I am using Stata 15.1 (last updated 15 oct 2018). I am asking for general and specific guidance for estimating multilevel survival models with "mi" (multiple imputation).
I have used "mi impute chained" to impute clinical data from a transplant registry. I would like to then estimate a multilevel survival model. To the best I can understand, "mestreg" does not work with the mi suite based on a prior post from Feb 2016, so I am using a Cox shared frailty model. Below is the output for the following commands.
My specific questions to the community are the following:Code:mi stset ptime_update, failure(death) scale(365.25) mi estimate: stcox i.race_granular $covariates mi estimate: stcox i.race_granular, strata(centre) mi estimate: stcox i.race_granular $covariates, shared(centre) stcox i.race_granular, shared(centre)
1. Can Stata estimate stcox, shared(cluster)with mi as I did below without concern?
2. If yes, can someone explain me how to confirm and evaluate the estimation? The "strata" command works clearly from the output, and the shared estimates look like my non mi estimates, so it seems to be working, but I'd like to have some better confirmation.
3. If no to #1, is there an alternative for a time-to-event model in Stata other than using strata(cluster)?
Many thanks for your guidance.
-Michael
Code:
*** Output for Statalist
. mi stset ptime_update, failure(death) scale(365.25)
failure event: death != 0 & death < .
obs. time interval: (0, ptime_update]
exit on or before: failure
t for analysis: time/365.25
------------------------------------------------------------------------------
21,217 total observations
0 exclusions
------------------------------------------------------------------------------
21,217 observations remaining, representing
8,743 failures in single-record/single-failure data
71,196.252 total analysis time at risk and under observation
at risk from t = 0
earliest observed entry t = 0
mi estimate, cmdok: mestreg i.race_granular || centre:, distribution(exponential) time tratio
command prefix mestreg i.race_granular || centre: not allowed
** covariates only: mi
. mi estimate: stcox i.race_granular $nmiss $miss
Multiple-imputation estimates Imputations = 10
Cox regression: Breslow method for ties Number of obs = 21,216
Average RVI = 0.0035
Largest FMI = 0.0394
DF adjustment: Large sample DF: min = 5,894.53
avg = 1.80e+09
max = 3.70e+10
Model F test: Equal FMI F( 27, 1.9e+07) = 21.34
Within VCE type: OIM Prob > F = 0.0000
---------------------------------------------------------------------------------------
_t | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------+----------------------------------------------------------------
race_granular |
Non-Hispanic Black | .0041659 .0390737 0.11 0.915 -.0724172 .080749
Hispanic | -.1450088 .050287 -2.88 0.004 -.2435694 -.0464481
Other | -.1068894 .0760553 -1.41 0.160 -.2559551 .0421763
|
tx_type_des | .2523575 .0246634 10.23 0.000 .2040182 .3006969
age | .0082351 .0010614 7.76 0.000 .0061548 .0103154
female | -.0854246 .0246798 -3.46 0.001 -.1337961 -.0370531
grouping_des | .0042175 .0098095 0.43 0.667 -.0150087 .0234437
insurance_trr | .0349039 .0104485 3.34 0.001 .0144253 .0553825
recipient_edu | -.0110632 .0082076 -1.35 0.178 -.0271497 .0050234
abo_cat | .0067155 .0077683 0.86 0.387 -.0085101 .0219411
end_match_las | .0010782 .0009063 1.19 0.234 -.0006981 .0028545
age_don | .0032827 .0008307 3.95 0.000 .0016545 .0049109
female_donor | .0530582 .0249816 2.12 0.034 .0040952 .1020212
race_don | .1408148 .0226417 6.22 0.000 .0964379 .1851917
pulm_inf_don | -.0314945 .0219263 -1.44 0.151 -.0744693 .0114803
cod_cad_don | -.000082 .0000711 -1.15 0.248 -.0002213 .0000572
end_creat | .0942102 .0161607 5.83 0.000 .0625358 .1258846
vent | .2152456 .0522129 4.12 0.000 .1129103 .317581
ecmo | .113633 .1279242 0.89 0.374 -.1370939 .3643598
vent_p_ecmo | .1212142 .1574985 0.77 0.442 -.1874772 .4299056
hist_cig_don_num | .1203965 .0341459 3.53 0.000 .0534698 .1873232
hist_oth_drug_don_num | .0597952 .0237674 2.52 0.012 .0132093 .106381
bmi_calc | .0021126 .0026663 0.79 0.428 -.0031132 .0073385
bmi_don_calc | -.0015305 .0021156 -0.72 0.469 -.0056771 .002616
six_min_walk | -.0001698 .0000279 -6.10 0.000 -.0002244 -.0001152
pa | .0011132 .0007483 1.49 0.137 -.0003538 .0025802
po2 | -.0000418 .0000725 -0.58 0.564 -.0001839 .0001002
---------------------------------------------------------------------------------------
*** strata works
. mi estimate: stcox i.race_granular, strata(centre)
Multiple-imputation estimates Imputations = 10
Stratified Cox regr.: Breslow method for ties Number of obs = 21,217
Average RVI = 0.0000
Largest FMI = 0.0000
DF adjustment: Large sample DF: min = .
avg = .
max = .
