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In phase II clinical trials, patients are recruited sequentially and consequently the time required to complete the clinical trial will become long if the accrual rate is low. To speed up the drug development process and account for ethical issues, stochastically and non-stochastically curtailed two-stage designs have been proposed in single-arm phase II clinical trials. More recently, randomized phase II clinical trials are being increasingly recommended to avoid biased evaluation of the treatment effect when compared with a historical control. The current patient population and the historical one may be quite heterogeneous. Moreover, it is impossible to randomly assign patients for treatments. Consequently, various two-stage designs have been presented for comparing two arms. Since the sample size required in a randomized phase II trial is usually larger than that required in a single-arm phase II trial, we introduce the concept of curtailed sampling procedure to develop curtailed two-stage design for two-armed, randomized phase II clinical trials. The proposed design does not require pairwise patient response comparison, yet it allows a trial to be stopped early as soon as the difference in therapeutic effect of the experimental therapy and the standard at the end of a trial is foreknown., (Copyright © 2017 Taylor & Francis Group, LLC.)

The purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data. The developed formula is based on robust non-parametric tests for comparing the marginal mean function of events between paired samples. This calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model. We evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations, homogeneous or nonhomogeneous processes, marginal hazard rates, censoring rate, accrual and follow-up times, as well as the sensitivity analysis for the assumption of the frailty distribution. The use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern Taiwan. Copyright © 2017 John Wiley & Sons, Ltd., (Copyright © 2017 John Wiley & Sons, Ltd.)

The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated., (© 2015, The International Biometric Society.)

Current status data arise naturally from tumorigenicity experiments, epidemiology studies, biomedicine, econometrics and demographic and sociology studies. Moreover, clustered current status data may occur with animals from the same litter in tumorigenicity experiments or with subjects from the same family in epidemiology studies. Because the only information extracted from current status data is whether the survival times are before or after the monitoring or censoring times, the nonparametric maximum likelihood estimator of survival function converges at a rate of n(1/3) to a complicated limiting distribution. Hence, semiparametric regression models such as the additive hazards model have been extended for independent current status data to derive the test statistics, whose distributions converge at a rate of n(1/2) , for testing the regression parameters. However, a straightforward application of these statistical methods to clustered current status data is not appropriate because intracluster correlation needs to be taken into account. Therefore, this paper proposes two estimating functions for estimating the parameters in the additive hazards model for clustered current status data. The comparative results from simulation studies are presented, and the application of the proposed estimating functions to one real data set is illustrated., (Copyright © 2013 John Wiley & Sons, Ltd.)

When phase I clinical trials were found to be unable to precisely estimate the frequency of toxicity, Brayan and Day proposed incorporating toxicity considerations into two-stage designs in phase II clinical trials. Conaway and Petroni further pointed out that it is important to evaluate the clinical activity and safety simultaneously in studying cancer treatments with more toxic chemotherapies in a phase II clinical trial. Therefore, they developed multi-stage designs with two dependent binary endpoints. However, the usual sample sizes in phase II trials make these designs difficult to control the type I error rate at a desired level over the entire null region and still have sufficient power against reasonable alternatives. Therefore, the curtailed sampling procedure summarized by Phatak and Bhatt will be applied to the two-stage designs with two dependent binary endpoints in this paper to reduce sample sizes and speed up the development process for drugs., (Copyright © 2011 John Wiley & Sons, Ltd.)

In clinical research, it is not uncommon to modify a trial procedure and/or statistical methods of ongoing clinical trials through protocol amendments. A major modification to the study protocol could result in a shift in target patient population. In addition, frequent and significant modifications could lead to a totally different study that is unable to address the medical questions that the original study intended to answer. In this article, we propose a logistic regression model for statistical inference based on a binary study endpoint for trials with protocol amendments. Under the proposed method, sample size adjustment is also derived.

In clinical trials, information about certain time points may be of interest in making decisions about treatment effectiveness. Rather than comparing entire survival curves, researchers can focus on the comparison at fixed time points that may have a clinical utility for patients. For two independent samples of right-censored data, Klein et al. (2007) compared survival probabilities at a fixed time point by studying a number of tests based on some transformations of the Kaplan-Meier estimators of the survival function. However, to compare the survival probabilities at a fixed time point for paired right-censored data or clustered right-censored data, their approach would need to be modified. In this paper, we extend the statistics to accommodate the possible within-paired correlation and within-clustered correlation, respectively. We use simulation studies to present comparative results. Finally, we illustrate the implementation of these methods using two real data sets.

