Utilization of treatment effect on a surrogate endpoint for planning a study to evaluate treatment effect on a final endpoint

To design a phase III study with a final endpoint and calculate the required sample size for the desired probability of success, we need a good estimate of the treatment effect on the endpoint. It is prudent to fully utilize all available information including the historical and phase II information of the treatment as well as external data of the other treatments. It is not uncommon that a phase II study may use a surrogate endpoint as the primary endpoint and has no or limited data for the final endpoint. On the other hand, external information from the other studies for the other treatments on the surrogate and final endpoints may be available to establish a relationship between the treatment effects on the two endpoints. Through this relationship, making full use of the surrogate information may enhance the estimate of the treatment effect on the final endpoint. In this research, we propose a bivariate Bayesian analysis approach to comprehensively deal with the problem. A dynamic borrowing approach is considered to regulate the amount of historical data and surrogate information borrowing based on the level of consistency. A much simpler frequentist method is also discussed. Simulations are conducted to compare the performances of different approaches. An example is used to illustrate the applications of the methods.     

Adapting the sample size planning of a phase III trial based on phase II data

Traditionally, in clinical development plan, phase II trials are relatively small and can be expected to result in a large degree of uncertainty in the estimates based on which Phase III trials are planned. Phase II trials are also to explore appropriate primary efficacy endpoint(s) or patient populations. When the biology of the disease and pathogenesis of disease progression are well understood, the phase II and phase III studies may be performed in the same patient population with the same primary endpoint, e.g. efficacy measured by HbA1c in non-insulin dependent diabetes mellitus trials with treatment duration of at least three months. In the disease areas that molecular pathways are not well established or the clinical outcome endpoint may not be observed in a short-term study, e.g. mortality in cancer or AIDS trials, the treatment effect may be postulated through use of intermediate surrogate endpoint in phase II trials. However, in many cases, we generally explore the appropriate clinical endpoint in the phase II trials. An important question is how much of the effect observed in the surrogate endpoint in the phase II study can be translated into the clinical effect in the phase III trial. Another question is how much of the uncertainty remains in phase III trials. In this work, we study the utility of adaptation by design (not by statistical test) in the sense of adapting the phase II information for planning the phase III trials. That is, we investigate the impact of using various phase II effect size estimates on the sample size planning for phase III trials. In general, if the point estimate of the phase II trial is used for planning, it is advisable to size the phase III trial by choosing a smaller alpha level or a higher power level. The adaptation via using the lower limit of the one standard deviation confidence interval from the phase II trial appears to be a reasonable choice since it balances well between the empirical power of the launched trials and the proportion of trials not launched if a threshold lower than the true effect size of phase III trial can be chosen for determining whether the phase III trial is to be launched.     

Methodological issues with adaptation of clinical trial design

Adaptation of clinical trial design generates many issues that have not been resolved for practical applications, though statistical methodology has advanced greatly. This paper focuses on some methodological issues. In one type of adaptation such as sample size re-estimation, only the postulated value of a parameter for planning the trial size may be altered. In another type, the originally intended hypothesis for testing may be modified using the internal data accumulated at an interim time of the trial, such as changing the primary endpoint and dropping a treatment arm. For sample size re-estimation, we make a contrast between an adaptive test weighting the two-stage test statistics with the statistical information given by the original design and the original sample mean test with a properly corrected critical value. We point out the difficulty in planning a confirmatory trial based on the crude information generated by exploratory trials. In regards to selecting a primary endpoint, we argue that the selection process that allows switching from one endpoint to the other with the internal data of the trial is not very likely to gain a power advantage over the simple process of selecting one from the two endpoints by testing them with an equal split of alpha (Bonferroni adjustment). For dropping a treatment arm, distributing the remaining sample size of the discontinued arm to other treatment arms can substantially improve the statistical power of identifying a superior treatment arm in the design. A common difficult methodological issue is that of how to select an adaptation rule in the trial planning stage. Pre-specification of the adaptation rule is important for the practicality consideration. Changing the originally intended hypothesis for testing with the internal data generates great concerns to clinical trial researchers.     

