Exponential of beta values for Multiple Imputation

[Chris Greenwood]

Hi all,

I am wanting to explore an additive interaction using some MI data.

To do this I have been using "mi est, eform(or) saving(savedata):" then "mi est (equation) using(savedata)".

The beta value stored from the the logistic regression is 0.3672391 and the OR value displayed in the output (using eform(or)) is 1.443743.
As a first check, when I run -- "mi est (eq1: _b[variable]) using savedata" -- I get the correct beta value returned.

However when I exponentiate this value within the "mi est" command, expecting to get the OR, I get a slightly different value from what is returned in the logistic regression output -- "mi est (eq1: exp(_b[variable])) using savedata" -- returns 1.450754 (output and correct exponential = 1.443743).


Am I doing something wrong here?
Is there a way I can view the "savedata"?

Any help with this would be very much appreciated.

Thanks,
Chris

[daniel klein]

The eform() option just displays the estimated coefficient in exponentiated form, it does not change the underlying estimation, i.e. exp(0.3672391) = 1.443743.

mi est (eq1: exp(_b[variable])) using savedata

gives you the average of M exponentiated coefficients, not the exponentiated average of M coefficients as mi does. The latter is the more appropriate as combining coefficients (or point estimates, in general) requires these quantities to be (approximately) normal. This is true for regression coefficients but probably not for odds ratios, given their truncation at 0.

To view the savedata look at estimates use and its number() option. Results from the individual models are stored in numbers 1, 2, ..., M. The combined estimates are saved in number M+1.

Best
Daniel

[Chris Greenwood]

Thanks Daniel for your quick responses to both my questions!

Do you know if there is a command or way in which I can work with the "exponentiated average of M coefficients" as opposed to the "average of M exponentiated coefficients" (as you have distinguished)? I am wanting to use this approach not simply to calculate an OR, but to obtain the associated p value.

Thanks again,
Chris

[daniel klein]

I do not fully understand the question. mi is giving you what you want and so is your first approach that replicates the correct point estimate. The p-values are there, too. What exactly is the problem you are facing?

Best
Daniel

[Chris Greenwood]

Sorry about my poor explanation.

Here is what I am trying to do in more detail.

I am trying to calculate the "relative excess risk due to interaction" in a logistic regression. My outcome is binary and I have 4 level predictor.
The predictor is a combined variable of A and B
0: A & B
1: A & not B
2: Not A & B
3: Not A & Not B

I am trying to see if (3) has excess risk, than level (2) and (1).

My regression syntax is:
mi est, eform(or) saving(savedata) : logistic outcome i.variable

The equation to calculate the excess risk due to interaction is this:
mi est (eq1: exp(_b[3.variable])-exp(_b[1.variable])-exp(_b[2.variable])+1) using savedata

This works for non-imputed data and gives an accurate OR and p value.

I hope this helps to explain my situation.
Thanks again!
Chris

[daniel klein]

Sorry, I have never dealt with excess risks. If nobody else has a better idea, you might want to stick to your current approach, despite the fact that what is described by eq1 might not be best suited for combination via Rubin's rules.

Best
Daniel

[Chris Greenwood]

Thanks again for all your help! Very much appreciated.

Chris