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We describe group sequential tests for a bivariate response. The tests are defined in terms of the two response components jointly, rather than through a single summary statistic. Such methods are appropriate when the two responses concern different aspects of a treatment; for example, one might wish to show that a new treatment is both as effective and as safe as the current standard. We present a formulation of the bivariate testing problem, introduce group sequential tests that satisfy Type I error conditions, and show how to find the sample size guaranteeing a specified power. We describe how properties of group sequential tests for bivariate normal observations can be computed by numerical integration.

We propose group sequential tests of the equivalence of two treatments based on ideas related to repeated confidence intervals. These tests adapt readily to unpredictable group sizes, to the possibility of continuing even though a boundary has been crossed, and to nonnormal observations. In comparing two binomial distributions, the required sample size depends strongly on the average success probability and an adaptive choice of group size is needed to produce an efficient test meeting specified error probability constraints. A special case is the experiment where interim analyses are performed, not for the purpose of early termination but simply to adjust the sample size so that nominal error rates will be guaranteed, despite the presence of a nuisance parameter.

We consider the statistical modeling and analysis of replicated multi-type point process data with covariates. Such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types. The underlying processes are modeled as nonhomogeneous mixed Poisson processes with random (subject) and fixed (covariate) effects. The method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients. Score tests and likelihood ratio statistics are used for covariate selection. A graphical test of goodness of fit of the selected model is based on generalized residuals. Measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed. An application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer.

We present a statistical test for the hypothesis of independence of two disease processes in animal carcinogenicity experiments. It is assumed that the diseases are occult (detectable only at death via necropsy), and progressive, in that each passes (potentially) through three states in each animal: absent, nonlethally present, and lethally present. The test is based on the combination of statistics from a series of age-stratified 3 x 3 tables in which the animals that die in each age interval are cross-classified into one of these three states for each disease. This test utilizes all the data, whether obtained by sacrifice or by "natural death." It avoids the biases due to lethality noted by Breslow et al. (1974, Journal of the National Cancer Institute 52, 233-239) for the test based on age-stratified 2 x 2 tables, where the nonlethal and lethal occurrences are pooled. In a simulation experiment, we show that such biases (which usually conceal true positive associations and produce spurious negative associations) can be very severe indeed, whereas our test preserves the nominal significance level quite well. The power of the test appears to vary widely, depending on the incidence, time to onset, and rate of progression of each disease. As an example of the application of our method, we assess the association between liver tumors and reticulum cell sarcoma in a radiocarcinogenesis experiment involving approximately 1,000 C3H female mice.

This paper considers the problem of analyzing disease prevalence data from survival experiments in which there may also be some serial sacrifice. The assumptions needed for "standard" analyses are reviewed in the context of a general model recently proposed by the authors. This model is then reparametrized in log-linear form, and a generalized EM algorithm is utilized to obtain maximum likelihood estimates of the parameters for a broad class of unsaturated models. Tests based on the relative likelihood are proposed to investigate the effects of treatment, time, and the presence of other diseases on the prevalences and lethalities of specific diseases of interest. An example is given, using data from a large experiment to investigate the effects of low-level radiation on laboratory mice. Finally, some possible directions for future research are indicated.

The paper considers the problem of analyzing disease prevalence data from survival experiments in which there may also be some serial sacrifice. The primary objective of the analysis is to describe the composition of the treated and control populations, in terms of age-dependent disease prevalences, by removing distortions in the data caused by the biased nature of the primary sampling mechanism (death). The statistical model which is utilized for this purpose is parameterized in terms of illness state prevalences and lethalities. It does not require determination of cause of death; nor does it assume that diseases progress independently. Methods are presented for estimating various quantities of interest, including disease-specific relative risks and measures of association among diseases. An application of this analysis is shown, using data from a large experiment to investigate the effects of low-level radiation on laboratory mice.

This paper concerns the analysis of an animal survival/sacrifice experiment designed to investigate the incidence of a particular disease of interest. The disease is assumed to be irreversible, and detectable only at death, for example by a necropsy. Each observation can be of one of three types: (i) death caused by the disease, (ii) death from a competing cause such as sacrifice, with the disease present, or (iii) death with the disease absent. A two-dimensional EM algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease. These can be compared with nonparametric estimators recently proposed by Kodell , Shaw and Johnson (1982, Biometrics 38, 43-58) and by Dinse and Lagakos (1982, Biometrics 38, 921-932). A slight modification of the algorithm permits the construction of likelihood-based interval estimates of quantiles of the distributions. Some extensions and generalizations are indicated.