Contents
How are proportional hazards used in discrete time?
We discuss briefly two extensions of the proportional hazards model to discrete time, starting with a definition of the hazard and survival functions in discrete time and then proceeding to models based on the logit and the complementary log-log transformations.
Why is the hazard ratio a function of time?
Since the hazard is a function of time, the hazard ratio, say, for exposed versus unexposed, is also a function of time; it may be different at different times of follow up. For example, if the exposure is some surgery (vs.
How to calculate the logit of the hazard?
Taking logs, we obtain a model on the logit of the hazard or conditional probability of dying at t j given survival up to that time, where α j = logit λ 0 ( t j) is the logit of the baseline hazard and x i ′ β is the effect of the covariates on the logit of the hazard.
How is the survival function written in discrete time?
However, the general result expressing the hazard as a ratio of the density to the survival function is still valid. A further result of interest in discrete time is that the survival function at time t j can be written in terms of the hazard at all prior times t 1, …, t j − 1 , as (7.18) S j = ( 1 − λ 1) ( 1 − λ 2) … ( 1 − λ j − 1).
Can a logistic regression fit a discrete time model?
In fact, the analogy with logistic regression goes further: we can fit the discrete-time proportional-hazards model by running a logistic regression on a set of pseudo observations generated as follows. Suppose individual i dies or is censored at time point t j ( i) .
Can you use Cox proportional hazards instead of logistic regression?
I am planning to use logistic regression and use the odd ratio to report the relative contribution of each independent variable to the dependent variable. Majority of my independent variables are categorical variables. Could any statistician explain why I should use cox proportional hazards model instead of Logistic regression?
How to fit the proportional hazards model 7.19?
The proportional hazards model 7.19 can then be fit by treating the d i j as independent Bernoulli observations with probability given by the hazard λ i j for individual i at time point t j . More generally, we can group pseudo-observations with identical covariate values.