principal stratification estimands: joint risks and marginal risks. Joint risks measure causal associations of treatment effects on S and Y, providing insight into the surrogate value of the biomarker, but are not statistically identifiable from vaccine trial data. While marginal risks do not measure causal associations of treatment effects, they nevertheless provide guidance for future research, and we describe a data collection scheme and assumptions under which the marginal risks are statistically identifiable. We show how different sets of assumptions affect the identifiability of these estimands; in particular, we depart from previous work by considering the consequences of relaxing the assumption of no individual treatment effects on Y before S is measured. Based on algebraic relationships between joint and marginal risks, we propose a sensitivity analysis approach for assessment of surrogate value, and show that in many cases the surrogate value of a biomarker may be hard to establish, even when the sample size is large.
PMCID: PMC3597127  PMID: 20105158
Estimated likelihood; Identifiability; Principal stratification; Sensitivity analysis; Surrogate endpoint; Vaccine trials

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