Joint modeling of longitudinal and survival data
Michael J. Crowther
Department of Health Sciences
University of Leicester
Leicester, UK
[email protected]
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Keith R. Abrams
Department of Health Sciences
University of Leicester
Leicester, UK
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Paul C. Lambert
Department of Health Sciences
University of Leicester
Leicester, UK
and
Department of Medical Epidemiology and Biostatistics
Karolinska Institutet
Stockholm, Sweden
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Abstract. The joint modeling of longitudinal and survival data has received
remarkable attention in the methodological literature over the past decade; however,
the availability of software to implement the methods lags behind. The most
common form of joint model assumes that the association between the survival
and the longitudinal processes is underlined by shared random effects. As a result,
computationally intensive numerical integration techniques such as adaptive
Gauss–Hermite quadrature are required to evaluate the likelihood. We describe a
new user-written command, stjm, that allows the user to jointly model a continuous
longitudinal response and the time to an event of interest. We assume a linear
mixed-effects model for the longitudinal submodel, allowing flexibility through the
use of fixed or random fractional polynomials of time. Four choices are available
for the survival submodel: the exponential, Weibull or Gompertz proportional
hazard models, and the flexible parametric model (stpm2). Flexible parametric
models are fit on the log cumulative-hazard scale, which has direct computational
benefits because it avoids the use of numerical integration to evaluate the cumulative
hazard. We describe the features of stjm through application to a dataset
investigating the effect of serum bilirubin level on time to death from any cause in
312 patients with primary biliary cirrhosis.
View all articles by these authors:
Michael J. Crowther, Keith R. Abrams, Paul C. Lambert
View all articles with these keywords:
stjm, stjmgraph, stjm postestimation, joint modeling, mixed effects, survival analysis, longitudinal data, adaptive Gauss–Hermite quadrature
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