A powerful test for Balaam's design

The crossover trial design (AB/BA design) is often used to compare the effects of two treatments in medical science because it performs within‐subject comparisons, which increase the precision of a treatment effect (i.e., a between‐treatment difference). However, the AB/BA design cannot be applied in the presence of carryover effects and/or treatments‐by‐period interaction. In such cases, Balaam's design is a more suitable choice. Unlike the AB/BA design, Balaam's design inflates the variance of an estimate of the treatment effect, thereby reducing the statistical power of tests. This is a serious drawback of the design. Although the variance of parameter estimators in Balaam's design has been extensively studied, the estimators of the treatment effect to improve the inference have received little attention. If the estimate of the treatment effect is obtained by solving the mixed model equations, the AA and BB sequences are excluded from the estimation process. In this study, we develop a new estimator of the treatment effect and a new test statistic using the estimator. The aim is to improve the statistical inference in Balaam's design. Simulation studies indicate that the type I error of the proposed test is well controlled, and that the test is more powerful and has more suitable characteristics than other existing tests when interactions are substantial. The proposed test is also applied to analyze a real dataset. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysing pharmacokinetic drug interaction or comparability studies with missing values in crossover design

In a pharmacokinetic drug interaction study using a three‐period, three‐treatment (drug A, drug B, and drugs A and B concomitantly) crossover design, pharmacokinetic parameters for either drug are only measured in two of the three periods. Similar missing data problems can arise for a four‐period, four‐treatment crossover pharmacokinetic comparability study. This paper investigates whether the usual ANOVA model for the crossover design can be applied under this pattern of missing data. It is shown that the model can still be used, contrary to a belief that a new one is needed. The effect of this type of missing data pattern on the statistical properties of treatment, period and carryover effect estimates was derived and illustrated by means of simulations and an example. Copyright © 2003 John Wiley & Sons, Ltd.     

Cost‐efficient higher‐order crossover designs for two‐treatment clinical trials

Higher‐order crossover designs have drawn considerable attention in clinical trials, because of their ability to test direct treatment effects in the presence of carry‐over effects. The important question, when applying higher‐order crossover designs in practice, is how to choose a design with both statistical and cost efficiencies from various alternatives. In this paper, we propose a general cost function and compare five statistically optimal or near‐optimal designs with this cost function for a two‐treatment study under different carry‐over models. Based on our study, to achieve both statistical and cost efficiencies, a four‐period, four‐sequence crossover design is generally recommended under the simple carry‐over or no carry‐over models, and a three‐period, two‐sequence crossover design is generally recommended under the steady‐state carry‐over models. Copyright © 2005 John Wiley & Sons, Ltd.     

Control of type 1 error in a hybrid complete two‐period vaccine efficacy trial

A complete two‐period experimental design has been defined as one in which subjects are randomized to treatment, observed for the occurrence of an event of interest, re‐randomized, and observed again for the event in a second period. A 4‐year vaccine efficacy trial was planned to compare a high‐dose vaccine with a standard dose vaccine. Subjects would be randomized each year, and subjects who had participated in a previous year would be allowed to re‐enroll in a subsequent year and would be re‐randomized. A question of interest is whether positive correlation between observations on subjects who re‐enrolled would inflate the variance of test statistics. The effect of re‐enrollment and correlation on type 1 error in a 4‐year trial is investigated by simulation. As conducted, the trial met its power requirements after two years. Subjects therefore included some who participated for a single year and others who participated in both years. Those who participated in both years constituted a complete two‐period design. An algebraic expression for the variance of the treatment difference in a complete two‐period design is derived. It is shown that under a ‘no difference’ null, correlation does not result in variance inflation in this design. When there is a treatment difference, there is variance inflation but it is small. In the vaccine efficacy trial, the effect of correlation on the statistical inference was negligible. Copyright © 2014 John Wiley & Sons, Ltd.     

The impact of period effects on dose level contrasts in alternating cross‐over designs for first‐time‐in‐human studies

For first‐time‐in‐human studies with small molecules alternating cross‐over designs are often employed and at study end are analyzed using linear models. We discuss the impact of including a period effect in the model on the precision with which dose level contrasts can be estimated and quantify the bias of least squares estimators if a period effect is inherent in the data that is not accounted for in the model. We also propose two alternative designs that allow a more precise estimation of dose level contrasts compared with the standard design when period effects are included in the model. Copyright © 2010 John Wiley & Sons, Ltd.     

