Properties of a nonparametric test for early comparison of treatments in clinical trials in the presence of surrogate endpoints

A nonparametric test is derived for comparing treatments with respect to the final endpoint in clinical trials in which the final endpoint has been observed for a random subset of patients, but results are available for a surrogate endpoint for a larger sample of patients. The test is an adaptation of the Wilcoxon-Mann-Whitney two-sample test, with an adjustment that involves a comparison of the ranks of the surrogate endpoints between patients with and without final endpoints. The validity of the test depends on the assumption that the patients with final endpoints represent a random sample of the patients registered in the study. This assumption is viable in trials in which the final endpoint is evaluated at a "landmark" timepoint in the patients' natural history. A small sample simulation study demonstrates that the test has a size that is close to the nominal value for all configurations evaluated. When compared with the conventional test based only on the final endpoints, the new test delivers substantial increases in power only when the surrogate endpoint is highly correlated with the true endpoint. Our research indicates that, in the absence of modeling assumptions, auxiliary information derived from surrogate endpoints can provide significant additional information only under special circumstances.     

Sample size calculation for the combination test under nonproportional hazards

For sample size calculation in clinical trials with survival endpoints, the logrank test, which is the optimal method under the proportional hazard (PH) assumption, is predominantly used. In reality, the PH assumption may not hold. For example, in immuno-oncology trials, delayed treatment effects are often expected. The sample size without considering the potential violation of the PH assumption may lead to an underpowered study. In recent years, combination tests such as the maximum weighted logrank test have received great attention because of their robust performance in various hazards scenarios. In this paper, we propose a flexible simulation-free procedure to calculate the sample size using combination tests. The procedure extends the Lakatos' Markov model and allows for complex situations encountered in a clinical trial, like staggered entry, dropouts, etc. We evaluate the procedure using two maximum weighted logrank tests, one projection-type test, and three other commonly used tests under various hazards scenarios. The simulation studies show that the proposed method can achieve the target power for all compared tests in most scenarios. The combination tests exhibit robust performance under correct specification and misspecification scenarios and are highly recommended when the hazard-changing patterns are unknown beforehand. Finally, we demonstrate our method using two clinical trial examples and provide suggestions about the sample size calculations under nonproportional hazards.     

An analysis for transient states with application to tumor shrinkage

The evaluation of therapies for chronic diseases is often based on the frequency and/or the duration of improvement. Treated separately, these endpoints may give contradictory impressions of the efficacy of the therapy. We propose a more unified method of summarizing improvement-related data--the probability of being in response, i.e., improved, as a function of time. Although improvement is not the only endpoint considered in most trials and this function will not always provide a clear answer to the question of which treatment has better improvement-related characteristics, it does combine the information on several endpoints usually considered separately into a single easily interpreted item. This function is estimated using the method of maximum likelihood on a distribution-free stochastic model of times to improvement and failure. Censored observations are taken into account. A detailed example using data from a cancer clinical trial is presented.     

Beyond mean modelling: Bias due to misspecification of dispersion in Poisson‐inverse Gaussian regression

In clinical trials one traditionally models the effect of treatment on the mean response. The underlying assumption is that treatment affects the response distribution through a mean location shift on a suitable scale, with other aspects of the distribution (shape/dispersion/variance) remaining the same. This work is motivated by a trial in Parkinson's disease patients in which one of the endpoints is the number of falls during a 10‐week period. Inspection of the data reveals that the Poisson‐inverse Gaussian (PiG) distribution is appropriate, and that the experimental treatment reduces not only the mean, but also the variability, substantially. The conventional analysis assumes a treatment effect on the mean, either adjusted or unadjusted for covariates, and a constant dispersion parameter. On our data, this analysis yields a non‐significant treatment effect. However, if we model a treatment effect on both mean and dispersion parameters, both effects are highly significant. A simulation study shows that if a treatment effect exists on the dispersion and is ignored in the modelling, estimation of the treatment effect on the mean can be severely biased. We show further that if we use an orthogonal parametrization of the PiG distribution, estimates of the mean model are robust to misspecification of the dispersion model. We also discuss inferential aspects that are more difficult than anticipated in this setting. These findings have implications in the planning of statistical analyses for count data in clinical trials.     

