Does the Prentice criterion validate surrogate endpoints?

Randomized Phase II or Phase III clinical trials that are powered based on clinical endpoints, such as survival time, may be prohibitively expensive, in terms of both the time required for their completion and the number of patients required. As such, surrogate endpoints, such as objective tumour response or markers including prostate specific antigen or CA-125, have gained widespread popularity in clinical trials. If an improvement in a surrogate endpoint does not itself confer patient benefit, then consideration must be given to the extent to which improvement in a surrogate endpoint implies improvement in the true clinical endpoint of interest. That this is not a trivial issue is demonstrated by the results of an NIH-sponsored trial of anti-arrhythmic drugs, in which the ability to correct an irregular heart beat not only did not correspond to a survival benefit but in fact led to excess mortality. One approach to the validation of surrogate endpoints involves ensuring that a valid between-group analysis of the surrogate endpoint constitutes also a valid analysis of the true clinical endpoint. The Prentice criterion is a set of conditions that essentially specify the conditional independence of the impact of treatment on the true endpoint, given the surrogate endpoint. It is shown that this criterion alone ensures that an observed effect of the treatment on the true endpoint implies a treatment effect also on the surrogate endpoint, but contrary to popular belief, it does not ensure the converse, specifically that the observation of a significant treatment effect on the surrogate endpoint can be used to infer a treatment effect on the true endpoint.     

Surrogate endpoints in clinical trials: cardiovascular diseases

A surrogate endpoint in a cardiovascular clinical trial is defined as endpoint measured in lieu of some other so-called 'true' endpoint. A surrogate is especially useful if it is easily measured and highly correlated with the true endpoint. Often the 'true' endpoint is one with clinical importance to the patient, for example, mortality or a major clinical outcome, while a surrogate is one biologically closer to the process of disease, for example, ejection fraction. Use of the surrogate can often lead to dramatic reductions in sample size and much shorter studies than use of the true endpoint. We discuss several problems common in trials with surrogate endpoints. Most important is the effect of missing data, especially in the face of informative censoring. Possible solutions are the assignment of scores or formal penalties to missing data.     

Surrogate endpoints in clinical trials: cancer

Investigators use a surrogate endpoint when the endpoint of interest is too difficult and/or expensive to measure routinely and when they can define some other, more readily measurable, endpoint, that is sufficiently well correlated with the first to justify its use as a substitute. A surrogate endpoint is usually proposed on the basis of a biologic rationale. In cancer studies with survival time as the primary endpoint, surrogate endpoints frequently employed are tumour response, time to progression, or time to reappearance of disease, since these events occur earlier and are unaffected by use of secondary therapies. In early drug development studies, tumour response is often the true primary endpoint. We discuss the investigation of the validity of carcinoembryonic antigen (a tumour marker present in the blood) as a surrogate for tumour response. In considering the validity of surrogate endpoints, one must distinguish between study endpoints that provide a basis for reliable comparisons of therapeutic effect, and clinical endpoints that are useful for patient management but have insufficient sensitivity and/or specificity to provide reproducible assessments of the effects of particular therapies.     

Evaluating the role of CD4-lymphocyte counts as surrogate endpoints in human immunodeficiency virus clinical trials

In human immunodeficiency virus clinical trials, the CD4-lymphocyte count has been regarded as a promising surrogate endpoint for clinical efficacy measures such as time to opportunistic infection and survival time. In the present paper, we test this hypothesis according to a criterion proposed by Prentice. This criterion requires the surrogate variable to capture the entire effect of treatment on the clinical endpoint, and it is satisfied if the hazard rate of the clinical endpoint is not affected by treatment among patients with the same preceding history of the surrogate variable. We analyse data from two completed zidovudine trials using the Cox regression model with the CD4-lymphocyte count as a time-varying covariate. The results indicate that the CD4-lymphocyte count captures part of the relationship between zidovudine and time to a first critical event but does not fulfil the Prentice criterion.     

Five criteria for using a surrogate endpoint to predict treatment effect based on data from multiple previous trials

A surrogate endpoint in a randomized clinical trial is an endpoint that occurs after randomization and before the true, clinically meaningful, endpoint that yields conclusions about the effect of treatment on true endpoint. A surrogate endpoint can accelerate the evaluation of new treatments but at the risk of misleading conclusions. Therefore, criteria are needed for deciding whether to use a surrogate endpoint in a new trial. For the meta‐analytic setting of multiple previous trials, each with the same pair of surrogate and true endpoints, this article formulates 5 criteria for using a surrogate endpoint in a new trial to predict the effect of treatment on the true endpoint in the new trial. The first 2 criteria, which are easily computed from a zero‐intercept linear random effects model, involve statistical considerations: an acceptable sample size multiplier and an acceptable prediction separation score. The remaining 3 criteria involve clinical and biological considerations: similarity of biological mechanisms of treatments between the new trial and previous trials, similarity of secondary treatments following the surrogate endpoint between the new trial and previous trials, and a negligible risk of harmful side effects arising after the observation of the surrogate endpoint in the new trial. These 5 criteria constitute an appropriately high bar for using a surrogate endpoint to make a definitive treatment recommendation.     

