Non-parametric group sequential designs in randomized clinical trials

This paper examines some non‐parametric group sequential designs applicable for randomized clinical trials, for comparing two continuous treatment effects taking the observations in matched pairs, or applicable in event‐based analysis. Two inverse binomial sampling schemes are considered, of which the second one is an adaptive data‐dependent design. These designs are compared with some fixed sample size competitors. Power and expected sample sizes are calculated for the proposed procedures.     

A simulation study on power comparisons for group sequential tests of non-parametric statistics

In this article, a group sequential test (GST) of non-parametric statistics for survival data is briefly reviewed. An asymptotic joint distribution of the test statistics, obtained after each interim analysis, is given to illustrate the applicability of the critical values of the GST procedures. It should be noted that censored observations are generally seen in survival data. Therefore, if one makes power calculations irrespective of censoring, reliable results may not be achieved, due to the lack of information about the censoring structure. A wide simulation study, covering different censoring rates and tied observations, is conducted to make the power comparisons under various scenarios. The simulation results are interpreted and compared with the results obtained by using power analysis and sample size (PASS) software.     

Nearly optimal truncated group sequential test on binomial proportions

In this article, we systematically study the optimal truncated group sequential test on binomial proportions. Through analysis of the cost structure, average test cost is introduced as a new optimality criterion. According to the new criterion, the optimal tests on different design parameters including the boundaries, success discriminant value, stage sample vector, stage size, and the maximum sample size are defined. Since the computation time in finding optimal designs by exhaustive search is intolerably long, group sequential sample space sorting method and procedures are developed to find the near-optimal ones. In comparison with the international standard ISO2859-1, the truncated group sequential designs proposed in this article can reduce the average test costs around 20%.     

Group sequential x2 statistic for testing the difference of two mean vectors in clinical trials

In this study we discuss the group sequential procedures for comparing two treatments based on multivariate observations in clinical trials. Also we suppose that a response vector on each of two treatments has a multivariate normal distribution with unknown covariance matrix. Then we propose a group sequential x² statistic in order to carry out repeated significance test for hypothesis of no difference between two population mean vectors. In order to realize the group sequential test where average sample number is reduced, we propose another modified group sequential x² statistic by extension of Jennison and Turnbull ( 1991 ). After construction of repeated confidence boundaries for making the repeated significance test, we compare two group sequential procedures based on two statistics regarding the average sample number and the power of the test in the simulations.     

Distribution-free partially sequential piacment procedures

The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions. In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample. Exact and asymptotic, as the fixed sample size in¬creases to infinity, properties of these sequential placements procedures are obtained, including statements about the power and expected number of sequentially obtained observations. The results of a Monte Carlo study are used to differentiate be¬tween various placement scoring schemes.     

Biopharmaceutical applications of group sequental designs

Methods are described for calculating the properties of a general class of group sequential designs. The procedures are based on direct enumeration of a11 possible outcomes thereby giving exact results. The test regions of these designs are closed, may be one- or two-sided and may include a variable number of groups or stages. The methods described can be applied in experimental situations where the responses can be dichotomized or ranked. Specific examples which are given to illustrate the procedures include drug screening, laboratory evaluation, and clinical trials.     

Optimal adaptive sequential designs for crossover bioequivalence studies

In prior works, this group demonstrated the feasibility of valid adaptive sequential designs for crossover bioequivalence studies. In this paper, we extend the prior work to optimize adaptive sequential designs over a range of geometric mean test/reference ratios (GMRs) of 70–143% within each of two ranges of intra‐subject coefficient of variation (10–30% and 30–55%). These designs also introduce a futility decision for stopping the study after the first stage if there is sufficiently low likelihood of meeting bioequivalence criteria if the second stage were completed, as well as an upper limit on total study size. The optimized designs exhibited substantially improved performance characteristics over our previous adaptive sequential designs. Even though the optimized designs avoided undue inflation of type I error and maintained power at 80%, their average sample sizes were similar to or less than those of conventional single stage designs. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimizing trial design in pharmacogenetics research: comparing a fixed parallel group,group sequential,and adaptive selection design on sample size requirements

