Point estimates and confidence regions for sequential trials involving selection

A number of authors have proposed clinical trial designs involving the comparison of several experimental treatments with a control treatment in two or more stages. At the end of the first stage, the most promising experimental treatment is selected, and all other experimental treatments are dropped from the trial. Provided it is good enough, the selected experimental treatment is then compared with the control treatment in one or more subsequent stages. The analysis of data from such a trial is problematic because of the treatment selection and the possibility of stopping at interim analyses. These aspects lead to bias in the maximum-likelihood estimate of the advantage of the selected experimental treatment over the control and to inaccurate coverage for the associated confidence interval. In this paper, we evaluate the bias of the maximum-likelihood estimate and propose a bias-adjusted estimate. We also propose an approach to the construction of a confidence region for the vector of advantages of the experimental treatments over the control based on an ordering of the sample space. These regions are shown to have accurate coverage, although they are also shown to be necessarily unbounded. Confidence intervals for the advantage of the selected treatment are obtained from the confidence regions and are shown to have more accurate coverage than the standard confidence interval based upon the maximum-likelihood estimate and its asymptotic standard error.

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.

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed. Copyright © 2005 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 group sequential design for phase II/III clinical trials that select a single treatment from several

There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

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.

Sequential genome-wide association studies for monitoring adverse events in the clinical evaluation of new drugs

Pharmacovigilance, the monitoring of adverse events (AEs), is an integral part in the clinical evaluation of a new drug. Until recently, attempts to relate the incidence of AEs to putative causes have been restricted to the evaluation of simple demographic and environmental factors. The advent of large-scale genotyping, however, provides an opportunity to look for associations between AEs and genetic markers, such as single nucleotides polymorphisms (SNPs). It is envisaged that a very large number of SNPs, possibly over 500 000, will be used in pharmacovigilance in an attempt to identify any genetic difference between patients who have experienced an AE and those who have not. We propose a sequential genome-wide association test for analysing AEs as they arise, allowing evidence-based decision-making at the earliest opportunity. This gives us the capability of quickly establishing whether there is a group of patients at high-risk of an AE based upon their DNA. Our method provides a valid test which takes account of linkage disequilibrium and allows for the sequential nature of the procedure. The method is more powerful than using a correction, such as idák, that assumes that the tests are independent. Copyright © 2006 John Wiley & Sons, Ltd.

How a sequential design would have affected the GAIN international study of Gavestinel in stroke

While planning the GAIN International Study of gavestinel in acute stroke, a sequential triangular test was proposed but not implemented. Before the trial commenced it was agreed to evaluate the sequential design retrospectively to evaluate the differences in the resulting analyses, trial durations and sample sizes in order to assess the potential of sequential procedures for future stroke trials. This paper presents four sequential reconstructions of the GAIN study made under various scenarios. For the data as observed, the sequential design would have reduced the trial sample size by 234 patients and shortened its duration by 3 or 4 months. Had the study not achieved a recruitment rate that far exceeded expectation, the advantages of the sequential design would have been much greater. Sequential designs appear to be an attractive option for trials in stroke. Copyright 2004 S. Karger AG, Basel

Comparing correlations of continuous observations from two independent populations using a sequential approach

A sequential study design generally makes more efficient use of available information than a fixed sample counterpart of equal power. This feature is gradually being exploited by researchers in genetic and epidemiological investigations that utilize banked biological resources and in studies where time, cost and ethics are prominent considerations. Recent work in this area has focussed on the sequential analysis of matched case-control studies with a dichotomous trait. In this paper, we extend the sequential approach to a comparison of the associations within two independent groups of paired continuous observations. Such a comparison is particularly relevant in familial studies of phenotypic correlation using twins. We develop a sequential twin method based on the intraclass correlation and show that use of sequential methodology can lead to a substantial reduction in the number of observations without compromising the study error rates. Additionally, our approach permits straightforward allowance for other explanatory factors in the analysis. We illustrate our method in a sequential heritability study of dysplasia that allows for the effect of body mass index and compares monozygotes with pairs of singleton sisters. Copyright (c) 2006 John Wiley & Sons, Ltd.

Microbe-associated molecular pattern (MAMP) signatures, synergy, size and charge: influences on perception or mobility and host defence responses

