Group sequential enrichment design incorporating subgroup selection.

An important component of clinical trials in drug development is the analysis of treatment efficacy in patient subgroups (subpopulations). Because of concerns of multiplicity and of the small sample sizes often involved, such analyses can present substantial statistical challenges and may lead to misleading conclusions. As a confirmatory seamless phase II/III design, we propose an adaptive enrichment group sequential procedure whereby resources can be concentrated on subgroups most likely to respond to treatment. Stopping boundaries are defined through upper and lower spending functions. The procedure is presented in terms of the efficient score, enabling the analysis of normal, binary, or time-to-event data. It addresses the dilution effect by eliminating populations at the first stage that appear likely to derive no therapeutic benefit. It subsequently proceeds with the definitive assessment of treatment efficacy among the remaining pooled populations using a group sequential design. The procedure provides strong protection of familywise type I error rate, and we employ a bootstrap algorithm to obtain point and interval estimates that are adjusted for the selection bias. We give examples to demonstrate how the design is used. We make comparisons with adaptive two-stage combination test procedures and with a group sequential test that does not account for the presence of subgroups. Numerical results show that the procedure has high power to detect subgroup-specific effects and the use of multiple interim analysis points can lead to substantial sample size savings.

On the multivariate probit model for exchangeable binary data with covariates.

This paper considers the use of a multivariate binomial probit model for the analysis of correlated exchangeable binary data. The model can naturally accommodate both cluster and individual level covariates, while keeping a fairly flexible intracluster association structure. We discuss Bayesian estimation when a sample of independent clusters of varying sizes are available, and show how Gibbs sampling may be used to derive the posterior densities of parameters. The methodology is illustrated with two examples: the first involves epidemiological data from a study of familial disease aggregation; the second uses teratological data from a developmental toxicity application.

Selenium supplementation and secondary prevention of nonmelanoma skin cancer in a randomized trial.

The Nutritional Prevention of Cancer Trial was a double-blind, randomized, placebo-controlled clinical trial designed to test whether selenium as selenized yeast (200 microg daily) could prevent nonmelanoma skin cancer among 1312 patients from the Eastern United States who had previously had this disease. Results from September 15, 1983, through December 31, 1993, showed no association between treatment and the incidence of basal and squamous cell carcinomas of the skin. This report summarizes the entire blinded treatment period, which ended on January 31, 1996. The association between treatment and time to first nonmelanoma skin cancer diagnosis and between treatment and time to multiple skin tumors overall and within subgroups, defined by baseline characteristics, was evaluated. Although results through the entire blinded period continued to show that selenium supplementation was not statistically significantly associated with the risk of basal cell carcinoma (hazard ratio [HR] = 1.09, 95% confidence interval [CI] = 0.94 to 1.26), selenium supplementation was associated with statistically significantly elevated risk of squamous cell carcinoma (HR = 1.25, 95% CI = 1.03 to 1.51) and of total nonmelanoma skin cancer (HR = 1.17, 95% CI = 1.02 to 1.34). Results from the Nutritional Prevention of Cancer Trial conducted among individuals at high risk of nonmelanoma skin cancer continue to demonstrate that selenium supplementation is ineffective at preventing basal cell carcinoma and that it increases the risk of squamous cell carcinoma and total nonmelanoma skin cancer.

Likelihood inference for exchangeable binary data with varying cluster sizes.

This article investigates maximum likelihood estimation with saturated and unsaturated models for correlated exchangeable binary data, when a sample of independent clusters of varying sizes is available. We discuss various parameterizations of these models, and propose using the EM algorithm to obtain maximum likelihood estimates. The methodology is illustrated by applications to a study of familial disease aggregation and to the design of a proposed group randomized cancer prevention trial.

Selenium supplementation and lung cancer incidence: an update of the nutritional prevention of cancer trial.

