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Re: st: Goodness of fit using Cox-snell residuals

From (Roberto G. Gutierrez, StataCorp)
Subject   Re: st: Goodness of fit using Cox-snell residuals
Date   Thu, 01 Jun 2006 11:37:30 -0500

Emelda Okiro <> wonders why her residual
analysis after -stcox- is failing:

> This is what my data looks like

[listing of multiple observation per subject data]

> . stset date_visit, id (rsv) failure(lrti) enter(time
> date_origin)origin(time d(31jan2002)) exit(time date_exit) scale(1)

[output omitted]

> . quietly xi: stcox i.currentagegrp sex i.siblings_un6 i.main_fuel
> i.hse_toilet i.babies_bor i.family_children
> i.interaction_un6 i.siblingssch_un6 i.siblingsroom_ov6 i.female_sibs
> poor  i.weaning i.job_desc, nohr mgale(mg)

> . predict cs, csnell

> . stset cs, failure(lrti)

which then signals a PROBABLE ERROR.

When you have multiple observations per subject, you need a residual that
is subject specific, in this case a residual that is summed over the 
observations within the subject.  These are known as cumulative Cox-Snell
residuals, and are obtained by option -ccsnell- to -predict- (note the 
extra c in ccsnell).

Once you get the cumulative Cox-Snell residuals, you can proceed with 
-stset-ting them and so on.  When you -stset- them, you can just ignore the
new PROBABLE ERROR message that you get due to missing values in the 
newly-created variable (cumulative Cox-Snell residuals are only recorded 
in one observation per subject).

To answer Nick's question, you -stset- Cox-Snell residuals so that you can
-sts generate- an estimated cumulative hazard for these residuals.  You see,
under a good-fitting model, the Cox-Snell residuals are distributed as unit
exponential for which the theoretical cumulative hazard is the identity
function, H(t) = t.  As such, if you plot the estimated cumulative hazard of
the Cox-Snell residuals, it _should_ look like a 45-degree line.

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