A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components

A composite endpoint consists of multiple endpoints combined in one outcome. It is frequently used as the primary endpoint in randomized clinical trials. There are two main disadvantages associated with the use of composite endpoints: a) in conventional analyses, all components are treated equally important; and b) in time‐to‐event analyses, the first event considered may not be the most important component. Recently Pocock et al. (2012) introduced the win ratio method to address these disadvantages. This method has two alternative approaches: the matched pair approach and the unmatched pair approach. In the unmatched pair approach, the confidence interval is constructed based on bootstrap resampling, and the hypothesis testing is based on the non‐parametric method by Finkelstein and Schoenfeld (1999). Luo et al. (2015) developed a close‐form variance estimator of the win ratio for the unmatched pair approach, based on a composite endpoint with two components and a specific algorithm determining winners, losers and ties. We extend the unmatched pair approach to provide a generalized analytical solution to both hypothesis testing and confidence interval construction for the win ratio, based on its logarithmic asymptotic distribution. This asymptotic distribution is derived via U‐statistics following Wei and Johnson (1985). We perform simulations assessing the confidence intervals constructed based on our approach versus those per the bootstrap resampling and per Luo et al. We have also applied our approach to a liver transplant Phase III study. This application and the simulation studies show that the win ratio can be a better statistical measure than the odds ratio when the importance order among components matters; and the method per our approach and that by Luo et al., although derived based on large sample theory, are not limited to a large sample, but are also good for relatively small sample sizes. Different from Pocock et al. and Luo et al., our approach is a generalized analytical method, which is valid for any algorithm determining winners, losers and ties. Copyright © 2016 John Wiley & Sons, Ltd.     

Treatment policy estimands for recurrent event data using data collected after cessation of randomised treatment

In the past, many clinical trials have withdrawn subjects from the study when they prematurely stopped their randomised treatment and have therefore only collected ‘on‐treatment’ data. Thus, analyses addressing a treatment policy estimand have been restricted to imputing missing data under assumptions drawn from these data only. Many confirmatory trials are now continuing to collect data from subjects in a study even after they have prematurely discontinued study treatment as this event is irrelevant for the purposes of a treatment policy estimand. However, despite efforts to keep subjects in a trial, some will still choose to withdraw. Recent publications for sensitivity analyses of recurrent event data have focused on the reference‐based imputation methods commonly applied to continuous outcomes, where imputation for the missing data for one treatment arm is based on the observed outcomes in another arm. However, the existence of data from subjects who have prematurely discontinued treatment but remained in the study has now raised the opportunity to use this ‘off‐treatment’ data to impute the missing data for subjects who withdraw, potentially allowing more plausible assumptions for the missing post‐study‐withdrawal data than reference‐based approaches. In this paper, we introduce a new imputation method for recurrent event data in which the missing post‐study‐withdrawal event rate for a particular subject is assumed to reflect that observed from subjects during the off‐treatment period. The method is illustrated in a trial in chronic obstructive pulmonary disease (COPD) where the primary endpoint was the rate of exacerbations, analysed using a negative binomial model.     

Estimation of the marginal survival time in the presence of dependent competing risks using inverse probability of censoring weighted (IPCW) methods

In medical studies, there is interest in inferring the marginal distribution of a survival time subject to competing risks. The Kyushu Lipid Intervention Study (KLIS) was a clinical study for hypercholesterolemia, where pravastatin treatment was compared with conventional treatment. The primary endpoint was time to events of coronary heart disease (CHD). In this study, however, some subjects died from causes other than CHD or were censored due to loss to follow-up. Because the treatments were targeted to reduce CHD events, the investigators were interested in the effect of the treatment on CHD events in the absence of causes of death or events other than CHD. In this paper, we present a method for estimating treatment group-specific marginal survival curves of time-to-event data in the presence of dependent competing risks. The proposed method is a straightforward extension of the Inverse Probability of Censoring Weighted (IPCW) method to settings with more than one reason for censoring. The results of our analysis showed that the IPCW marginal incidence for CHD was almost the same as the lower bound for which subjects with competing events were assumed to be censored at the end of all follow-up. This result provided reassurance that the results in KLIS were robust to competing risks.     

