The longitudinal submodel was fitted using mixed effects logistic regression, and the survival submodel was a Cox model adjusted for age, gender, severity of disease (SAPS II, KDIGO grade) and use of life support (norepinephrine, mechanical ventilation and dialysis).
A joint model of longitudinal and survival data consists of two component submodels: the longitudinal submodel and the survival submodel.
The longitudinal submodel allows us to model the trajectory of a repeatedly measured biomarker over time, adjusting for baseline covariates.
For example, we can link the subject specific baseline biomarker values through the intercept association structure, where (5) h i (t ) = h 0 (t ) exp α 2 (β 0 + b 0 i ) + ϕ v i in this expression α2 now estimates the strength of the association between the patient specific baseline biomarker values, as estimated by the longitudinal submodel, and the time-to-event.
For illustration, we let W i (t ij ), the longitudinal submodel, be a linear function of time where the intercept and slope varies between subjects (4) W i (t ij ) = (β 0 + b 0 i ) + (β 1 + b 1 i ) t ij giving a model with a random intercept and random linear slope.
The most commonly used association structures include the current value parameterisation [ 5]; whereby we directly link the value of the biomarker, as estimated by the longitudinal submodel, to survival, and the first derivative or slope [ 10]; allowing the investigation of the effect that the rate of change of the biomarker has on survival.
Longitudinal Section through House, Feb. 25, 1930.
Black squares and red circles indicate the longitudinal cut through the northern and southern chimneys, respectively.
This image represents a longitudinal section through WT and end-stage mSOD1G93A mouse gastrocnemius muscle.
The first are excitatory neurons that mediate cholinergic contraction of circular and longitudinal muscle through muscarinic M2 and M3 receptors.
