Correlation coefficient in logistic regression

[Henrik Lauridsen]

Dear Stata experts.

I am trying to calculate the ‘Minimal important change’ in a dataset by reproducing the method outlined in the article:

Terluin B, Eekhout I, Terwee CB, de Vet HC. Minimal important change (MIC) based on a predictive modeling approach was more precise than MIC based on ROC analysis. J Clin Epidemiol. 2015;68(12):1388-96.

The method makes use of a logistic regression model: ln(odds_post) = C + B_X * X
and this was translated into the following Stata command:

glm anc change, family(binomial) link(logit)

The article describes that the correlation r_c-bx (i.e. the correlation between C and B_x) is needed to determine the MIC, however, I am not sure how to obtain this correlation using Stata?

Can anyone help me obtaining this correlation coefficient?

[Richard Williams]

Something like this, maybe?

. webuse nhanes2f, clear

. logit diabetes i.black, nolog

Logistic regression                             Number of obs     =     10,335
                                                LR chi2(1)        =      21.79
                                                Prob > chi2       =     0.0000
Log likelihood =  -1988.172                     Pseudo R2         =     0.0054

------------------------------------------------------------------------------
    diabetes |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     1.black |    .609734   .1231356     4.95   0.000     .3683926    .8510754
       _cons |  -3.063142   .0503436   -60.84   0.000    -3.161814    -2.96447
------------------------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of logit model

             | diabetes           
             |        1.          
        e(V) |    black     _cons 
-------------+--------------------
diabetes     |                    
     1.black |   1.0000           
       _cons |  -0.4088    1.0000

[Henrik Lauridsen]

Dear Richard.

This is exactly what I needed. I thank you for taking the time to help me. I can now proceed to determine the MIC.

Many thanks