Two‐stage clinical trial designs may be efficient in pharmacogenetics research when there is some but inconclusive evidence of effect modification by a genomic marker. Two‐stage designs allow to stop early for efficacy or futility and can offer the additional opportunity to enrich the study population to a specific patient subgroup after an interim analysis. This study compared sample size requirements for fixed parallel group, group sequential, and adaptive selection designs with equal overall power and control of the family‐wise type I error rate. The designs were evaluated across scenarios that defined the effect sizes in the marker positive and marker negative subgroups and the prevalence of marker positive patients in the overall study population. Effect sizes were chosen to reflect realistic planning scenarios, where at least some effect is present in the marker negative subgroup. In addition, scenarios were considered in which the assumed ‘true’ subgroup effects (i.e., the postulated effects) differed from those hypothesized at the planning stage. As expected, both two‐stage designs generally required fewer patients than a fixed parallel group design, and the advantage increased as the difference between subgroups increased. The adaptive selection design added little further reduction in sample size, as compared with the group sequential design, when the postulated effect sizes were equal to those hypothesized at the planning stage. However, when the postulated effects deviated strongly in favor of enrichment, the comparative advantage of the adaptive selection design increased, which precisely reflects the adaptive nature of the design. Copyright © 2013 John Wiley & Sons, Ltd.     

On a class of partially sequential two-sample test procedures for multivariate continuous data

In a two-sample testing problem, sometimes one of the sample observations are difficult and/or costlier to collect compared to the other one. Also, it may be the situation that sample observations from one of the populations have been previously collected and for operational advantages we do not wish to collect any more observations from the second population that are necessary for reaching a decision. Partially sequential technique is found to be very useful in such situations. The technique gained its popularity in statistics literature due to its very nature of capitalizing the best aspects of both fixed and sequential procedures. The literature is enriched with various types of partially sequential techniques useable under different types of data set-up. Nonetheless, there is no mention of multivariate data framework in this context, although very common in practice. The present paper aims at developing a class of partially sequential nonparametric test procedures for two-sample multivariate continuous data. For this we suggest a suitable stopping rule adopting inverse sampling technique and propose a class of test statistics based on the samples drawn using the suggested sampling scheme. Various asymptotic properties of the proposed tests are explored. An extensive simulation study is also performed to study the asymptotic performance of the tests. Finally the benefit of the proposed test procedure is demonstrated with an application to a real-life data on liver disease.     

A Bayesian sequential design with adaptive randomization for 2‐sided hypothesis test

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2‐arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size.     

Asyhptotic efficiency of sequential and non-sequential procedures based on fisher's method of combining tests

In this paper we propose test statistics based on Fisher's method of combining tests for hypotheses involving two or more parameters simultaneously, It Is shown that these tests are asymptotically efficient In the sense of Bahadur, It is then shown how these tests can be modified to give sequential test procedures which are efficient in the sense of Berk and Brown (1978).

The results in section 3 generalize the work of Perng (1977) and Durairajan (1980).     

Efficient estimators for adaptive stratified sequential sampling

In stratified sampling, methods for the allocation of effort among strata usually rely on some measure of within-stratum variance. If we do not have enough information about these variances, adaptive allocation can be used. In adaptive allocation designs, surveys are conducted in two phases. Information from the first phase is used to allocate the remaining units among the strata in the second phase. Brown et al. [Adaptive two-stage sequential sampling, Popul. Ecol. 50 (2008), pp. 239–245] introduced an adaptive allocation sampling design – where the final sample size was random – and an unbiased estimator. Here, we derive an unbiased variance estimator for the design, and consider a related design where the final sample size is fixed. Having a fixed final sample size can make survey-planning easier. We introduce a biased Horvitz–Thompson type estimator and a biased sample mean type estimator for the sampling designs. We conduct two simulation studies on honey producers in Kurdistan and synthetic zirconium distribution in a region on the moon. Results show that the introduced estimators are more efficient than the available estimators for both variable and fixed sample size designs, and the conventional unbiased estimator of stratified simple random sampling design. In order to evaluate efficiencies of the introduced designs and their estimator furthermore, we first review some well-known adaptive allocation designs and compare their estimator with the introduced estimators. Simulation results show that the introduced estimators are more efficient than available estimators of these well-known adaptive allocation designs.     

