Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-11T02:03:22.998Z Has data issue: false hasContentIssue false
  • English
  • Français

Latent Class Dynamic Mediation Model with Application to Smoking Cessation Data

Published online by Cambridge University Press:  01 January 2025

Jing Huang ,
Ying Yuan  and
David Wetter
Jing Huang
Affiliation:
The University of Pennsylvania
Ying Yuan*
Affiliation:
The University of Texas MD Anderson Cancer Center
David Wetter
Affiliation:
The University of Utah
*
Correspondence should be made to Ying Yuan, Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA. Email: yyuan@mdanderson.org
Get access Rights & Permissions [Opens in a new window]

Abstract

Traditional mediation analysis assumes that a study population is homogeneous and the mediation effect is constant over time, which may not hold in some applications. Motivated by smoking cessation data, we propose a latent class dynamic mediation model that explicitly accounts for the fact that the study population may consist of different subgroups and the mediation effect may vary over time. We use a proportional odds model to accommodate the subject heterogeneities and identify latent subgroups. Conditional on the subgroups, we employ a Bayesian hierarchical nonparametric time-varying coefficient model to capture the time-varying mediation process, while allowing each subgroup to have its individual dynamic mediation process. A simulation study shows that the proposed method has good performance in estimating the mediation effect. We illustrate the proposed methodology by applying it to analyze smoking cessation data.

Keywords

Bayesian inferencedynamic mediationlatent classtime-varying coefficients

Information

Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 1 , 15 March 2019 , pp. 1 - 18
Copyright
Copyright © 2019 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-09653-2) contains supplementary material, which is available to authorized users.

