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st: Non-zero covariance of orthogonal covariates with 'streg'


From   "Ng, Edmond" <Edmond.Ng@mhra.gsi.gov.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Non-zero covariance of orthogonal covariates with 'streg'
Date   Thu, 17 Jan 2013 15:04:20 +0000

Dear listers,

I am using 'streg' to fit a three-paramter generalized gamma model. I am fitting my model using two orthogonal dummy indicators for the control and treatment (b0 and b1) groups. I was expecting a zero covariance between b0 and b1 (i.e. covariance between [_t]b0 and [_t]b1)  in the resultant variance-covariance matrix but found a non-zero entry instead. Please see output below. 

I am not sure why it is  non-zero. Could anyone shed any light on this please? Many thanks in advance. 

BW, Edmond 
 
*************** OUTPUT EXCERPT ***************

. tab b0 b1, m

           |       tmt
 control   |         0          1 |     Total
-----------+----------------------+----------
         0 |         0     30,798 |    30,798 
         1 |    31,711          0 |    31,711 
-----------+----------------------+----------
     Total |    31,711     30,798 |    62,509 


. streg b0 b1 , distribution(gamma) nocons

         failure _d:  case
   analysis time _t:  dur_yr
Fitting full model:

Iteration 0:   log likelihood = -93650.975  (not concave)
(output omitted) 

Iteration 38:  log likelihood = -15654.639  
Iteration 39:  log likelihood = -15654.639  

Gamma regression -- accelerated failure-time form 

No. of subjects =        62509                     Number of obs   =     62509
No. of failures =         3456
Time at risk    =  207216.3121
                                                   Wald chi2(2)    =    209.00
Log likelihood  =   -15654.639                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          b0 |   3.683094   .2574147    14.31   0.000     3.178571    4.187618
          b1 |   3.716548   .2571747    14.45   0.000     3.212495    4.220601
-------------+----------------------------------------------------------------
     /ln_sig |  -1.035381   1.714809    -0.60   0.546    -4.396346    2.325584
      /kappa |   2.573081   4.412193     0.58   0.560    -6.074658    11.22082
-------------+----------------------------------------------------------------
       sigma |   .3550909   .6089133                      .0123223    10.23265
------------------------------------------------------------------------------


. matrix list e(V)

symmetric e(V)[4,4]
                      _t:         _t:     ln_sig:      kappa:
                      b0          b1       _cons       _cons
       _t:b0   .06626235
       _t:b1   .06575357   .06613882
ln_sig:_cons  -.43555213  -.43556342   2.9405716
 kappa:_cons    1.121996    1.121986  -7.5657866   19.467448


*************** END OF OUTPUT EXCERPT ***************







***********************************************************************
Edmond Ng 
Research Statistician 
Clinical Practice Research Datalink (CPRD), MHRA,
151 Buckingham Palace Road, Victoria, London, SW1W 9SZ, United Kingdom. 
Email:edmond.ng@mhra.gsi.gov.uk
 
CPRD Knowledge Centre 
Email:kc@cprd.com; tel: +44 (0) 20 3080 6383; www.CPRD.com 
***********************************************************************


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