Model F test: Equal FMI F( 3, .) = 3.67
Within VCE type: OIM Prob > F = 0.0117
-------------------------------------------------------------------------------------
_t | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
race_granular |
Non-Hispanic Black | -.0517968 .0389612 -1.33 0.184 -.1281594 .0245658
Hispanic | -.1552613 .0511899 -3.03 0.002 -.2555916 -.0549309
Other | -.0756223 .0763356 -0.99 0.322 -.2252372 .0739927
-------------------------------------------------------------------------------------
*** trying a mi shared frailty model. It estimates, but no indication that it is multilevel. Estimates are different than covariate only model.
mi estimate: stcox i.race_granular $nmiss $miss, shared(centre)
Multiple-imputation estimates Imputations = 10
Cox regression: Breslow method for ties Number of obs = 21,216
Average RVI = 0.0037
Largest FMI = 0.0400
DF adjustment: Large sample DF: min = 5,709.24
avg = 1.49e+09
max = 3.08e+10
Model F test: Equal FMI F( 27, 1.8e+07) = 19.97
Within VCE type: OIM Prob > F = 0.0000
---------------------------------------------------------------------------------------
_t | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------+----------------------------------------------------------------
race_granular |
Non-Hispanic Black | -.0223719 .0397676 -0.56 0.574 -.1003149 .0555711
Hispanic | -.1831117 .0516951 -3.54 0.000 -.2844321 -.0817912
Other | -.1199062 .0764192 -1.57 0.117 -.2696851 .0298728
tx_type_des | .2595752 .0263676 9.84 0.000 .2078957 .3112546
age | .007673 .0010875 7.06 0.000 .0055416 .0098044
female | -.0880246 .0248277 -3.55 0.000 -.136686 -.0393632
grouping_des | .0065191 .0099099 0.66 0.511 -.0129039 .0259422
insurance_trr | .0368581 .0106699 3.45 0.001 .0159454 .0577708
recipient_edu | -.0020136 .0085693 -0.23 0.814 -.0188091 .0147818
abo_cat | .0050944 .0077766 0.66 0.512 -.0101475 .0203363
end_match_las | .0011873 .0009394 1.26 0.206 -.000654 .0030285
age_don | .0035487 .0008396 4.23 0.000 .0019031 .0051943
female_donor | .0560035 .025171 2.22 0.026 .0066693 .1053377
race_don | .1262233 .0231297 5.46 0.000 .0808898 .1715567
pulm_inf_don | -.0365005 .02236 -1.63 0.103 -.0803252 .0073243
cod_cad_don | -.0000799 .0000712 -1.12 0.262 -.0002194 .0000597
end_creat | .0894781 .0167006 5.36 0.000 .0567456 .1222107
vent | .2415701 .0539368 4.48 0.000 .1358559 .3472844
ecmo | .1160986 .128481 0.90 0.366 -.1357195 .3679167
vent_p_ecmo | .094155 .1582924 0.59 0.552 -.2160923 .4044024
hist_cig_don_num | .1158391 .034369 3.37 0.001 .0484747 .1832036
hist_oth_drug_don_num | .0535818 .0238907 2.24 0.025 .0067546 .1004091
bmi_calc | .0015292 .0026879 0.57 0.569 -.0037389 .0067974
bmi_don_calc | -.0020372 .0021261 -0.96 0.338 -.0062043 .0021299
six_min_walk | -.0001853 .0000314 -5.90 0.000 -.0002468 -.0001238
pa | .0013551 .0007552 1.79 0.073 -.0001255 .0028357
po2 | -7.80e-06 .0000749 -0.10 0.917 -.0001545 .0001389
---------------------------------------------------------------------------------------
** complete case model, which shows center estimation
. stcox i.race_granular, shared(centre)
failure _d: death
analysis time _t: ptime_update/365.25
Fitting comparison Cox model:
Estimating frailty variance:
Iteration 0: log profile likelihood = -79831.26
Iteration 1: log profile likelihood = -79827.878
Iteration 2: log profile likelihood = -79827.866
Iteration 3: log profile likelihood = -79827.866
Fitting final Cox model:
Iteration 0: log likelihood = -79962.988
Iteration 1: log likelihood = -79829.421
Iteration 2: log likelihood = -79827.867
Iteration 3: log likelihood = -79827.866
Refining estimates:
Iteration 0: log likelihood = -79827.866
Cox regression -- Breslow method for ties
Gamma shared frailty Number of obs = 21,217
Group variable: centre Number of groups = 78
Obs per group:
No. of subjects = 21,217 min = 1
No. of failures = 8,743 avg = 272.01282
Time at risk = 71196.25188 max = 1,190
Wald chi2(3) = 9.69
Log likelihood = -79827.866 Prob > chi2 = 0.0214
-------------------------------------------------------------------------------------
_t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
race_granular |
Non-Hispanic Black | .9632818 .0371996 -0.97 0.333 .8930628 1.039022
Hispanic | .8613009 .0436307 -2.95 0.003 .7798944 .9512047
Other | .9370008 .0712056 -0.86 0.392 .8073364 1.08749
--------------------+----------------------------------------------------------------
theta | .0350027 .0087813
-------------------------------------------------------------------------------------
LR test of theta=0: chibar2(01) = 168.80 Prob >= chibar2 = 0.000
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