On sample size and inference for two-stage adaptive designs

Proschan and Hunsberger (1995, Biometrics 51, 1315-1324) proposed a two-stage adaptive design that maintains the Type I error rate. For practical applications, a two-stage adaptive design is also required to achieve a desired statistical power while limiting the maximum overall sample size. In our proposal, a two-stage adaptive design is comprised of a main stage and an extension stage, where the main stage has sufficient power to reject the null under the anticipated effect size and the extension stage allows increasing the sample size in case the true effect size is smaller than anticipated. For statistical inference, methods for obtaining the overall adjusted p-value, point estimate and confidence intervals are developed. An exact two-stage test procedure is also outlined for robust inference.

Efficacy evaluation for monotherapies in two-by-two factorial trials

For factorial clinical trials in which two monotherapy treatments under study can interact only in the presence of treatment effects for each treatment, the always-pooled test statistic using data from all four groups has a correct size in detecting the simple effect of an individual treatment used alone. However, this test statistic may have an unbounded bias in estimation of the simple effect. The never-pooled test statistic that uses only data from the treatment group not receiving the other treatment has poor precision for estimating the simple effect. Two alternative test statistics under consideration are the two-stage statistic involving a preliminary test of treatment interaction and the maximum test statistic taking the larger of the always-pooled and the never-pooled statistics. The power, bias, and mean square error of all four tests are compared. When negative interactions exist, the two-stage and maximum statistics are generally superior to the always-pooled statistic and compare reasonably well with the never-pooled statistic; the maximum statistic seems slightly more favorable than the two-stage statistic. The two-stage statistic is the best choice when a treatment interaction can be large.

Testing for the existence of a desirable dose combination

We consider the problem of studying several dose combinations of two drugs for a therapeutic endpoint in a multilevel factorial clinical trial. Two test statistics are constructed to test whether there exists at least one dose combination that is more effective than its component doses. Their distributions involve nuisance parameters quantifying the mean differences among the doses of the two component drugs. It is shown that their power functions achieve maxima as all the nuisance parameters approach infinity in absolute value. The significance levels of the two tests are derived and two alpha-level tests are proposed. Tables are given to provide the alpha-level critical values for these tests and to gain insights into their power performances.

Designing a clinical trial to demonstrate prevention of ulcer recurrence: modelling simulation approaches

We describe a Markov chain model for the ulcer recurrence and healing process, review the available literature to obtain appropriate parameter estimates, and use this model to evaluate alternative clinical trial designs. We focus on designs aimed at supporting recurrence prevention claims for a duodenal ulcer maintenance treatment. Our results show that a trial with endoscopies scheduled only at four month intervals is inadequate to support recurrence prevention claims; discrimination between the null and alternative hypotheses is impossible because of the size and direction of expected biases in observed recurrences. Our results suggest that endoscopy intervals should be at most four weeks to establish a claim of ulcer prevention.

A computer program for the generalized chi-square analysis of competing risks grouped survival data (CRISCAT)

CRISCAT is a computer program for the analysis of grouped survival data with competing risks via weighted least squares methods. Competing risks adjustments are obtained from general matrix operations using many of the strategies employed in a previously developed program (GENCAT) for multivariate categorical data. CRISCAT computes survival rates at several time points for multiple causes of failure, where each rate is adjusted for other causes in the sense that failure due to thes other causes has been eliminated as a risk. The program can generate functions of the adjusted survival rates, to which asymptotic regression models may be fit. CRISCAT yields test statistics for hypotheses involving either these functions or estimated model parameters. Thus, this computational algorithm links competing risks theory to linear models methods for contingency table analysis and provides a unified approach to estimation and hypothesis testing of functions involving competing risks adjusted rates.