Surrogacy assessment using principal stratification when surrogate and outcome measures are multivariate normal

Flexible evaluation of surrogate markers with Bayesian model averaging

When long-term follow up is required for a primary endpoint in a randomized clinical trial, a valid surrogate marker can help to estimate the treatment effect and accelerate the decision process. Several model-based methods have been developed to evaluate the proportion of the treatment effect that is explained by the treatment effect on the surrogate marker. More recently, a nonparametric approach has been proposed allowing for more flexibility by avoiding the restrictive parametric model assumptions required in the model-based methods. While the model-based approaches suffer from potential mis-specification of the models, the nonparametric method fails to give desirable estimates when the sample size is small, or when the range of the data does not follow certain conditions. In this paper, we propose a Bayesian model averaging approach to estimate the proportion of treatment effect explained by the surrogate marker. Our procedure offers a compromise between the model-based approach and the nonparametric approach by introducing model flexibility via averaging over several candidate models and maintains the strength of parametric models with respect to inference. We compare our approach with previous model-based methods and the nonparametric method. Simulation studies demonstrate the advantage of our method when surrogate supports are inconsistent and sample sizes are small. We illustrate our method using data from the Diabetes Prevention Program study to examine hemoglobin A1c as a surrogate marker for fasting glucose.

A rank-based approach to evaluate a surrogate marker in a small sample setting

In clinical studies of chronic diseases, the effectiveness of an intervention is often assessed using "high cost" outcomes that require long-term patient follow-up and/or are invasive to obtain. While much progress has been made in the development of statistical methods to identify surrogate markers, that is, measurements that could replace such costly outcomes, they are generally not applicable to studies with a small sample size. These methods either rely on nonparametric smoothing which requires a relatively large sample size or rely on strict model assumptions that are unlikely to hold in practice and empirically difficult to verify with a small sample size. In this paper, we develop a novel rank-based nonparametric approach to evaluate a surrogate marker in a small sample size setting. The method developed in this paper is motivated by a small study of children with nonalcoholic fatty liver disease (NAFLD), a diagnosis for a range of liver conditions in individuals without significant history of alcohol intake. Specifically, we examine whether change in alanine aminotransferase (ALT; measured in blood) is a surrogate marker for change in NAFLD activity score (obtained by biopsy) in a trial, which compared Vitamin E ($n=50$) versus placebo ($n=46$) among children with NAFLD.

Surrogacy validation for time-to-event outcomes with illness-death frailty models

A common practice in clinical trials is to evaluate a treatment effect on an intermediate outcome when the true outcome of interest would be difficult or costly to measure. We consider how to validate intermediate outcomes in a causally-valid way when the trial outcomes are time-to-event. Using counterfactual outcomes, those that would be observed if the counterfactual treatment had been given, the causal association paradigm assesses the relationship of the treatment effect on the surrogate outcome with the treatment effect on the true, primary outcome. In particular, we propose illness-death models to accommodate the censored and semicompeting risk structure of survival data. The proposed causal version of these models involves estimable and counterfactual frailty terms. Via these multistate models, we characterize what a valid surrogate would look like using a causal effect predictiveness plot. We evaluate the estimation properties of a Bayesian method using Markov chain Monte Carlo and assess the sensitivity of our model assumptions. Our motivating data source is a localized prostate cancer clinical trial where the two survival outcomes are time to distant metastasis and time to death.

Time-to-event surrogate endpoint validation using mediation analysis and meta-analytic data

With the ongoing development of treatments and the resulting increase in survival in oncology, clinical trials based on endpoints such as overall survival may require long follow-up periods to observe sufficient events and ensure adequate statistical power. This increase in follow-up time may compromise the feasibility of the study. The use of surrogate endpoints instead of final endpoints may be attractive for these studies. However, before a surrogate can be used in a clinical trial, it must be statistically validated. In this article, we propose an approach to validate surrogates when both the surrogate and final endpoints are censored event times. This approach is developed for meta-analytic data and uses a mediation analysis to decompose the total effect of the treatment on the final endpoint as a direct effect and an indirect effect through the surrogate. The meta-analytic nature of the data is accounted for in a joint model with random effects at the trial level. The proportion of the indirect effect over the total effect of the treatment on the final endpoint can be computed from the parameters of the model and used as a measure of surrogacy. We applied this method to investigate time-to-relapse as a surrogate endpoint for overall survival in resectable gastric cancer.