Assessment of the information theory approach to evaluating time-to-event surrogate and true endpoints in a meta-analytic setting

In many disease areas, commonly used long-term clinical endpoints are becoming increasingly difficult to implement due to long follow-up times and/or increased costs. Shorter-term surrogate endpoints are urgently needed to expedite drug development, the evaluation of which requires robust and reliable statistical methodology to drive meaningful clinical conclusions about the strength of relationship with the true long-term endpoint. This paper uses a simulation study to explore one such previously proposed method, based on information theory, for evaluation of time to event surrogate and long-term endpoints, including the first examination within a meta-analytic setting of multiple clinical trials with such endpoints. The performance of the information theory method is examined for various scenarios including different dependence structures, surrogate endpoints, censoring mechanisms, treatment effects, trial and sample sizes, and for surrogate and true endpoints with a natural time-ordering. Results allow us to conclude that, contrary to some findings in the literature, the approach provides estimates of surrogacy that may be substantially lower than the true relationship between surrogate and true endpoints, and rarely reach a level that would enable confidence in the strength of a given surrogate endpoint. As a result, care is needed in the assessment of time to event surrogate and true endpoints based only on this methodology.     

Approaches to evaluation of treatment effect in randomized clinical trials with genomic subset

With the advances in human genomic/genetic studies, the clinical trial community gradually recognizes that phenotypically homogeneous patients may be heterogeneous at the genomic level. The genomic technology brings a possible avenue for developing a genomic (composite) biomarker to predict a genomically responsive patient subset that may have a (much) higher likelihood of benefiting from a treatment. Randomized controlled trial is the mainstay to provide scientifically convincing evidence of a purported effect a new treatment may demonstrate. In conventional clinical trials, the primary clinical hypothesis pertains to the therapeutic effect in all patients who are eligible for the study defined by the primary efficacy endpoint. The aspect of one-size-fits-all surrounding the conventional design has been challenged, particularly when the diseases may be heterogeneous due to observable clinical characteristics and/or unobservable underlying the genomic characteristics. Extension from the conventional single population design objective to an objective that encompasses two possible patient populations will allow more informative evaluation in the patients having different degrees of responsiveness to medication. Building in conventional clinical trials, an additional genomic objective can generate an appealing conceptual framework from the patient's perspective in addressing personalized medicine in well-controlled clinical trials. There are many perceived benefits of personalized medicine that are based on the notion of being genomically proactive in the identification of disease and prevention of disease or recurrence. In this paper, we show that an adaptive design approach can be constructed to study a clinical hypothesis of overall treatment effect and a hypothesis of treatment effect in a genomic subset more efficiently than the conventional non-adaptive approach.     

Another view on the analysis of cardiovascular morbidity/mortality trials

In many morbidity/mortality studies, composite endpoints are considered. Although the primary interest is to demonstrate that an invention delays death, the expected death rate is often that low that studies focussing on survival exclusively are not feasible. Components of the composite endpoint are chosen such that their occurrence is predictive for time to death. Therefore, if the time to non-fatal events is censored by death, censoring is no longer independent. As a consequence, the analysis of the components of a composite endpoint cannot be reasonably performed using classical methods for the analysis of survival times like Kaplan-Meier estimates or log-rank tests. In this paper we visualize the impact of disregarding dependent censoring during the analysis and discuss practicable alternatives for the analysis of morbidity/mortality studies. In the context of simulations we provide evidence that copula-based methods have the potential to deliver practically unbiased estimates of hazards of components of a composite endpoint. At the same time, they require minimal assumptions, which is important since not all assumptions are generally verifiable because of censoring. Therefore, there are alternative ways to analyze morbidity/mortality studies more appropriately by accounting for the dependencies among the components of composite endpoints. Despite the limitations mentioned, these alternatives can at minimum serve as sensitivity analyses to check the robustness of the currently used methods.     

