On two approximations to the F-distribution: Application to testing for intraclass correlation in family studies

Two approximations to the F-distribution are evaluated in the context of testing for intraclass correlation in the analysis of family data. The evaluation is based on a computation of empirical significance levels and a comparison between p-values associated with these approximations and the corresponding exact p-values. It is found that the approximate methods may give very unsatisfactory results, and exact methods are therefore recommended for general use.     

Efficiency of reduced logistic regression models

One feature of the usual polychotomous logistic regression model for categorical outcomes is that a covariate must be included in all the regression equations. If a covariate is not important in all of them, the procedure will estimate unnecessary parameters. More flexible approaches allow different subsets of covariates in different regressions. One alternative uses individualized regressions which express the polychotomous model as a series of dichotomous models. Another uses a model in which a reduced set of parameters is simultaneously estimated for all the regressions. Large-sample efficiencies of these procedures were compared in a variety of circumstances in which there was a common baseline category for the outcome and the covariates were normally distributed. For a correctly specified model, the reduced estimates were over 100% efficient for nonzero slope parameters and up to 500% efficient when the baseline frequency and the effect of interest were small. The individualized estimates could have efficiencies less than 50% when the effect of interest was large, but were also up to 130% efficient when the baseline frequency was large and the effect of interest was small. Efficiency was usually enhanced by correlation among the covariates. For an underspecified reduced model, asymptotic bias in the reduced estimates was approximately proportional to the magnitude of the omitted parameter and to the reciprocal of the baseline frequency.     

The design of a clinical trial when there are two categories of patients

Strategies are investigated for selecting one of two medical treatments when patients may be stratified into two distinct categories on the basis of their expected difference in response to the two treatments. The relative effectiveness of the following three strategies are assessed: (1) separate decisions made independently for the two categories, (2) a single overall decision made on the basis of simple pooling, and (3) the Bayes strategy.     

A characterization of the efficiency of individualized logistic regressions

The use of individualized regressions, which reduces the polychotomous logistic regression model to several dichotomous models, has been proposed as a solution to some practical difficulties for binary covariates (Begg and Gray 1984, Biometrika, 71, 11–18). Its disadvantages, however, include loss of efficiency and the complexity of making comparisons among regressions. Using expressions for the large-sample distribution of the maximum-likelihood estimates, the efficiency of the individualized procedure relative to the polychotomous procedure is evaluated for the case in which the covariates are assumed to follow a multivariate normal distribution. The relative efficiency when the logistic slope vectors from different regressions are collinear can be substantially lower compared to the efficiency with orthogonal slope vectors. Further evaluations for binary covariates using collinear and orthogonal slope parametrizations lead to a similar characterization.     

Power of the adjusted Q statistic to evaluate heterogeneity in meta-analyses of cluster randomized trials

Because of its simplicity, the Q statistic is frequently used to test the heterogeneity of the estimated intervention effect in meta-analyses of individually randomized trials. However, it is inappropriate to apply it directly to the meta-analyses of cluster randomized trials without taking clustering effects into account. We consider the properties of the adjusted Q statistic for testing heterogeneity in the meta-analyses of cluster randomized trials with binary outcomes. We also derive an analytic expression for the power of this statistic to detect heterogeneity in meta-analyses, which can be useful when planning a meta-analysis. A simulation study is used to assess the performance of the adjusted Q statistic, in terms of its Type I error rate and power. The simulation results are compared to that obtained from the proposed formula. It is found that the adjusted Q statistic has a Type I error rate close to the nominal level of 5%, as compared to the unadjusted Q statistic commonly used to test for heterogeneity in the meta-analyses of individually randomized trials with an inflated Type I error rate. Data from a meta-analysis of four cluster randomized trials are used to illustrate the procedures.     

Misogyny: It’s Still the Law—An Empirical Assessment of the Missouri Juvenile Court System’s Processing of Rape and Robbery Offenders

Patriarchal societies have long used their legal systems as a vehicle of oppression. This article examines the extent to which bias against women can still be discerned in the content of the criminal law by comparing and contrasting Missouri??s forcible rape and robbery in the first degree statutes. The study then analyzes the application of these statutes by examining all of the forcible rape and robbery in the first degree cases processed by Missouri??s juvenile court system between January 1, 2001 and December 31, 2004 (N?=?617). The results of these analyses suggest that Missouri??s robbery statute is more protective of victims than is its rape statute. They also indicate that at least among juveniles, robbery offenders are sanctioned more severely than rape offenders in terms of detention, informal adjustment and adjudication.     

Some aspects of the design and analysis of cluster randomization trials

Trials which randomize intact social groups, or clusters, to different interventions are becoming increasingly widespread. Although statistically less efficient than trials which randomize individuals, such designs are often preferred from a practical or ethical point of view, particularly in the evaluation of health care or educational strategies. We discuss selected issues that arise in the conduct of such trials, including the choice of design, ethical implications, sample size estimation and approaches to the analysis. The discussion is closely tied to methodological issues that have arisen in a recent evaluation trial of a new antenatal care programme, as sponsored by the Special Programme of Research, Development and Research Training in Human Reproduction of the World Health Organization.     

The design of a clinical trial with several patient categories

Various strategies are investigated for selecting one of two medical treatments when patients may be divided into k ≥ 2 categories on the basis of their expected differences in response to the two treatments. The strategies compared are (1) k independent decisions, (2) a single overall decision made on the basis of simple pooling, and (3) the Bayes strategy. The optimal clinical trial size is supplied for each strategy, and conditions delineated under which each of the strategies is to be preferred.