[PDF] hrcomprisk: Nonparametric Assessment Between Competing Risks

What is a constant hazard ratio model?

• The model may therefore be called "a constant hazard ratio model", but someone thought that "proportional" is a better word to describe a fixed ratio of two hazards over time. (When the ratio of two quantities is fixed, we may say that one quantity is proportional to the other, say, 1.5 times the other.)

What is the point estimate for the hazard ratio?

• The point estimate for the hazard ratio is where ? ˆis the maximum likelihood estimate of ?. We can construct(1??)100%con?dence intervals for thehazard ratio as ??exp{(X?X)ˆ?±Z1??/2se((Xˆ?X)ˆ?)}. is a semiparametric model makes no assumptions about the form of assumes parametric form for the e?ect of the predictors onthe hazard

How do you calculate proportional hazards?

• (When the ratio of two quantities is fixed, we may say that one quantity is proportional to the other, say, 1.5 times the other.) To get a visual impression of the proportional hazards feature, let's assume that E is a binary (0,1) exposure. Plugging in the value of E, we first derive two log-hazard functions: =log h0(t) + 1 =log h0(t)

Can a predictor satisfy the proportional hazards assumption?

• Predictor may not satisfy proportional hazards assumption,and it may be too complicated to model the hazard ratio forthat predictor as a function of time. Can be used to make graphical checks of the proportionalhazards assumption. We will look at this more later.