A Frailty Model in Crossover Studies with Time-to-Event Response Variable

In this article, we develop a model to study treatment, period, carryover, and other applicable effects in a crossover design with a time-to-event response variable. Because time-to-event outcomes on different treatment regimens within the crossover design are correlated for an individual, we adopt a proportional hazards frailty model. If the frailty is assumed to have a gamma distribution, and the hazard rates are piecewise constant, then the likelihood function can be determined via closed-form expressions. We illustrate the methodology via an application to a data set from an asthma clinical trial and run simulations that investigate sensitivity of the model to data generated from different distributions.     

Carryover negligibility and relevance in bioequivalence studies

The carryover effect is a recurring issue in the pharmaceutical field. It may strongly influence the final outcome of an average bioequivalence study. Testing a null hypothesis of zero carryover is useless: not rejecting it does not guarantee the non‐existence of carryover, and rejecting it is not informative of the true degree of carryover and its influence on the validity of the final outcome of the bioequivalence study. We propose a more consistent approach: even if some carryover is present, is it enough to seriously distort the study conclusions or is it negligible? This is the central aim of this paper, which focuses on average bioequivalence studies based on 2 × 2 crossover designs and on the main problem associated with carryover: type I error inflation. We propose an equivalence testing approach to these questions and suggest reasonable negligibility or relevance limits for carryover. Finally, we illustrate this approach on some real datasets. Copyright © 2015 John Wiley & Sons, Ltd.     

Use of baseline measurements in the two-period crossover design

It is proposed that baseline measurements be obtained prior to each period in a two-period crossover design. These measurements are used in a preliminary test for determining the validity of a test for treatment comparison and also for testing the hypothesis of equal treatment effects. The null hypothesis in this preliminary test consists of the following three hypotheses: that there is no difference in disease conditions prior to the two periods, no difference in residual effects of the drugs, and no treatment × period interaction.. A numerical example is given and the efficiencies of several methods are computed.     

Practical approaches for design and analysis of clinical trials of infertility treatments: crossover designs and the Mantel–Haenszel method are recommended

Crossover designs have some advantages over standard clinical trial designs and they are often used in trials evaluating the efficacy of treatments for infertility. However, clinical trials of infertility treatments violate a fundamental condition of crossover designs, because women who become pregnant in the first treatment period are not treated in the second period. In previous research, to deal with this problem, some new designs, such as re‐randomization designs, and analysis methods including the logistic mixture model and the beta‐binomial mixture model were proposed. Although the performance of these designs and methods has previously been evaluated in large‐scale clinical trials with sample sizes of more than 1000 per group, the actual sample sizes of infertility treatment trials are usually around 100 per group. The most appropriate design and analysis for these moderate‐scale clinical trials are currently unclear. In this study, we conducted simulation studies to determine the appropriate design and analysis method of moderate‐scale clinical trials for irreversible endpoints by evaluating the statistical power and bias in the treatment effect estimates. The Mantel–Haenszel method had similar power and bias to the logistic mixture model. The crossover designs had the highest power and the smallest bias. We recommend using a combination of the crossover design and the Mantel–Haenszel method for two‐period, two‐treatment clinical trials with irreversible endpoints. Copyright © 2015 John Wiley & Sons, Ltd.     

Two‐Sample Bootstrap Hypothesis Tests for Three‐Dimensional Labelled Landmark Data

Abstract. We investigate resampling methodologies for testing the null hypothesis that two samples of labelled landmark data in three dimensions come from populations with a common mean reflection shape or mean reflection size‐and‐shape. The investigation includes comparisons between (i) two different test statistics that are functions of the projection onto tangent space of the data, namely the James statistic and an empirical likelihood statistic; (ii) bootstrap and permutation procedures; and (iii) three methods for resampling under the null hypothesis, namely translating in tangent space, resampling using weights determined by empirical likelihood and using a novel method to transform the original sample entirely within refection shape space. We present results of extensive numerical simulations, on which basis we recommend a bootstrap test procedure that we expect will work well in practise. We demonstrate the procedure using a data set of human faces, to test whether humans in different age groups have a common mean face shape.     

Carry‐over in cross‐over trials in bioequivalence: theoretical concerns and empirical evidence

There is now general agreement that pre‐testing for carry‐over in the AB/BA design is harmful and that efficient analysis of this design must proceed on the assumption that carry‐over has not affected the results to any appreciable degree. A general consensus has not been achieved in the case of higher‐order designs. Since particular forms of carry‐over can be estimated on a within‐patient basis and unbiased within‐patient treatment estimators are possible, some statisticians favour pre‐testing and some favour automatic adjustment for carry‐over. We present theoretical arguments that show that, just as in the AB/BA case, the strategy of pre‐testing is biased as a whole and also that the loss in terms of efficiency in adjusting is not negligible. We also present data from two large series of bioequivalence studies to provide empirical evidence that in this context carry‐over is either absent or rare. We conclude that adjusting or testing for carry‐over in bioequivalence studies is at worst harmful and at best pointless, and that this may also apply to other kinds of study. Copyright © 2004 John Wiley & Sons, Ltd.     