An investigation into the two‐stage meta‐analytic copula modelling approach for evaluating time‐to‐event surrogate endpoints which comprise of one or more events of interest

Clinical trials of experimental treatments must be designed with primary endpoints that directly measure clinical benefit for patients. In many disease areas, the recognised gold standard primary endpoint can take many years to mature, leading to challenges in the conduct and quality of clinical studies. There is increasing interest in using shorter‐term surrogate endpoints as substitutes for costly long‐term clinical trial endpoints; such surrogates need to be selected according to biological plausibility, as well as the ability to reliably predict the unobserved treatment effect on the long‐term endpoint. A number of statistical methods to evaluate this prediction have been proposed; this paper uses a simulation study to explore one such method in the context of time‐to‐event surrogates for a time‐to‐event true endpoint. This two‐stage meta‐analytic copula method has been extensively studied for time‐to‐event surrogate endpoints with one event of interest, but thus far has not been explored for the assessment of surrogates which have multiple events of interest, such as those incorporating information directly from the true clinical endpoint. We assess the sensitivity of the method to various factors including strength of association between endpoints, the quantity of data available, and the effect of censoring. In particular, we consider scenarios where there exist very little data on which to assess surrogacy. Results show that the two‐stage meta‐analytic copula method performs well under certain circumstances and could be considered useful in practice, but demonstrates limitations that may prevent universal use.     

Hypotheses testing for generalized order statistics with simple order restrictions on model parameters under the alternative

In applications of generalized order statistics as, for instance, reliability analysis of engineering systems, prior knowledge about the order of the underlying model parameters is often available and may therefore be incorporated in inferential procedures. Taking this information into account, we establish the likelihood ratio test, Rao's score test, and Wald's test for test problems arising from the question of appropriate model selection for ordered data, where simple order restrictions are put on the parameters under the alternative hypothesis. For simple and composite null hypothesis, explicit representations of the corresponding test statistics are obtained along with some properties and their asymptotic distributions. A simulation study is carried out to compare the order restricted tests in terms of their power. In the set-up considered, the adapted tests significantly improve the power of the associated omnibus versions for small sample sizes, especially when testing a composite null hypothesis.     

Conditional approval: discussion points from the PSI conditional approval expert group

The European Agency for the Evaluation of Medicinal Products has recently completed the consultation of a draft guidance on how to implement conditional approval. This route of application is available for orphan drugs, emergency situations and serious debilitating or life-threatening diseases. Although there has been limited experience in implementing conditional approval to date, PSI (Statisticians in the Pharmaceutical Industry) sponsored a meeting of pharmaceutical statisticians with an interest in the area to discuss potential issues. This article outlines the issues raised and resulting discussions, based on the group's interpretation of the legislation. Conditional approval seems to fit well with the accepted regulatory strategy in HIV. In oncology, conditional approval may be most likely when (a) compelling phase II data are available using accepted clinical outcomes (e.g. progression/recurrence-free survival or overall survival) and Phase III has been planned or started, or (b) when data are available using a surrogate endpoint for clinical outcome (e.g. response rate or biochemical measures) from a single-arm study in rare tumours with high response, compared with historical data. The use of interim analyses in Phase III for supporting conditional approval raises some challenging issues regarding dissemination of information, maintenance of blinding, potential introduction of bias, ethics, switching, etc.     