Validation of surrogate markers in multiple randomized clinical trials with repeated measurements: canonical correlation approach

Part of the recent literature on the evaluation of biomarkers as surrogate endpoints starts from a multitrial context, which leads to a definition of validity in terms of the quality of both trial-level and individual-level association between the surrogate and true endpoints (Buyse et al., 2000, Biostatistics1, 49-67). These authors concentrated on cross-sectional continuous responses. However, in many randomized clinical studies, repeated measurements are encountered on either or both endpoints. A challenge in this setting is the formulation of a simple and meaningful concept of "surrogacy."Alonso et al. (2003, Biometrical Journal45, 931-945) proposed the variance reduction factor (VRF) to evaluate surrogacy at the individual level. They also showed how and when this concept should be extended to study surrogacy at the trial level. Here, we approach the problem from the natural canonical correlation perspective. We define a class of canonical correlation functions that can be used to study surrogacy at the trial and individual level. We show that the VRF and the R2 measure defined by Buyse et al. (2000) follow as special cases. Simulations are conducted to evaluate the performance of different members of this family. The methodology is illustrated on data from a meta-analysis of five clinical trials comparing antipsychotic agents for the treatment of chronic schizophrenia.     

One-Sided Tests in Clinical Trials with Multiple Endpoints

Treatment comparisons in clinical trials often involve several endpoints. For example, one might wish to demonstrate that a new treatment is superior to the current standard for some components of the multivariate response vector and is not inferior, modulo biologically unimportant difference to the standard treatment for all other components. We introduce a new approach to multiple-endpoint testing that incorporates the essential univariate and multivariate features of the treatment effects. This approach is compared with existing methods in a simulation study and applied to data on rheumatoid arthritis patients receiving one of two treatments.     

Influence of trial duration on the bias of the estimated treatment effect in clinical trials when individual heterogeneity is ignored

In randomized clinical trials where the times to event of two treatment groups are compared under a proportional hazards assumption, it has been established that omitting prognostic factors from the model entails an underestimation of the hazards ratio. Heterogeneity due to unobserved covariates in cancer patient populations is a concern since genomic investigations have revealed molecular and clinical heterogeneity in these populations. In HIV prevention trials, heterogeneity is unavoidable and has been shown to decrease the treatment effect over time. This article assesses the influence of trial duration on the bias of the estimated hazards ratio resulting from omitting covariates from the Cox analysis. The true model is defined by including an unobserved random frailty term in the individual hazard that reflects the omitted covariate. Three frailty distributions are investigated: gamma, log‐normal, and binary, and the asymptotic bias of the hazards ratio estimator is calculated. We show that the attenuation of the treatment effect resulting from unobserved heterogeneity strongly increases with trial duration, especially for continuous frailties that are likely to reflect omitted covariates, as they are often encountered in practice. The possibility of interpreting the long‐term decrease in treatment effects as a bias induced by heterogeneity and trial duration is illustrated by a trial in oncology where adjuvant chemotherapy in stage 1B NSCLC was investigated.     

Designs for single- or multiple-agent phase I trials

Phase I trials of cytotoxic agents in oncology are usually dose-finding studies that involve a single cytotoxic agent. Many statistical methods have been proposed for these trials, all of which are based on the assumption of a monotonic dose-toxicity curve. For single-agent trials, this is a valid assumption. In many trials, however, investigators are interested in finding the maximally tolerated dose based on escalating multiple cytotoxic agents. When there are multiple agents, monotonicity of the dose-toxicity curve is not clearly defined. In this article we present a design for phase I trials in which the toxicity probabilities follow a partial order, meaning that there are pairs of treatments for which the ordering of the toxicity probabilities is not known at the start of the trial. We compare the new design to existing methods for simple orders and investigate the properties of the design for two partial orders.     

Using secondary outcome to sharpen bounds for treatment harm rate in characterizing heterogeneity

In a clinical trial, statistical reports are typically concerned about the mean difference in two groups. Now there is increasing interest in the heterogeneity of the treatment effect, which has important implications in treatment evaluation and selection. The treatment harm rate (THR), which is defined by the proportion of people who has a worse outcome on the treatment compared to the control, was used to characterize the heterogeneity. Since THR involves the joint distribution of the two potential outcomes, it cannot be identified without further assumptions even in the randomized trials. We can only derive the simple bounds with the observed data. But the simple bounds are usually too wide. In this paper, we use a secondary outcome that satisfies the monotonicity assumption to tighten the bounds. It is shown that the bounds we derive cannot be wider than the simple bounds. We also construct some simulation studies to assess the performance of our bounds in finite sample. The results show that a secondary outcome, which is more closely related to the primary outcome, can lead to narrower bounds. Finally, we illustrate the application of the proposed bounds in a randomized clinical trial of determining whether the intensive glycemia could reduce the risk of development or progression of diabetic retinopathy.     