Procedure for determining sample size at each stage in group sequential test

The purpose of our study is to propose a. procedure for determining the sample size at each stage of the repeated group significance, tests intended to compare the efficacy of two treatments when a response variable is normal. It is necessary to devise a procedure for reducing the maximum sample size because a large number of sample size are often used in group sequential test. In order to reduce the sample size at each stage, we construct the repeated confidence boundaries which enable us to find which of the two treatments is the more effective at an early stage. Thus we use the recursive formulae of numerical integrations to determine the sample size at the intermediate stage. We compare our procedure with Pocock's in terms of maximum sample size and average sample size in the simulations.     

Adaptive choice of scale tests in flexible two-stage designs with applications in experimental ecology and clinical trials

In this paper, the two-sample scale problem is addressed within the rank framework which does not require to specify the underlying continuous distribution. However, since the power of a rank test depends on the underlying distribution, it would be very useful for the researcher to have some information on it in order to use the possibly most suitable test. A two-stage adaptive design is used with adaptive tests where the data from the first stage are used to compute a selector statistic to select the test statistic for stage 2. More precisely, an adaptive scale test due to Hall and Padmanabhan and its components are considered in one-stage and several adaptive and non-adaptive two-stage procedures. A simulation study shows that the two-stage test with the adaptive choice in the second stage and with Liptak combination, when it is not more powerful than the corresponding one-stage test, shows, however, a quite similar power behavior. The test procedures are illustrated using two ecological applications and a clinical trial.     

Generalized sequential ranks and tests of randomness

Generalized sequential ranks are defined and are proved to be independent and uniformly distributed under the hypothesis of randomness. By comparison with a Spear-MAsr-type statistic it is shown that in certain cases the test based on the sum of all sequential ranks is an asymptotically optimum test for trend against logistic regression. The test is equivalent to tests proposed by Jonckheere and Terpstra and has a high efficiency when compared with the optimal parametric test for normal regression alternatives.     

Bayes sequential estimation for a time-transformed exponential model

A problem of Bayesian sequential estimating an unknown parameter of a time-transformed exponential model is considered. It is supposed that the loss associated with the error of estimation is weighted squared or precautionary and the cost of observing the process is a function of time and the number of observations. Bayes sequential procedures for estimating the unknown parameter are presented.     

On group sequential tests for data in unequally sized groups and with unknown variance

We present a method to generalise the scope of application of group sequential tests designed for equally sized groups of normal observations with known variance. Preserving the significance levels against which standardised statistics are compared leads to tests for unequally grouped data which maintain Type I error probabilities to a high degree of accuracy. The same approach can be followed when observations have unknown variance by setting critical values for Studentised statistics at percentiles of the appropriate t-distributions. This significance level approach is equally applicable to group sequential one-sided tests and two-sided tests, possibly with early stopping permitted to accept the null hypothesis. In applications to equivalence testing, tests are required to maintain a specified power, rather than Type I error rate: such tests can be constructed by defining the standardised test statistics used in the significance level approach with respect to appropriately chosen hypotheses.     

On sequential closed testing dose groups with a control

Methods for a sequential test of a dose-response effect in pre-clinical studies are investigated. The objective of the test procedure is to compare several dose groups with a zero-dose control. The sequential testing is conducted within a closed family of one-sided tests. The procedures investigated are based on a monotonicity assumption. These closed procedures strongly control the familywise error rate while providing information about the shape of the dose-responce relationship. Performance of sequential testing procedures are compared via a Monte Carlo simulation study. We illustrae the procedures by application to a real data set.     

A bayesian group sequential analysis procedure

In this work a method is developed for determining the expected sample size, 2nN, required by a group sequential test using a Bayesian approach. This method is proved to be superior to some recently developed methods. It gives a specific technique to determine the maximum number of groups, N, as well as the group, size, 2n. The proposed method allows a very early termination of the experiment when the alternative hypothesis is true, i.e. when i there is real difference between the treatments under consideration.     

Robust inference for group sequential trials

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests.