Confidence intervals for the risk ratio under cluster sampling based on the beta-binomial model

A new regression model for overdispersed binomial data accounting for outliers and an excess of zeros

Binary outcomes are extremely common in biomedical research. Despite its popularity, binomial regression often fails to model this kind of data accurately due to the overdispersion problem. Many alternatives can be found in the literature, the beta-binomial (BB) regression model being one of the most popular. The additional parameter of this model enables a better fit to overdispersed data. It also exhibits an attractive interpretation in terms of the intraclass correlation coefficient. Nonetheless, in many real data applications, a single additional parameter cannot handle the entire excess of variability. In this study, we propose a new finite mixture distribution with BB components, namely, the flexible beta-binomial (FBB), which is characterized by a richer parameterization. This allows us to enhance the variance structure to account for multiple causes of overdispersion while also preserving the intraclass correlation interpretation. The novel regression model, based on the FBB distribution, exploits the flexibility and large variety of the distribution's possible shapes (which includes bimodality and various tail behaviors). Thus, it succeeds in accounting for several (possibly concomitant) sources of overdispersion stemming from the presence of latent groups in the population, outliers, and excessive zero observations. Adopting a Bayesian approach to inference, we perform an intensive simulation study that shows the superiority of the new regression model over that of the existing ones. Its better performance is also confirmed by three applications to real datasets extensively studied in the biomedical literature, namely, bacteria data, atomic bomb radiation data, and control mice data.

Prediction intervals for overdispersed binomial data with application to historical controls

Bioassays are highly standardized trials for assessing the impact of a chemical compound on a model organism. In that context, it is standard to compare several treatment groups with an untreated control. If the same type of bioassay is carried out several times, the amount of information about the historical controls rises with every new study. This information can be applied to predict the outcome of one future control using a prediction interval. Since the observations are counts of success out of a given sample size, like mortality or histopathological findings, the data can be assumed to be binomial but may exhibit overdispersion caused by the variability between historical studies. We describe two approaches that account for overdispersion: asymptotic prediction intervals using the quasi-binomial assumption and prediction intervals based on the quantiles of the beta-binomial distribution. Both interval types were α-calibrated using bootstrap methods. For an assessment of the intervals coverage probabilities, a simulation study based on various numbers of historical studies and sample sizes as well as different binomial proportions and varying levels of overdispersion was run. It could be shown that α-calibration can improve the coverage probabilities of both interval types. The coverage probability of the calibrated intervals, calculated based on at least 10 historical studies, was satisfactory close to the nominal 95%. In a last step, the intervals were computed based on a real data set from the NTP homepage, using historical controls from bioassays with the mice strain B6C3F1.

Procedures for testing the homogeneity of relative difference in sparse data

To quantify the excess effect of an experimental treatment over a placebo group in clinical trials, we often consider use of the relative difference, defined as the proportion of patients who would respond to the experimental treatment among those who would not otherwise if they were assigned to the placebo group. To control the effects due to confounders on the response of interest, we frequently employ stratified analysis in practice. Before obtaining a summary estimate of the relative difference, it is desirable to assess whether this measure is constant across strata. Based on the beta-binomial model, we develop simple procedures for testing the homogeneity of relative difference for sparse data in which we have many strata but few patients per stratum. Using Monte Carlo simulations, we demonstrate that the proposed test procedures can generally perform well with respect to type I error in a variety of situations. We further evaluate and study the power of these test procedures. Finally, we note some robustness in using the test procedures proposed here.

Relação de risco como indicador do número de animais necessário no mapeamento genético de características binárias complexas em bovinos

Este estudo de simulação de dados objetiva avaliar a relação de risco (lambda R) como indicador do número de animais genotipados necessário para o mapeamento genético de características binárias, tais como a mastite bovina. Dados foram simulados para diferentes prevalências, modelos genéticos e seus parâmetros, em famílias com aproximadamente cinco meios-irmãos afetados. Analisaram os dados gerados em pares de meios-irmãos afetados ("affected sib pairs analysis"). O número necessário de famílias genotipadas aumenta com a prevalência, enquanto os valores de lambda R decrescem, validando lambdaR como indicador do número de animais necessário para o mapeamento para diferentes prevalências. São necessárias mais famílias para características dominantes em relação às recessivas. Penetrância incompleta exerce pouca influência, enquanto fenocópias aumentam o número necessário de animais. Um segundo locus diminui o poder de detecção de genes, especialmente em modelos com heterogeneidade de locus. Pode-se concluir que lambda R é indicador útil para determinar o número de animais necessários em experimentos de mapeamento genético com famílias de meios-irmãos.

