Interpretation of results of a paired analysis

[Bree Shi]

Hello Everyone,

I am doing a paired kidney analysis to look at the effect of obesity on post-transplant outcomes (e.g. death). The pairs were transplant pairs where one kidney was allocated to an obese recipient and the other to a non-obese recipient.
For the main analyisis, I used a stratified Cox model, with each pair as a stratum.
Now I am doing a dose response analysis to look at whether more severely obesed patients had a greater risk of death.
So I categorised patient cohort from "not obese VS obese" to "not obese VS obese class I or VS obese class II and III". The pairs remain the same as main analyisis, just with one more category.

My questions are:
1. From the lincom command, there is not enough evidence to conclude that obese II and III patients have a greater risk of death compared to obese class I. However, as the pair was not obese VS obese, I'm not sure if it is correct to interpret obese I VS obese II and III using lincom.

2. When comparing class I to not obese, HR=1.28, CI 1.07-1.66, p=0.008; When comparing class II and III to not obese, HR=1.42, CI 0.95-2.11, p=0.087. I think it is incorrect to say that there's an increased risk of death for obese II and III just because the point estimates are higher as the CIs are overlappping. How should I interpret it correctly?

Many thanks for any thoughts on this. Appreciate any help in advance.

Best Regards,
Bree


Below are the output.

 stcox i.obese_cat i.agecat_tx   i.durationcat   i.hlam  i.cv  i.diabetes i.gfstatus , strata(groupid) hr nolog vce(robust) baselevels

         failure _d:  death
   analysis time _t:  (enddate-origin)/365.25
             origin:  time transplantdate
                 id:  id

Stratified Cox regr. -- no ties

No. of subjects      =        3,038             Number of obs    =     836,725
No. of failures      =          601
Time at risk         =  19741.05681
                                                Wald chi2(13)    =      145.49
Log pseudolikelihood =   -255.51969             Prob > chi2      =      0.0000

                                      (Std. Err. adjusted for 3,038 clusters in id)
-----------------------------------------------------------------------------------
                  |               Robust
               _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
        obese_cat |
       Not obese  |          1  (base)
         Obese I  |   1.284755   .1213985     2.65   0.008     1.067552     1.54615
Obese II and III  |   1.417494    .289101     1.71   0.087     .9504223      2.1141
                  |
        agecat_tx |
           18-34  |          1  (base)
           35-49  |    3.26754    .914541     4.23   0.000     1.887908    5.655369
           50-65  |   5.446535   1.598246     5.78   0.000     3.064372    9.680532
             65+  |   8.810133   2.826903     6.78   0.000     4.697403    16.52369
                  |
      durationcat |
           0-1yr  |          1  (base)
           1-3yr  |   1.533406   .3224166     2.03   0.042     1.015505    2.315433
            3yr+  |   2.151468    .455557     3.62   0.000     1.420691    3.258145
                  |
             hlam |
               0  |          1  (base)
             1-2  |   1.148471    .502754     0.32   0.752     .4869658    2.708579
             3-4  |   .8541231   .3995813    -0.34   0.736     .3414333    2.136658
             5-6  |   .5942201   .2849043    -1.09   0.278     .2321833    1.520771
                  |
               cv |
   No or missing  |          1  (base)
Yes or suspected  |   2.161482   .3009532     5.54   0.000     1.645261    2.839673
                  |
         diabetes |
   No or missing  |          1  (base)
             Yes  |   1.863112   .2779249     4.17   0.000     1.390795    2.495829
                  |
         gfstatus |
               0  |          1  (base)
               1  |   2.990554   .5347461     6.13   0.000     2.106429     4.24577
-----------------------------------------------------------------------------------
                                                         Stratified by groupid



testparm i.obese_cat

 ( 1)  1.obese_cat = 0
 ( 2)  2.obese_cat = 0

           chi2(  2) =    9.87
         Prob > chi2 =    0.0072



 lincom 2.obese_cat-1.obese_cat

 ( 1)  - 1.obese_cat + 2.obese_cat = 0

------------------------------------------------------------------------------
          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .0983221   .2238869     0.44   0.661    -.3404881    .5371324
------------------------------------------------------------------------------

[Clyde Schechter]

I'm assuming that the variable obese_cat is coded 0 = not obese, 1 = class I obese, 2 = class 2 or 3 obese.

The fact that the confidence intervals for the hazard ratios for Obese I and Obese II and III do not overlap actually doesn't really shed much light on your question. It is the relative hazard ratio, Obese II and III vs Obese I that matters. That information will actually be found at the very end of the output you show:

lincom 2.obese_cat-1.obese_cat

 ( 1)  - 1.obese_cat + 2.obese_cat = 0

------------------------------------------------------------------------------
          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .0983221   .2238869     0.44   0.661    -.3404881    .5371324
------------------------------------------------------------------------------

This result, 0.0983221 is the log of the hazard ratio for obese II and III vs Obese 1. If you exponentiate it you will get the hazard ratio. Actually, rather than doing that by hand, just re-run the lincom command adding the -hr- ratio and Stata will give you the result in the hazard ratio metric. From that you will see that the confidence interval (which is roughly from 0.71 to 1.71) for this includes 1, so you can conclude that your data are consistent with the hazard ratio for Obese II and III being either greater than, equal to, or less than that for Obese I. Your data do not pin down the directionality of whatever the difference may be.

[Bree Shi]

Thank you Clyde for the quick reply.

I have another question that I hope you can answer.
For this paired analysis, I used Conditional Poisson regression to compare count data, using Ramsey Regression Equation Specification Error Test (RESET) to check model fit.
I used stratified Cox model to compare time to event data, using Cox-Snell residuals to check model fit.
Are those two goodness-of-fit tests suitable for the paired analyisis?

Many Thanks!
Bree

[Clyde Schechter]

I don't know. Perhaps somebody else will respond. If you don't get a response in a reasonable amount of time, repost this question as a New Topic with a title that describes this question well.