interpreting logistic regression

[GS2]

Hello,

I ran the following code for a logistic regression

proc logisitic data = mlc.comps;
class assoc_head;
model postop_comp (event = 'Yes') = assoc_head / rsquare;
run;

This produced the following output:

The SAS System

The LOGISTIC Procedure

Model Information
Data Set	MLC.COMPS
Response Variable	postop_comp	Post-operative Complications?
Number of Response Levels	2
Model	binary logit
Optimization Technique	Fisher's scoring

Number of Observations Read	301
Number of Observations Used	301

Response Profile
Ordered Value	postop_comp	Total Frequency
1	No	211
2	Yes	90

Probability modeled is postop_comp='Yes'.

Class Level Information
Class	Value	Design Variables
assoc_head	No	1
	Yes	-1

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion	Intercept Only	Intercept and Covariates
AIC	369.231	365.240
SC	372.938	372.655
-2 Log L	367.231	361.240

R-Square	0.0197	Max-rescaled R-Square	0.0280

Testing Global Null Hypothesis: BETA=0
Test	Chi-Square	DF	Pr > ChiSq
Likelihood Ratio	5.9901	1	0.0144
Score	4.9036	1	0.0268
Wald	4.1188	1	0.0424

Type 3 Analysis of Effects
Effect	DF	Wald Chi-Square	Pr > ChiSq
assoc_head	1	4.1188	0.0424

Analysis of Maximum Likelihood Estimates
Parameter		DF	Estimate	Standard Error	Wald Chi-Square	Pr > ChiSq
Intercept		1	-1.5388	0.3764	16.7158	<.0001
assoc_head	No	1	0.7638	0.3764	4.1188	0.0424

Odds Ratio Estimates
Effect	Point Estimate	95% Wald Confidence Limits
assoc_head No vs Yes	4.607	1.054	20.145

Association of Predicted Probabilities and Observed Responses
Percent Concordant	9.3	Somers' D	0.073
Percent Discordant	2.0	Gamma	0.643
Percent Tied	88.7	Tau-a	0.031
Pairs	18990	c	0.536

My question is if this model is acceptable? Given the small R2 and 0.5 C statistic it doesn't look good. Is there I do anything about it given I am looking at 2 variables? Thank you

[PaigeMiller]

You should plot the results and see what they show.

C close to 0.5 isn't good.

[StatDave · Accepted solution]

Your data is just a 2x2 table. No real need for a modeling procedure. You could just use the CHISQ option in PROC FREQ  to compare the two probabilities. If you want a model that does a good job predicting the response, you would need to have more predictors in the model.

[GS2]

We were looking to put an OR with each. That was the reason for modeling but your point is taken that I could get that from the proc freq procedure.