longitudinal and competing risks data. Stat Med. 2008;27: 6426–6438. 2 Elashoff RM et al. A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics. 2008;64: 762–771. 3 Rizopoulos D. Joint Models for Longitudinal and Time-to-Event Data, with Applications in R. Boca Raton, FL: Chapman & Hall/CRC; 2012. 4 Proust-Lima C et al. Joint modelling of repeated multivariate cognitive measures and competing risks of dementia and death: a latent process and latent class approach. Stat Med. 2015; In press. Only ones with code / software packages available* * at time of writing the manuscript
latent process parameterization &# ! " ' (%) 2 Random effects parameterization &# *" with &' = 1, Cov ." , *" = Σ23 and Var * = 73 8 3a Current value parameterization &# 9" % 3b Time-dependent slopes parameterization &# (')9" % + &# (8) ; ;% 9" % 3c Lagged-effects parameterization &# 9" max{% − @, 0} 3d Cumulative effects parameterization &# C D E 9" F ;F 3e Weighted-cumulative effects parameterization &# C D E G(% − F)9" F ;F 3f Special case of the random effects parameterization (with fixed component) &# H ' ' + ."' 4 Association between sub-models accounted entirely for by latent classes N/A
β3 (1)) βg (2) Y(t) μ(t) X Z(t)Tb T ε ⍺ g (β2 (1), β3 (1)) βg (2) Model 1 Models 3a, c Y(t) μ(t) X Z(t)Tb T ε ⍺ g (1) (β2 (1), β3 (1)) βg (2) Models 3b, d, e ⍺ g (2) Y(t) μ(t) X Z(t)Tb T ε ⍺ g (β2 (1), β3 (1)) βg (2) Model 3f
– wasn’t in an R package • SEs estimated by bootstrap can be slow • Extends the seminal model by Henderson et al. (2000) 2 • Currently only available as C code files – not standard software choice of biostatisticians • Slow to converge • Constraints on latent association structure complicates interpretation 3 • Available as a comprehensive joint model package in R • Very fast • Flexible range of latent association structures • Fits a contrasts model; i.e. estimates ! and " such that # $ $ = # & $ + ! and ($ = (& + ", respectively 4 • Available as a comprehensive joint model package in R • Need to fit multiple models with different number of classes – moderately slow • Need to fit final model from multiple initial values to ensure reached global maximum – slow • Flexible choice of survival models • Can’t quantify the association between two sub-models • Don’t need to worry about correctly specifying form of ) *+ , -