References

Anatchkova, M. D., Velicer, W. F., & Prochaska, J. O. (2006). Replication of subtypes for smoking cessation within the precontemplation stage of change Addictive Behaviors. 31. (7), 1101– 1115. CrossRefGoogle ScholarPubMed
Baker, T. B., Piper, M. E., McCarthy, D. E., Majeskie, M. R., & Fiore, M. C. (2004). Addiction motivation reformulated: An effective processing model of negative reinforcement. Psychological Review, 111. (1), 33– CrossRefGoogle Scholar
Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51. (6), 1173 CrossRefGoogle ScholarPubMed
Bind, M. A., Vanderweele, T. J., Coull, B. A., & Schwartz, J. D. (2015). Causal mediation analysis for longitudinal data with exogenous exposure. Biostatistics, 17. (1), 122– 134. CrossRefGoogle ScholarPubMed
Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology, 53. 605– 634. CrossRefGoogle ScholarPubMed
Bommelé, J., Kleinjan, M., Schoenmakers, T. M., Burk, W. J., Van Den Eijnden, R., & Van De Mheen, D. (2015). Identifying subgroups among hardcore smokers: A latent profile approach. PLoS ONE, 10. (7), e0133570 CrossRefGoogle ScholarPubMed
Brandon, T. H., Wetter, D. W., & Baker, T. B. (1996). Affect, expectancies, urges, and smoking: Do they conform to models of drug motivation and relapse?. Experimental and Clinical Psychopharmacology, 4. (1), 29 CrossRefGoogle Scholar
Brown, R. L. (1997). Assessing specific mediational effects in complex theoretical models. Structural Equation Modeling: A Multidisciplinary Journal, 4. (2), 142– 156. CrossRefGoogle Scholar
Chmura Kraemer, H., Kiernan, M., Essex, M., & Kupfer, D. J. (2008). How and why criteria defining moderators and mediators differ between the Baron & Kenny and MacArthur approaches. Health Psychology, 27. (2S). S101 CrossRefGoogle Scholar
Cole, D. A., & Maxwell, S. E. (2003). Testing mediational models with longitudinal data: Questions and tips in the use of structural equation modeling. Journal of Abnormal Psychology, 112. (4), 558 14674869 CrossRefGoogle ScholarPubMed
Daniels, M. J., Roy, J. A., Kim, C., Hogan, J. W., Perri, M. G. (2012). Bayesian inference for the causal effect of mediation. Biometrics, 68. (4), 1028– 1036. CrossRefGoogle ScholarPubMed
Didelez, V., Dawid, P., & Geneletti, S. (2012). arXiv:1206.6840 Direct and indirect effects of sequential treatments.Google Scholar
Dijkstra, A., & De Vries, H. (2000). Clusters of precontemplating smokers defined by the perception of the pros, cons, and self-efficacy. Addictive Behaviors, 25. (3), 373– 385. CrossRefGoogle ScholarPubMed
Elliott, M. R., Gallo, J. J., Ten Have, T. R., Bogner, H. R., & Katz, I. R. (2005). Using a Bayesian latent growth curve model to identify trajectories of positive affect and negative events following myocardial infarction. Biostatistics, 6. (1), 119– 143. CrossRefGoogle ScholarPubMed
Eilers, P. H., & Marx, B. D. Flexible smoothing with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B$$\end{document} -splines and penalties. (1996). Statistical Science, 11. (2), 89– 102. Google Scholar
Foshee, V. A., Bauman, K. E., & Linder, G. F. (1999). Family violence and the perpetration of adolescent dating violence: Examining social learning and social control processes. Journal of Marriage and the Family, 61. (2), 331– 342. CrossRefGoogle Scholar
Garrett, E. S., & Zeger, S. L. (2000). Latent class model diagnosis. Biometrics, 56. (4), 1055– 1067. CrossRefGoogle ScholarPubMed
Gelman, A., Meng, X. L., & Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6. (4), 733– 760. Google Scholar
Geneletti, S. (2007). Identifying direct and indirect effects in a non-counterfactual framework. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69. (2), 199– 215. CrossRefGoogle Scholar
Gollob, H., & Reichardt, C. Collins, L., & Horn, J. (1991). Interpreting and estimating indirect effects assuming time lags really matter. Best methods for the analysis of change: Recent advances, unanswered questions, future directions, Washington, D.C: American Psychological Association. 243– 259. CrossRefGoogle Scholar
Green, D. E. (1979). Teenage smoking: Immediate and long-term patterns. Washington, D.C: U.S. Government Printing Office.Google Scholar
Hafeman, D. M., & VanderWeele, T. J. (2011). Alternative assumptions for the identification of direct and indirect effects. Epidemiology, 22. (6), 753– 764. CrossRefGoogle ScholarPubMed