Triggering of defences by microbes has mainly been investigated using single elicitors or microbe-associated molecular patterns (MAMPs), but MAMPs are released in planta as complex mixtures together with endogenous oligogalacturonan (OGA) elicitor. We investigated the early responses in Arabidopsis of calcium influx and oxidative burst induced by non-saturating concentrations of bacterial MAMPs, used singly and in combination: flagellin peptide (flg22), elongation factor peptide (elf18), peptidoglycan (PGN) and component muropeptides, lipo-oligosaccharide (LOS) and core oligosaccharides. This revealed that some MAMPs have additive (e.g. flg22 with elf18) and even synergistic (flg22 and LOS) effects, whereas others mutually interfere (flg22 with OGA). OGA suppression of flg22-induced defences was not a result of the interference with the binding of flg22 to its receptor flagellin-sensitive 2 (FLS2). MAMPs induce different calcium influx signatures, but these are concentration dependent and unlikely to explain the differential induction of defence genes [pathogenesis-related gene 1 (PR1), plant defensin gene 1.2 (PDF1.2) and phenylalanine ammonia lyase gene 1 (PAL1)] by flg22, elf18 and OGA. The peptide MAMPs are potent elicitors at subnanomolar levels, whereas PGN and LOS at high concentrations induce low and late host responses. This difference might be a result of the restricted access by plant cell walls of MAMPs to their putative cellular receptors. flg22 is restricted by ionic effects, yet rapidly permeates a cell wall matrix, whereas LOS, which forms supramolecular aggregates, is severely constrained, presumably by molecular sieving. Thus, MAMPs can interact with each other, whether directly or indirectly, and with the host wall matrix. These phenomena, which have not been considered in detail previously, are likely to influence the speed, magnitude, versatility and composition of plant defences.

Evaluation of a sequential global test of improved recovery following stroke as applied to the ICTUS trial of citicoline

The International Citicoline Trial in acUte Stroke is a sequential phase III study of the use of the drug citicoline in the treatment of acute ischaemic stroke, which was initiated in 2006 in 56 treatment centres. The primary objective of the trial is to demonstrate improved recovery of patients randomized to citicoline relative to those randomized to placebo after 12 weeks of follow-up. The primary analysis will take the form of a global test combining the dichotomized results of assessments on three well-established scales: the Barthel Index, the modified Rankin scale and the National Institutes of Health Stroke Scale. This approach was previously used in the analysis of the influential National Institute of Neurological Disorders and Stroke trial of recombinant tissue plasminogen activator in stroke. The purpose of this paper is to describe how this trial was designed, and in particular how the simultaneous objectives of taking into account three assessment scales, performing a series of interim analyses and conducting treatment allocation and adjusting the analyses to account for prognostic factors, including more than 50 treatment centres, were addressed. Copyright (C) 2008 John Wiley & Sons, Ltd.

Urban mammals: what does the future hold? An analysis of the factors affecting patterns of use of residential gardens in Great Britain

1Urban areas are predicted to grow significantly in the foreseeable future because of increasing human population growth. Predicting the impact of urban development and expansion on mammal populations is of considerable interest due to possible effects on biodiversity and human-wildlife conflict. 2The British government has recently announced a substantial housing programme to meet the demands of its growing population and changing socio-economic profile. This is likely to result in the construction of high-density, low-cost housing with small residential gardens. To assess the potential effects of this programme, we analysed the factors affecting the current pattern of use of residential gardens by a range of mammal species using a questionnaire distributed in wildlife and gardening magazines and via The Mammal Society. 3Twenty-two species/species groups were recorded. However, the pattern of garden use by individual species was limited, with only six species/species groups (bats, red fox Vulpes vulpes, grey squirrel Sciurus carolinensis, hedgehog Erinaceus europaeus, mice, voles) recorded as frequent visitors to > 20% of gardens in the survey. 4There was a high degree of association between the variables recorded in the study, such that it was difficult to quantify the effects of individual variables. However, all species/species groups appeared to be negatively affected by the increased fragmentation and reduced proximity of natural and semi-natural habitats, decreasing garden size and garden structure, but to differing degrees. Patterns of garden use were most clearly affected by house location (city, town, village, rural), with garden use declining with increasing urbanization for the majority of species/species groups, except red foxes and grey squirrels. Increasing urbanization is likely to be related to a wide range of interrelated factors, any or all of which may affect a range of mammal species. 5Overall, the probable effects of the planned housing development programme in Britain are not likely to be beneficial to mammal populations, although the pattern of use examined in this study may represent patterns of habitat selection by species rather than differences in distribution or abundance. Consequently, additional data are required on the factors affecting the density of species within urban environments.

The automation of nested clade phylogeographic analysis

ANeCA is a fully automated implementation of Nested Clade Phylogeographic Analysis. This was originally developed by Templeton and colleagues, and has been used to infer, from the pattern of gene sequence polymorphisms in a geographically structured population, the historical demographic processes that have shaped its evolution. Until now it has been necessary to perform large parts of the procedure manually. We provide a program that will take data in Nexus sequential format, and directly output a set of inferences. The software also includes TCS v1.18 and GeoDis v2.2 as part of automation.

A 25-year review of sequential methodology in clinical studies

This paper explores the theoretical developments and subsequent uptake of sequential methodology in clinical studies in the 25 years since Statistics in Medicine was launched. The review examines the contributions which have been made to all four phases into which clinical trials are traditionally classified and highlights major statistical advancements, together with assessing application of the techniques. The vast majority of work has been in the setting of phase III clinical trials and so emphasis will be placed here. Finally, comments are given indicating how the subject area may develop in the future.