Predictive comparison of joint longitudinal-survival modeling: a case study illustrating competing approaches

Abstract

The joint modeling of longitudinal and survival data has received extraordinary attention in the statistics literature recently, with models and methods becoming increasingly more complex. Most of these approaches pair a proportional hazards survival with longitudinal trajectory modeling through parametric or nonparametric specifications. In this paper we closely examine one data set previously analyzed using a two parameter parametric model for Mediterranean fruit fly (medfly) egg-laying trajectories paired with accelerated failure time and proportional hazards survival models. We consider parametric and nonparametric versions of these two models, as well as a proportional odds rate model paired with a wide variety of longitudinal trajectory assumptions reflecting the types of analyses seen in the literature. In addition to developing novel nonparametric Bayesian methods for joint models, we emphasize the importance of model selection from among joint and non joint models. The default in the literature is to omit at the outset non joint models from consideration. For the medfly data, a predictive diagnostic criterion suggests that both the choice of survival model and longitudinal assumptions can grossly affect model adequacy and prediction. Specifically for these data, the simple joint model used in by Tseng et al. (Biometrika 92:587-603, 2005) and models with much more flexibility in their longitudinal components are predictively outperformed by simpler analyses. This case study underscores the need for data analysts to compare on the basis of predictive performance different joint models and to include non joint models in the pool of candidates under consideration.

How many longitudinal covariate measurements are needed for risk prediction?

“…Bias is a less serious concern in risk prediction because the calibration of the model can be checked, and if necessary, the model can be recalibrated. There are also cases where timedependent Cox models are appropriate [21]. Furthermore, although some specialized methods have been proposed for joint modeling with multiple longitudinal covariates, including conditional score estimator [22], latent class approach [23], and Bayesian methods [24,25], the computational methods and software for multivariate joint modeling are not fully developed.…”

Survival Analysis

“…Bayesian nonparametric approaches for the PO model have been based on Bernstein polynomials (Banerjee and Dey 2005), B-splines (Wang and Dunson 2011), and Polya trees (Hanson 2006a;Hanson and Yang 2007;Zhao et al 2009;Hanson et al 2011).…”

“…An important aspect associated with the BNP formulation of these models is that, by assuming the same, flexible model for the baseline survival function, they can be placed on a common ground (Hanson 2006a;Hanson and Yang 2007;Zhang and Davidian 2008;Zhao et al 2009;Hanson et al 2011). Compare Fig.…”

“…Hanson (2006a), Hanson and Yang (2007), Zhao et al (2009) and Hanson et al (2011) considered several variations of PT-based BNP models for survival regression. Of these models, the PO model was chosen over the PH and AFT models on the basis of the LPML criterion (Geisser and Eddy 1979).…”

Multilevel Bayesian Models for Survival Times and Longitudinal Patient-Reported Outcomes With Many Zeros

“…Examples of non-clinical settings in which joint modeling is useful include degradation measurements paired with time-to-failure data in reliability (Lu and Meeker 1993), and fruit fly reproductive fertility and lifespan measurements in fecundity studies (Hanson et al 2011). …”