What is multivariate Cox analysis?
The Cox (proportional hazards or PH) model (Cox, 1972) is the most commonly used multivariate approach for analysing survival time data in medical research. It is a survival analysis regression model, which describes the relation between the event incidence, as expressed by the hazard function and a set of covariates.
How are Cox proportional hazards used in multilevel survival analysis?
First, Cox proportional hazards models with mixed effects incorporate cluster-specific random effects that modify the baseline hazard function. Second, piecewise exponential survival models partition the duration of follow-up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval.
How are time survival models used in multilevel analysis?
Third, after partitioning the duration of follow-up into mutually exclusive intervals, one can use discrete time survival models that use a complementary log–log generalised linear model to model the occurrence of the outcome of interest within each interval. Random effects can be incorporated to account for within-cluster homogeneity in outcomes.
How are random effects incorporated in the Cox model?
When random effects are incorporated in the Cox model, these random effects denote increased or decreased hazard for distinct classes (e.g. clusters such as hospitals, schools or workplaces). Assume that subjects are nested in one of M classes or clusters (e.g. hospitals).
How does a piecewise exponential survival model work?
Second, piecewise exponential survival models partition the duration of follow-up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval. This is equivalent to a Poisson regression model that incorporates the duration of exposure within each interval.