# Adjusted odds ratio question

I have a question about adjusted odds ratios for matched data. Let's assume that we have a binary variable that we want to determine the odds ratios for (let's say smoking or not smoking, this is the exposure variable), and we also want to control for gender and weight. We have previously done matching on the other two variables, so the gender is the same within our strata and the weight is reasonably close (but not matched exactly).

Then we have a model in the form logit(P) = alpha + beta_1 * SMK + beta_2 * GEND + beta_3 * WEIGHT.

My question is, even though there is still some small variance in WEIGHT in our data, is the adjusted odds ratio for smoking status still simply exp(beta_1)?

And just to clarify, does the expression "adjusted for weight" simply mean that we have included the variable weight in our model?

## 1 Answer

Why aren't you using conditional logistic regression? You've gone through the effort of matching, so drop the covariates from the analysis and estimate effects in the matched sets.

If you fit the analysis with logistic regression then the matching doesn't count for anything and you can interpret all the coefficients the same as you would in an unmatched analysis. So yes, exp(beta_1) is the odds ratio for weight, and yes if the other matching variables are also included as covariates you can say it's been "adjusted for".

• Just a heads up: Neil Pearce recently argued that it is a misconception that matched case-control studies must be analyzed using a "matched analysis". I found it quite an interesting read. – COOLSerdash Nov 15 '18 at 15:52
• Thanks for your advice! I am using conditional logistic regression, I just wanted to clarify the basics first. But do i understand it correctly that the difference when using conditional LR is that I would drop the covariates that I matched exactly, but I'd still include WEIGHT in the above example, plus the "dummy" variables that show which stratum the datapoint belongs to? I'm using clogit BTW from the survival package in R, so the dummy variables are added automatically. – Salmon Nov 15 '18 at 19:15
• @Salmon I'm puzzled how you can adjust for sex in a Clogit model which should have no within-cluster variability... – AdamO Nov 15 '18 at 19:40
• No, the Clogit model only includes the continuous covariates that haven't been matched exactly. It is working fine for me, I just want to make sure I understand the theory behind it. So conditional logistic regression uses the same logistic model 1/(1 + e^-z) as logistic regression, where z is a linear combination of the covariates, right? And the difference is that in the conditional case, z only includes covariates with within-cluster variability plus the dummy variables. And the odds ratio of a given covariate is still calculated as exp(coefficient), right? Thanks! – Salmon Nov 15 '18 at 22:06