Proportion of treatment effect mediated by surrogate endpoints

One of the central aims in randomized clinical trials is to find well‐validated surrogate endpoints to reduce the sample size and/or duration of trials. Clinical researchers and practitioners have proposed various surrogacy measures for assessing candidate surrogate endpoints. However, most existing surrogacy measures have the following shortcomings: (i) they often fall outside the range [0,1], (ii) they are imprecisely estimated, and (iii) they ignore the interaction associations between a treatment and candidate surrogate endpoints in the evaluation of the surrogacy level. To overcome these difficulties, we propose a new surrogacy measure, the proportion of treatment effect mediated by candidate surrogate endpoints (PMS), based on the decomposition of the treatment effect into direct, indirect, and interaction associations mediated by candidate surrogate endpoints. In addition, we validate the advantages of PMS through Monte Carlo simulations and the application to empirical data from ORIENT (the Olmesartan Reducing Incidence of Endstage Renal Disease in Diabetic Nephropathy Trial).     

Sample Size Reassessment and Hypothesis Testing in Adaptive Survival Trials

Mid-study design modifications are becoming increasingly accepted in confirmatory clinical trials, so long as appropriate methods are applied such that error rates are controlled. It is therefore unfortunate that the important case of time-to-event endpoints is not easily handled by the standard theory. We analyze current methods that allow design modifications to be based on the full interim data, i.e., not only the observed event times but also secondary endpoint and safety data from patients who are yet to have an event. We show that the final test statistic may ignore a substantial subset of the observed event times. An alternative test incorporating all event times is found, where a conservative assumption must be made in order to guarantee type I error control. We examine the power of this approach using the example of a clinical trial comparing two cancer therapies.     

Extension of the rank sum test for clustered data: two-group comparisons with group membership defined at the subunit level

The Wilcoxon rank sum test is widely used for two-group comparisons for nonnormal data. An assumption of this test is independence of sampling units both between and within groups. In ophthalmology, data are often collected on two eyes of an individual, which are highly correlated. In ophthalmological clinical trials, randomization is usually performed at the subject level, but the unit of analysis is the eye. If the eye is used as the unit of analysis, then a modification to the usual Wilcoxon rank sum variance formula must be made to account for the within-cluster dependence. For some clustered data designs, where the unit of analysis is the subunit, group membership may be defined at the subunit level. For example, in some randomized ophthalmologic clinical trials, different treatments may be applied to fellow eyes of some patients, while the same treatment may be applied to fellow eyes of other patients. In general, binary eye-specific covariates may be present (scored as exposed or unexposed) and one wishes to compare nonnormally distributed outcomes between exposed and unexposed eyes using the Wilcoxon rank sum test while accounting for the clustering. In this article, we present a corrected variance formula for the Wilcoxon rank sum statistic in the setting of eye (subunit)-specific covariates. We apply it to compare ocular itching scores in ocular allergy patients between eyes treated with active versus placebo eye drops, where some patients receive the same eye drop in both eyes, while other patients receive different eye drops in fellow eyes. We also present comparisons between the clustered Wilcoxon test and each of the signed rank tests and mixed model approaches and show dramatic differences in power in favor of the clustered Wilcoxon test for some designs.     

The analysis of multiple endpoints in clinical trials

Treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall Type I error rate. One option is to select a single primary endpoint for formal statistical inference, but this is not always feasible. Another approach is to apply Bonferroni correction (i.e., multiply each P-value by the total number of endpoints). Its conservatism for correlated endpoints is examined for multivariate normal data. A third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics. Quantitative, binary, and survival endpoints are all considered within this general framework. Two examples are presented and the relative merits of the proposed strategies are discussed.     