Optimal composite scores for longitudinal clinical trials under the linear mixed effects model

Clinical trials of chronic, progressive conditions use rate of change on continuous measures as the primary outcome measure, with slowing of progression on the measure as evidence of clinical efficacy. For clinical trials with a single prespecified primary endpoint, it is important to choose an endpoint with the best signal‐to‐noise properties to optimize statistical power to detect a treatment effect. Composite endpoints composed of a linear weighted average of candidate outcome measures have also been proposed. Composites constructed as simple sums or averages of component tests, as well as composites constructed using weights derived from more sophisticated approaches, can be suboptimal, in some cases performing worse than individual outcome measures. We extend recent research on the construction of efficient linearly weighted composites by establishing the often overlooked connection between trial design and composite performance under linear mixed effects model assumptions and derive a formula for calculating composites that are optimal for longitudinal clinical trials of known, arbitrary design. Using data from a completed trial, we provide example calculations showing that the optimally weighted linear combination of scales can improve the efficiency of trials by almost 20% compared with the most efficient of the individual component scales. Additional simulations and analytical results demonstrate the potential losses in efficiency that can result from alternative published approaches to composite construction and explore the impact of weight estimation on composite performance. Copyright © 2016. The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.     

Surrogate threshold effect: an alternative measure for meta-analytic surrogate endpoint validation

In many therapeutic areas, the identification and validation of surrogate endpoints is of prime interest to reduce the duration and/or size of clinical trials. Buyse et al. [Biostatistics 2000; 1:49-67] proposed a meta-analytic approach to the validation. In this approach, the validity of a surrogate is quantified by the coefficient of determination Rtrial2 obtained from a model, which allows for prediction of the treatment effect on the endpoint of interest ('true' endpoint) from the effect on the surrogate. One problem related to the use of Rtial2 is the difficulty in interpreting its value. To address this difficulty, in this paper we introduce a new concept, the so-called surrogate threshold effect (STE), defined as the minimum treatment effect on the surrogate necessary to predict a non-zero effect on the true endpoint. One of its interesting features, apart from providing information relevant to the practical use of a surrogate endpoint, is its natural interpretation from a clinical point of view.     

A semiparametric pseudo-score method for analysis of two-phase studies with continuous phase-I covariates

Two-phase study designs can reduce cost and other practical burdens associated with large scale epidemiologic studies by limiting ascertainment of expensive covariates to a smaller but informative sub-sample (phase-II) of the main study (phase-I). During the analysis of such studies, however, subjects who are selected at phase-I but not at phase-II, remain informative as they may have partial covariate information. A variety of semi-parametric methods now exist for incorporating such data from phase-I subjects when the covariate information can be summarized into a finite number of strata. In this article, we consider extending the pseudo-score approach proposed by Chatterjee et al. (J Am Stat Assoc 98:158–168, 2003) using a kernel smoothing approach to incorporate information on continuous phase-I covariates. Practical issues and algorithms for implementing the methods using existing software are discussed. A sandwich-type variance estimator based on the influence function representation of the pseudo-score function is proposed. Finite sample performance of the methods are studies using simulated data. Advantage of the proposed smoothing approach over alternative methods that use discretized phase-I covariate information is illustrated using two-phase data simulated within the National Wilms Tumor Study (NWTS).     

Dynamic path analysis for event time data: large sample properties and inference

We consider the situation with a survival or more generally a counting process endpoint for which we wish to investigate the effect of an initial treatment. Besides the treatment indicator we also have information about a time-varying covariate that may be of importance for the survival endpoint. The treatment may possibly influence both the endpoint and the time-varying covariate, and the concern is whether or not one should correct for the effect of the dynamic covariate. Recently Fosen et al. (Biometrical J 48:381–398, 2006a) investigated this situation using the notion of dynamic path analysis and showed under the Aalen additive hazards model that the total effect of the treatment indicator can be decomposed as a sum of what they termed a direct and an indirect effect. In this paper, we give large sample properties of the estimator of the cumulative indirect effect that may be used to draw inferences. Small sample properties are investigated by Monte Carlo simulation and two applications are provided for illustration. We also consider the Cox model in the situation with recurrent events data and show that a similar decomposition of the total effect into a sum of direct and indirect effects holds under certain assumptions.     

