Table 5 Summary of joint modelling approaches used to incorporate longitudinal data and survival data
From: Modelling of longitudinal data to predict cardiovascular disease risk: a methodological review
Method N(%)[refs] | Longitudinal outcome type | Disease outcome type | How the longitudinal data were used in the analysis N (%) [refs] | Reason for the use of method | Assumptions | Pros | Cons |
|---|---|---|---|---|---|---|---|
Frequentist joint model, N = 6 (75.0) [86, 87, 89, 91,92,93] | Continuous | Time to event | Longitudinal data were modelled in LME. Survival data were modelled in Cox PH. N = 5 (62.5) [86, 87, 91,92,93] Association structures: Current value, N = 2 (25.0) [86, 93] Current value and 1st derivative, N = 2 (25.0) [91, 92] 1st derivative, N = 1 (12.5) [87] | To predict changes in risk score over time using repeated measures | None considered | Includes all measured values of longitudinal variable | Computationally very hard model to fit |
Continuous | Time to event | Structured equation model incorporated in survival model as covariate, N = 1 (12.5) [89] | To incorporate a constant change or variation in the survival model | PH; Change is linear | Incorporates information from all time points | Does not allow for adjustment by other covariates as it cannot calculate overall coefficients | |
Latent class model, N = 1 (12.5) [88] | Continuous | Time to event | Latent class model used to calculate trajectory of longitudinal variable. Trajectory class incorporated in model as covariate, N = 1 (12.5) [88] | To find groups for the trajectories based on the data | PH; Population of trajectories arises from a finite mixture | Very effective at summarizing trajectories | Cannot place patients into trajectory groups easily in clinical practice; Computationally very hard model to fit |
Bayesian approach, N = 1 (12.5) [90] | Ordinal | Time to event | Item response theory models were used to model ordinal data from a multi-question survey using a latent parameter. This latent parameter was modelled using a linear growth model and was incorporated in a multi-state Gompertz survival model as a covariate, N = 1 (12.5) [90] | To model ordinal survey data with the correct distribution | Values constant between observations | Incorporates data from complex survey accounting for ordinal data modelling the data directly rather than modelling the sum of the responses | Complex and requires Bayesian code to be used to define the model |