Hayes, A. F., & Preacher, K. J. (2014). Statistical mediation analysis with a multicategorical independent variable. British Journal of Mathematical and Statistical Psychology, 67. (3), 451– 470. CrossRefGoogle ScholarPubMed
Heagerty, P. J., & Comstock, B. A. (2013). Exploration of lagged associations using longitudinal data. Biometrics, 69. (1), 197– 205. CrossRefGoogle ScholarPubMed
Hoyle, R. H., & Kenny, D. A. Hoyle, R. H. (1999). Sample size, reliability, and tests of statistical mediation. Statistical strategies for small sample research, Thousand Oaks: Sage. 195– 222. Google Scholar
Huang, J., & Yuan, Y. (2017). Bayesian dynamic mediation analysis. Psychological Methods, 22. (4), 667– CrossRefGoogle ScholarPubMed
Husten, C. G., McCarty, M. C., Giovino, G. A., Chrismon, J. H., & Zhu, B. P. (1998). Intermittent smokers: A descriptive analysis of persons who have never smoked daily. American Journal of Public Health, 88. (1), 86– 89. CrossRefGoogle ScholarPubMed
Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15. (4), 309– CrossRefGoogle ScholarPubMed
Imai, K., Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25. (1), 51– 71. CrossRefGoogle Scholar
Jarvis, M. J. (2004). Why people smoke. BMJ, 328. (7434), 277– 279. CrossRefGoogle ScholarPubMed
Jullion, A., & Lambert, P. Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P$$\end{document} -splines models. (2007). Computational Statistics & Data Analysis, 51. (5), 2542– 2558. CrossRefGoogle Scholar
Joffe, M. M., Small, D., & Hsu, C. Y. (2007). Defining and estimating intervention effects for groups that will develop an auxiliary outcome. Statistical Science, 22. (1), 74– 97. CrossRefGoogle Scholar
Kirchner, T. R., & Sayette, M. A. (2007). Effects of smoking abstinence and alcohol consumption on smoking-related outcome expectancies in heavy smokers and tobacco chippers. Nicotine & Tobacco Research, 9. (3), 365– 376. CrossRefGoogle ScholarPubMed
Lau, R. S., & Cheung, G. W. (2010). https://10.1177/1094428110391673. Estimating and comparing specific mediation effects in complex latent variable models. Organizational Research Methods.Google Scholar
Lu, Z., & Song, X. (2012). Finite mixture varying coefficient models for analyzing longitudinal heterogenous data. Statistics in Medicine, 31. (6), 544– 560. CrossRefGoogle ScholarPubMed
MacKinnon, D. P. Rose, J. S., Chassin, L., Presson, C. C., & Sherman, S. J. (2000). Contrasts in multiple mediator models. Multivariate applications in substance use research: New methods for new questions, Mahwah: Lawrence Erlbaum Associates Publishers. 141– 160. Google Scholar
MacKinnon, D. P., Lockwood, C. M., Homan, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7. (1), 83 CrossRefGoogle ScholarPubMed
MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30. (1), 41– 62. CrossRefGoogle ScholarPubMed
Norman, G. J., Velicer, W. F., Fava, J. L., & Prochaska, J. O. (2000). Cluster subtypes within stage of change in a representative sample of smokers. Addictive Behaviors, 25. (2), 183– 204. CrossRefGoogle Scholar
Pearl, J. (2001). Direct and indirect effects. In Proceedings of the seventeenth conference on uncertainty in artificial intelligence (pp. 411–420). Morgan Kaufmann Publishers Inc.Google Scholar
Petersen, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology, 17. (3), 276– 284. CrossRefGoogle ScholarPubMed
Poland, B. D., Cohen, J. E., Ashley, M. J., Adlaf, E., Ferrence, R., Pederson, L. L., & Raphael, D. (2000). Heterogeneity among smokers and non-smokers in attitudes and behaviour regarding smoking and smoking restrictions. Tobacco Control, 9. (4), 364– 371. CrossRefGoogle ScholarPubMed
Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40. (3), 879– 891. CrossRefGoogle ScholarPubMed
Reitzel, L. R., Cromley, E. K., & Li, Y. et al. (2011). The effect of tobacco outlet density and proximity on smoking relapse during a specific quit attempt. American Journal of Public Health, 101. 315– 320. CrossRefGoogle Scholar
Roberts, G. O., & Rosenthal, J. S. (2009). Examples of adaptive MCMC. Journal of Computational and Graphical Statistics, 18. (2), 349– 367. CrossRefGoogle Scholar
Robins, J. M. Green, P. J., Hjort, N. L., & Richardson, S. (2003). Semantics of casual DAG models and the identification of direct and indirect effects. Highly structured stochastic systems, Oxford: Oxford University Press. 70– 81. CrossRefGoogle Scholar
Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability for direct andindirect effects. Epidemiology, 3. (2), 143– 155. CrossRefGoogle Scholar
Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11. 550– 560. CrossRefGoogle ScholarPubMed
Robins, J. M. Richardson, T. S. (2010). Alternative graphical causal models and the identification of direct effects. In Causality and psychopathology: Finding the determinants of disorders and their cures (pp. 103–158).Google Scholar
Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66. (5), 688– 701. CrossRefGoogle Scholar
Rubin, D. B. (1990). Comment: Neyman (1923) and causal inference in experiments and observational studies. Statistical Science, 5. (4), 472– 480. CrossRefGoogle Scholar
Rubin, D. B. (2000). Causal inference without counterfactuals: Comment. Journal of the American Statistical Association, 95. (450), 435– 438. Google Scholar
Rubin, D. B. (2004). Direct and indirect causal effects via potential outcomes. Scandinavian Journal of Statistics, 31. (2), 161– 170. CrossRefGoogle Scholar
Ruppert, D. (2002). Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics, 11. (4), 735– 757. CrossRefGoogle Scholar
Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression, New York: Cambridge University Press. CrossRefGoogle Scholar
Schneider, J. E., Reid, R. J., Peterson, N. A., Lowe, J. B., & Hughey, J. (2005). Tobacco outlet density and demographics at the tract level of analysis in Iowa: Implications for environmentally based prevention initiatives. Prevention Science, 6. (4), 319–325. CrossRefGoogle ScholarPubMed
Shiyko, M. P., Lanza, S. T., Tan, X., Li, R., & Shiffman, S. (2012). Using the time-varying effect model (TVEM) to examine dynamic associations between negative affect and self-confidence on smoking urges: Differences between successful quitters and relapsers. Prevention Science, 13. (3), 288– 299. CrossRefGoogle ScholarPubMed
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64. (4), 583– 639. CrossRefGoogle Scholar
Sullivan, P. F., & Kendler, K. S. (1999). The genetic epidemiology of smoking. Nicotine & Tobacco Research, 1. Suppl2 S51– S57. CrossRefGoogle ScholarPubMed
Ten Have, T. R., Elliott, M. R., Joffe, M., Zanutto, E., & Datto, C. (2004). Causal models for randomized physician encouragement trials in treating primary care depression. Journal of the American Statistical Association, 99. (465), 16– 25. CrossRefGoogle Scholar
Ten Have, T. R., Joffe, M. M., Lynch, K. G., Brown, G. K., Maisto, S. A., & Beck, A. T. (2007). Causal mediation analyses with rank preserving models. Biometrics, 63. (3), 926– 934. CrossRefGoogle Scholar
Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure-mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 18. (2), 137– CrossRefGoogle ScholarPubMed
VanderWeele, T. J., Tchetgen, EJT, Cornelis, M., & Kraft, P. (2014). Methodological challenges in Mendelian randomization. Epidemiology, 25. (3), 427– CrossRefGoogle ScholarPubMed
VanderWeele, T., Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2. 457– 468. CrossRefGoogle Scholar
VanderWeele, T. J., & Vansteelandt, S. (2010). Odds ratios for mediation analysis for a dichotomous outcome. American Journal of Epidemiology, 172. (12), 1339– 1348. CrossRefGoogle ScholarPubMed
Velicer, W. F., Redding, C. A., Sun, X., & Prochaska, J. O. (2007). Demographic variables, smoking variables, and outcome across five studies. Health Psychology, 26. (3), 278– CrossRefGoogle ScholarPubMed
West, S. G., & Aiken, L. S. Bryant, K. J., Windle, M., & West, S. G. (1997). Toward understanding individual effects in multicomponent prevention programs: Design and analysis strategies. The science of prevention: Methodological advances from alcohol and substance abuse research, Washington, D.C: American Psychological Association. 167– 209. CrossRefGoogle Scholar
Wetter, D. W., McClure, J. B., Cofta-Woerpel, L., Costello, T. J., Reitzel, L. R., Businelle, M. S., & Cinciripini, P. M. (2011). A randomized clinical trial of a palmtop computer-delivered treatment for smoking relapse prevention among women. Psychology of Addictive Behaviors, 25. (2), 365 CrossRefGoogle ScholarPubMed
Yuan, Y., & MacKinnon, D. P. (2009). Bayesian mediation analysis. Psychological Methods, 14. (4), 301 CrossRefGoogle ScholarPubMed
Supplementary material: File

Huang et al. supplementary material

Supplementary Materials for “Latent Class Dynamic Mediation Model with Application to Smoking Cessation Data”
Download Huang et al. supplementary material(File)
File 211.7 KB