An overview of group sequential methods in longitudinal clinical trials

Group sequential designs for pragmatic clinical trials with early outcomes: methods and guidance for planning and implementation

BACKGROUND

Group sequential designs are one of the most widely used methodologies for adaptive design in randomized clinical trials. In settings where early outcomes are available, they offer large gains in efficiency compared to a fixed design. However, such designs are underused and used predominantly in therapeutic areas where there is expertise and experience in implementation. One barrier to their greater use is the requirement to undertake simulation studies at the planning stage that require considerable knowledge, coding experience and additional costs. Based on some modest assumptions about the likely patterns of recruitment and the covariance structure of the outcomes, some simple analytic expressions are presented that negate the need to undertake simulations.

METHODS

A model for longitudinal outcomes with an assumed approximate multivariate normal distribution and three contrasting simple recruitment models are described, based on fixed, increasing and decreasing rates. For assumed uniform and exponential correlation models, analytic expressions for the variance of the treatment effect and the effects of the early outcomes on reducing this variance at the primary outcome time-point are presented. Expressions for the minimum and maximum values show how the correlations and timing of the early outcomes affect design efficiency.

RESULTS

Simulations showed how patterns of information accrual varied between correlation and recruitment models, and consequentially to some general guidance for planning a trial. Using a previously reported group sequential trial as an exemplar, it is shown how the analytic expressions given here could have been used as a quick and flexible planning tool, avoiding the need for extensive simulation studies based on individual participant data.

CONCLUSIONS

The analytic expressions described can be routinely used at the planning stage of a putative trial, based on some modest assumptions about the likely number of outcomes and when they might occur and the expected recruitment patterns. Numerical simulations showed that these models behaved sensibly and allowed a range of design options to be explored in a way that would have been difficult and time-consuming if the previously described method of simulating individual trial participant data had been used.

Changing the Paradigm for the Treatment and Development of New Therapies for FSGS

Focal segmental glomerulosclerosis (FSGS) is a renal pathology finding that represents a constellation of rare kidney diseases, which manifest as proteinuria, edema nephrotic syndrome, hypertension, and increased risk for kidney failure. Therapeutic options for FSGS are reviewed displaying the expected efficacy from 25 to 69% depending on specific therapy, patient characteristics, cost, and common side effects. This variability in treatment response is likely caused, in part, by the heterogeneity in the etiology and active molecular mechanisms of FSGS. Clinical trials in FSGS have been scant in number and slow to recruit, which may stem, in part, from reliance on classic clinical trial design paradigms. Traditional clinical trial designs based on the "learn and confirm" paradigm may not be appropriate for rare diseases, such as FSGS. Future drug development and testing will require novel approaches to trial designs that have the capacity to enrich study populations and adapt the trial in a planned way to gain efficiencies in trial completion timelines. A clinical trial simulation is provided that compares a classical and more modern design to determine the maximum tolerated dose in FSGS.

A comparison of methods for treatment selection in seamless phase II/III clinical trials incorporating information on short-term endpoints

In an adaptive seamless phase II/III clinical trial interim analysis, data are used for treatment selection, enabling resources to be focused on comparison of more effective treatment(s) with a control. In this paper, we compare two methods recently proposed to enable use of short-term endpoint data for decision-making at the interim analysis. The comparison focuses on the power and the probability of correctly identifying the most promising treatment. We show that the choice of method depends on how well short-term data predict the best treatment, which may be measured by the correlation between treatment effects on short- and long-term endpoints.

Natural killer cell differentiation from hematopoietic stem cells: a comparative analysis of heparin- and stromal cell-supported methods

Natural killer (NK) cells differentiated from hematopoietic stem cells (HSCs) may have significant clinical benefits over NK cells from adult donors, including the ability to choose alloreactive donors and potentially more robust in vivo expansion. Stromal-based methods have been used to study the differentiation of NK cells from HSCs. Stroma and cytokines support NK cell differentiation, but may face considerable regulatory hurdles. A recently reported clinical-grade, heparin-based method could serve as an alternative. How the stromal-based and heparin-based approaches compare in terms of NK cell generating efficiency or function is unknown. We show that compared with heparin-based cultures, stroma significantly increases the yield of HSC-derived NK cells by differentiating less-committed progenitors into the NK lineage. NK cells generated by both approaches were similar for most NK-activating and -inhibiting receptors. Although both approaches resulted in a phenotype consistent with CD56(bright) stage IV NK cells, heparin-based cultures favored the development of CD56(+)CD16(+) cells, whereas stroma produced more NK cell immunoglobulin-like receptor-expressing NK cells, both of which are markers of terminal maturation. At day 21, stromal-based cultures demonstrated significantly more IL-22 production, and both methods yielded similar amounts of IFN-γ production and cytotoxicity by day 35. These findings suggest that heparin-based cultures are an effective replacement for stroma and may facilitate clinical trials testing HSC-derived NK cells.