Clustered right-censored data often arise from tumorigenicity experiments and clinical trials. For testing the equality of two survival functions, Jung and Jeong extended weighted logrank (WLR) tests to two independent samples of clustered right-censored data, while the weighted Kaplan-Meier (WKM) test can be derived from the work of O'Gorman and Akritas. The weight functions in both classes of tests (WLR and WKM) can be selected to be more sensitive to detect a certain alternative; however, since the exact alternative is unknown, it is difficult to specify the selected weights in advance. Since WLR is rank-based, it is not sensitive to the magnitude of the difference in survival times. Although WKM is constructed to be more sensitive to the magnitude of the difference in survival times, it is not sensitive to late hazard differences. Therefore, in order to combine the advantages of these two classes of tests, this paper developed a class of versatile tests based on simultaneously using WLR and WKM for two independent samples of clustered right-censored data. The comparative results from a simulation study are presented and the implementation of the versatile tests to two real data sets is illustrated.

In clinical development, an adaptive design combining results from two separate studies (e.g., a seamless adaptive design with a dose finding study phase and a confirmatory study phase) is commonly considered. The purpose of an adaptive design is not only to reduce lead time between the two studies, but also to evaluate the treatment effect in a more efficient way. In this paper, the focus is on the case where the study objectives are the same but the time durations of the study periods are different in the two stages. In particular, event data are collected in both stages. Statistical procedure for combining data observed from the two different stages is discussed. Furthermore, results on hypotheses testing and sample size calculation are derived for the comparison of two treatments.

When the accrual rate is low and the treatment period is long, a long observational period is required before information concerning the primary end point, such as binary response, becomes available in the study. Simon's two-stage designs are often employed in Phase II clinical trials to avoid giving patient an ineffective drug. Thus, if the new drug is ineffective then this design would certainly accelerate the process of drug discovery and development. However, for a promising new drug this design may still require a long observational period. Therefore, when drug safety is not a primary concern, this paper proposes curtailed two-stage designs to shorten the drug development process as soon as the treatment either shows lack of efficacy or is very effective. The proposed design is superior to Simon's two-stage designs in terms of savings in expected sample size and is much easier to implement in practice than stochastically curtailed Simon's designs.

Generally, a two-stage design is employed in Phase II clinical trials to avoid giving patients an ineffective drug. If the number of patients with significant improvement, which is a binomial response, is greater than a pre-specified value at the first stage, then another binomial response at the second stage is also observed. This paper considers interval estimation of the response probability when the second stage is allowed to continue. Two asymptotic interval estimators, Wald and score, as well as two exact interval estimators, Clopper-Pearson and Sterne, are constructed according to the two binomial responses from this two-stage design, where the binomial response at the first stage follows a truncated binomial distribution. The mean actual coverage probability and expected interval width are employed to evaluate the performance of these interval estimators. According to the comparison results, the score interval is recommended for both Simon's optimal and minimax designs., (Copyright (c) 2007 John Wiley & Sons, Ltd.)

To compare the survival functions based on right-truncated data, Lagakos et al. proposed a weighted logrank test based on a reverse time scale. This is in contrast to Bilker and Wang, who suggested a semi-parametric version of the Mann-Whitney test by assuming that the distribution of truncation times is known or can be estimated parametrically. The approach of Lagakos et al. is simple and elegant, but the weight function in their method depends on the underlying cumulative hazard functions even under proportional hazards models. On the other hand, a semi-parametric test may have better efficiency, but it may be sensitive to misspecification of the distribution of truncation times. Therefore, this paper proposes a non-parametric test statistic based on the integrated weighted difference between two estimated survival functions in forward time. The comparative results from a simulation study are presented and the implementation of these methods to a real data set is demonstrated., (Copyright 2006 John Wiley & Sons, Ltd.)

In clinical trials or drug development studies, researchers are often interested in identifying which treatments or dosages are more effective than the standard one. Recently, several multiple testing procedures based on weighted logrank tests have been proposed to compare several treatments with a control in a one-way layout where survival data are subject to random right-censorship. However, weighted logrank tests are based on ranks, and these tests might not be sensitive to the magnitude of the difference in survival times against a specific alternative. Therefore, it is desirable to develop a more robust and powerful multiple testing procedure. This paper proposes multiple testing procedures based on two-sample weighted Kaplan-Meier statistics, each comparing an individual treatment with the control, to determine which treatments are more effective than the control. The comparative results from a simulation study are presented and the implementation of these methods to the prostate cancer clinical trial and the renal carcinoma tumour study are presented., (2004 John Wiley & Sons, Ltd.)