Can earlier biomarker measurements explain a treatment effect on diabetes incidence? A robust comparison of five surrogate markers

INTRODUCTION

We measured and compared five individual surrogate markers-change from baseline to 1 year after randomization in hemoglobin A1c (HbA1c), fasting glucose, 2-hour postchallenge glucose, triglyceride-glucose index (TyG) index, and homeostatic model assessment of insulin resistance (HOMA-IR)-in terms of their ability to explain a treatment effect on reducing the risk of type 2 diabetes mellitus at 2, 3, and 4 years after treatment initiation.

RESEARCH DESIGN AND METHODS

Study participants were from the Diabetes Prevention Program study, randomly assigned to either a lifestyle intervention (n=1023) or placebo (n=1030). The surrogate markers were measured at baseline and 1 year, and diabetes incidence was examined at 2, 3, and 4 years postrandomization. Surrogacy was evaluated using a robust model-free estimate of the proportion of treatment effect explained (PTE) by the surrogate marker.

RESULTS

Across all time points, change in fasting glucose and HOMA-IR explained higher proportions of the treatment effect than 2-hour glucose, TyG index, or HbA1c. For example, at 2 years, glucose explained the highest (80.1%) proportion of the treatment effect, followed by HOMA-IR (77.7%), 2-hour glucose (76.2%), and HbA1c (74.6%); the TyG index explained the smallest (70.3%) proportion.

CONCLUSIONS

These data suggest that, of the five examined surrogate markers, glucose and HOMA-IR were the superior surrogate markers in terms of PTE, compared with 2-hour glucose, HbA1c, and TyG index.

Solutions for surrogacy validation with longitudinal outcomes for a gene therapy

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.

Testing for heterogeneity in the utility of a surrogate marker

In studies that require long-term and/or costly follow-up of participants to evaluate a treatment, there is often interest in identifying and using a surrogate marker to evaluate the treatment effect. While several statistical methods have been proposed to evaluate potential surrogate markers, available methods generally do not account for or address the potential for a surrogate to vary in utility or strength by patient characteristics. Previous work examining surrogate markers has indicated that there may be such heterogeneity, that is, that a surrogate marker may be useful (with respect to capturing the treatment effect on the primary outcome) for some subgroups, but not for others. This heterogeneity is important to understand, particularly if the surrogate is to be used in a future trial to replace the primary outcome. In this paper, we propose an approach and estimation procedures to measure the surrogate strength as a function of a baseline covariate W and thus examine potential heterogeneity in the utility of the surrogate marker with respect to W. Within a potential outcome framework, we quantify the surrogate strength/utility using the proportion of treatment effect on the primary outcome that is explained by the treatment effect on the surrogate. We propose testing procedures to test for evidence of heterogeneity, examine finite sample performance of these methods via simulation, and illustrate the methods using AIDS clinical trial data.

Informed decision-making: Statistical methodology for surrogacy evaluation and its role in licensing and reimbursement assessments

The desire, by patients and society, for faster access to therapies has driven a long tradition of the use of surrogate endpoints in the evaluation of pharmaceuticals and, more recently, biologics and other innovative medical technologies. The consequent need for statistical validation of potential surrogate outcome measures is a prime example on the theme of statistical support for decision-making in health technology assessment (HTA). Following the pioneering methodology based on hypothesis testing that Prentice presented in 1989, a host of further methods, both frequentist and Bayesian, have been developed to enable the value of a putative surrogate outcome to be determined. This rich methodological seam has generated practical methods for surrogate evaluation, the most recent of which are based on the principles of information theory and bring together ideas from the causal effects and causal association paradigms. Following our synopsis of statistical methods, we then consider how regulatory authorities (on licensing) and payer and HTA agencies (on reimbursement) use clinical trial evidence based on surrogate outcomes. We review existing HTA surrogate outcome evaluative frameworks. We conclude with recommendations for further steps: (1) prioritisation by regulators and payers of the application of formal surrogate outcome evaluative frameworks, (2) application of formal Bayesian decision-analytic methods to support reimbursement decisions, and (3) greater utilization of conditional surrogate-based licensing and reimbursement approvals, with subsequent reassessment of treatments in confirmatory trials based on final patient-relevant outcomes.

