Sequential methods for pharmacogenetic studies

A study or experiment can be described as sequential if its design includes one or more interim analyses at which it is possible to stop the study, having reached a definitive conclusion concerning the primary question of interest. The potential of the sequential study to terminate earlier than the equivalent fixed sample size study means that, typically, there are ethical and economic advantages to be gained from using a sequential design. These advantages have secured a place for the methodology in the conduct of many clinical trials of novel therapies. Recently, there has been increasing interest in pharmacogenetics: the study of how DNA variation in the human genome affects the safety and efficacy of drugs. The potential for using sequential methodology in pharmacogenetic studies is considered and the conduct of candidate gene association studies, family-based designs and genome-wide association studies within the sequential setting is explored. The objective is to provide a unified framework for the conduct of these types of studies as sequential designs and hence allow experimenters to consider using sequential methodology in their future pharmacogenetic studies.

A practical comparison of group-sequential and adaptive designs

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Interim analyses and sequential designs in phase III studies

Recruitment of patients to a clinical trial usually occurs over a period of time, resulting in the steady accumulation of data throughout the trial's duration. Yet, according to traditional statistical methods, the sample size of the trial should be determined in advance, and data collected on all subjects before analysis proceeds. For ethical and economic reasons, the technique of sequential testing has been developed to enable the examination of data at a series of interim analyses. The aim is to stop recruitment to the study as soon as there is sufficient evidence to reach a firm conclusion. In this paper we present the advantages and disadvantages of conducting interim analyses in phase III clinical trials, together with the key steps to enable the successful implementation of sequential methods in this setting. Examples are given of completed trials, which have been carried out sequentially, and references to relevant literature and software are provided.

Sequentially testing for a gene-drug interaction in a genomewide analysis

Assaying a large number of genetic markers from patients in clinical trials is now possible in order to tailor drugs with respect to efficacy. The statistical methodology for analysing such massive data sets is challenging. The most popular type of statistical analysis is to use a univariate test for each genetic marker, once all the data from a clinical study have been collected. This paper presents a sequential method for conducting an omnibus test for detecting gene-drug interactions across the genome, thus allowing informed decisions at the earliest opportunity and overcoming the multiple testing problems from conducting many univariate tests. We first propose an omnibus test for a fixed sample size. This test is based on combining F-statistics that test for an interaction between treatment and the individual single nucleotide polymorphism (SNP). As SNPs tend to be correlated, we use permutations to calculate a global p-value. We extend our omnibus test to the sequential case. In order to control the type I error rate, we propose a sequential method that uses permutations to obtain the stopping boundaries. The results of a simulation study show that the sequential permutation method is more powerful than alternative sequential methods that control the type I error rate, such as the inverse-normal method. The proposed method is flexible as we do not need to assume a mode of inheritance and can also adjust for confounding factors. An application to real clinical data illustrates that the method is computationally feasible for a large number of SNPs. Copyright (c) 2007 John Wiley & Sons, Ltd.

Flexible selection of a single treatment incorporating short-term endpoint information in a phase II/III clinical trial

Seamless phase II/III clinical trials in which an experimental treatment is selected at an interim analysis have been the focus of much recent research interest. Many of the methods proposed are based on the group sequential approach. This paper considers designs of this type in which the treatment selection can be based on short-term endpoint information for more patients than have primary endpoint data available. We show that in such a case, the familywise type I error rate may be inflated if previously proposed group sequential methods are used and the treatment selection rule is not specified in advance. A method is proposed to avoid this inflation by considering the treatment selection that maximises the conditional error given the data available at the interim analysis. A simulation study is reported that illustrates the type I error rate inflation and compares the power of the new approach with two other methods: a combination testing approach and a group sequential method that does not use the short-term endpoint data, both of which also strongly control the type I error rate. The new method is also illustrated through application to a study in Alzheimer's disease. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Incorporating data received after a sequential trial has stopped into the final analysis: implementation and comparison of methods

In a sequential clinical trial, accrual of data on patients often continues after the stopping criterion for the study has been met. This is termed “overrunning.” Overrunning occurs mainly when the primary response from each patient is measured after some extended observation period. The objective of this article is to compare two methods of allowing for overrunning. In particular, simulation studies are reported that assess the two procedures in terms of how well they maintain the intended type I error rate. The effect on power resulting from the incorporation of “overrunning data” using the two procedures is evaluated.