Calculating sample size for studies with expected all-or-none nonadherence and selection bias

Summary .  We develop sample size formulas for studies aiming to test mean differences between a treatment and control group when all-or-none nonadherence (noncompliance) and selection bias are expected. Recent work by Fay, Halloran, and Follmann (2007, Biometrics 63, 465–474) addressed the increased variances within groups defined by treatment assignment when nonadherence occurs, compared to the scenario of full adherence, under the assumption of no selection bias. In this article, we extend the authors' approach to allow selection bias in the form of systematic differences in means and variances among latent adherence subgroups. We illustrate the approach by performing sample size calculations to plan clinical trials with and without pilot adherence data. Sample size formulas and tests for normally distributed outcomes are also developed in a Web Appendix that account for uncertainty of estimates from external or internal pilot data.     

Bronchiolectasis-a complication of artificial ventilation.

Pulmonary barotrauma associated with artificial ventilation is recognised clinically as pneumothorax, pneumo-mediastinum, or subcutaneous emphysema. Eleven patients who died in the intensive therapy unit after artificial ventilation were found at necropsy to have pronounced bronchiolectasis, which was associated with a greatly increased physiological dead space during life. The condition was best predicted by the maximum level of positive end expiratory pressure and the duration of application of positive end expiratory pressure. The clinical course of the lesion in survivors is not known. Further detailed studies are needed, but it is suggested that high levels of positive end expiratory pressure should be used with caution.     

Clinical and biomarker endpoint analysis in neoadjuvant endocrine therapy trials

Neoadjuvant endocrine therapy trials for breast cancer are now a widely accepted investigational approach for oncology cooperative group and pharmaceutical company research programs. However, there remains considerable uncertainty regarding the most suitable endpoints for these studies, in part, because short-term clinical, radiological or biomarker responses have not been fully validated as surrogate endpoints that closely relate to long-term breast cancer outcome. This shortcoming must be addressed before neoadjuvant endocrine treatment can be used as a triage strategy designed to identify patients with endocrine therapy “curable” disease. In this summary, information from published studies is used as a basis to critique clinical trial designs and to suggest experimental endpoints for future validation studies. Three aspects of neoadjuvant endocrine therapy designs are considered: the determination of response; the assessment of surgical outcomes; and biomarker endpoint analysis. Data from the letrozole 024 (LET 024) trial that compared letrozole and tamoxifen is used to illustrate a combined endpoint analysis that integrates both clinical and biomarker information. In addition, the concept of a “cell cycle response” is explored as a simple post-treatment endpoint based on Ki67 analysis that might have properties similar to the pathological complete response endpoint used in neoadjuvant chemotherapy trials.     

K‐Sample comparisons using propensity analysis

In this paper, we investigate K‐group comparisons on survival endpoints for observational studies. In clinical databases for observational studies, treatment for patients are chosen with probabilities varying depending on their baseline characteristics. This often results in noncomparable treatment groups because of imbalance in baseline characteristics of patients among treatment groups. In order to overcome this issue, we conduct propensity analysis and match the subjects with similar propensity scores across treatment groups or compare weighted group means (or weighted survival curves for censored outcome variables) using the inverse probability weighting (IPW). To this end, multinomial logistic regression has been a popular propensity analysis method to estimate the weights. We propose to use decision tree method as an alternative propensity analysis due to its simplicity and robustness. We also propose IPW rank statistics, called Dunnett‐type test and ANOVA‐type test, to compare 3 or more treatment groups on survival endpoints. Using simulations, we evaluate the finite sample performance of the weighted rank statistics combined with these propensity analysis methods. We demonstrate these methods with a real data example. The IPW method also allows us for unbiased estimation of population parameters of each treatment group. In this paper, we limit our discussions to survival outcomes, but all the methods can be easily modified for any type of outcomes, such as binary or continuous variables.     

Are cancer risks associated with exposures to ionising radiation from internal emitters greater than those in the Japanese A-bomb survivors?

