Hi everyone,

I read the previous threads on correlation structure for xtgee command, and was not able to find an answer to my question.

https://www.statalist.org/forums/for...-correlation-1


I am mostly a clinician with some training in biostatistics. I have a dataset of patients with several repeated measures of cardiac function (fac). Based on what I know clinically about their disease I expect the cardiac function to deteriorate overtime (a negative change). When I look at the association between time from enrollment and cardiac function (fac) and adjust for baseline variables such as age, gender, and race using default correlation structure in xtgee, I get a clinically meaningful result showing a drop in FAC as time goes by. When I try to adjust for additional confounding variables such as patients genetic composition, history of syncope, etc I get an error saying "estimates diverging (correlation > 1)". I consulted with a biostatistician and changed the correlation structure to independent. The full model runs without error but does not make any clinical sense.

We assume that the observations on a given person are more correlated than those between different persons and that's one of the reasons why we used xtgee.
when is it truly appropriate to use "independent" correlation? is this an appropriate analysis in this setting?


***CARDIAC FUNCTION CHANGE FROM BASELINE***
. sum facpchange

Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
facpchange | 232 -.544104 34.8395 -54.31739 213.3658



****BASIC MODELS****

. xtgee facpchange baselinefac baselineage timefromenrollment gender racecat, vce(robust)

Iteration 1: tolerance = 2.81232
Iteration 2: tolerance = .25599286
Iteration 3: tolerance = .02040117
Iteration 4: tolerance = .00172463
Iteration 5: tolerance = .00014646
Iteration 6: tolerance = .00001244
Iteration 7: tolerance = 1.057e-06
Iteration 8: tolerance = 8.980e-08

GEE population-averaged model Number of obs = 232
Group variable: newid Number of groups = 64
Link: identity Obs per group:
Family: Gaussian min = 1
Correlation: exchangeable avg = 3.6
max = 16
Wald chi2(5) = 21.59
Scale parameter: 855.6729 Prob > chi2 = 0.0006

(Std. Err. adjusted for clustering on newid)
------------------------------------------------------------------------------------
| Robust
facpchange | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
baselinefac | -1.602184 .6847695 -2.34 0.019 -2.944308 -.2600603
baselineage | -.2671689 .2613979 -1.02 0.307 -.7794995 .2451616
timefromenrollment | -.7846865 .3421002 -2.29 0.022 -1.455191 -.1141824
gender | -2.404015 5.010766 -0.48 0.631 -12.22494 7.416906
racecat | -11.40566 8.440595 -1.35 0.177 -27.94892 5.1376
_cons | 79.95015 37.58321 2.13 0.033 6.288417 153.6119
------------------------------------------------------------------------------------



. xtgee facpchange baselinefac baselineage timefromenrollment gender racecat,corr(independent) vce(robust)

Iteration 1: tolerance = 3.782e-14

GEE population-averaged model Number of obs = 232
Group variable: newid Number of groups = 64
Link: identity Obs per group:
Family: Gaussian min = 1
Correlation: independent avg = 3.6
max = 16
Wald chi2(5) = 15.80
Scale parameter: 771.9043 Prob > chi2 = 0.0074

Pearson chi2(232): 179081.79 Deviance = 179081.79
Dispersion (Pearson): 771.9043 Dispersion = 771.9043

(Std. Err. adjusted for clustering on newid)
------------------------------------------------------------------------------------
| Robust
facpchange | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
baselinefac | -2.397221 .8351175 -2.87 0.004 -4.034021 -.7604205
baselineage | -.4212535 .3186779 -1.32 0.186 -1.045851 .2033436
timefromenrollment | .2670995 .4395776 0.61 0.543 -.5944567 1.128656
gender | .9083245 6.08238 0.15 0.881 -11.01292 12.82957
racecat | -1.920435 9.90207 -0.19 0.846 -21.32814 17.48727
_cons | 103.8621 43.79236 2.37 0.018 18.03065 189.6935
------------------------------------------------------------------------------------



***MODELS WITH FURTHER ADJUSTMENT***
. xtgee facpchange baselinefac baselineage timefromenrollment syncscd fhx gender racecat i.gencat bbcat aad
> cat2 trcat , vce(robust)

Iteration 1: tolerance = .93023682
Iteration 2: tolerance = 3.2229013
estimates diverging (correlation > 1)
r(430);


. xtgee facpchange baselinefac baselineage timefromenrollment syncscd fhx gender racecat i.gencat bbcat aad
> cat2 trcat, corr(independent) vce(robust)

Iteration 1: tolerance = 3.940e-14

GEE population-averaged model Number of obs = 223
Group variable: newid Number of groups = 63
Link: identity Obs per group:
Family: Gaussian min = 1
Correlation: independent avg = 3.5
max = 16
Wald chi2(14) = 51.03
Scale parameter: 580.4958 Prob > chi2 = 0.0000

Pearson chi2(223): 129450.56 Deviance = 129450.56
Dispersion (Pearson): 580.4958 Dispersion = 580.4958

(Std. Err. adjusted for clustering on newid)
------------------------------------------------------------------------------------
| Robust
facpchange | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
baselinefac | -3.15892 .7322048 -4.31 0.000 -4.594016 -1.723825
baselineage | -.3453198 .2363296 -1.46 0.144 -.8085174 .1178778
timefromenrollment | .0480247 .370433 0.13 0.897 -.6780107 .7740601
syncscd | -5.437768 6.341163 -0.86 0.391 -17.86622 6.990683
fhx | 4.274889 6.512604 0.66 0.512 -8.489581 17.03936
gender | -4.556462 5.105886 -0.89 0.372 -14.56381 5.450891
racecat | 7.997929 6.919319 1.16 0.248 -5.563687 21.55955
|
gencat |
1 | -5.551725 6.803133 -0.82 0.414 -18.88562 7.78217
2 | 5.892378 8.544308 0.69 0.490 -10.85416 22.63891
3 | -28.07365 9.018601 -3.11 0.002 -45.74978 -10.39752
4 | -1.416394 6.241017 -0.23 0.820 -13.64856 10.81577
|
bbcat | -6.143254 5.617134 -1.09 0.274 -17.15263 4.866125
aadcat2 | -5.09861 5.885905 -0.87 0.386 -16.63477 6.437553
trcat | -30.83395 7.747186 -3.98 0.000 -46.01815 -15.64974
_cons | 188.6057 46.43338 4.06 0.000 97.59791 279.6134
------------------------------------------------------------------------------------

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