An adaptive approach to implementing bivariate group sequential clinical trial designs

In clinical trials, situations often arise where more than one response from each patient is of interest; and it is required that any decision to stop the study be based upon some or all of these measures simultaneously. Theory for the design of sequential experiments with simultaneous bivariate responses is described by Jennison and Turnbull (Jennison, C., Turnbull, B. W. (1993). Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints. Biometrics 49:741-752) and Cook and Farewell (Cook, R. J., Farewell, V. T. (1994). Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 50:1146-1152) in the context of one efficacy and one safety response. These expositions are in terms of normally distributed data with known covariance. The methods proposed require specification of the correlation, ρ between test statistics monitored as part of the sequential test. It can be difficult to quantify ρ and previous authors have suggested simply taking the lowest plausible value, as this will guarantee power. This paper begins with an illustration of the effect that inappropriate specification of ρ can have on the preservation of trial error rates. It is shown that both the type I error and the power can be adversely affected. As a possible solution to this problem, formulas are provided for the calculation of correlation from data collected as part of the trial. An adaptive approach is proposed and evaluated that makes use of these formulas and an example is provided to illustrate the method. Attention is restricted to the bivariate case for ease of computation, although the formulas derived are applicable in the general multivariate case.

Sequential designs for phase III clinical trials incorporating treatment selection

Most statistical methodology for phase III clinical trials focuses on the comparison of a single experimental treatment with a control. An increasing desire to reduce the time before regulatory approval of a new drug is sought has led to development of two-stage or sequential designs for trials that combine the definitive analysis associated with phase III with the treatment selection element of a phase II study. In this paper we consider a trial in which the most promising of a number of experimental treatments is selected at the first interim analysis. This considerably reduces the computational load associated with the construction of stopping boundaries compared to the approach proposed by Follman, Proschan and Geller (Biometrics 1994; 50: 325-336). The computational requirement does not exceed that for the sequential comparison of a single experimental treatment with a control. Existing methods are extended in two ways. First, the use of the efficient score as a test statistic makes the analysis of binary, normal or failure-time data, as well as adjustment for covariates or stratification straightforward. Second, the question of trial power is also considered, enabling the determination of sample size required to give specified power. Copyright © 2003 John Wiley & Sons, Ltd.

Problems in the coupling of eye and hand in the sequential movements of children with developmental coordination disorder

Background: Shifting gaze and attention ahead of the hand is a natural component in the performance of skilled manual actions. Very few studies have examined the precise co-ordination between the eye and hand in children with Developmental Coordination Disorder (DCD). Methods This study directly assessed the maturity of eye-hand co-ordination in children with DCD. A double-step pointing task was used to investigate the coupling of the eye and hand in 7-year-old children with and without DCD. Sequential targets were presented on a computer screen, and eye and hand movements were recorded simultaneously. Results There were no differences between typically developing (TD) and DCD groups when completing fast single-target tasks. There were very few differences in the completion of the first movement in the double-step tasks, but differences did occur during the second sequential movement. One factor appeared to be the propensity for the DCD children to delay their hand movement until some period after the eye had landed on the target. This resulted in a marked increase in eye-hand lead during the second movement, disrupting the close coupling and leading to a slower and less accurate hand movement among children with DCD. Conclusions In contrast to skilled adults, both groups of children preferred to foveate the target prior to initiating a hand movement if time allowed. The TD children, however, were more able to reduce this foveation period and shift towards a feedforward mode of control for hand movements. The children with DCD persevered with a look-then-move strategy, which led to an increase in error. For the group of DCD children in this study, there was no evidence of a problem in speed or accuracy of simple movements, but there was a difficulty in concatenating the sequential shifts of gaze and hand required for the completion of everyday tasks or typical assessment items.

