# Jake's Website

## Testing Proportional Hazards

In a previous post we covered the assumptions of the Cox Proportional Hazards model. The model places very little restriction on the shape of the baseline hazard function or on the linear predictor, however, it does assume that the linear predictor has a constant proportional effect on the hazard function. $$\frac{h(t|x_0)}{h(t|x_1)} = \frac{h_0(t)e^{x_0\beta}} {h_0(t)e^{x_1\beta}} = e^{(x_0 - x_1)\beta}$$ This assumption is definitely non-trivial, and can be prone to fail. An interesting thing to note is that this assumptions can fail even if every member of the population actually meets proportional hazard individually.

## Cox Proportional Hazard

The Cox Proprtional hazard model is perhaps the most common survival model. In a number of ways it has similarities to traditional linear regression. There are two main differences: 1 - We are regressing against hazard rate (probability of dying conditional on being alive) 2 - We use the exponent of xb instead of just xb to ensure the values are always positive. The key concept is of members of the population at risk.

## Cox Proportional Hazard

The Cox Proprtional hazard model is perhaps the most common survival model. In a number of ways it has similarities to traditional linear regression. There are two main differences: 1 - We are regressing against hazard rate (probability of dying conditional on being alive) 2 - We use the exponent of xb instead of just xb to ensure the values are always positive. The key concept is of members of the population at risk.