Estimation of the proportion of treatment effect explained by a high-dimensional surrogate

Clinical studies examining the effectiveness of a treatment with respect to some primary outcome often require long-term follow-up of patients and/or costly or burdensome measurements of the primary outcome of interest. Identifying a surrogate marker for the primary outcome of interest may allow one to evaluate a treatment effect with less follow-up time, less cost, or less burden. While much clinical and statistical work has focused on identifying and validating surrogate markers, available approaches tend to focus on settings in which only a single surrogate marker is of interest. Limited work has been done to accommodate the high-dimensional surrogate marker setting where the number of potential surrogates is greater than the sample size. In this article, we develop methods to estimate the proportion of treatment effect explained by high-dimensional surrogates. We study the asymptotic properties of our proposed estimator, propose inference procedures, and examine finite sample performance via a simulation study. We illustrate our proposed methods using data from a randomized study comparing a novel whey-based oral nutrition supplement with a standard supplement with respect to change in body fat percentage over 12 weeks, where the surrogate markers of interest are gene expression probesets.

Evaluation of Surrogate Endpoints Using Information-Theoretic Measure of Association Based on Havrda and Charvat Entropy

Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials. Using information theory, Alonso et al. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. The new model is illustrated through the analysis of data from a completed clinical trial. It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis.

Quantifying the feasibility of shortening clinical trial duration using surrogate markers

The potential benefit of using a surrogate marker in place of a long-term primary outcome is very attractive in terms of the impact on study length and cost. Many available methods for quantifying the effectiveness of a surrogate endpoint either rely on strict parametric modeling assumptions or require that the primary outcome and surrogate marker are fully observed that is, not subject to censoring. Moreover, available methods for quantifying surrogacy typically provide a proportion of treatment effect explained (PTE) measure and do not directly address the important questions of whether and how the trial can be ended earlier using the surrogate marker. In this article, we specifically address these important questions by proposing a PTE measure to quantify the feasibility of ending trials early based on endpoint information collected at an earlier landmark point t 0 in a time-to-event outcome setting. We provide a framework for deriving an optimally predicted outcome for individual patients at t 0 based on a combination of surrogate marker and event time information in the presence of censoring. We propose a non-parametric estimator for the PTE measure and derive the asymptotic properties of our estimators. Finite sample performance of our estimators are illustrated via extensive simulation studies and a real data application examining the potential of hemoglobin A1c and fasting plasma glucose to predict treatment effects on long term diabetes risk based on the Diabetes Prevention Program study.

Incorporating baseline covariates to validate surrogate endpoints with a constant biomarker under control arm

A surrogate endpoint S in a clinical trial is an outcome that may be measured earlier or more easily than the true outcome of interest T. In this work, we extend causal inference approaches to validate such a surrogate using potential outcomes. The causal association paradigm assesses the relationship of the treatment effect on the surrogate with the treatment effect on the true endpoint. Using the principal surrogacy criteria, we utilize the joint conditional distribution of the potential outcomes T, given the potential outcomes S. In particular, our setting of interest allows us to assume the surrogate under the placebo, S ( 0 ) , is zero-valued, and we incorporate baseline covariates in the setting of normally distributed endpoints. We develop Bayesian methods to incorporate conditional independence and other modeling assumptions and explore their impact on the assessment of surrogacy. We demonstrate our approach via simulation and data that mimics an ongoing study of a muscular dystrophy gene therapy.

Using multiple imputation to classify potential outcomes subgroups

With medical tests becoming increasingly available, concerns about over-testing, over-treatment and health care cost dramatically increase. Hence, it is important to understand the influence of testing on treatment selection in general practice. Most statistical methods focus on average effects of testing on treatment decisions. However, this may be ill-advised, particularly for patient subgroups that tend not to benefit from such tests. Furthermore, missing data are common, representing large and often unaddressed threats to the validity of most statistical methods. Finally, it is often desirable to conduct analyses that can be interpreted causally. Using the Rubin Causal Model framework, we propose to classify patients into four potential outcomes subgroups, defined by whether or not a patient's treatment selection is changed by the test result and by the direction of how the test result changes treatment selection. This subgroup classification naturally captures the differential influence of medical testing on treatment selections for different patients, which can suggest targets to improve the utilization of medical tests. We can then examine patient characteristics associated with patient potential outcomes subgroup memberships. We used multiple imputation methods to simultaneously impute the missing potential outcomes as well as regular missing values. This approach can also provide estimates of many traditional causal quantities of interest. We find that explicitly incorporating causal inference assumptions into the multiple imputation process can improve the precision for some causal estimates of interest. We also find that bias can occur when the potential outcomes conditional independence assumption is violated; sensitivity analyses are proposed to assess the impact of this violation. We applied the proposed methods to examine the influence of 21-gene assay, the most commonly used genomic test in the United States, on chemotherapy selection among breast cancer patients.

