Mixed model repeated measures with missing covariate data

[patrick handcock]

Hi there - quick question on GLMM with repeated measures (crossover) design and how to deal with missing covariate data.

In this context, 28 participants complete 2 conditions (crossover design with 1 week washout between conditions) comparing glucose effect (AUC) of 1) sugary drink vs. 2) water. I am adjusting for several covariates in the model (e.g. BMI, age, fasting values, physical activity before each trial condition).

For the physical activity covariate - I have some for BOTH conditions in 6 participants and PARTIAL missing data in a further 4 participants (i.e. have data for only 1 condition).

I see when I control for prior physical activity as a covariate - my total observations are 22 (suggesting that the participants with fully missing PA data are being dropped).

e.g.

mixed glucoseAUC i.condition glu_baseline age i.sex bmi i.trialorder || id: , mle var
margins i.condition

(PA_leadin covariate with missing data added below)

mixed glucoseAUC i.condition glu_baseline age i.sex bmi i.trialorder PA_leadin || id: , mle var
margins i.condition


QU1: Is there a way to 'deal with this' or keep these participants in somehow to avoid this loss of sample size (imputation?) - or does one just have to concede this as a limitation?

QU2: What is the mixed model actually doing with the participants with partially missing PA data (i.e. only missing for one of the conditions) - as I see these seem to be kept in the model?

Many thanks!

Patrick

[Clyde Schechter]

Let's deal with 2) first, because it's more straightforward. The rules for -mixed- are the same as for any other estimation command. If an observation has missing values on any variable that appears in the regression command (or, not relevant here, in an analysis with weights if the weight is 0 or missing), it is excluded from the estimation sample. Otherwise, it is included. So for the people where you have information on PA in one condition and not the other, the observation for the condition where the information is not missing is included, and the other is excluded. This is actually a nice feature of using mixed models, instead of repeated measures ANOVA. (Repeated measures ANOVA plays by different rules and omits all observations on a person if any of that person's observations have missing data.)

Turning to 1, the answer depends on why the data is missing, how it came to be missing. Broadly speaking, there are three types of missingness: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). These terms do not mean what the ordinary meaning of their words and English syntax would imply, so I recommend that you read Paul Allison's thorough and readable explanation at https://pdfs.semanticscholar.org/58d...c218e126e4.pdf.

If your data are MCAR, you can just proceed with the analysis that includes the PA variable and omits some of the observations. If your data are MAR, your best bet is probably to do multiple imputation. If your date are MNAR, that is the hardest case and, in my opinion, the best approach is to create a variety of scenarios for the missing data and see if you can demonstrate that your findings are robust to reasonable assumptions about missingness.

But clearly the first step is to establish which category your missing data falls into. I can't emphasize enough that there is no statistical test that can be performed on the data itself to answer this question. You have to infer it based on your understanding of the processes that led to the missing responses, and your understanding of the extent to which the complicated condition of MAR might be satisfied with the variables that are at your disposal. I'm sorry I can't be more specific, but this is a very big topic with many possibilities, and only you know how your data came into being.

[patrick handcock]

Thanks so much Clyde - this is perfect!