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I have a database in which a group of patients was assigned to one of two treatment arms. I have to find out if there is a difference in the evolution of a particular biomarker between these two treatment modalities along the study (3 repeated measurements at 3 different time-points). My first problem is that I have missing values (because some of the patients died, were lost to follow-up...etc). And my second one is that this biomarker has a non-normally distribution. Is it correct to use a generalized linear mixed model to analyse the data? Do I have to make some corrections because of the distribution of the data? Thank you.

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    $\begingroup$ Can you please give more information on what you mean by "non-normally". Do you mean it has outliers? That is only positive? That is discrete? etc. Generally speaking, yes, your intuition is correct. You could use a 'gamma' or a 'inverse-gaussian' family if you have only positive values with some extreme values (see ?family). Depending on your encoding missing values should not be a massive problem for a GLMM as they can be assumed MCAR. Nevertheless if you are doing survival analysis the missing value mechanism should be explored further. $\endgroup$
    – usεr11852
    Commented May 25, 2015 at 23:34
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    $\begingroup$ This biomarker has only positive values, and these values are positively skewed. I can do the GLMM analysis without any other corrections? I must say I am more familiar with SPSS than with R (but if you could describe the exact steps, I think I could do this analysis in R too). Thank you $\endgroup$
    – Dimitrie
    Commented May 31, 2015 at 9:14

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My first problem is that I have missing values (because some of the patients died, were lost to follow-up...etc)

You should consider imputing the missing values using multiple imputation. It is important that you have a good idea about WHY the data are missing. I won't go into detail since this is an old question and there are lots of resources here on CrossValidated for imputation.

my second one is that this biomarker has a non-normally distribution

The distribution of the response is not important. It's the conditional distribution that might - and for that we would inspect the residuals and assess them for normality.

Is it correct to use a generalized linear mixed model to analyse the data? Do I have to make some corrections because of the distribution of the data? Thank you.

If the residuals are plausibly normally distributed then you should be fine with a linear mixed model. However, if they are not, then indeed, an appropriate GLMM would be indicated.

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