On the individual surrogate paradox

When the primary outcome is difficult to collect, a surrogate endpoint is typically used as a substitute. It is possible that for every individual, the treatment has a positive effect on the surrogate, and the surrogate has a positive effect on the primary outcome, but for some individuals, the treatment has a negative effect on the primary outcome. For example, a treatment may be substantially effective in preventing the stroke for everyone, and lowering the risk of stroke is universally beneficial for life expectancy; however, the treatment may still cause death for some individuals. We define such paradoxical phenomenon as the individual surrogate paradox. The individual surrogate paradox is proposed to capture the treatment effect heterogeneity, which is unable to be described by either the surrogate paradox based on average causal effect or that based on distributional causal effect. We investigate the existing surrogate criteria in terms of whether the individual surrogate paradox could manifest. We find that only the strong binary surrogate can avoid such paradox without additional assumptions. Utilizing the sharp bounds, we propose novel criteria to exclude the individual surrogate paradox. Our methods are illustrated in an application to determine the effect of the intensive glycemia on the risk of development or progression of diabetic retinopathy.

Robust methods to correct for measurement error when evaluating a surrogate marker

The identification of valid surrogate markers of disease or disease progression has the potential to decrease the length and costs of future studies. Most available methods that assess the value of a surrogate marker ignore the fact that surrogates are often measured with error. Failing to adjust for measurement error can erroneously identify a useful surrogate marker as not useful or vice versa. We investigate and propose robust methods to correct for the effect of measurement error when evaluating a surrogate marker using multiple estimators developed for parametric and nonparametric estimates of the proportion of treatment effect explained by the surrogate marker. In addition, we quantify the attenuation bias induced by measurement error and develop inference procedures to allow for variance and confidence interval estimation. Through a simulation study, we show that our proposed estimators correct for measurement error in the surrogate marker and that our inference procedures perform well in finite samples. We illustrate these methods by examining a potential surrogate marker that is measured with error, hemoglobin A1c, using data from the Diabetes Prevention Program clinical trial.

Evaluating multiple surrogate markers with censored data

The utilization of surrogate markers offers the opportunity to reduce the length of required follow-up time and/or costs of a randomized trial examining the effectiveness of an intervention or treatment. There are many available methods for evaluating the utility of a single surrogate marker including both parametric and nonparametric approaches. However, as the dimension of the surrogate marker increases, a completely nonparametric procedure becomes infeasible due to the curse of dimensionality. In this paper, we define a quantity to assess the value of multiple surrogate markers in a time-to-event outcome setting and propose a robust estimation approach for censored data. We focus on surrogate markers that are measured at some landmark time, t₀ , which occurs earlier than the end of the study. Our approach is based on a dimension reduction procedure with an option to incorporate weights to guard against potential misspecification of the working model, resulting in three different proposed estimators, two of which can be shown to be double robust. We examine the finite sample performance of the estimators under various scenarios using a simulation study. We illustrate the estimation and inference procedures using data from the Diabetes Prevention Program (DPP) to examine multiple potential surrogate markers for diabetes.

Assessing the value of a censored surrogate outcome

Assessing the potential of surrogate markers and surrogate outcomes for replacing a long term outcome is an active area of research. The interest in this topic is partly motivated by increasing pressure from stakeholders to shorten the time required to evaluate the safety and/or efficacy of a treatment or intervention such that treatments deemed safe and effective can be made available to those in need more quickly. Most existing methods in surrogacy evaluation either require strict model assumptions or that primary outcome and surrogate outcome information is available for all study participants. In this paper, we focus on a setting where the primary outcome is subject to censoring and the aim is to quantify the surrogacy of an intermediate outcome, which is also subject to censoring. We define the surrogacy as the proportion of treatment effect on the primary outcome that is explained by the intermediate surrogate outcome information and propose two robust methods to estimate this quantity. We propose both a nonparametric approach that uses a kernel smoothed Nelson-Aalen estimator of conditional survival, and a semiparametric method that derives conditional survival estimates from a landmark Cox proportional hazards model. Simulation studies demonstrate that both approaches perform well in finite samples. Our methodological development is motivated by our interest in investigating the use of a composite cardiovascular endpoint as a surrogate outcome in a randomized study of the effectiveness of angiotensin-converting enzyme inhibitors on survival. We apply the proposed methods to quantify the surrogacy of this potential surrogate outcome for the primary outcome, time to death.