After ingestion or inhalation of radionuclides, internal organs of the human body will be exposed to ionising radiation. Current risk estimates of radiation-associated cancer from internal emitters are largely based on extrapolation of risk from high-dose externally exposed groups. Concerns have been expressed that extrapolated risk estimates from internal emitters are greatly underestimated, by factors of ten or more, thus implying a severe underestimation of the true risks. Therefore, data on cancer mortality and incidence in a number of groups who received exposure predominantly from internal emitters are examined and excess relative risks per Sv are compared with comparable (age at exposure, time since exposure, gender) matched subsets of the Japanese atomic bomb survivor cohort. Risks are examined separately for low LET and high LET internal emitters. There are eight studies informative for the effects of internal low LET radiation exposure and 12 studies informative for the effects of internal high LET radiation. For 11 of the 20 cancer endpoints (subgroups of particular study cohorts) examined in the low LET internal emitter studies, the best estimate of the excess relative risk is greater than the corresponding estimate in the Japanese atomic bomb survivors and for the other nine it is less. For four of these 20 studies, the relative risk is significantly (2-sided P < 0.05) different from that in the Japanese atomic bomb survivors, in three cases greater than the atomic bomb survivor relative risk and in one case less. Considering only those six low LET studies/endpoints with 100 or more deaths or cases, for four out of six studies/endpoints the internal emitter risk is greater than that in the Japanese atomic bomb survivors. For seven of the 24 cancer endpoints examined in the high LET internal emitter studies the best estimate of the ERR in the internal emitter study is greater than the corresponding estimate in the Japanese atomic bomb survivors and for the other 17 it is less. For six studies, the relative risk is significantly (2-sided P < 0.05) different from that in the Japanese atomic bomb survivors, in one case greater than the atomic bomb survivor relative risk and in five cases less. Considering only those eight high LET studies/endpoints with 100 or more deaths or cases, for five out of eight studies/endpoints the internal emitter risk is greater than that in the Japanese atomic bomb survivors. These results suggest that excess relative risks in the internal emitter studies do not appreciably differ from those in the Japanese atomic bomb survivors. However, there are substantial uncertainties in estimates of risks in the internal emitter studies, particularly in relation to lung cancer associated with radon daughter (alpha particle) exposure, so a measure of caution should be exercised in these conclusions.     

Clinical trials in systemic sclerosis: lessons learned and outcomes

The pathogenesis of systemic sclerosis (SSc) is complex and largely unclear. The clinical heterogeneity of the disease and its progression over a number of years makes the choice of endpoints in the design of clinical trials difficult. The overwhelming need in this disease is to diagnose it early and identify those patients who will benefit most from early, aggressive treatment that potentially can alter the clinical disease course. To achieve this, innumerable challenges must be overcome. This article reviews data from recent clinical trials and the lessons derived from retrospective observational studies, databases, and patient registries. Taken together, these observations will help to improve our understanding of the diverse clinical course of SSc and permit refinement of existing outcome measures for the design of future clinical trials, in which the likelihood of observing a positive treatment effect with the drugs at our disposal will be maximized.     

A Systematic Review of the Efficacy and Safety Experience Reported for Sorafenib in Advanced Renal Cell Carcinoma (RCC) in the Post-Approval Setting

Background

Sorafenib was FDA approved in 2005 for treatment of renal cell carcinoma (RCC) based on the results of the pivotal phase 3 clinical trial, TARGET (Treatment Approaches in Renal Cancer Global Evaluation Trial). Since that time, numerous clinical studies have been undertaken that substantially broaden our knowledge of the use of sorafenib for this indication.

Methods

We systematically reviewed PubMed, Web of Science, Embase, Cochrane Library, and www.clinicaltrials.gov for prospective clinical studies using single agent sorafenib in RCC and published since 2005. Primary endpoints of interest were progression-free survival (PFS) and safety. PROSPERO International prospective register of systematic reviews #CRD42014010765.

Results

We identified 30 studies in which 2182 patients were treated with sorafenib, including 1575 patients who participated in randomized controlled phase 3 trials. In these trials, sorafenib was administered as first-, second- or third-line treatment. Heterogeneity among trial designs and reporting of data precluded statistical comparisons among trials or with TARGET. The PFS appeared shorter in second- vs. first-line treatment, consistent with the more advanced tumor status in the second-line setting. In some trials, incidences of grade 3/4 hypertension or hand-foot skin reaction (HFSR) were more than double that seen in TARGET (4% and 6%, respectively). These variances may be attributable to increased recognition of HFSR, or potentially differences in dose adjustments, that could be consequences of increased familiarity with sorafenib usage. Several small studies enrolled exclusively Asian patients. These studies reported notably longer PFS than was observed in TARGET. However, no obvious corresponding differences in disease control rate and overall survival were seen.

Conclusions

Collectively, more recent experiences using sorafenib in RCC are consistent with results reported for TARGET with no marked changes of response endpoints or new safety signals observed.