Trajectory Modelling Techniques Useful to Epidemiological Research: A Comparative Narrative Review of Approaches

Figures & data

Figure 1 Pain intensity modelling methods: population average models (top) and trajectory modelling approaches (bottom).

Table 1 Overview of the Trajectory Modelling Techniques

	Latent Class modelling approaches				Cluster Analysis	Sequence Analysis
	GMM	GBTM	LTA	LCA
Statistical technique	Parametric finite mixture model; Allows heterogeneity within subgroups	Semi-parametric finite mixture model; Do not allow heterogeneity within subgroups	Semi-parametric finite mixture model	Semi-parametric finite mixture model	Nonparametric approach	Nonparametric approach
Rationale of use	Statistical modelling of repeated measures of a given variable			Modelling of a variable at one point in time	Modelling of a variable at one point in time	Modelling of sequences of states or events that unfold over a period of time
Possibility to include covariates	yes	yes	Yes	yes	yes	yes
Study design	Longitudinal	Longitudinal	Longitudinal	Cross-sectional	Cross-sectional	Longitudinal
Type of variables	Continuous; Categorical (nominal or ordinal)	Continuous; Categorical (nominal or ordinal)	Categorical (nominal or ordinal)	Categorical	Continuous; Categorical (nominal or ordinal); Mixed	Categorical (sequential)
Type of distributions	Normal; Binary; Censored; normal; Poisson; Zero-inflated Poisson	Binary; Censored normal; Poisson; Zero-inflated Poisson	Binary; Multinomial	Binary; Multinomial	N/A	N/A
Methodological choices to be made	Class-membership probability thresholds Number of classes/trajectories in the study population/Indicators: Bayesian Information Criterion (BIC), Clinical judgment, Parsimony, Minimum acceptable % of patients in each class				Algorithm to be used	States to be prioritized when multiple states occur simultaneously
Available statistical software programs	lcmm R-package; Mplus	SAS Proc traj; CrimCV R-package; Mplus; traj Stata-plugin	SAS Proc lta; poLCA and depmixs4 R-package, Mpus	SAS Proc LCA; poLCA and depmixs4R-package; Mplus, Others	SAS Proc cluster; R; SPSS Cluster analysis; Stata Cluster and Clustermat; Others	SAS, TraMineR R-package
Examples of applications (variables)	Clinical symptoms (eg, pain intensity or interference); Developmental trajectories; Acculturative changes; Perceived racial discrimination; Self-Esteem; Behaviours	Clinical symptoms (eg, pain intensity or interference); Quality of life; Healthcare visits; Body mass; Developmental trajectories of physical aggression	Alcohol use; Sexual behaviours; Racial identity; Adolescents’ beliefs about parental authority	Behaviours (eg, alcohol, substances, sexual, behavioural obesity risk factors)	Clinical symptoms (eg, pain interference, depression); Healthcare visits; Expectations	Healthcare visits
Examples of studies reporting the use of the approach	^Citation12,Citation42,Citation45,Citation48,Citation132	^Citation11,Citation26,Citation27,Citation30,Citation62,Citation133,Citation134	^Citation68,Citation135-^Citation138	^Citation85,Citation87,Citation90	^Citation103^–^Citation105	^Citation18,Citation51,Citation115-^Citation117,Citation124

Notes: R: A language and environment for statistical computing (R Core Team, Vienna, Austria); Mplus: Mplus Computer Software (Muthén & Muthén, Los Angeles, CA, USA); SAS: SAS software (SAS Institute, Cary, NC, USA); Stata: Stata Statistical Software (StataCorp LLC., College Station, TX, USA); SPSS: IBM SPSS Statistics for Windows (IBM Corp., Armonk, NY, US).

Abbreviations: GMM, growth mixture modelling; GBTM, group-based trajectory modelling; LTA, latent transition analysis; LCA, latent class analysis.

Pagé MG, Katz J, Escobar ER, et al. Distinguishing problematic from nonproblematic postsurgical pain: a pain trajectory analysis after total knee arthroplasty. PAIN. 2015;156(3):460–468. doi:10.1097/01.j.pain.0000460327.10515.2d25599235

 PubMed Web of Science ®Google Scholar

Connell AM, Frye AA. Growth mixture modelling in developmental psychology: overview and demonstration of heterogeneity in developmental trajectories of adolescent antisocial behaviour. Infant Child Dev. 2006;15(6):609–621. doi:10.1002/icd.481

 Web of Science ®Google Scholar

Masterson Creber R, Lee CS, Lennie TA, Topaz M, Riegel B. Using growth mixture modeling to identify classes of sodium adherence in adults with heart failure. J Cardiovasc Nurs. 2014;29(3):209–217.23416937

 PubMed Web of Science ®Google Scholar

McDevitt-Petrovic O, Shevlin M, Kirby K. Modelling changes in anxiety and depression during low-intensity cognitive behavioural therapy: an application of growth mixture models. British J Clin Psychol. 2020;59(2):169–185. doi:10.1111/bjc.12237

 Web of Science ®Google Scholar

Li MM, Ocay DD, Teles AR, et al. Acute postoperative opioid consumption trajectories and long-term outcomes in pediatric patients after spine surgery. J Pain Res. 2019;12:1673. doi:10.2147/JPR.S19118331190974

 PubMed Web of Science ®Google Scholar

Deyo RA, Bryan M, Comstock BA, et al. Trajectories of symptoms and function in older adults with low back disorders. SPINE. 2015;40(17):1352–1362. doi:10.1097/BRS.000000000000097525996537