Using a surrogate marker for early testing of a treatment effect

The development of methods to identify, validate, and use surrogate markers to test for a treatment effect has been an area of intense research interest given the potential for valid surrogate markers to reduce the required costs and follow-up times of future studies. Several quantities and procedures have been proposed to assess the utility of a surrogate marker. However, few methods have been proposed to address how one might use the surrogate marker information to test for a treatment effect at an earlier time point, especially in settings where the primary outcome and the surrogate marker are subject to censoring. In this paper, we propose a novel test statistic to test for a treatment effect using surrogate marker information measured prior to the end of the study in a time-to-event outcome setting. We propose a robust nonparametric estimation procedure and propose inference procedures. In addition, we evaluate the power for the design of a future study based on surrogate marker information. We illustrate the proposed procedure and relative power of the proposed test compared to a test performed at the end of the study using simulation studies and an application to data from the Diabetes Prevention Program.

Links between causal effects and causal association for surrogacy evaluation in a gaussian setting

Two paradigms for the evaluation of surrogate markers in randomized clinical trials have been proposed: the causal effects paradigm and the causal association paradigm. Each of these paradigms rely on assumptions that must be made to proceed with estimation and to validate a candidate surrogate marker (S) for the true outcome of interest (T). We consider the setting in which S and T are Gaussian and are generated from structural models that include an unobserved confounder. Under the assumed structural models, we relate the quantities used to evaluate surrogacy within both the causal effects and causal association frameworks. We review some of the common assumptions made to aid in estimating these quantities and show that assumptions made within one framework can imply strong assumptions within the alternative framework. We demonstrate that there is a similarity, but not exact correspondence between the quantities used to evaluate surrogacy within each framework, and show that the conditions for identifiability of the surrogacy parameters are different from the conditions, which lead to a correspondence of these quantities.

Validation of surrogate endpoints in cancer clinical trials via principal stratification with an application to a prostate cancer trial

Increasing attention has been focused on the use and validation of surrogate endpoints in cancer clinical trials. Previous literature on validation of surrogate endpoints are classified into four approaches: the proportion explained approach; the indirect effects approach; the meta-analytic approach; and the principal stratification approach. The mainstream in cancer research has seen the application of a meta-analytic approach. However, VanderWeele (2013) showed that all four of these approaches potentially suffer from the surrogate paradox. It was also shown that, if a principal surrogate satisfies additional criteria called one-sided average causal sufficiency, the surrogate cannot exhibit a surrogate paradox. Here, we propose a method for estimating principal effects under a monotonicity assumption. Specifically, we consider cancer clinical trials which compare a binary surrogate endpoint and a time-to-event clinical endpoint under two naturally ordered treatments (e.g. combined therapy vs. monotherapy). Estimation based on a mean score estimating equation will be implemented by the expectation-maximization algorithm. We will also apply the proposed method as well as other surrogacy criteria to evaluate the surrogacy of prostate-specific antigen using data from a phase III advanced prostate cancer trial, clarifying the complementary roles of both the principal stratification and meta-analytic approaches in the evaluation of surrogate endpoints in cancer. Copyright © 2017 John Wiley & Sons, Ltd.

Evaluating surrogate marker information using censored data

Given the long follow-up periods that are often required for treatment or intervention studies, the potential to use surrogate markers to decrease the required follow-up time is a very attractive goal. However, previous studies have shown that using inadequate markers or making inappropriate assumptions about the relationship between the primary outcome and surrogate marker can lead to inaccurate conclusions regarding the treatment effect. Currently available methods for identifying and validating surrogate markers tend to rely on restrictive model assumptions and/or focus on uncensored outcomes. The ability to use such methods in practice when the primary outcome of interest is a time-to-event outcome is difficult because of censoring and missing surrogate information among those who experience the primary outcome before surrogate marker measurement. In this paper, we propose a novel definition of the proportion of treatment effect explained by surrogate information collected up to a specified time in the setting of a time-to-event primary outcome. Our proposed approach accommodates a setting where individuals may experience the primary outcome before the surrogate marker is measured. We propose a robust non-parametric procedure to estimate the defined quantity using censored data and use a perturbation-resampling procedure for variance estimation. Simulation studies demonstrate that the proposed procedures perform well in finite samples. We illustrate the proposed procedures by investigating two potential surrogate markers for diabetes using data from the Diabetes Prevention Program. Copyright © 2017 John Wiley & Sons, Ltd.