Design and analysis of group-randomized trials: a review of recent methodological developments

We review recent developments in the design and analysis of group-randomized trials (GRTs). Regarding design, we summarize developments in estimates of intraclass correlation, power analysis, matched designs, designs involving one group per condition, and designs in which individuals are randomized to receive treatments in groups. Regarding analysis, we summarize developments in marginal and conditional models, the sandwich estimator, model-based estimators, binary data, survival analysis, randomization tests, survey methods, latent variable methods and nonlinear mixed models, time series methods, global tests for multiple endpoints, mediation effects, missing data, trial reporting, and software. We encourage investigators who conduct GRTs to become familiar with these developments and to collaborate with methodologists who can strengthen the design and analysis of their trials.

Eight interval estimators of a common rate ratio under stratified poisson sampling

Under the assumption that the rate ratio (RR) is constant across strata, we consider eight interval estimators of RR under stratified Poisson sampling: the weighted least-squares (WLS) interval estimator with the logarithmic transformation, the interval estimator using the principle analogous to that of Fieller's Theorem, the interval estimators using Wald's statistic with and without the logarithmic transformation, the interval estimators using the Mantel-Haenszel statistic with and without the logarithmic transformation, the score test-based interval estimator, and the asymptotic likelihood ratio test-based interval estimator. We apply Monte Carlo simulation to evaluate and compare the performance of these estimators with respect to the coverage probability and the average length in a variety of situations. We find that the coverage probability of the commonly used WLS interval estimator tends to be smaller than the desired confidence level, especially when we have a large number of strata with a small expected total number of cases (ETNC) per stratum and the underlying RR is far away from 1 (i.e. RR18 or RR8). We further find that the two estimators with the logarithmic transformation, as well as the two test-based estimators can consistently perform well in a variety of situations. When RR1 with a given reasonable size of ETNC per stratum, we note that the interval estimators without the logarithmic transformation can be preferable to the corresponding ones with the logarithmic transformation in the situations considered here. However, when evaluating the non-coverage probability in the two tails, we find that the former tends to shift the left, while the latter is generally not subject to this concern. We also note that interval estimator using the Mantel-Haenszel (MH) statistic with the logarithmic transformation is likely less efficient than the two test-based interval estimators using the score and the likelihood ratio tests. Finally, we use the data taken from a study of the postmenopausal hormone use on the risk of breast cancer in women as an example to illustrate the use of these interval estimators considered here.

Methods for the analysis of incidence rates in cluster randomized trials

BACKGROUND

The published literature on cluster randomized trials focuses on outcomes that are either continuous or binary. In many trials, the outcome is an incidence rate, such as mortality, based on person-years data. In this paper we review methods for the analysis of such data in cluster randomized trials and present some simple approaches.

METHODS

We discuss the choice of the measure of intervention effect and present methods for confidence interval estimation and hypothesis testing which are conceptually simple and easy to perform using standard statistical software. The method proposed for hypothesis testing applies a t-test to cluster observations. To control confounding, a Poisson regression model is fitted to the data incorporating all covariates except intervention status, and the analysis is carried out on the residuals from this model. The methods are presented for unpaired data, and extensions to paired or stratified clusters are outlined.

RESULTS

The methods are evaluated by simulation and illustrated by application to data from a trial of the effect of insecticide-impregnated bednets on child mortality.

CONCLUSIONS

The techniques provide a straightforward approach to the analysis of incidence rates in cluster randomized trials. Both the unadjusted analysis and the analysis adjusting for confounders are shown to be robust, even for very small numbers of clusters, in situations that are likely to arise in randomized trials.