I’m trying to figure out multivariate analysis and trying to understand the nuts and bolts underlying it.
Is it always true that the adjusted OR will be lower than the crude OR?
How does one do the actual MV analysis? With a list of univariate OR’s? Or can it only be done with the original dataset?
Which function in R does this?
Thanks so much for any help…
Is it always true that the adjusted OR will be lower than the crude OR?
No. The effect of adjusting depends on which direction the confounder influences the association. If the confounder influences the exposure (E) and the outcome (O) in the same direction, this would increase the strength of the E-O association, and adjusting would attenuate it (remove the confounding). If the confounder influences E and O in opposite directions (e.g. increases the chance of the outcome while lowering the chance of being exposed), the confounder would attenuate the observed E-O association and adjusting would increase your effect size.
How does one do the actual MV analysis? With a list of univariate OR’s? Or can it only be done with the original dataset?
You have to put in the original data, the univariate OR’s are not used for the adjusted analysis.
In R you could add covariates with +. For linear regression, the code would look something like lm(x~y + a + b, data = data), where x is the outcome, y is the predictor and a and b are covariates.
Which function in R does this?
Depending on what type of analysis you want to do, there are many options. For logistic regression, you could check out the glm() function. For linear regression lm() does the trick.
I hope this points you in the right direction!
Helps very much, thank you!
The answer above is right about confounding, as adjusting for a confounder moves the estimate toward or away from the null depending on the direction of confounding, and for a collapsible measure (risk difference, risk ratio) that’s the whole story.
But the OR is noncollapsible, which adds a second shift unrelated to confounding. Even in a confounding-free RCT, the conditional (adjusted) OR is always at least as far from the null as the marginal (unadjusted) OR (|β_marginal| ≤ |β_conditional|) whenever the covariate is associated with the outcome conditional on treatment. This follows from the nonlinearity of the logit link (Jensen’s inequality) and is unidirectional regardless of the effect’s sign.
So an unadjusted-to-adjusted treatment effect estimand change in an observational study combines (a) confounding correction (either direction) and (b) noncollapsibility (always away from the null). They can oppose each other, which is why such a change can’t be read as evidence about confounding in a logistic model.
On a related notes, ordinary unadjusted ORs were designed for the case where there is outcome homogeneity within each exposure group, e.g. when everything is captured in a 2\times 2 table. Similarly, the Pearson \chi^2 test for a contingency table assumes within-group homogeneity, i.e., no risk factors exist except the one displayed in the table. A similar assumption applies to the Kaplan-Meier estimator. Since outcome homogeneity assumptions are never true, crude estimates are seldom applicable.
I am not sure what you mean by second shift. Surely the effect in men+women must be different from the effect in men alone as well as the effect in women alone if gender is prognostic for the outcome. In which case the estimated effect of the intervention can only move away from the null after adjustment for gender - an expected logical result regardless of the nonlinearity of the logit link on the probability scale.
More generally, “the effect in men+women” is an ill-defined concept that does not result in a useful estimate, since ORs were never meant to be applied in such outcome-heterogeneous settings.