Abstract
Time-dependent (TD) covariates have proven to be extremely useful in the Cox model. From a clinical point of view, when assessing the hazard for a subject why not make use of our most up-to-date information? And indeed, models with TD covariates can often have much better loglikelihood. An important complement to hazard ratios, particularly in multi-state models, are the 3 measures of absolute risk (of which the first is most familiar)
- probability in state k at time t
- expexted number of visits to state k
- expected sojourn time in state k
Creating honest estimates of absolute risk, when the model has TD covariates, has been a baffling problem; with mostly bad ideas in the literature. We were motivated to address the issue by analysis of data from the Mayo Clinic Study of Aging and a simple 3 state model of cognitively unimpaired, dementia, and death. The affects of age, sex, amyloid burden (time dependent), APOE e4 genotype, and comorid conditions (time dependent) on both the rates of transition between states and on the absolute rates (lifetime risk of dementia, expected years in dementia) were of key interest. An approach based on classic observed/expected events in epidemiology studies led us to an approach takes explicit advantage of multistate models and seems to work well. Several important theory and technical issues remain open.