Dear Statalist members,

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.
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)
My specific questions to the community are the following:
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