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I was hoping for some assistance regarding performing a multi-variable logistic regression for a matched data set. I am not formally trained as a statistician (biology trained with basic stats/SPSS training), so am struggling a little bit.

I have a data set with ~300 propensity score matched pairs. I am interested in outcome "X", and seeing if any of my variables were independent predictors of outcome X.

In the unmatched data set (prior to propensity matching) I performed a multivariable logistic regression, and was interested in doing the same for my matched model. I am currently using SPSS for my data analysis.

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  • $\begingroup$ You just need to run a mixed model using subject ID as fixed effect and logit link... $\endgroup$
    – Giuseppe Biondi-Zoccai
    Commented Feb 12, 2020 at 13:42
  • $\begingroup$ Do you have time-to-outcome data, or just yes/no for outcome? What are you trying to accomplish with the propensity matching? Often you lose information by throwing away cases. What did you match on? $\endgroup$
    – EdM
    Commented Feb 12, 2020 at 16:58
  • $\begingroup$ Outcome X is yes/no. I used propensity matching as I am trying to compare two similar (but quite different) technical methods that can be performed to fix for a certain problem. Propensity matching was used to try and account (as much as possible) for any bias that may be present in choosing one method over another $\endgroup$
    – sunny_aus
    Commented Feb 13, 2020 at 13:09
  • $\begingroup$ @Joe_74 conditional logistic regression is better. Using subjid as a fixed effect do you mean random effect? $\endgroup$
    – AdamO
    Commented Feb 14, 2020 at 18:50
  • $\begingroup$ @sunny_aus the point of propensity matching is reducing the influence of confounders and precision variables. Are you proposing to continue to adjust for those effects even though they have an expected odds ratio of association of 1? $\endgroup$
    – AdamO
    Commented Feb 14, 2020 at 18:51

2 Answers 2

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Although you could use a common ID for each matched pair, as suggested in a comment on the question, I would recommend that you use (inverse) propensity-score weighting rather than propensity-score matching to deal any bias resulting from how the method was chosen in each case.

When you match you are necessarily throwing away all the information included in the discarded cases and decreasing the number of degrees of freedom for your ultimate statistical tests. If your original logistic multiple regression model was well specified, close to the "true" model, then you wouldn't need to correct at all. The propensity adjustment provides an additional control in case your model wasn't actually well specified.

You can correct for the bias that you fear by including all cases but weighting each case inversely to its propensity score. Also, for generating the propensity score, it can be best to use a rich modeling approach that allows for nonlinearities and for interactions among covariates, like gradient boosting, as provided by the twang package in R. (I don't know what the equivalent is in SPSS.) That can provide superior performance to, say, determining propensity scores via a logistic regression without interactions. The threads listed as "Related" on this page and links from them provide further guidance. I've found answers from @Noah particularly helpful on issues regarding propensity scores.

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Propensity matching is designed to reduce the influence of variables you would normally adjust for. Propensity matching will "balance" variables exactly that were used for matching. Propensity matching will also approximately "balance" variables that were not matched for depending on how well they're predicted by the matching. Basically, there should be very little reason to perform further adjustment...

Regardless, conditional logistic regression is a standard way of analyzing such data. Input the matched pair ID as a cluster variable and calculate the conditional OR of association for the appropriate exposure.

You can further adjust for covariates if there's residual confounding to account for, but the tendency of the conditional logistic regression to behave erratically in finely stratified data is more nefarious than in standard logistic regression.

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