Adaptive designs with correlated test statistics

In clinical trials, the collected observations such as clustered data or repeated measurements are often correlated. As a consequence, test statistics in a multistage design are correlated. Adaptive designs were originally developed for independent test statistics. We present a general framework for two-stage adaptive designs with correlated test statistics. We show that the significance level for the Bauer-Köhne design is inflated for positively correlated test statistics from a bivariate normal distribution. The decision boundary for the second stage can be modified so that type one error is controlled. This general concept is expandable to other adaptive designs. In order to use these designs, the correlation between test statistics has to be estimated. For a known covariance matrix, we show how correlation can be determined within the framework of linear mixed models. A sample size reassessment rule is proposed and evaluated for an unknown covariance matrix by simulation. As Wald test statistics in linear mixed models have independent increments, we use this property to create valid test procedures. We compare these procedures with the proposed design in our simulations.

Group sequential methods for cluster randomization trials with binary outcomes

BACKGROUND

Cluster randomization trials in which intact social units are randomly assigned to different intervention groups have become very popular in recent years, particularly for the evaluation of innovations in the delivery of health care. An extensive literature dealing with the associated methodological challenges has also appeared. Although the monitoring of such trials using formal stopping rules is clearly indicated when the outcomes are irreversible and individual-level data are available sequentially, simple and reliable statistical methods that may be used for this purpose are currently not available.

PURPOSE

To investigate the validity of standard group sequential methods when applied to cluster randomization trials having binary outcomes.

METHODS

The large sample distributions for each of five test statistics computed from sequentially accumulated data are derived. A simulation study is performed to evaluate the finite sample properties of these statistics when applied to the interim analysis of cluster randomization trials. Data from the World Health Organization antenatal care trial are used to illustrate the methods.

RESULTS

Each of the joint distributions is shown to be characterized by a covariance structure that asymptotically satisfies an independent increments structure, a foundation that simplifies group sequential methods. The simulation study reveals that four of the five test statistics evaluated provide satisfactory performance with as few as 10 clusters allocated to each of two interventions.

LIMITATIONS

The applicability of our results to effect estimation following a group sequential cluster randomization trial is not investigated, although a theoretical foundation which may be used for this purpose is presented.

CONCLUSIONS

Standard group sequential methods can be applied to cluster randomization trials when interim analyses are warranted.

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.

Group sequential large sampleT2-like?2 tests for multivariate observations

In many studies, a K degree of freedom large sample chi2 test is used to assess the effect of treatment on a multivariate response, such as an omnibus T2-like test of a difference between two treatment groups in any of K repeated measures. Alternately, a K df chi2 test may be used to test the equality of K+1 groups in a single outcome measure. Jennison and Turnbull (Biometrika 1991; 78: 133-141) describe group sequential chi2 and F-tests for normal errors linear models, and Proschan, Follmann and Geller (Statist. Med. 1994; 13: 1441-1452) describe group sequential tests for K+1 group comparisons. These methods apply to sequences of statistics that can be characterized as having an independent increments variance-covariance structure, thus simplifying the computation of the sequential variance-covariance matrix and the resulting sequential test boundaries. However, many commonly used statistics do not share this structure, including a Liang-Zeger (Biometrika 1986; 73: 13-22) GEE longitudinal analysis with an independence working correlation structure and a Wei-Lachin (J. Amer. Statist. Assoc. 1984; 79: 653-661) multivariate Wilcoxon rank test, among others. For such analyses, this paper describes the computation of group sequential boundaries for the interim analysis of emerging results using K df tests that are expressed as quadratic forms in a statistics vector that is distributed as multivariate normal, at least asymptotically. We derive the elements of the covariance matrix of multiple successive K df chi2 statistics based on established theorems on the distribution of quadratic forms. This covariance matrix is estimated by augmenting the data from the successive interim analyses into a single analysis from which the component sequential tests and their variance-covariance matrix can then be extracted. Boundary values for the sequential statistics can then be computed using the method of Slud and Wei (J. Amer. Statist. Assoc. 1982; 77: 862-868) or using the alpha-spending function of Lan and DeMets (Biometrika 1983; 70: 659-663) with a surrogate measure of information. An example is presented using the analysis of repeated cholesterol measurements in a clinical trial.

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.

A comparison of group sequential methods for binary longitudinal data

Interim analyses are conducted to allow for early termination of the trial, for ethical as well as economical reasons. Here we consider interim analyses in repeated measurements studies where the measurements are binary. Two methods for analysing this kind of data are compared according to their operating characteristics. A subject-specific approach based on the logistic random-effects model is compared with the population-averaged approach based on the generalized estimating equations. The comparison is illustrated with simulations using a randomized clinical trial for toenail fungal infection.