Multistage sampling for latent variable models

I consider the design of multistage sampling schemes for epidemiologic studies involving latent variable models, with surrogate measurements of the latent variables on a subset of subjects. Such models arise in various situations: when detailed exposure measurements are combined with variables that can be used to assign exposures to unmeasured subjects; when biomarkers are obtained to assess an unobserved pathophysiologic process; or when additional information is to be obtained on confounding or modifying variables. In such situations, it may be possible to stratify the subsample on data available for all subjects in the main study, such as outcomes, exposure predictors, or geographic locations. Three circumstances where analytic calculations of the optimal design are possible are considered: (i) when all variables are binary; (ii) when all are normally distributed; and (iii) when the latent variable and its measurement are normally distributed, but the outcome is binary. In each of these cases, it is often possible to considerably improve the cost efficiency of the design by appropriate selection of the sampling fractions. More complex situations arise when the data are spatially distributed: the spatial correlation can be exploited to improve exposure assignment for unmeasured locations using available measurements on neighboring locations; some approaches for informative selection of the measurement sample using location and/or exposure predictor data are considered.     

Strategies for Cohort Sampling Under the Cox Proportional Hazards Model,Application to an AIDS Clinical Trial

In some studies that relate covariates to times of failure it is not feasible to observe all covariates for all subjects. For example, some covariates may be too costly in terms of time, money, or effect on the subject to record for all subjects. This paper considers the relative efficiencies of several designs for sampling a portion of the cohort on which the costly covariates will be observed. Such designs typically measure all covariates for each failure and control for covariates of lesser interest. Control subjects are sampled either from risk sets at times of observed failures or from the entire cohort. A new design in which the sampling probability for each individual depends on the amount of information that the individual can contribute to estimated coefficients is shown to be superior to other sampling designs under certain conditions. Primary focus of our designs is on time-invariant covariates, but some methods easily generalize to the time-varying setting. Data from a study conducted by the AIDS Clinical Trials Group are used to illustrate the new sampling procedure and to explore the relative efficiency of several sampling schemes.     

Power and sample size considerations in clinical trials with competing risk endpoints

In clinical trials with a time-to-event endpoint, subjects are often at risk for events other than the one of interest. When the occurrence of one type of event precludes observation of any later events or alters the probably of subsequent events, the situation is one of competing risks. During the planning stage of a clinical trial with competing risks, it is important to take all possible events into account. This paper gives expressions for the power and sample size for competing risks based on a flexible parametric Weibull model. Nonuniform accrual to the study is considered and an allocation ratio other than one may be used. Results are also provided for the case where two or more of the competing risks are of primary interest.     

The correlation structure of longitudinal measurements of vision in patients with macular degeneration

Background: In age‐related macular degeneration (ARMD) trials, the FDA‐approved endpoint is the loss (or gain) of at least three lines of vision as compared to baseline. The use of such a response endpoint entails a potentially severe loss of information. A more efficient strategy could be obtained by using longitudinal measures of the change in visual acuity. In this paper we investigate, by using data from two randomized clinical trials, the mean and variance–covariance structures of the longitudinal measurements of the change in visual acuity. Methods: Individual patient data were collected in 234 patients in a randomized trial comparing interferon‐ α with placebo and in 1181 patients in a randomized trial comparing three active doses of pegaptanib with sham. A linear model for longitudinal data was used to analyze the repeated measurements of the change in visual acuity. Results: For both trials, the data were adequately summarized by a model that assumed a quadratic trend for the mean change in visual acuity over time, a power variance function, and an antedependence correlation structure. The power variance function was remarkably similar for the two datasets and involved the square root of the measurement time. Conclusions: The similarity of the estimated variance functions and correlation structures for both datasets indicates that these aspects may be a genuine feature of the measurements of changes in visual acuity in patients with ARMD. The feature can be used in the planning and analysis of trials that use visual acuity as the clinical endpoint of interest. Copyright © 2010 John Wiley & Sons, Ltd.