Addressing potential prior‐data conflict when using informative priors in proof‐of‐concept studies

Bayesian methods are increasingly used in proof‐of‐concept studies. An important benefit of these methods is the potential to use informative priors, thereby reducing sample size. This is particularly relevant for treatment arms where there is a substantial amount of historical information such as placebo and active comparators. One issue with using an informative prior is the possibility of a mismatch between the informative prior and the observed data, referred to as prior‐data conflict. We focus on two methods for dealing with this: a testing approach and a mixture prior approach. The testing approach assesses prior‐data conflict by comparing the observed data to the prior predictive distribution and resorting to a non‐informative prior if prior‐data conflict is declared. The mixture prior approach uses a prior with a precise and diffuse component. We assess these approaches for the normal case via simulation and show they have some attractive features as compared with the standard one‐component informative prior. For example, when the discrepancy between the prior and the data is sufficiently marked, and intuitively, one feels less certain about the results, both the testing and mixture approaches typically yield wider posterior‐credible intervals than when there is no discrepancy. In contrast, when there is no discrepancy, the results of these approaches are typically similar to the standard approach. Whilst for any specific study, the operating characteristics of any selected approach should be assessed and agreed at the design stage; we believe these two approaches are each worthy of consideration. Copyright © 2015 John Wiley & Sons, Ltd.     

Tests for Coefficients in High‐dimensional Additive Hazard Models

We consider hypothesis testing problems for low‐dimensional coefficients in a high dimensional additive hazard model. A variance reduced partial profiling estimator (VRPPE) is proposed and its asymptotic normality is established, which enables us to test the significance of each single coefficient when the data dimension is much larger than the sample size. Based on the p‐values obtained from the proposed test statistics, we then apply a multiple testing procedure to identify significant coefficients and show that the false discovery rate can be controlled at the desired level. The proposed method is also extended to testing a low‐dimensional sub‐vector of coefficients. The finite sample performance of the proposed testing procedure is evaluated by simulation studies. We also apply it to two real data sets, with one focusing on testing low‐dimensional coefficients and the other focusing on identifying significant coefficients through the proposed multiple testing procedure.     

Statistical Inference for Single‐index Panel Data Models

We study estimation and hypothesis testing in single‐index panel data models with individual effects. Through regressing the individual effects on the covariates linearly, we convert the estimation problem in single‐index panel data models to that in partially linear single‐index models. The conversion is valid regardless of the individual effects being random or fixed. We propose an estimating equation approach, which has a desirable double robustness property. We show that our method is applicable in single‐index panel data models with heterogeneous link functions. We further design a chi‐squared test to evaluate whether the individual effects are random or fixed. We conduct simulations to demonstrate the finite sample performance of the method and conduct a data analysis to illustrate its usefulness.     

Sequential parallel comparison design with two coprimary endpoints

A placebo‐controlled randomized clinical trial is required to demonstrate that an experimental treatment is superior to its corresponding placebo on multiple coprimary endpoints. This is particularly true in the field of neurology. In fact, clinical trials for neurological disorders need to show the superiority of an experimental treatment over a placebo in two coprimary endpoints. Unfortunately, these trials often fail to detect a true treatment effect for the experimental treatment versus the placebo owing to an unexpectedly high placebo response rate. Sequential parallel comparison design (SPCD) can be used to address this problem. However, the SPCD has not yet been discussed in relation to clinical trials with coprimary endpoints. In this article, our aim was to develop a hypothesis‐testing method and a method for calculating the corresponding sample size for the SPCD with two coprimary endpoints. In a simulation, we show that the proposed hypothesis‐testing method achieves the nominal type I error rate and power and that the proposed sample size calculation method has adequate power accuracy. In addition, the usefulness of our methods is confirmed by returning to an SPCD trial with a single primary endpoint of Alzheimer disease‐related agitation.     

Two‐stage phase II survival trial design

Recently, molecularly targeted agents and immunotherapy have been advanced for the treatment of relapse or refractory cancer patients, where disease progression‐free survival or event‐free survival is often a primary endpoint for the trial design. However, methods to evaluate two‐stage single‐arm phase II trials with a time‐to‐event endpoint are currently processed under an exponential distribution, which limits application of real trial designs. In this paper, we developed an optimal two‐stage design, which is applied to the four commonly used parametric survival distributions. The proposed method has advantages compared with existing methods in that the choice of underlying survival model is more flexible and the power of the study is more adequately addressed. Therefore, the proposed two‐stage design can be routinely used for single‐arm phase II trial designs with a time‐to‐event endpoint as a complement to the commonly used Simon's two‐stage design for the binary outcome.     

