Sample size requirements for testing treatment effect heterogeneity in cluster randomized trials with binary outcomes.

Cluster randomized trials (CRTs) refer to a popular class of experiments in which randomization is carried out at the group level. While methods have been developed for planning CRTs to study the average treatment effect, and more recently, to study the heterogeneous treatment effect, the development for the latter objective has currently been limited to a continuous outcome. Despite the prevalence of binary outcomes in CRTs, determining the necessary sample size and statistical power for detecting differential treatment effects in CRTs with a binary outcome remain unclear. To address this methodological gap, we develop sample size procedures for testing treatment effect heterogeneity in two-level CRTs under a generalized linear mixed model. Closed-form sample size expressions are derived for a binary effect modifier, and in addition, a computationally efficient Monte Carlo approach is developed for a continuous effect modifier. Extensions to multiple effect modifiers are also discussed. We conduct simulations to examine the accuracy of the proposed sample size methods. We present several numerical illustrations to elucidate features of the proposed formulas and to compare our method to the approximate sample size calculation under a linear mixed model. Finally, we use data from the Strategies and Opportunities to Stop Colon Cancer in Priority Populations (STOP CRC) CRT to illustrate the proposed sample size procedure for testing treatment effect heterogeneity.

Health and Economic Impact of Intensive Surveillance for Distant Recurrence After Curative Treatment of Colon Cancer: A Mathematical Modeling Study.

BACKGROUND: Intensive surveillance strategies are currently recommended for patients after curative treatment of colon cancer, with the aim of secondary prevention of recurrence. Yet, intensive surveillance has not yielded improvements in overall patient survival compared with minimal follow-up, and more intensive surveillance may be costlier. OBJECTIVE: The purpose of this study was to estimate the quality-adjusted life-years, economic costs, and cost-effectiveness of various surveillance strategies after curative treatment of colon cancer. DESIGN: A Markov model was calibrated to reflect the natural history of colon cancer recurrence and used to estimate surveillance costs and outcomes. SETTINGS: This was a decision-analytic model. PATIENTS: Individuals entered the model at age 60 years after curative treatment for stage I, II, or III colon cancer. Other initial age groups were assessed in secondary analyses. MAIN OUTCOME MEASURES: We estimated the gains in quality-adjusted life-years achieved by early detection and treatment of recurrence, as well as the economic costs of surveillance under various strategies. RESULTS: Cost-effective strategies for patients with stage I colon cancer improved quality-adjusted life-expectancy by 0.02 to 0.06 quality-adjusted life-years at an incremental cost of $1702 to $13,019. For stage II, they improved quality-adjusted life expectancy by 0.03 to 0.09 quality-adjusted life-years at a cost of $2300 to $14,363. For stage III, they improved quality-adjusted life expectancy by 0.03 to 0.17 quality-adjusted life-years for a cost of $1416 to $17,631. At a commonly cited willingness-to-pay threshold of $100,000 per quality-adjusted life-year, the most cost-effective strategy for patients with a history of stage I or II colon cancer was liver ultrasound and chest x-ray annually. For those with a history of stage III colon cancer, the optimal strategy was liver ultrasound and chest x-ray every 6 months with CEA measurement every 6 months. LIMITATIONS: The study was limited by model structure assumptions and uncertainty around the values of the model's parameters. CONCLUSIONS: Given currently available data and within the limitations of a model-based decision-analytic approach, the effectiveness of routine intensive surveillance for patients after treatment of colon cancer appears, on average, to be small. Compared with testing using lower cost imaging, currently recommended strategies are associated with cost-effectiveness ratios that indicate low value according to well-accepted willingness-to-pay thresholds in the United States. See Video Abstract at http://links.lww.com/DCR/A921.