Interest in the chemopreventive effects of the trace element selenium has spanned the past three decades. Of >100 studies that have investigated the effects of selenium in carcinogen-exposed animals, two-thirds have observed a reduction in tumor incidence and/or preneoplastic endpoints (G. F. Combs and S. B. Combs, The Role of Selenium in Nutrition Chapter 10, pp. 413-462. San Diego, CA: Academic Press, 1986, and B. H. Patterson and O. A. Levander, Cancer Epidemiol. Biomark. Prev., 6: 63-69, 1997). The Nutritional Prevention of Cancer Trial, a randomized clinical trial reported by Clark et al. (L. C. Clark et al., JAMA, 276: 1957-1963, 1996), showed as a secondary end point, a statistically significant decrease in lung cancer incidence with selenium supplementation. The adjusted hazard ratio (HR) was 0.56 [95% confidence interval (CI), 0.31-1.01; P = 0.05]. These results were based on active follow-up of 1312 participants. This reanalysis used an extended Nutritional Prevention of Cancer Trial participant follow-up through the end of the blinded clinical trial on February 1, 1996. The additional 3 years added 8 cases to the selenium-treated group and 4 cases to the placebo group, and increased follow-up to 7.9 years. The relative risk of 0.70 (95% CI, 0.40-1.21; P = 0.18) is not statistically significant. Whereas the overall adjusted HR is not significant (HR = 0.74; 95% CI, 0.44-1.24; P = 0.26), and the HR for current and former smokers was not significant, the trend is toward a reduction in risk of incident lung cancer with selenium supplementation. In a subgroup analysis there was a nominally significant HR among subjects with baseline plasma selenium in the lowest tertile (HR = 0.42; 95% CI, 0.18-0.96; P = 0.04). The analysis for the middle and highest tertiles of baseline showed HRs of 0.91 and 1.25. The current reanalysis indicates that selenium supplementation did not significantly decrease lung cancer incidence in the full population, but a significant decrease among individuals with low baseline selenium concentrations was observed.

Baseline characteristics and the effect of selenium supplementation on cancer incidence in a randomized clinical trial: a summary report of the Nutritional Prevention of Cancer Trial.

The Nutritional Prevention of Cancer Trial was a randomized, clinical trial designed to evaluate the efficacy of selenium as selenized yeast (200 microg daily) in preventing the recurrence of nonmelanoma skin cancer among 1312 residents of the Eastern United States. Original secondary analyses through December 31, 1993 showed striking inverse associations between treatment and the incidence of total [hazard ratio (HR) = 0.61, 95% confidence interval (CI) = 0.46-0.82], lung, prostate, and colorectal cancer and total cancer mortality. This report presents results through February 1, 1996, the end of blinded treatment. Effect modification by baseline characteristics is also evaluated. The effects of treatment overall and within subgroups of baseline age, gender, smoking status, and plasma selenium were examined using incidence rate ratios and Cox proportional hazards models. Selenium supplementation reduced total (HR = 0.75, 95% CI = 0.58-0.97) and prostate (HR = 0.48, 95% CI = 0.28-0.80) cancer incidence but was not significantly associated with lung (HR = 0.74, 95% CI = 0.44-1.24) and colorectal (HR = 0.46, 95% CI = 0.21-1.02) cancer incidence. The effects of treatment on other site-specific cancers are also described. The protective effect of selenium was confined to males (HR = 0.67, 95% CI = 0.50-0.89) and was most pronounced in former smokers. Participants with baseline plasma selenium concentrations in the lowest two tertiles (<121.6 ng/ml) experienced reductions in total cancer incidence, whereas those in the highest tertile showed an elevated incidence (HR = 1.20, 95% CI = 0.77-1.86). The Nutritional Prevention of Cancer trial continues to show a protective effect of selenium on cancer incidence, although not all site-specific cancers exhibited a reduction in incidence. This treatment effect was restricted to males and to those with lower baseline plasma selenium concentrations.