Glenn - I think you've almost answered your own question. You wrote
". . . directly modelling the correlation (shared frailty)
should be better than correcting for it in the calculation of standard
errors. . ."
I would preface that by "If the correlation model is correct . ."
In other words, the "correction" approach is general and assumes no
particular model - thus you will be protected over a wide range of possible
correlation models. On the other hand, if you know the shared frailty model
is correct, you would do better using it. It's basically the same tradeoff
of using parameteric vs nonparameteric inference.
Al Feiveson
-----Original Message-----
From: Hoetker, Glenn [mailto:[email protected]]
Sent: Thursday, May 15, 2003 2:51 PM
To: [email protected]
Subject: st: Streg: cluster(patient) vs shared frailty
Hi all.
Stata now offers two approaches to correlation across observations in
survival analysis: clustered (robust) standard errors and shared frailty
models.
Using the example from the STREG entry (pages 222-4 of the V8 survival
analysis manual) I discover that they yield different results (see
below). The magnitude & significance of the FEMALE variable differ
across models. When the lnormal distribution is used, resulting in the
finding of no shared frailty, both models give essentially the same
results.
Can anyone offer theoretical or practical advice on when to favor one
means of dealing with correlation across observations over another? My
intuition is that directly modelling the correlation (shared frailty)
should be better than correcting for it in the calculation of standard
errors, but I have no real basis for that intuition.
Many thanks.
Glenn Hoetker
Assistant Professor of Strategy
College of Business Administration
University of Illinois at Urbana-Champaign
217-265-4081
[email protected]
"Success is going from failure to failure without a loss of enthusiasm."
Sir Winston Churchill
***OUTPUT FOLLOWS***
. use http://www.stata-press.com/data/r8/catheter, clear
(Kidney data, McGilchrist and Aisbett, Biometrics, 1991)
. stset time, fail(infect)
. streg age female, d(weibull) frailty(invgauss) shared(patient) nolog
failure _d: infect
analysis time _t: time
Weibull regression --
log-relative hazard form Number of obs =
76
Inverse-Gaussian shared frailty Number of groups =
38
Group variable: patient
No. of subjects = 76 Obs per group: min =
2
No. of failures = 58 avg =
2
Time at risk = 7424 max =
2
LR chi2(2) =
9.84
Log likelihood = -99.093527 Prob > chi2 =
0.0073
------------------------------------------------------------------------
------
_t | Haz. Ratio Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
age | 1.006918 .013574 0.51 0.609 .9806623
1.033878
female | .2331376 .1046382 -3.24 0.001 .0967322
.5618928
-------------+----------------------------------------------------------
------
/ln_p | .1900625 .1315342 1.44 0.148 -.0677398
.4478649
/ln_the | .0357272 .7745362 0.05 0.963 -1.482336
1.55379
-------------+----------------------------------------------------------
------
p | 1.209325 .1590676 .9345036
1.564967
1/p | .8269074 .1087666 .638991
1.070087
theta | 1.036373 .8027085 .2271066
4.729362
------------------------------------------------------------------------
------
Likelihood-ratio test of theta=0: chibar2(01) = 8.70 Prob>=chibar2 =
0.002
. streg age female, d(weibull) cluster(patient)
failure _d: infect
analysis time _t: time
Weibull regression -- log relative-hazard form
No. of subjects = 76 Number of obs =
76
No. of failures = 58
Time at risk = 7424
Wald chi2(2) =
2.97
Log pseudo-likelihood = -103.44362 Prob > chi2 =
0.2260
(standard errors adjusted for clustering on
patient)
------------------------------------------------------------------------
------
| Robust
_t | Haz. Ratio Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
age | 1.004122 .0088484 0.47 0.641 .9869283
1.021615
female | .4361966 .2249636 -1.61 0.108 .1587393
1.198616
-------------+----------------------------------------------------------
------
/ln_p | -.1028083 .0798087 -1.29 0.198 -.2592305
.053614
-------------+----------------------------------------------------------
------
p | .9023 .0720114 .7716451
1.055077
1/p | 1.108279 .0884503 .9477979
1.295933
------------------------------------------------------------------------
------
Glenn Hoetker
Assistant Professor of Strategy
College of Business Administration
University of Illinois at Urbana-Champaign
217-265-4081
[email protected]
"Success is going from failure to failure without a loss of enthusiasm."
Sir Winston Churchill
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