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  • Penalized maximum likelihood estimation method to reduce bias in generalized linear models

    Dear Stata Forum Users, do really need your help. Hope you will not regard my question as a stupid one.

    I am reporting results of my randomized study on medication adjustment and faced a challenge to adjust for the baseline values. I got many valueable suggestions here in Forum. I try to summarize some of them below.

    Dataset:

    1) I have 400 patients: 200 control/200 intervention, variables recorded: id (patient study number), r_treat (intervention or control group); nmedicine1 and nmedicine3 (number of medications received at day 3 and day 90), polypharmacy1 and polypharmacy3 - at day 3 and 90 (generated dichotome variables: if 10 and more drugs - polypharmacy==1, if 0-9 drugs polypharmacy==0)

    2) As my study is a randomized controlled study --

    I try to estimate a regression model that has polypharmacy3 as the outcome, and with r_treat and polypharmacy1 as explanatory variables. Is that right? If it is, one option would be to use -logit- to estimate a logistic regression model.

    As my explanatory variables does not vary - they are constants and baseline counts are perfect predictor for outcome - så I get kiicked out of the model - glm-

    3) I used as suggested a different analysis that does not use maximum likelihood estimation. Joseph Coveney's -firthlogit-, available from SSC, can handle this.


    I got challenged by others on the question: why did I chosed this way - were the assumptions behind model met?


    His against arguments were:

    1) This is not nessessary baseline medication I adjust for, but a baseline level or baseline value? -- why not analyze as repeated measurements?

    2) I assume that my baseline medication (polypharmacy) is a fixed value and not as unsure measurements ad the outcome measure --I am not quet sure what does it mean?

    3) I assume that the effect of the intervention is the same in patient with many drugs (polypharmacy) and in the patient with no drugs at baseline ---?

    Here some suggested to introduce a ny variable which include both baseline and follow-up values and a time-variable with 2 levels-this will give intervention between intervention and time amd cluster (id) as an option.


    Does anyone can help with the arguments for -firthlogit- in my case? What are the assumptions behind?

    Thanks alot in advance if any gives a comment. All advices and thoughts are higly appreciated.

    Sincerely, Natallia

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