Optimal adaptive promising zone designs.

We develop optimal decision rules for sample size re-estimation in two-stage adaptive group sequential clinical trials. It is usual for the initial sample size specification of such trials to be adequate to detect a realistic treatment effect δa with good power, but not sufficient to detect the smallest clinically meaningful treatment effect δmin . Moreover it is difficult for the sponsors of such trials to make the up-front commitment needed to adequately power a study to detect δmin . It is easier to justify increasing the sample size if the interim data enter a so-called "promising zone" that ensures with high probability that the trial will succeed. We have considered promising zone designs that optimize unconditional power and promising zone designs that optimize conditional power and have discussed the tension that exists between these two objectives. Where there is reluctance to base the sample size re-estimation rule on the parameter δmin we propose a Bayesian option whereby a prior distribution is assigned to the unknown treatment effect δ , which is then integrated out of the objective function with respect to its posterior distribution at the interim analysis.

Solutions to problems of nonexistence of parameter estimates and sparse data bias in Poisson regression.

Poisson regression can be challenging with sparse data, in particular with certain data constellations where maximum likelihood estimates of regression coefficients do not exist. This paper provides a comprehensive evaluation of methods that give finite regression coefficients when maximum likelihood estimates do not exist, including Firth's general approach to bias reduction, exact conditional Poisson regression, and a Bayesian estimator using weakly informative priors that can be obtained via data augmentation. Furthermore, we include in our evaluation a new proposal for a modification of Firth's approach, improving its performance for predictions without compromising its attractive bias-correcting properties for regression coefficients. We illustrate the issue of the nonexistence of maximum likelihood estimates with a dataset arising from the recent outbreak of COVID-19 and an example from implant dentistry. All methods are evaluated in a comprehensive simulation study under a variety of realistic scenarios, evaluating their performance for prediction and estimation. To conclude, while exact conditional Poisson regression may be confined to small data sets only, both the modification of Firth's approach and the Bayesian estimator are universally applicable solutions with attractive properties for prediction and estimation. While the Bayesian method needs specification of prior variances for the regression coefficients, the modified Firth approach does not require any user input.

A comparison of confidence distribution approaches for rare event meta-analysis.

Meta-analysis of rare event data has recently received increasing attention due to the challenging issues rare events pose to traditional meta-analytic methods. One specific way to combine information and analyze rare event meta-analysis data utilizes confidence distributions (CDs). While several CD methods exist, no comparisons have been made to determine which method is best suited for homogeneous or heterogeneous meta-analyses with rare events. In this article, we review several CD methods: Fisher's classic P-value combination method, one that combines P-value functions, another that combines confidence intervals, and one that combines confidence log-likelihood functions. We compare these CD approaches, and we propose and compare variations of these methods to determine which method produces reliable results for homogeneous or heterogeneous rare event meta-analyses. We find that for homogeneous rare event data, most CD methods perform very well. On the other hand, for heterogeneous rare event data, there is a clear split in performance between some CD methods, with some performing very poorly and others performing reasonably well.

A permutation-based approach for heterogeneous meta-analyses of rare events.

The increasingly widespread use of meta-analysis has led to growing interest in meta-analytic methods for rare events and sparse data. Conventional approaches tend to perform very poorly in such settings. Recent work in this area has provided options for sparse data, but these are still often hampered when heterogeneity across the available studies differs based on treatment group. We propose a permutation-based approach based on conditional logistic regression that accommodates this common contingency, providing more reliable statistical tests when such patterns of heterogeneity are observed. We find that commonly used methods can yield highly inflated Type I error rates, low confidence interval coverage, and bias when events are rare and non-negligible heterogeneity is present. Our method often produces much lower Type I error rates and higher confidence interval coverage than traditional methods in these circumstances. We illustrate the utility of our method by comparing it to several other methods via a simulation study and analyzing an example data set, which assess the use of antibiotics to prevent acute rheumatic fever.

Theory and Inference for Regression Models with Missing Responses and Covariates.

In this paper, we carry out an in-depth theoretical investigation for inference with missing response and covariate data for general regression models. We assume that the missing data are Missing at Random (MAR) or Missing Completely at Random (MCAR) throughout. Previous theoretical investigations in the literature have focused only on missing covariates or missing responses, but not both. Here, we consider theoretical properties of the estimates under three different estimation settings: complete case analysis (CC), a complete response analysis (CR) that involves an analysis of those subjects with only completely observed responses, and the all case analysis (AC), which is an analysis based on all of the cases. Under each scenario, we derive general expressions for the likelihood and devise estimation schemes based on the EM algorithm. We carry out a theoretical investigation of the three estimation methods in the normal linear model and analytically characterize the loss of information for each method, as well as derive and compare the asymptotic variances for each method assuming the missing data are MAR or MCAR. In addition, a theoretical investigation of bias for the CC method is also carried out. A simulation study and real dataset are given to illustrate the methodology.

Exact analysis of dose response for multiple correlated binary outcomes.

The neurotoxicity of a substance is often tested using animal bioassays. In the functional observational battery, animals are exposed to a test agent and multiple outcomes are recorded to assess toxicity, using approximately 40 animals measured on up to 30 different items. This design gives rise to a challenging statistical problem: a large number of outcomes for a small sample of subjects. We propose an exact test for multiple binary outcomes, under the assumption that the correlation among these items is equal. This test is based upon an exponential model described by Molenberghs and Ryan (1999, Environmetrics 10, 279-300) and extends the methods developed by Corcoran et al. (2001, Biometrics 57, 941-948) who developed an exact test for exchangeably correlated binary data for groups (clusters) of correlated observations. We present a method that computes an exact p-value testing for a joint dose-response relationship. An estimate of the parameter for dose response is also determined along with its 95% confidence bound. The method is illustrated using data from a neurotoxicity bioassay for the chemical perchlorethylene.