Power calculations for cluster randomized trials (CRTs) with right-truncated Poisson-distributed outcomes: a motivating example from a malaria vector control trial

Inferring the epidemiological benefit of indoor vector control interventions against malaria from mosquito data

The cause of malaria transmission has been known for over a century but it is still unclear whether entomological measures are sufficiently reliable to inform policy decisions in human health. Decision-making on the effectiveness of new insecticide-treated nets (ITNs) and the indoor residual spraying of insecticide (IRS) have been based on epidemiological data, typically collected in cluster-randomised control trials. The number of these trials that can be conducted is limited. Here we use a systematic review to highlight that efficacy estimates of the same intervention may vary substantially between trials. Analyses indicate that mosquito data collected in experimental hut trials can be used to parameterize mechanistic models for Plasmodium falciparum malaria and reliably predict the epidemiological efficacy of quick-acting, neuro-acting ITNs and IRS. Results suggest that for certain types of ITNs and IRS using this framework instead of clinical endpoints could support policy and expedite the widespread use of novel technologies.

Estimating the effectiveness of malaria vector control interventions has typically relied on resource-intensive cluster randomised trials. Here, the authors estimate changes in malaria prevalence using entomological data from experimental hut trials, which may provide an alternative route to approval of interventions in some situations.

Sample size considerations for matched-pair cluster randomization design with incomplete observations of binary outcomes

Multiple public health and medical research studies have applied matched-pair cluster randomization design to the evaluation of the intervention and/or prevention effects. One of the most common and severe problems faced by researchers when conducting cluster randomized trials (CRTs) is incomplete observations, which are associated with various reasons causing the individuals to discontinue participating in the trials. Although statistical methods to remedy the problems of missing data have already been proposed, there are still methodological gaps in research concerning the determination of sample size in matched-pair CRTs with incomplete binary outcomes. One conventional method for adjusting for missing data in the sample size determination is to divide the sample size under complete data by the expected follow-up rate. However, such crude adjustment ignores the impact of the structure and strength of correlations regarding both outcome data and missing data mechanism. This article provides a closed-form sample size formula for matched-pair CRTs with incomplete binary outcomes, which appropriately accounts for different missing patterns and magnitudes as well as the effects of matching and clustering on the outcome and missing data. The generalized estimating equation (GEE) approach treats incomplete observations as missing data in a marginal logistic regression model, which flexibly accommodates various types of intraclass correlation, missing patterns, and missing proportions. In the presence of missing data, the proposed GEE sample size method provides higher accuracy as compared with the conventional method. The performance of the proposed method is assessed by simulation studies. This article also illustrates how the proposed method can be used to design a real-world matched-pair CRT to examine the effect of a team-based approach on controlling blood pressure (BP).

Design and analysis of a 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria: Small sample considerations for cluster-randomized trials with count data

BACKGROUND

Cluster-randomized trials allow for the evaluation of a community-level or group-/cluster-level intervention. For studies that require a cluster-randomized trial design to evaluate cluster-level interventions aimed at controlling vector-borne diseases, it may be difficult to assess a large number of clusters while performing the additional work needed to monitor participants, vectors, and environmental factors associated with the disease. One such example of a cluster-randomized trial with few clusters was the "efficacy and risk of harms of repeated ivermectin mass drug administrations for control of malaria" trial. Although previous work has provided recommendations for analyzing trials like repeated ivermectin mass drug administrations for control of malaria, additional evaluation of the multiple approaches for analysis is needed for study designs with count outcomes.

METHODS

Using a simulation study, we applied three analysis frameworks to three cluster-randomized trial designs (single-year, 2-year parallel, and 2-year crossover) in the context of a 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria. Mixed-effects models, generalized estimating equations, and cluster-level analyses were evaluated. Additional 2-year parallel designs with different numbers of clusters and different cluster correlations were also explored.

RESULTS

Mixed-effects models with a small sample correction and unweighted cluster-level summaries yielded both high power and control of the Type I error rate. Generalized estimating equation approaches that utilized small sample corrections controlled the Type I error rate but did not confer greater power when compared to a mixed model approach with small sample correction. The crossover design generally yielded higher power relative to the parallel equivalent. Differences in power between analysis methods became less pronounced as the number of clusters increased. The strength of within-cluster correlation impacted the relative differences in power.

CONCLUSION

Regardless of study design, cluster-level analyses as well as individual-level analyses like mixed-effects models or generalized estimating equations with small sample size corrections can both provide reliable results in small cluster settings. For 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria, we recommend a mixed-effects model with a pseudo-likelihood approximation method and Kenward-Roger correction. Similarly designed studies with small sample sizes and count outcomes should consider adjustments for small sample sizes when using a mixed-effects model or generalized estimating equation for analysis. Although the 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria is already underway as a parallel trial, applying the simulation parameters to a crossover design yielded improved power, suggesting that crossover designs may be valuable in settings where the number of available clusters is limited. Finally, the sensitivity of the analysis approach to the strength of within-cluster correlation should be carefully considered when selecting the primary analysis for a cluster-randomized trial.

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation

Cluster randomized trials (CRTs) are widely used in epidemiological and public health studies assessing population-level effect of group-based interventions. One important application of CRTs is the control of vector-borne disease, such as malaria. However, a particular challenge for designing these trials is that the primary outcome involves counts of episodes that are subject to right truncation. While sample size formulas have been developed for CRTs with clustered counts, they are not directly applicable when the counts are right truncated. To address this limitation, we discuss two marginal modeling approaches for the analysis of CRTs with truncated counts and develop two corresponding closed-form sample size formulas to facilitate the design of such trials. The proposed sample size formulas allow investigators to explore the power under a large number of scenarios without computationally intensive simulations. The proposed formulas are validated in extensive simulations. We further explore the implication of right truncation on power and apply the proposed formulas to illustrate the power calculation for a malaria control CRT where the primary outcome is subject to right truncation.