Sample Size for Joint Testing of Indirect Effects
This paper presents methods to calculate sample size for evaluating mediation by joint testing of both links in an indirect pathway from exposure to mediator to outcome. Calculations rely on simulations of the underlying data structure, with testing of the two links performed under the simplifying assumption that the two test statistics are asymptotically independent. Simulations show that the proposed methods are accurate. Continuous and binary exposures and mediators, as well as continuous, binary, count, and survival outcomes are accommodated, along with over-dispersion of count outcomes, design effects, and confounding of the exposure-mediator and mediator-outcome relationships. An illustrative example is provided, and a documented R program implementing the calculations is available online.
KeywordsMediation Indirect pathway Sample size Power Generalized linear models.
- Hauck, W., & Donner, A. (1977). Wald’s test as applied to hypotheses in logit analyses. Journal of the American Statistical Association, 72, 851–853.Google Scholar
- Hicks, R., & Tingley, D. (2011). Causal mediation analysis. The Stata Journal, 11, 605–619.Google Scholar
- Kalbfleisch, J., & Prentice, R. (1980). The Statistical Analysis of Failure Time Data. New York: Wiley.Google Scholar
- Kenny, D. (2013). PowMedR. R program to compute power of joint test for continuous exposure, mediator, and outcome. Available at http://davidakenny.net/progs/PowMedR.txt.
- Kohler, U., Karlson, K., Holm, A. (2011). Comparing coefficients of nested nonlinear probability models. The Stata Journal, 11, 420–438.Google Scholar
- Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. Available at http://www.statmodel.com/examples/penn.shtml#extendSEM.
- Pearl, J. (2001). Direct and indirect effects. In: Proceedings of the Seventeenth Conference on Uncertainty and Artificial Intelligence. CA, San Francisco.Google Scholar
- Pearl, J. (2011). The mediation formula: A guide to the assessment of causal pathways in nonlinear models. Tech. rep. University of California, Los Angeles: Computer Science Department.Google Scholar
- R Development Core Team. (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Austria: Vienna. http://www.R-project.org.
- Sobel, M. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhardt (Ed.), Sociological Methodology (pp. 290–312). American Sociological Association .Google Scholar
- Valeri, L., & VanderWeele, T. (2013). Mediation analysis allowing for exposure-mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological methods, 18, 1–14.Google Scholar
- Wang, E., & Xue, X. (2012). Power and sample size calculations for evaluating mediation effects in longitudinal studies. Statistical Methods in Medical Research. Available at http://www.smm.sagepub.com/content/early/2012/12/05/0962280212465163.full.pdf+html.