Dear all, In a matched case-control study, the outcome is case (0/1), the predictor variable is the continuous substance1. The best model had two fractional polynomials, i.e., substance1 squared (named substance1_2) and substance1 raised to the power of 3 (named substance1_3). I ran PROC LOGISTIC with model case = substance1_2 substance1_3. I managed to calculate the odds ratio for a change in substance1 from 15 to 5 units. In order to calculate the 90% CI, I will need the standard error. How can I calculate the standard error for this OR? I believe that the UNITS or ODDSRATIO statement may be helpful, but I don't know how to do it (https://documentation.sas.com/?docsetId=statug&docsetTarget=statug_logistic_syntax36.htm&docsetVersion=15.1&locale=en). It would be great if someone can help me! * Example (real dataset is much longer);
DATA dataset;
INPUT case matchgroup substance1 substance1_2 substance1_3;
DATALINES;
1 1 2 4 8
0 2 5 25 125
0 3 10 100 1000
1 4 20 400 8000
0 1 15 225 3375
0 2 8 64 512
0 3 3 9 27
0 4 17 289 4913
1 1 12 144 1728
RUN;
title Univariate logistic regression on dataset - substance1_2 substance1_3;
proc logistic data=dataset outest=betas_substance1;
strata matchgroup;
model case(event='1')= substance1_2 substance1_3 / alpha=0.1;
run;
* Intermediate step: Regression coefficients in output betas_substance1 were renamed to beta_substance1_2 and beta_substance1_3
....;
DATA dataset;
SET dataset;
* log odds and odds ratio;
log_odds_substance1 = beta_substance1_2*(15**2-5**2) + beta_substance1_3*(15**3-5**3);
OR_substance1 = exp(log_odds_substance1);
* 90% CI;
Standard_error_substance1 = ????;
LCI_OR_substance1 = exp(log_odds_substance1 - Standard_error_substance1*1.645);
UCI_OR_substance1 = exp(log_odds_substance1 + Standard_error_substance1*1.645);
RUN;
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