IIs there a significant difference between these curves?

What is aCox model?What is aCox model?

WWhat is a Cox Model?

Stephen J. Walters.What is a Cox Model? Hayward Medical Communications 2009.

GFirst, determine the survival curves!

((Quick review of the Kaplan-Meier Method for

survival analysis)

Consider 10 subjects being treated for a fatal disease….

The Cox Model - also known as the proportional hazards regression analysis

proportional: the ratio between the treatment group and control group

hazard: instantaneous risk of an event

regression: an iterative process whereby the effects of selected explanatory factors are adjusted to create a model (equation) which fits the empiric survival curve

The “Hazard” function h(t) where t represents time

Mathematically, the hazard function is estimated by:

h(t) = h0(t)exp(ẞ1x1 +…..+

ẞkxk)

where X = 0 for control groupX = 1 for intervention group

h(t) = h0(t)exp(ẞ1x1 +…..+ ẞkxk) h(t) = h0(t)exp(ẞX)

h0 = risk of event for control group at time t

Which when we take the natural log of both sides we get:

= ẞX

Now just try different values of ẞ until the function best approximates the actual survival data.

Now we just plug in our value of ẞ with X = 0 then X = 1 to solve for the ratio between the hazard of dying for the intervention group divided by the hazard of dying for the control group

Nota Bene!!

There is no time-dependent term on the right-hand side of the equation, thus the ratio is independent of time, hence constant throughout the length of the survival curve.

Remember what this was all about? Recall our study and the survival curve:

The median survival timewas lower in the intensive-control group than inthe conventional-control group (hazard ratio, 1.11;95% CI, 1.01 to 1.23; P = 0.03)

Having an equation for the hazard ratio we can thus derive P values for the results!