# st: Streg: cluster(patient) vs shared frailty

 From "Hoetker, Glenn" To Subject st: Streg: cluster(patient) vs shared frailty Date Thu, 15 May 2003 14:51:18 -0500

```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
University of Illinois at Urbana-Champaign
217-265-4081
ghoetker@uiuc.edu
"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
University of Illinois at Urbana-Champaign
217-265-4081
ghoetker@uiuc.edu
"Success is going from failure to failure without a loss of enthusiasm."
Sir Winston Churchill

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```