A sequential two meal challenge reveals abnormalities in postprandial TAG but not glucose in men with increasing numbers of metabolic syndrome components

Objective To examine the impact of increasing numbers of metabolic syndrome (MetS) components on postprandial lipaemia. Methods Healthy men (n = 112) underwent a sequential meal postprandial investigation, in which blood samples were taken at regular intervals after a test breakfast (0 min) and lunch (330 min). Lipids and glucose were measured in the fasting sample, with triacylglycerol (TAG), non-esterified fatty acids and glucose analysed in the postprandial samples. Results Subjects were grouped according to the number of MetS components regardless of the combinations of components (0/1, 2, 3 and 4/5). As expected, there was a trend for an increase in body mass index, blood pressure, fasting TAG, glucose and insulin, and a decrease in fasting high-density lipoprotein cholesterol with increasing numbers of MetS components (P≤0.0004). A similar trend was observed for the summary measures of the postprandial TAG and glucose responses. For TAG, the area under the curve (AUC) and maximum concentration (maxC) were significantly greater in men with ≥ 3 than < 3 components (P < 0.001), whereas incremental AUC was greater in those with 3 than 0/1 and 2, and 4/5 compared with 2 components (P < 0.04). For glucose, maxC after the test breakfast (0-330 min) and total AUC (0-480 min) were higher in men with ≥ 3 than < 3 components (P≤0.001). Conclusions Our data analysis has revealed a linear trend between increasing numbers of MetS components and magnitude (AUC) of the postprandial TAG and glucose responses. Furthermore, the two meal challenge discriminated a worsening of postprandial lipaemic control in subjects with ≥ 3 MetS components.

Fine-root turnover rates of European forests revisited: an analysis of data from sequential coring and ingrowth cores

Background and Aims Forest trees directly contribute to carbon cycling in forest soils through the turnover of their fine roots. In this study we aimed to calculate root turnover rates of common European forest tree species and to compare them with most frequently published values. Methods We compiled available European data and applied various turnover rate calculation methods to the resulting database. We used Decision Matrix and Maximum-Minimum formula as suggested in the literature. Results Mean turnover rates obtained by the combination of sequential coring and Decision Matrix were 0.86 yr−1 for Fagus sylvatica and 0.88 yr−1 for Picea abies when maximum biomass data were used for the calculation, and 1.11 yr−1 for both species when mean biomass data were used. Using mean biomass rather than maximum resulted in about 30 % higher values of root turnover. Using the Decision Matrix to calculate turnover rate doubled the rates when compared to the Maximum-Minimum formula. The Decision Matrix, however, makes use of more input information than the Maximum-Minimum formula. Conclusions We propose that calculations using the Decision Matrix with mean biomass give the most reliable estimates of root turnover rates in European forests and should preferentially be used in models and C reporting.

An investigation of the shortcomings of the CONSORT 2010 statement for the reporting of group sequential randomised controlled trials: a methodological systematic review

Background It can be argued that adaptive designs are underused in clinical research. We have explored concerns related to inadequate reporting of such trials, which may influence their uptake. Through a careful examination of the literature, we evaluated the standards of reporting of group sequential (GS) randomised controlled trials, one form of a confirmatory adaptive design. Methods We undertook a systematic review, by searching Ovid MEDLINE from the 1st January 2001 to 23rd September 2014, supplemented with trials from an audit study. We included parallel group, confirmatory, GS trials that were prospectively designed using a Frequentist approach. Eligible trials were examined for compliance in their reporting against the CONSORT 2010 checklist. In addition, as part of our evaluation, we developed a supplementary checklist to explicitly capture group sequential specific reporting aspects, and investigated how these are currently being reported. Results Of the 284 screened trials, 68(24%) were eligible. Most trials were published in “high impact” peer-reviewed journals. Examination of trials established that 46(68%) were stopped early, predominantly either for futility or efficacy. Suboptimal reporting compliance was found in general items relating to: access to full trials protocols; methods to generate randomisation list(s); details of randomisation concealment, and its implementation. Benchmarking against the supplementary checklist, GS aspects were largely inadequately reported. Only 3(7%) trials which stopped early reported use of statistical bias correction. Moreover, 52(76%) trials failed to disclose methods used to minimise the risk of operational bias, due to the knowledge or leakage of interim results. Occurrence of changes to trial methods and outcomes could not be determined in most trials, due to inaccessible protocols and amendments. Discussion and Conclusions There are issues with the reporting of GS trials, particularly those specific to the conduct of interim analyses. Suboptimal reporting of bias correction methods could potentially imply most GS trials stopping early are giving biased results of treatment effects. As a result, research consumers may question credibility of findings to change practice when trials are stopped early. These issues could be alleviated through a CONSORT extension. Assurance of scientific rigour through transparent adequate reporting is paramount to the credibility of findings from adaptive trials. Our systematic literature search was restricted to one database due to resource constraints.