Evaluating treatment effects in group sequential multivariate longitudinal studies with covariate adjustment

Jeffries et al. (2018) investigated testing for a treatment difference in the setting of a randomized clinical trial with a single outcome measured longitudinally over a series of common follow-up times while adjusting for covariates. That paper examined the null hypothesis of no difference at any follow-up time versus the alternative of a difference for at least one follow-up time. We extend those results here by considering multivariate outcome measurements, where each individual outcome is examined at common follow-up times. We consider the case where there is interest in first testing for a treatment difference in a global function of the outcomes (e.g., weighted average or sum) with subsequent interest in examining the individual outcomes, should the global function show a treatment difference. Testing is conducted for each follow-up time and may be performed in the setting of a group sequential trial. Testing procedures are developed to determine follow-up times for which a global treatment difference exists and which individual combinations of outcome and follow-up time show evidence of a difference while controlling for multiplicity in outcomes, follow-up, and interim analyses. These approaches are examined in a study evaluating the effects of tissue plasminogen activator on longitudinally obtained stroke severity measurements.

Detecting treatment differences in group sequential longitudinal studies with covariate adjustment

In longitudinal studies comparing two treatments over a series of common follow-up measurements, there may be interest in determining if there is a treatment difference at any follow-up period when there may be a non-monotone treatment effect over time. To evaluate this question, Jeffries and Geller (2015) examined a number of clinical trial designs that allowed adaptive choice of the follow-up time exhibiting the greatest evidence of treatment difference in a group sequential testing setting with Gaussian data. The methods are applicable when a few measurements were taken at prespecified follow-up periods. Here, we test the intersection null hypothesis of no difference at any follow-up time versus the alternative that there is a difference for at least one follow-up time. Results of Jeffries and Geller (2015) are extended by considering a broader range of modeled data and the inclusion of covariates using generalized estimating equations. Testing procedures are developed to determine a set of follow-up times that exhibit a treatment difference that accounts for multiplicity in follow-up times and interim analyses.

More data, less information? Potential for nonmonotonic information growth using GEE

Statistical intuition suggests that increasing the total number of observations available for analysis should increase the precision with which parameters can be estimated. Such monotonic growth of statistical information is of particular importance when data are analyzed sequentially, such as in confirmatory clinical trials. However, monotonic information growth is not always guaranteed, even when using a valid, but inefficient estimator. In this article, we demonstrate the theoretical possibility of nonmonotonic information growth when using generalized estimating equations (GEE) to estimate a slope and provide intuition for why this possibility exists. We use theoretical and simulation-based results to characterize situations that may result in nonmonotonic information growth. Nonmonotonic information growth is most likely to occur when (1) accrual is fast relative to follow-up on each individual, (2) correlation among measurements from the same individual is high, and (3) measurements are becoming more variable further from randomization. In situations that may lead to nonmonotonic information growth, study designers should plan interim analyses to avoid situations most likely to result in nonmonotonic information growth.

A double-blind, placebo-controlled study of atomoxetine in young children with ADHD

OBJECTIVE

To evaluate the efficacy and tolerability of atomoxetine for the treatment of attention-deficit/hyperactivity disorder (ADHD) in 5- and 6-year-old children.

METHODS

This was an 8-week, double-blind, placebo-controlled randomized clinical trial of atomoxetine in 101 children with ADHD. Atomoxetine or placebo was flexibly titrated to a maximum dose of 1.8 mg/kg per day. The pharmacotherapist reviewed psychoeducational material on ADHD and behavioral-management strategies with parents during each study visit.

RESULTS

Significant mean decreases in parent (P = .009) and teacher (P = .02) ADHD-IV Rating Scale scores were demonstrated with atomoxetine compared with placebo. A total of 40% of children treated with atomoxetine met response criteria (Clinical Global Impression-Improvement Scale indicating much or very much improved) compared with 22% of children on placebo, which was not significant (P = .1). Decreased appetite, gastrointestinal upset, and sedation were significantly more common with atomoxetine than placebo. Although some children demonstrated a robust response to atomoxetine, for others the response was more attenuated. Sixty-two percent of subjects who received atomoxetine were moderately, markedly, or severely ill according to the Clinical Global Impression-Severity Scale at study completion.

