Principles of latent variable mixture modeling and its value in clinical research applications_Chinese Journal of Evidence-Based Medicine

Authors：

LI Bingzhe ^1,2 , JIANG Qijing ³ , LU Zhenzhen ^1,2 ,  HUANG Lihong ^1,2

1. Department of Biostatistics, Zhongshan Hospital, Fudan University, Shanghai 200032, P. R. China;
2. Clinical Research Unit, Institute of Clinical Science, Zhongshan Hospital, Fudan University, Shanghai 200032, P. R. China;
3. School of Public Health, Fudan University, Shanghai 200032, P. R. China;

Corresponding author：

HUANG Lihong, Email: huang.lihong@zs-hospital.sh.cn

Keywords：

Latent variable mixture modeling; Latent class analysis; Growth mixture modeling; Latent class growth modeling; Clinical research

DOI：

10.7507/1672-2531.202402003

Video：

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In medical research, latent subgroups often emerge with characteristics or trends distinct from the general population, yet identifying them directly remain challenging. The latent variable mixture modeling, grounded in the idea that a population consists of a limited mixture of subgroups, assigns latent categories to individuals based on posterior probabilities. This model is suitable for both cross-sectional and longitudinal datasets. Approaching from a statistical perspective, this paper thoroughly explicates the foundational principles of four prevalent methods within the latent variable mixture modeling realm, outlining the essential modeling workflow. By integrating insights from previous cases and real-world data, we review the rational applications of these methods. The latent variable mixture modeling stands as a flexible classification tool for identifying and analyzing latent categories within research populations, further facilitating the in-depth exploration of predictors influencing these latent categories and their consequent effects on outcome variables.

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15.	Diallo TM, Morin AJ, Lu H. The impact of total and partial inclusion or exclusion of active and inactive time invariant covariates in growth mixture models. Psychol Methods, 2017, 22(1): 166-190.
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21.	Ni Y, Tein JY, Zhang M, et al. Changes in depression among older adults in China: A latent transition analysis. J Affect Disord, 2017, 209: 3-9.
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1. Berlin KS, Williams NA, Parra GR. An introduction to latent variable mixture modeling (part 1): overview and cross-sectional latent class and latent profile analyses. J Pediatr Psychol, 2014, 39(2): 174-187.
2. Muthén BO. Latent variable mixture modeling. New developments and techniques in structural equation modeling. Lawrence Erlbaum Associates, 2001.
3. Nagin D, Tremblay RE. Trajectories of boys' physical aggression, opposition, and hyperactivity on the path to physically violent and nonviolent juvenile delinquency. Child Dev, 1999, 70(5): 1181-1196.
4. Jackson KM, Sher KJ. Similarities and differences of longitudinal phenotypes across alternate indices of alcohol involvement: a methodologic comparison of trajectory approaches. Psychol Addict Behav, 2005, 19(4): 339-351.
5. MacCallum RC, Austin JT. Applications of structural equation modeling in psychological research. Annu Rev Psychol, 2000, 51: 201-26.
6. McNeish D, Harring JR. Improving convergence in growth mixture models without covariance structure constraints. Stat Methods Med Res, 2021, 30(4): 994-1012.
7. Davies CE, Glonek GF, Giles LC. The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure. Stat Methods Med Res, 2017, 26(4): 1982-1991.
8. Feldman BJ, Masyn KE, Conger RD. New approaches to studying problem behaviors: a comparison of methods for modeling longitudinal, categorical adolescent drinking data. Dev Psychol, 2009, 45(3): 652-676.
9. Lanza ST. Latent class analysis for developmental research. Child Dev Perspect, 2016, 10(1): 59-64.
10. Lanza ST, Tan X, Bray BC. Latent class analysis with distal outcomes: a flexible model-based approach. Struct Equ Modeling, 2013, 20(1): 1-26.
11. Ryoo JH, Wang C, Swearer SM, et al. Longitudinal model building using latent transition analysis: an example using school bullying data. Front Psychol, 2018, 9: 675.
12. Sotres-Alvarez D, Herring AH, Siega-Riz AM. Latent transition models to study women's changing of dietary patterns from pregnancy to 1 year postpartum. Am J Epidemiol, 2013, 177(8): 852-861.
13. Herle M, Micali N, Abdulkadir M, et al. Identifying typical trajectories in longitudinal data: modelling strategies and interpretations. Eur J Epidemiol, 2020, 35(3): 205-222.
14. Lennon H, Kelly S, Sperrin M, et al. Framework to construct and interpret latent class trajectory modelling. BMJ Open, 2018, 8(7): e020683.
15. Diallo TM, Morin AJ, Lu H. The impact of total and partial inclusion or exclusion of active and inactive time invariant covariates in growth mixture models. Psychol Methods, 2017, 22(1): 166-190.
16. van der Nest G, Lima Passos V, Candel MJJM, et al. An overview of mixture modelling for latent evolutions in longitudinal data: modelling approaches, fit statistics and software. Adv Life Course Res, 2020, 43: 100323.
17. van de Schoot R, Sijbrandij M, Winter SD, et al. The GRoLTS-checklist: guidelines for reporting on latent trajectory studies. Struct Equ Modeling, 2017, 24(3): 451-467.
18. Peto J. That the effects of smoking should be measured in pack-years: misconceptions 4. Br J Cancer, 2012, 107(3): 406-407.
19. Loupy A, Coutance G, Bonnet G, et al. Identification and characterization of trajectories of cardiac allograft vasculopathy after heart transplantation: a population-based study. Circulation, 2020, 141(24): 1954-1967.
20. Zhang YB, Chen C, Pan XF, et al. Associations of healthy lifestyle and socioeconomic status with mortality and incident cardiovascular disease: two prospective cohort studies. BMJ, 2021, 373: n604.
21. Ni Y, Tein JY, Zhang M, et al. Changes in depression among older adults in China: A latent transition analysis. J Affect Disord, 2017, 209: 3-9.
22. Nagin D. Overview of a semiparametric, group-based approach for analyzing trajectories of development. Punishment, places and perpetrators: developments in criminology and criminal justice research. 2004.
23. Neely ML, Pieper CF, Gu B, et al. Exploration of model misspecification in latent class methods for longitudinal data: Correlation structure matters. Stat Med, 2023, 42(14): 2420-2438.
24. Proust-lima C, Philipps V, Liquet B. Estimation of extended mixed models using latent classes and latent processes: the r package lcmm. J Stat Softw, 2017, 78(2): 1-56.
25. Proust-lima C, Philipps V, Liquet B. Estimation of extended mixed models using latent classes and latent processes: the R package lcmm. 2015.

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