 PubMed Web of Science ®Google Scholar

Rabbitts JA, Zhou C, Groenewald CB, Durkin L, Palermo TM. Trajectories of postsurgical pain en children: risk factors and impact of late pain recovery on long-term health outcomes after major surgery. Pain. 2015;156(11):2383–2389. doi:10.1097/j.pain.000000000000028126381701

 PubMed Web of Science ®Google Scholar

Sieberg CB, Simons LE, Edelstein MR, et al. Pain prevalence and trajectories following pediatric spinal fusion surgery. J Pain. 2013;14(12):1694–1702. doi:10.1016/j.jpain.2013.09.00524290449

 PubMed Web of Science ®Google Scholar

Shi Q, Mendoza TR, Gunn GB, Wang XS, Rosenthal DI, Cleeland CS. Using group-based trajectory modeling to examine heterogeneity of symptom burden in patients with head and neck cancer undergoing aggressive non-surgical therapy. Quality Life Res. 2013;22:2331–2339. doi:10.1007/s11136-013-0380-2

 PubMed Web of Science ®Google Scholar

Flint KM, Schmiege SJ, Allen LA, Fendler TJ, Rumsfeld J, Bekelman D. Health status trajectories among outpatients with heart failure. J Pain Symptom Manage. 2017;53(2):224–231.27756621

 PubMed Web of Science ®Google Scholar

Arling G, Ofner S, Reeves MJ, et al. Care trajectories of veterans in the 12 months after hospitalization for acute ischemic stroke. Circ Cardiovasc Qual Outcomes. 2015;8(6 Suppl 3):S131–140. doi:10.1161/CIRCOUTCOMES.115.00206826515201

 PubMed Web of Science ®Google Scholar

Barnett TA, Gauvin L, Craig CL, Katzmarzyk PT. Distinct trajectories of leisure time physical activity and predictors of trajectory class membership: a 22 year cohort study. Int J Behavioral Nutrition Physical Activity. 2008;5(1):57. doi:10.1186/1479-5868-5-57

 PubMed Web of Science ®Google Scholar

Guo J, Collins LM, Hill KG, Hawkins JD. Developmental pathways to alcohol abuse and dependence in young adulthood. J Stud Alcohol. 2000;61(6):799–808. doi:10.15288/jsa.2000.61.79911188485

 PubMed Web of Science ®Google Scholar

Seaton EK, Yip T, Morgan-Lopez A, Sellers RM. Racial discrimination and racial socialization as predictors of African American adolescents’ racial identity development using latent transition analysis. Dev Psychol. 2012;48(2):448–458. doi:10.1037/a002532821875184

 PubMed Web of Science ®Google Scholar

Cumsille P, Darling N, Flaherty B, Loreto Martinez M. Heterogeneity and change in the patterning of adolescents’ perceptions of the legitimacy of parental authority: a latent transition model. Child Dev. 2009;80(2):418–432. doi:10.1111/j.1467-8624.2009.01269.x19467001

 PubMed Web of Science ®Google Scholar

Huh J, Riggs NR, Spruijt-Metz D, Chou CP, Huang Z, Pentz M. Identifying patterns of eating and physical activity in children: a latent class analysis of obesity risk. Obesity. 2011;19(3):652–658. doi:10.1038/oby.2010.22820930718

 PubMed Web of Science ®Google Scholar

Kuramoto SJ, Bohnert AS, Latkin CA. Understanding subtypes of inner-city drug users with a latent class approach. Drug Alcohol Depend. 2011;118(23):237–243. doi:10.1016/j.drugalcdep.2011.03.03021530105

 PubMed Web of Science ®Google Scholar

Vasilenko SA, Kugler KC, Butera NM, Lanza ST. Patterns of adolescent sexual behavior predicting young adult sexually transmitted infections: a latent class analysis approach. Arch Sex Behav. 2015;44(3):705–715. doi:10.1007/s10508-014-0258-624449152

 PubMed Web of Science ®Google Scholar

Leroy C, Van Leeuw V, Chihi A, Englert Y, Zhang WH. Clusters analysis: new approach for identifying mother’s profiles with similar characteristics. Revue de médecine périnatale. 2017;1–8.

 Google Scholar

Liao M, Li Y, Kianifard F, Obi E, Arcona S. Cluster analysis and its application to healthcare claims data: a study of end-stage renal disease patients who initiated hemodialysis. BMC Nephrol. 2016;17:25. doi:10.1186/s12882-016-0238-226936756

 PubMed Web of Science ®Google Scholar

Han SY, Liefbroer AC, Elzinga CH. Comparing methods of classifying life courses: sequence analysis and latent class analysis. Longit Life Course Stud. 2017;8(4):319–341. doi:10.14301/llcs.v8i4.409

 Web of Science ®Google Scholar

Martin TF. Advancing dynamic family theories: applying optimal matching analysis to family research. J Fam Theory Rev. 2015;7(4):482–497. doi:10.1111/jftr.12120

 Web of Science ®Google Scholar

Le Meur N, Gao F, Bayat S. Mining care trajectories using health administrative information systems: the use of state sequence analysis to assess disparities in prenatal care consumption. BMC Health Serv Res. 2015;15(1):200. doi:10.1186/s12913-015-0857-525976089

 PubMed Web of Science ®Google Scholar

Haenssgen MJ, Ariana P. Healthcare access: A sequence-sensitive approach. SSM Popul Health. 2017;3:37–47. doi:10.1016/j.ssmph.2016.11.00829349202

 PubMed Web of Science ®Google Scholar

Vanasse A, Courteau J, Courteau M, et al. Healthcare utilization after a first hospitalization for COPD: a new approach of State Sequence Analysis based on the’6W’multidimensional model of care trajectories. BMC Health Serv Res. 2020;20(1):1–15. doi:10.1186/s12913-020-5030-0

 Web of Science ®Google Scholar