CONCLUSIONS

To our knowledge, this is the first randomized controlled trial of atomoxetine in children as young as 5 years. Atomoxetine generally was well tolerated and reduced core ADHD symptoms in the children on the basis of parent and teacher reports. Reductions in the ADHD-IV Rating Scale scores, however, did not necessarily translate to overall clinical and functional improvement, as demonstrated on the Clinical Global Impression-Severity Scale and the Clinical Global Impression-Improvement Scale. Despite benefits, the children in the atomoxetine group remained, on average, significantly impaired at the end of the study.

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.

Group sequential clinical trials for longitudinal data with analyses using summary statistics

Longitudinal endpoints are used in clinical trials, and the analysis of the results is often conducted using within-individual summary statistics. When these trials are monitored, interim analyses that include subjects with incomplete follow-up can give incorrect decisions due to bias by non-linearity in the true time trajectory of the treatment effect. Linear mixed-effects models can be used to remove this bias, but there is a lack of software to support both the design and implementation of monitoring plans in this setting. This paper considers a clinical trial in which the measurement time schedule is fixed (at least for pre-trial design), and the scientific question is parameterized by a contrast across these measurement times. This setting assures generalizable inference in the presence of non-linear time trajectories. The distribution of the treatment effect estimate at the interim analyses using the longitudinal outcome measurements is given, and software to calculate the amount of information at each interim analysis is provided. The interim information specifies the analysis timing thereby allowing standard group sequential design software packages to be used for trials with longitudinal outcomes. The practical issues with implementation of these designs are described; in particular, methods are presented for consistent estimation of treatment effects at the interim analyses when outcomes are not measured according to the pre-trial schedule. Splus/R functions implementing this inference using appropriate linear mixed-effects models are provided. These designs are illustrated using a clinical trial of statin treatment for the symptoms of peripheral arterial disease.

Interim analysis of continuous long-term endpoints in clinical trials with longitudinal outcomes

This paper discusses interim analysis for clinical trials where the primary endpoint is observed at a specific long-term follow-up time, but where repeated measures of the same outcome are also taken at earlier times. Methods are considered for improving the efficiency with which the long-term treatment difference is estimated, making use of information from shorter-term follow-up times. This approach to interim analysis has previously been studied for binary endpoints assessed at two time points during follow-up. Here we adapt and extend this methodology to include continuous endpoints assessed at an arbitrary number of follow-up times, making use of methods for analysing multivariate normal data subject to monotone missingness and unstructured mean and covariance relationships. The magnitude of efficiency gains obtained by using short-term measurements is considered, as well as how these gains depend on the number and timing of the short-term measurements. Sequential analysis of treatment differences is discussed, including the extent to which efficiency gains translate into reductions in the expected duration of a sequentially monitored trial. The methods are illustrated on a data set involving a placebo-controlled comparison of longitudinal cholesterol measurements.

Interim monitoring of clinical trials based on long-term binary endpoints

This paper discusses interim analysis of randomized clinical trials for which the primary endpoint is observed at a specific long-term follow-up time. For such trials subjects only yield direct information on the primary endpoint once they have been followed through to the long-term follow-up time, potentially eliminating a large proportion of the accrued sample from an interim analysis of the primary endpoint. We advocate more efficient interim analysis of long-term endpoints by augmenting long-term information with short-term information on subjects who have not yet been followed through to the long-term follow-up time. While retaining the long-term endpoint as the subject of the analysis, methods of jointly analysing short- and long-term data are discussed for reversible binary endpoints. It is shown theoretically and by simulation that the use of short-term information improves the efficiency with which long-term treatment differences are assessed based on interim data. Sequential analysis of treatment differences is discussed based on spending functions, and is illustrated with a numerical example from a cholesterol treatment trial.

Longitudinal data analysis (repeated measures) in clinical trials

Longitudinal data is often collected in clinical trials to examine the effect of treatment on the disease process over time. This paper reviews and summarizes much of the methodological research on longitudinal data analysis from the perspective of clinical trials. We discuss methodology for analysing Gaussian and discrete longitudinal data and show how these methods can be applied to clinical trials data. We illustrate these methods with five examples of clinical trials with longitudinal outcomes. We also discuss issues of particular concern in clinical trials including sequential monitoring and adjustments for missing data. A review of current software for analysing longitudinal data is also provided. Published in 1999 by John Wiley & Sons, Ltd. This article is a US Government work and is the public domain in the United States.