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Published in:

01-11-2015

Sample Size for Joint Testing of Indirect Effects

Authors: Eric Vittinghoff, Torsten B. Neilands

Published in: Prevention Science | Issue 8/2015

Abstract

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.

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Baron, R., & Kenny, D. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.CrossRefPubMed

Bernardo, M., Lipsitz, S., Harrington, D., Catalano, P. (2000). Sample size calculations for failure time random variables in non-randomized studies. Journal of the Royal Statistical Society (Series D): The Statistician, 49, 31–40.CrossRef

Breen, R., Karlson, K., Holm, A. (2013). Total, direct, and indirect effects in logit and probit models. Sociological Methods & Research, 42, 164–191.CrossRef

Carrico, A., Woods, W., Siever, M., Discepola, M., Dilworth, S., Neilands, T., Miller, N., Moskowitz, J. (2013). Positive affect and processes of recovery among treatment-seeking methamphetamine users. Drug and Alcohol Dependence, 132, 624–629.PubMedCentralCrossRefPubMed

Cole, S., & Hernán, M. (2002). Fallibility in estimating direct effects. International Journal of Epidemiology, 31, 163–165.CrossRefPubMed

Demidenko, E. (2007). Sample size determination for logistic regression revisited. Statistics in Medicine, 26, 3385–3397.CrossRefPubMed

Freedman, L., & Schatzkin, A. (1992). Sample size for studying intermediate endpoints within intervention trials or observational studies. American Journal of Epidemiology, 136, 1148–1159.PubMed

Fritz, M., & MacKinnon, D. (2007). Required sample size to detect the mediated effect. Psychological Science, 18, 233–239.PubMedCentralCrossRefPubMed

Fritz, M., Taylor, A., MacKinnon, D. (2012). Explanation of two anomalous results in statistical mediation research. Multivariate Behavioral Research, 47, 61–87.PubMedCentralCrossRefPubMed

Glueck, D., & Muller, K. (2003). Adjusting power for a baseline covariate in linear models. Statistics in Medicine, 22, 2535–2551.PubMedCentralCrossRefPubMed

Hauck, W., & Donner, A. (1977). Wald’s test as applied to hypotheses in logit analyses. Journal of the American Statistical Association, 72, 851–853.

Hicks, R., & Tingley, D. (2011). Causal mediation analysis. The Stata Journal, 11, 605–619.

Hsieh, F., Bloch, D., Larsen, M. (1998). A simple method of sample size calculation for linear and logistic regression. Statistics in Medicine, 17, 1623–1634.CrossRefPubMed

Hsieh, F., & Lavori, P. (2000). Sample-size calculations for the Cox proportional hazards regression model with nonbinary covariates. Controlled Clinical Trials, 21, 552–560.CrossRefPubMed

Imai, K., Keele, L., Yamamoto, T. (2010). Identification inference, and sensitivity analysis for causal mediation effects. Statistical Science, 25, 51–71.CrossRef

Judd, C., & Kenny, D. (1981). Process analysis: Estimating mediation in treatment evaluations. Evaluation Review, 5, 602–619.CrossRef

Kalbfleisch, J., & Prentice, R. (1980). The Statistical Analysis of Failure Time Data. New York: Wiley.

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.

Lyles, R., Lin, H.-M., Williamson, J. (2007). A practical approach to computing power for generalized linear models with nominal, count, or ordinal responses. Statistics in Medicine, 26, 1632–1648.CrossRefPubMed

MacKinnon, D., Lockwood, C., Brown, C., Wang, W., Hoffman, J. (2007). The intermediate endpoint effect in logistic and probit regression. Clinical Trials, 4, 499–513.PubMedCentralCrossRefPubMed

MacKinnon, D., Lockwood, C., Hoffman, J., West, S., Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83–104.PubMedCentralCrossRefPubMed

Mallinckrodt, B., Abraham, W., Wei, M., Russell, D. (2006). Advances in testing the statistical significance of mediation effects. Journal of Counseling Psychology, 53, 372–378.CrossRef

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. (1998). Graphs, causality, and structural equation models. Sociological Methods and Research, 27, 226–284.CrossRef

Pearl, J. (2001). Direct and indirect effects. In: Proceedings of the Seventeenth Conference on Uncertainty and Artificial Intelligence. CA, San Francisco.

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.

Pearl, J. (2012). The causal mediation formula—a guide to the assessment of pathways and mechanisms. Prevention Science, 13, 426–436.CrossRefPubMed

Petersen, M., Sinisi, S., van der Laan, M. (2006). Estimation of direct causal effects. Epidemiology, 17, 276–284.CrossRefPubMed

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.

Robins, J., & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143–155.CrossRefPubMed

Schmoor, C., Sauerbrei, W., Schumacher, M. (2000). Sample size considerations for the evaluation of prognostic factors in survival analysis. Statistics in Medicine, 19, 441–452.CrossRefPubMed

Schoenfeld, D., & Borenstein, M. (2005). Calculating the power or sample size for the logistic and proportional hazards models. Journal of Statistical Computation and Simulation, 75, 771–785.CrossRef

Self, S., & Mauritsen, R. (1988). Power/sample size calculations for generalized linear models. Biometrics, 44, 79–86.CrossRef

Self, S., Mauritsen, R., Ohara, J. (1992). Power calculations for likelihood ratio tests in generalized linear models. Biometrics, 48, 31–39.CrossRef

Shieh, G. (2000). On power and sample size calculations for likelihood ratio tests in generalized linear models. Biometrics, 56, 1192–1196.CrossRefPubMed

Shieh, G. (2005). On power and sample size calculations for wald tests in generalized linear models. Journal of Statistical Planning and Inference, 128, 43–59.CrossRef

Signorini, D. (1991). Sample size for Poisson regression. Biometrika, 78, 446–450.CrossRef

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 .

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.

VanderWeele, T. (2009). Marginal structural models for the estimation of direct and indirect effects. Epidemiology, 20, 18–26.CrossRefPubMed

Vittinghoff, E., Sen, S., McCulloch, C. (2008). Sample size calculations for evaluating mediation. Statistics in Medicine, 28, 541–557.CrossRef

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.

Whittemore, A. (1981). Sample size for logistic regression with small response probability. Journal of the American Statistical Association, 76, 27–32.CrossRef

Wilson, S., & Gordon, I. (1986). Calculating sample sizes in the presence of confounding variables. Applied Statistics, 35, 207–213.CrossRef

Title: Sample Size for Joint Testing of Indirect Effects
Authors: Eric Vittinghoff
Torsten B. Neilands
Publication date: 01-11-2015
Publisher: Springer US
Published in: Prevention Science / Issue 8/2015
Print ISSN: 1389-4986
Electronic ISSN: 1573-6695
DOI: https://doi.org/10.1007/s11121-014-0528-5

At a glance: The STEP trials

Springer Medicine

Sample Size for Joint Testing of Indirect Effects

Abstract

At a glance: The STEP trials

Springer Medicine

Abstract

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