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I have a run a linear mixed effects model in R to model clinical data. However, this model is heteroscedastic (as there excess zeros in the response variable).

I have tried transforming the data (log transform) and (sqrt). Still, neither transformation resolves the issue (see residual versus fitted value plot). I have not used Cox proportional hazards model as the data is not time-to-event data, the data measures force and there are a large number of observations have a reading of zero. I cannot exclude these readings as they are valid.

I have found an R package that runs Tobit regression (AER). Nevertheless, this will not accommodate the random effects in the model. I cannot find any R packages that run Weibull mixed effects models (or gamma mixed effects models)...

Does anyone know if there is a package to run these type of models? (or can they suggest any alternative approach).

Many thanks

Etn

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Regarding an alternative approach, would a zero-inflated model work? A zero-inflated model will account for the fact that there are excess zeros in your model. The punch line is that there are two processes at work: one that generates zeros and one that generates the remainder of your data.

This is a contrived (and sort of silly) example, but say you are examining the rates of ovarian cancer and collect a random sample of 1,000 people where 500 of these people are male. Of course males cannot have ovarian cancer, so a response $Y_{cancer}$ will always equal 0 for men. This will bias any sort of estimates due to the overwhelming number of zeros and will render your model less meaningful and less accurate for the question you likely seek to answer.

You want to be careful, however. You want to make sure that there is a pragmatic reason for including the zero-inflated piece. If the data generating process genuinely produces a large number of zeros, then a zero-inflated model is inappropriate. If there are ostensibly two processes at work such that one process will generate the majority of the zeros, then a ZIN model may address your concerns. Having a bit more background on the clinical trial and the question you seek to answer might help to clarify whether or not a ZIN model is appropriate.

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    $\begingroup$ @ Matt, many thanks or your response - the clinical data: patients force is recorded using a machine, this force reading is recorded 5 times for each patient at each time point (4 different visiting times). Sometimes the machine has a reading of zero (for all 5 reps) and other times it has a zero reading for e.g. 1st rep, 3rd rep. If there is a full zero reading (for all 5 reps) this is due to the patient having no force (true reading). If there is zero reading (for some of the 5 reps) then this could be due to the patient not pushing hard enough for that reading and the machine recorded zero. $\endgroup$
    – Etn
    Commented Oct 23, 2015 at 11:19

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