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# st: Developing a Predictive Risk Equation from stcox survival analysis

 From Tom Robinson To statalist@hsphsun2.harvard.edu Subject st: Developing a Predictive Risk Equation from stcox survival analysis Date Wed, 19 Sep 2012 08:53:45 +1200

```Hi,

I am using stcox to develop a predictive risk model but am unsure about how
to formulate the final equation.  I am using Stata 12.1

I have independent variables that were collected by family physicians as
part of routine care e.g. blood pressure, lipids, renal function,
demographic variables, time since developing diabetes . These come from a
single review and I am using this review date as onset. The outcome is new
onset of end-stage renal failure which is collected from a range of
national datasets (in New Zealand).

I have developed a model using stcox which I'm happy with but need to turn
this into a risk prediction equation for risk at 5 years after which I can
use in a validation dataset. I have centered all the variables around their
mean.

What I have done so far is: (following Tangri N, Stevens LA, Griffith J, et
al. A predictive model for progression of chronic kidney disease to kidney
failure. JAMA. 2011;305(15):1553-1559.appendix)

- use predict *newvar*, xb to calculate each individuals overall hazard
coefficient
- confirmed for myself that this is equivalent to the sum of each
variable multiplied by its coefficient from the model
- confirmed that a dummy individual X with all the independent variables
set at 0 (in other words at the means) has a overall hazard of 0 (*newvar
*)
- used predict *newvar2*, basesurv to calculate the baseline survivals
- set individual X _t to 5 years which is the time period I'm interested
in predicting risk at.  This individuals baseline survival is Y
- Used this survival in the equation gen risk5yr=1-(Y)^exp(*newvar*) to
calculate each persons risk of the event at 5 years

My problem is that the when I run an estat concordance on my model I get a
higher Harrel's C than I do when I run roctab on my outcome and the risks
I have calculated (using the development dataset still).

I have also run a calibration analysis on my calculated risks which is
wildly wrong (the predicted risks in each decile are about half of the
actual risks)

Clearly I'm doing something wrong but I can't see what.  Thanks for any