Power of Testing Mediation Effects with Censored Continuous-Time and Discrete-Time Survival Data

Interest in using survival analyses for estimating mediation effects have grown in the last decade.  It is a useful tool to analyze direct and indirect effects for time-to-event data. For example, a growing number of drug abuse prevention and intervention studies suggest that early-onset alcohol or substance use is associated with heightened risk for numerous adverse social, psychological and behavioral outcomes including later accelerated substance use (e.g., Gil, Wagner, & Tubman, 2004; Hawkins et al., 1997).  Preventive interventions have been developed to reduce or delay substance involvement initiation by manipulating pertinent behavioral determinants of early onset for the aim of reducing risk for later adverse outcomes and to ease the associated economic costs.  A potential social-environmental behavioral determinant might be family cohesion or social norms of tolerance for drug use (e.g., Brook, Brook, Richter, & Whiteman, 2003). A potential intrapersonal behavioral determinant might be academic achievement or self efficacy (e.g., Ellickson et al., 2003). To evaluate the efficacy of the prevention program in reducing or delaying the onset of substance involvement and to examine the mechanism of how the prevention program works, researchers apply mediation models with survival data.  The purpose of the study is to use the results of a simulation study to provide a general guideline of power and necessary sample sizes for conducting survival analyses to estimate mediation effects and to investigate whether the required sample sizes differ by various data structures such as 1) time in a continuous scale vs. time in discrete scales (small vs. large interval) and 2) data with 0% vs. 20% vs. 40% censored data.

Original samples that have continuous-time with no censored data varying by the sample sizes and regression coefficients/hazard ratios for the mediation model of X (independent variable) to M (mediator) to Y (time to event) are first simulated.  Samples with censored data and/or discrete time are extracted from the original samples.  The joint significance test method, multivariate delta method, and (percentile and bias-corrected) bootstrap methods are applied to examine the mediation effect for each sample. We then compare the mediation effects across samples by data structure, sample size, and regression coefficients.

Across various data structures, the preliminary results show that a sample size of 50 is adequate to detect a large effect (i.e., B=.59 & HR=1.8), 100 is adequate to detect a medium effect (B=.41 & HR=1.5) and over 500 is needed to detect a small effect (B=.14 & HR=1.15). Power increases or decreases slightly for data with more censoring or with larger intervals, depending on the method of testing the mediation effect.

Back to: New Methods to Investigate Statistical Mediation: Time to Event Models and Methods to Improve Confidence Limit Estimation and Power

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