START: single‐to‐double arm transition design for phase II clinical trials

Phase II clinical trials designed for evaluating a drug's treatment effect can be either single‐arm or double‐arm. A single‐arm design tests the null hypothesis that the response rate of a new drug is lower than a fixed threshold, whereas a double‐arm scheme takes a more objective comparison of the response rate between the new treatment and the standard of care through randomization. Although the randomized design is the gold standard for efficacy assessment, various situations may arise where a single‐arm pilot study prior to a randomized trial is necessary. To combine the single‐ and double‐arm phases and pool the information together for better decision making, we propose a Single‐To‐double ARm Transition design (START) with switching hypotheses tests, where the first stage compares the new drug's response rate with a minimum required level and imposes a continuation criterion, and the second stage utilizes randomization to determine the treatment's superiority. We develop a software package in R to calibrate the frequentist error rates and perform simulation studies to assess the trial characteristics. Finally, a metastatic pancreatic cancer trial is used for illustrating the decision rules under the proposed START design.     

A win ratio approach to comparing continuous non‐normal outcomes in clinical trials

Clinical trials are often designed to compare continuous non‐normal outcomes. The conventional statistical method for such a comparison is a non‐parametric Mann–Whitney test, which provides a P‐value for testing the hypothesis that the distributions of both treatment groups are identical, but does not provide a simple and straightforward estimate of treatment effect. For that, Hodges and Lehmann proposed estimating the shift parameter between two populations and its confidence interval (CI). However, such a shift parameter does not have a straightforward interpretation, and its CI contains zero in some cases when Mann–Whitney test produces a significant result. To overcome the aforementioned problems, we introduce the use of the win ratio for analysing such data. Patients in the new and control treatment are formed into all possible pairs. For each pair, the new treatment patient is labelled a ‘winner’ or a ‘loser’ if it is known who had the more favourable outcome. The win ratio is the total number of winners divided by the total numbers of losers. A 95% CI for the win ratio can be obtained using the bootstrap method. Statistical properties of the win ratio statistic are investigated using two real trial data sets and six simulation studies. Results show that the win ratio method has about the same power as the Mann–Whitney method. We recommend the use of the win ratio method for estimating the treatment effect (and CI) and the Mann–Whitney method for calculating the P‐value for comparing continuous non‐Normal outcomes when the amount of tied pairs is small. Copyright © 2016 John Wiley & Sons, Ltd.     

Weighted log‐rank test for time‐to‐event data in immunotherapy trials with random delayed treatment effect and cure rate

A cancer clinical trial with an immunotherapy often has 2 special features, which are patients being potentially cured from the cancer and the immunotherapy starting to take clinical effect after a certain delay time. Existing testing methods may be inadequate for immunotherapy clinical trials, because they do not appropriately take the 2 features into consideration at the same time, hence have low power to detect the true treatment effect. In this paper, we proposed a piece‐wise proportional hazards cure rate model with a random delay time to fit data, and a new weighted log‐rank test to detect the treatment effect of an immunotherapy over a chemotherapy control. We showed that the proposed weight was nearly optimal under mild conditions. Our simulation study showed a substantial gain of power in the proposed test over the existing tests and robustness of the test with misspecified weight. We also introduced a sample size calculation formula to design the immunotherapy clinical trials using the proposed weighted log‐rank test.     

Statistical considerations in a delayed‐start design to demonstrate disease modification effect in neurodegenerative disorders

There has been a paradigm shift in diagnostic conceptualization of Alzheimer's disease (AD) based on the current evidence suggesting that structure and biology changes start to occur before clinical symptoms emerge. Consequently, therapeutic drug development is also shifting to treat early AD patients using biomarkers for enrichment in clinical trials. A similar paradigm shift is occurring for Parkinson disease. In the absence of acceptable biomarkers that could be combined with a clinical endpoint to demonstrate a disease modification (DM) effect in neurodegenerative disorders, a delayed‐start design can be applied to demonstrate a lasting effect on the disease course. The delayed‐start design includes two treatment periods, where in period 1, patients are randomized to receive an active treatment or placebo, and in period 2, placebo patients are switched to the active treatment while patients in the active treatment arm will continue the same treatment. The hypothesis is that patients who start the active treatment later will fail to catch up to the treatment benefit achieved by patients who receive the active treatment in both periods. A usual analytical approach has sought to demonstrate the divergence of slope during period 1 and the parallelism of slopes during period 2 as the DM effect. However, due to heterogeneity in timing and the magnitude of maximal effect among patients, nonlinear response over time could be observed within the two treatment arms in both periods. We propose an approach to evaluate the DM effect with the linearity assumption for treatment differences, but not for each arm separately.