I'm working on a model which has been fitted to longitudinal data (using mixed effects regression). I'm also investigating the effects of about 6 covariates on this model. Covariate A (continuous variable) is quite important in my investigation but the problem I have is that about 50% of these covariates are missing from my population. The question is at what percentage would you consider excluding a covariate completely? I'm a bit concerned that if I include only half of the covariate into my analysis, the result is likely to be unreliable or biased. I hope my question is clear enough but I would be happy to clarify anything. I've read here that $10\%$ is a good cut off. Is this correct?
If you are confident that your data are missing completely at random (MCAR), or even just that the probability of a value's being missing is independent of what its value would have been ("missing at random," technically different from MCAR and a less restrictive requirement), then you should consider multiple imputation.
In this process, several sets of stochastic estimates (imputations) are made of what the missing values might have been, based on the relations within the data you have. You have some ability to determine which inter-variable relations will be used for imputation.
You then perform your analyses on each of these imputed data sets, and combine the analyses among the multiple imputations. This approach includes estimates of error arising from the imputation process, in addition to the errors always inherent in modeling. So the error estimates will include errors due to your missing half of the data on your important continuous covariate.
When the necessary assumptions are met, multiple imputation will perform better than limiting analyses to cases having complete data or relying on some arbitrary cutoff for deciding whether to include a variable at all. The web site linked above has links to tools for performing multiple imputation, including the
mice package in R, and there is a
multiple-imputation tag on this site that you can follow for further discussion.