I'm trying to wrap my head around Cox models as well as how to express them in the form of hazard functions when you have both categorical AND numeric covariates. I need some assistance with this question below.
In a study, the following covariates were collected on a number of subjects.
• z1: Treatment status: 0 if control, 1 if treatment
• z2: Sex: 0 if male, 1 if female
• z3: Age in years
• z4: Height in inches
A Cox proportional hazards model will be constructed to estimate the effect of treatment on the hazard. It is thought that the effect of treatment may be different for men and women. It is further thought that hazard increases with age, but that the effect of treatment does not vary with age. However, the treatment group is slightly older, on the average, than the control group. It is not thought that the hazard function varies with height, but the control group is slightly taller, on average, than the treatment group, and men are somewhat taller, on average, than women.
Express the hazard in terms of the covariates and parameters.
How do you express the hazard in the form below when you have so many different covariates? I know that I need to include the baseline hazard but I'm unsure has to how many beta parameters I need, or what covariates need to be multiplied by those beta parameters.