Analysis of dichotomous outcome data for community intervention studies

Design and analysis of trials with a partially nested design and a binary outcome measure

Where treatments are administered to groups of patients or delivered by therapists, outcomes for patients in the same group or treated by the same therapist may be more similar, leading to clustering. Trials of such treatments should take account of this effect. Where such a treatment is compared with an un-clustered treatment, the trial has a partially nested design. This paper compares statistical methods for this design where the outcome is binary. Investigation of consistency reveals that a random coefficient model with a random effect for group or therapist is not consistent with other methods for a null treatment effect, and so this model is not recommended for this design. Small sample performance of a cluster-adjusted test of proportions, a summary measures test and logistic generalised estimating equations and random intercept models are investigated through simulation. The expected treatment effect is biased for the logistic models. Empirical test size of two-sided tests is raised only slightly, but there are substantial biases for one-sided tests. Three formulae are proposed for calculating sample size and power based on (i) the difference of proportions, (ii) the log-odds ratio or (iii) the arc-sine transformation of proportions. Calculated power from these formulae is compared with empirical power from a simulations study. Logistic models appeared to perform better than those based on proportions with the likelihood ratio test performing best in the range of scenarios considered. For these analyses, the log-odds ratio method of calculation of power gave an approximate lower limit for empirical power.

Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcomes: a simulation study

Abstracts

Analysis of group randomized trials with multiple binary endpoints and small number of groups

The group randomized trial (GRT) is a common study design to assess the effect of an intervention program aimed at health promotion or disease prevention. In GRTs, groups rather than individuals are randomized into intervention or control arms. Then, responses are measured on individuals within those groups. A number of analytical problems beset GRT designs. The major problem emerges from the likely positive intraclass correlation among observations of individuals within a group. This paper provides an overview of the analytical method for GRT data and applies this method to a randomized cancer prevention trial, where multiple binary primary endpoints were obtained. We develop an index of extra variability to investigate group-specific effects on response. The purpose of the index is to understand the influence of individual groups on evaluating the intervention effect, especially, when a GRT study involves a small number of groups. The multiple endpoints from the GRT design are analyzed using a generalized linear mixed model and the stepdown Bonferroni method of Holm.

Modeling adolescent drug-use patterns in cluster-unit trials with multiple sources of correlation using robust latent class regressions

PURPOSE

The purpose of the study is to examine variation in adolescent drug-use patterns by using latent class regression analysis and evaluate the properties of an estimating-equations approach under different cluster-unit trial designs.

METHODS

A set of second-order estimating equations for latent class models under the cluster-unit trial design are proposed. This approach models the correlation within subclusters (drug-use behaviors), but ignores the correlation within clusters (communities). A robust covariance estimator is proposed that accounts for within-cluster correlation. Performance of this approach is addressed through a Monte Carlo simulation study, and practical implications are illustrated by using data from the National Evaluation of the Enforcing Underage Drinking Laws Randomized Community Trial.

RESULTS

The example shows that the proposed method provides useful information about the heterogeneous nature of drug use by identifying two subtypes of adolescent problem drinkers. A Monte Carlo simulation study supports the proposed estimation method by suggesting that the latent class model parameters were unbiased for 30 or more clusters. Consistent with other studies of generalized estimating equation (GEE) estimators, the robust covariance estimator tended to underestimate the true variance of regression parameters, but the degree of inflation in the test size was relatively small for 70 clusters and only slightly inflated for 30 clusters.

CONCLUSIONS

The proposed model for studying adolescent drug use provides an alternative to standard diagnostic criteria, focusing on the nature of the drug-use profile, rather than relying on univariate symptom counts. The second-order GEE-type estimation procedure provided a computationally feasible approach that performed well for a moderate number of clusters and was consistent with prior studies of GEE under the generalized linear model framework.

Multilevel analysis of group-randomized trials with binary outcomes

OBJECTIVES

Many dental studies have assessed the effectiveness of community- or group-based interventions such as community water fluoridation. These cluster trials, of which group-randomized trials (GRTs) are one type, have design and analysis considerations not found in studies with randomization of treatments to individuals (randomized controlled trials, RCTs). The purpose of this paper is to review analytic methods used for the analysis of binary outcomes from cluster trials and to illustrate these concepts and analytical methods using a school-based GRT.

METHODS

We examine characteristics of GRTs including intra-class correlation (ICC), their most distinctive feature, and review analytical methods for GRTs including group-level analysis, adjusted chi-square test and multivariable analysis (mixed effect models and generalized estimating equations) for correlated binary data. We consider two- and three-level modeling of data from a cross-sectional cluster design. We apply the concepts reviewed using a GRT designed to determine the effect of incentives on response rates in a school-based dental study. We compare the results of analyses using methods for correlated binary data with those from traditional methods that do not account for ICC.

RESULTS

Application of traditional analytic methods to the dental GRT used as an example for this paper led to a substantial overstatement of the effectiveness of the intervention.

CONCLUSIONS

Ignoring the ICC among members of the same group in the analysis of public health intervention studies can lead to erroneous conclusions where groups are the unit of assignment. Special consideration is needed in the analysis of data from these cluster trials. Randomization of treatments to groups also should receive more consideration in the design of cluster trials in dental public health.

Planning a cluster randomized trial with unequal cluster sizes: practical issues involving continuous outcomes

Background

Cluster randomization design is increasingly used for the evaluation of health-care, screeening or educational interventions. At the planning stage, sample size calculations usually consider an average cluster size without taking into account any potential imbalance in cluster size. However, there may exist high discrepancies in cluster sizes.

Methods

We performed simulations to study the impact of an imbalance in cluster size on power. We determined by simulations to which extent four methods proposed to adapt the sample size calculations to a pre-specified imbalance in cluster size could lead to adequately powered trials.

Results

We showed that an imbalance in cluster size can be of high influence on the power in the case of severe imbalance, particularly if the number of clusters is low and/or the intraclass correlation coefficient is high. In the case of a severe imbalance, our simulations confirmed that the minimum variance weights correction of the variation inflaction factor (VIF) used in the sample size calculations has the best properties.

Conclusion

Publication of cluster sizes is important to assess the real power of the trial which was conducted and to help designing future trials. We derived an adaptation of the VIF from the minimum variance weights correction to be used in case the imbalance can be a priori formulated such as "a proportion (γ) of clusters actually recruit a proportion (τ) of subjects to be included (γ ≤ τ)".