Sufficient conditions for concluding surrogacy based on observed data

In this paper, we show that Prentice's criteria for surrogates can be strengthened to remedy some weaknesses of the criteria, and we also propose some sufficient conditions under which the treatment effects on a surrogate and on the true endpoint have qualitative implication and equivalence relations. With or without requiring Prentice's criteria, we discuss what conditions are required to qualitatively assess the causal effect of treatment on an unobserved endpoint in terms of an observed surrogate. Rather than a correlation between a surrogate and an endpoint, we require stricter measurements of association for the qualitative assessment. Further we show that these conditions can be satisfied by commonly used models, such as generalized linear models and Cox's proportional hazard models.     

A rank test for bivariate time‐to‐event outcomes when one event is a surrogate

In many clinical settings, improving patient survival is of interest but a practical surrogate, such as time to disease progression, is instead used as a clinical trial's primary endpoint. A time‐to‐first endpoint (e.g., death or disease progression) is commonly analyzed but may not be adequate to summarize patient outcomes if a subsequent event contains important additional information. We consider a surrogate outcome very generally as one correlated with the true endpoint of interest. Settings of interest include those where the surrogate indicates a beneficial outcome so that the usual time‐to‐first endpoint of death or surrogate event is nonsensical. We present a new two‐sample test for bivariate, interval‐censored time‐to‐event data, where one endpoint is a surrogate for the second, less frequently observed endpoint of true interest. This test examines whether patient groups have equal clinical severity. If the true endpoint rarely occurs, the proposed test acts like a weighted logrank test on the surrogate; if it occurs for most individuals, then our test acts like a weighted logrank test on the true endpoint. If the surrogate is a useful statistical surrogate, our test can have better power than tests based on the surrogate that naively handles the true endpoint. In settings where the surrogate is not valid (treatment affects the surrogate but not the true endpoint), our test incorporates the information regarding the lack of treatment effect from the observed true endpoints and hence is expected to have a dampened treatment effect compared with tests based on the surrogate alone. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.     

An extension of the single threshold design for monitoring efficacy and safety in phase II clinical trials

Tan and Machin (biStat. Med. 2002; 21:1991-2012) introduce a Bayesian two-stage design for phase II clinical trials where the binary endpoint of interest is treatment efficacy. In this paper we propose an extension of their design to incorporate safety considerations. At each stage we define the treatment successful and deserving of further study if the total number of adverse events is sufficiently small and the number of responders who simultaneously do not experience any toxicity is sufficiently large. Therefore, our criterion is based on the joint posterior probability that the true overall toxicity rate and the true efficacy-and-safety rate are, respectively, smaller and larger than conveniently pre-specified target values. The optimal two-stage sample sizes are determined specifying a minimum threshold for the above-mentioned posterior probability, computed under the assumption that favorable outcomes have occurred. Besides describing the proposed design, we suggest how to construct informative prior scenarios and we also apply the reference algorithm to derive a non-informative prior distribution. Finally, some numerical results are provided and a real data application is illustrated.     

Comparing and combining biomarkers as principal surrogates for time‐to‐event clinical endpoints

Principal surrogate endpoints are useful as targets for phase I and II trials. In many recent trials, multiple post‐randomization biomarkers are measured. However, few statistical methods exist for comparison of or combination of biomarkers as principal surrogates, and none of these methods to our knowledge utilize time‐to‐event clinical endpoint information. We propose a Weibull model extension of the semi‐parametric estimated maximum likelihood method that allows for the inclusion of multiple biomarkers in the same risk model as multivariate candidate principal surrogates. We propose several methods for comparing candidate principal surrogates and evaluating multivariate principal surrogates. These include the time‐dependent and surrogate‐dependent true and false positive fraction, the time‐dependent and the integrated standardized total gain, and the cumulative distribution function of the risk difference. We illustrate the operating characteristics of our proposed methods in simulations and outline how these statistics can be used to evaluate and compare candidate principal surrogates. We use these methods to investigate candidate surrogates in the Diabetes Control and Complications Trial. Copyright © 2014 John Wiley & Sons, Ltd.     

Surrogate and auxiliary endpoints in clinical trials,with potential applications in cancer and aids research

Surrogate endpoints have been defined by Prentice as response variables that can substitute for a ‘true’ endpoint for the purpose of comparing specific interventions or treatments in a clinical trial. The applicability of this definition, and of related surrogate endpoint criteria, is discussed, with emphasis on cancer and AIDS research settings. Auxiliary endpoints are defined as response variables, or covariates, that can strengthen true endpoint analyses. Specifically, such response variables provide some additional information on true endpoint occurrence times for study subjects having censored values for such times. Auxiliary variables will very frequently be available, and they may be able to be used without making additional strong assumptions. Approaches to the use of auxiliary variables using ideas based on augmented score and augmented likelihood methods are described.