Surrogacy assessment using principal stratification and a Gaussian copula model

In clinical trials, a surrogate outcome ( S) can be measured before the outcome of interest ( T) and may provide early information regarding the treatment ( Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al.

Augmented trial designs for evaluation of principal surrogates

Observation of counterfactual intermediate responses, and evaluation of them as candidate surrogates, is complicated in a standard randomized trial as half of the responses are systematically missing by design. Although some augmentation procedures exist for obtaining counterfactual responses, they are specific to vaccine trials. We outline extensions to the existing augmentations and suggest augmentations of three trial designs outside the setting of vaccines. We outline the assumptions needed to identify the causal estimands of interest under each augmented design, under which standard likelihood-based methods can be used to evaluate intermediate responses as principal surrogates. Two of these designs, crossover and individual stepped-wedge, allow for the observation of clinical endpoints under both treatment and control for some subset of subjects and can therefore improve efficiency over standard parallel trial designs. The third, the treatment run-in design, allows for the observation of a baseline measure that may be as useful a surrogate as the true counterfactual intermediate response. As the evaluation methods rely on several assumptions, we also outline a remediation analysis, which can be used to help overcome assumption violations. We illustrate our suggested methods in an example from a drug-resistant tuberculosis treatment trial.

Exploring the relationship between the causal-inference and meta-analytic paradigms for the evaluation of surrogate endpoints

Nowadays, two main frameworks for the evaluation of surrogate endpoints, based on causal-inference and meta-analysis, dominate the scene. Earlier work showed that the metrics of surrogacy introduced in both paradigms are related, although in a complex way that is difficult to study analytically. In the present work, this relationship is further examined using simulations and the analysis of a case study. The results indicate that the extent to which both paradigms lead to similar conclusions regarding the validity of the surrogate, depends on a complex interplay between multiple factors like the ratio of the between and within trial variability and the unidentifiable correlations between the potential outcomes. All the analyses were carried out using the newly developed R package Surrogate, which is freely available via CRAN.

Surrogacy assessment using principal stratification with multivariate normal and Gaussian copula models

BACKGROUND

The validation of intermediate markers as surrogate markers (S) for the true outcome of interest (T) in clinical trials offers the possibility for trials to be run more quickly and cheaply by using the surrogate endpoint in place of the true endpoint.

PURPOSE

Working within a principal stratification framework, we propose causal quantities to evaluate surrogacy using a Gaussian copula model for an ordinal surrogate and time-to-event final outcome. The methods are applied to data from four colorectal cancer clinical trials, where S is tumor response and T is overall survival.

METHODS

For the Gaussian copula model, a Bayesian estimation strategy is used and, as some parameters are not identifiable from the data, we explore the use of informative priors that are consistent with reasonable assumptions in the surrogate marker setting to aid in estimation.

RESULTS

While there is some bias in the estimation of the surrogacy quantities of interest, the estimation procedure does reasonably well at distinguishing between poor and good surrogate markers.

LIMITATIONS

Some of the parameters of the proposed model are not identifiable from the data, and therefore, assumptions must be made in order to aid in their estimation.

CONCLUSIONS

The proposed quantities can be used in combination to provide evidence about the validity of S as a surrogate marker for T.

Hard, harder, hardest: principal stratification, statistical identifiability, and the inherent difficulty of finding surrogate endpoints

In many areas of clinical investigation there is great interest in identifying and validating surrogate endpoints, biomarkers that can be measured a relatively short time after a treatment has been administered and that can reliably predict the effect of treatment on the clinical outcome of interest. However, despite dramatic advances in the ability to measure biomarkers, the recent history of clinical research is littered with failed surrogates. In this paper, we present a statistical perspective on why identifying surrogate endpoints is so difficult. We view the problem from the framework of causal inference, with a particular focus on the technique of principal stratification (PS), an approach which is appealing because the resulting estimands are not biased by unmeasured confounding. In many settings, PS estimands are not statistically identifiable and their degree of non-identifiability can be thought of as representing the statistical difficulty of assessing the surrogate value of a biomarker. In this work, we examine the identifiability issue and present key simplifying assumptions and enhanced study designs that enable the partial or full identification of PS estimands. We also present example situations where these assumptions and designs may or may not be feasible, providing insight into the problem characteristics which make the statistical evaluation of surrogate endpoints so challenging.