Tests for homogeneity of the risk ratio in a series of 2x2 tables

Construction of confidence intervals for the risk differences in stratified design with correlated bilateral data

A stratified study is often designed for adjusting a confounding effect or effect of different centers/groups in two treatments or diagnostic tests, and the risk difference is one of the most frequently used indices in comparing efficiency between two treatments or diagnostic tests. This article presented five simultaneous confidence intervals (CIs) for risk differences in stratified bilateral designs accounting for the intraclass correlation and developed seven CIs for the common risk difference under the homogeneity assumption. The performance of the CIs is evaluated with respect to the empirical coverage probabilities, empirical coverage widths and ratios of mesial noncoverage probability and the noncoverage probability under various scenarios. Empirical results show that Wald simultaneous CI, Haldane simultaneous CI, Score simultaneous CI based on Bonferroni method and simultaneous CI based on bootstrap-resampling method perform satisfactorily and hence be recommended for applications, the CI based on the weighted-least-square (WLS) estimator, the CIs based on Mantel-Haenszel estimator, the CI based on Cochran statistic and the CI based on Score statistic for the common risk difference behave well even under small sample sizes. A real data example is used to demonstrate the proposed methodologies.

HELOW: a program for testing extreme homogeneity in meta-analysis

Meta-analysis aims to synthesize results from different studies. Although, in a meta-analysis the presence of large between-study heterogeneity is routinely evaluated, in some instances is also important to probe whether there is extreme between-study homogeneity (i.e. extreme low between-study heterogeneity). HELOW (HEterogeneity LOW) is a program for testing extreme homogeneity in a meta-analysis of risk ratios when binary outcome and Mantel-Haenszel fixed effects summary risk ratio estimate are employed. The significance of extreme homogeneity is assessed using a Monte Carlo test. Extreme homogeneity may yield insights for the statistical and clinical interpretation of the data.

Risk of autism and increasing maternal and paternal age in a large north American population

Previous studies are inconsistent regarding whether there are independent effects of maternal and paternal age on the risk of autism. Different biologic mechanisms are suggested by maternal and paternal age effects. The study population included all California singletons born in 1989-2002 (n = 7,550,026). Children with autism (n = 23,311) were identified through the California Department of Developmental Services and compared with the remainder of the study population, with parental ages and covariates obtained from birth certificates. Adjusted odds ratios and 95% confidence intervals were used to evaluate the risk of autism associated with increasing maternal and paternal age. In adjusted models that included age of the other parent and demographic covariates, a 10-year increase in maternal age was associated with a 38% increase in the odds ratio for autism (odds ratio = 1.38, 95% confidence interval: 1.32, 1.44), and a 10-year increase in paternal age was associated with a 22% increase (odds ratio = 1.22, 95% confidence interval: 1.18, 1.26). Maternal and paternal age effects were seen in subgroups defined by race/ethnicity and other covariates and were of greater magnitude among first-born compared with later-born children. Further studies are needed to help clarify the biologic mechanisms involved in the independent association of autism risk with increasing maternal and paternal age.

Testing homogeneity of the risk ratio in stratified noncompliance randomized trials

The risk ratio (RR), defined as the ratio of probabilities of having an adverse event between an experimental treatment and a control treatment, is one of the most commonly used indices to measure the efficacy of an experimental treatment in a randomized clinical trial (RCT). When we want to obtain a summary estimator of the RR in stratified analysis, it is important that we can examine the assumption whether the underlying RR varies between strata. Although we can find a few publications on testing the homogeneity of RR, all these papers focus the ideal situation in which every patient complies with his/her assigned treatment. The research on testing the homogeneity of RR for a noncompliance RCT is limited. In this paper, we develop three simple test statistics for testing homogeneity of the RR under a noncompliance stratified RCT with large strata. To evaluate the performance of these statistics, we apply Monte Carlo simulation to calculate Type I error and power in a variety of situations. Based on the findings, we provide a general guideline of selecting a preferable test statistic under various situations. Finally, we include a large field trial studying the effect of a multifactor intervention program on the mortality of coronary heart disease (CHD) in middle-aged men to illustrate the practical use of these test statistics.

Extreme between-study homogeneity in meta-analyses could offer useful insights

OBJECTIVES

Meta-analyses are routinely evaluated for the presence of large between-study heterogeneity. We examined whether it is also important to probe whether there is extreme between-study homogeneity.

STUDY DESIGN

We used heterogeneity tests with left-sided statistical significance for inference and developed a Monte Carlo simulation test for testing extreme homogeneity in risk ratios across studies, using the empiric distribution of the summary risk ratio and heterogeneity statistic. A left-sided P=0.01 threshold was set for claiming extreme homogeneity to minimize type I error.

RESULTS

Among 11,803 meta-analyses with binary contrasts from the Cochrane Library, 143 (1.21%) had left-sided P-value <0.01 for the asymptotic Q statistic and 1,004 (8.50%) had left-sided P-value <0.10. The frequency of extreme between-study homogeneity did not depend on the number of studies in the meta-analyses. We identified examples where extreme between-study homogeneity (left-sided P-value <0.01) could result from various possibilities beyond chance. These included inappropriate statistical inference (asymptotic vs. Monte Carlo), use of a specific effect metric, correlated data or stratification using strong predictors of outcome, and biases and potential fraud.

CONCLUSION

Extreme between-study homogeneity may provide useful insights about a meta-analysis and its constituent studies.

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.

Synthesizing medical evidence: systematic reviews and metaanalyses

Systematic reviews and metaanalyses have become increasingly popular ways of summarizing, and sometimes extending, existing medical knowledge. In this review the authors summarize current methods of performing meta-analyses, including the following: formulating a research question; performing a structured literature search and a search for trials not published in the formal medical literature; summarizing and, where appropriate, combining results from several trials; and reporting and presenting results. Topics such as cumulative and Bayesian metaanalysis and metaregression are also addressed. References to textbooks, articles, and Internet resources are also provided. The goal is to assist readers who wish to perform their own metaanalysis or to interpret critically a published example.