**Description of concordant and discordant in SAS PROC LOGISTIC**

Part of the default output from PROC LOGISTIC is a table that has entries including`percent concordant’ and `percent discordant’. To me, this implies the percent that would correctly be assigned, based on the results of the logistic regression. But that is not what it is. It looks at all possible pairs of observations. A pair is concordant if the observation with the larger value of X also has the larger value of Y. A pair is discordant if the observation with the larger value of X has the smaller value of Y; here, X and Y are the predicted value and the actual value.

**Example concordant and discordant**

For our first example from these data, the output looks like this:

Association of Predicted Probabilities and Observed Responses

Percent Concordant | 25.0 | Somers’ D | 0.000 |

Percent Discordant | 25.0 | Gamma | 0.000 |

Percent tied | 50.0 | Tai-A | 0.0000 |

Pairs | 4 | c | 0.500 |

**Evidence of concordant and discordant in PROC LOGISTIC**

It is hard to find documentation of this.

I couldn’t find it explained in the LOGISTIC documentation. I found a mention of `concordant’ and `discordant’ in the FREQ documentation, but it was not clear what X and Y were, until I

searched SAS-L and found an explanation from David Cassell.

**Solution to the problem of concordant and discordant in PROC LOGISTIC**

For what I was thinking of, you need the CTABLE option on the MODEL statement, which gives the proportion correctly classified, the sensitivity, the specificity, and other

measures for each of a number of cutpoints of the predicted probability level. By default, it gives probability levels from 0 to 1 at intervals of .02, but if you just want a few, you can get them:

`proc logistic data = today3; class race sex/param = ref;`

` model disease(event = '1') = race sex/ctable pprob = (.25 .5 .75);`

weight weight;

run;

which yields sensitivity. specificity, false positive and false negative rates at various probability levels.

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This is very useful information. Thanks.

Wow this is a great resource.. I’m enjoying it.. good article

Peter,

i am curious as to how Pairs is calculated. i thought that ‘Pairs’ has to be the sum of first n integers. But that is not the case.

I believe ‘pairs’ is just the total number of comparisons used in concordant and discordant

Found the same issue, reason explained in detail here -

http://opinions5.blogspot.com/2011/09/sas-logistic-regression-shows-all-tied.html