How to interpret coefficients from weibull regression for variables of proportion?

Question

I want to fit a weibull regression model. The variables are however given as proportions (i.e. they are in interval <0,1> ... is this compositional data if they do not sum up to 1?). An example would be a proportion of blue balls in the bag or a proportion of patients of a clinic having some health condition.

How can I then interpret the outcome of this regression and is it even OK to fit it as if they were absolute numbers, just with function weibreg for example?

EDIT: To provide more detailed idea about the covariates, I will stick to an easy example with balls and bag. Lets assume we are measuring number of balls of different colours in multiple bags over time. Each bag is measured different number of times, because they came into the study earlier/later. Moreover, each bag has different number of balls in it, some have only under 10, some have more than 1000. Also other variables are measured, such as quality of bag (lets assume this is numeric value, e.g. percentage of cotton ...). Now lets assume that someone punch into each bag every day. Some of them will tear up (=death of bag). I want to model the probability of survival / tearing up , and estimate the effect of colours of balls and other quantities. My first idea was to start by taking only one time point and model time to tear up. In order to have comparable values, I am not using absolute values of numbers of balls of different colours, but rather proportions (3 blue out of 10 are not the same as 3 blue out of 1000). After this simple model I would like to extend my model o longitudinal survival model.

Answer 1

There is no inherent problem in using a proportion as a predictor in a survival model, if that is what your understanding of the subject matter indicates. From your description, it seems that keeping track of the total number of "balls," in addition to the fractions of individual "colors," might help. If you know the number of "balls" of all "colors" then the "color" proportions aren't all linearly independent (that would be compositional data), so you can't use all of them as predictors. In that case, just pick one to ignore. If all you care about is the fraction of a particular "color" like "blue" there is no problem at all. You might need to use some transformation of the numbers and proportions to meet the requirement of linearity in the predictors, but that's the case in all generalized linear models.

That said, I have a few concerns related to your apparent time-varying covariates. The modeling requires that the current covariate values determine the current hazard or acceleration in time of your Weibull survival model. In your example, if having a large number of "balls" over a long period of time makes the "bags" flimsier, then you might need to use some integrated measure of the number of "balls" over time as a covariate, instead of the current number. There is also a risk of survivorship bias, if some covariate takes on values that change systematically with time. In your example, if the proportion of "blue balls" increases with time, it might mean that long survival due to other reasons is really a predictor of the "blue-ball" proportion. If you then used the proportion of "blue balls" as a predictor, you would get into trouble.

Also, in your example "each bag is measured different number of times, because they came into the study earlier/later." So think carefully about the time reference from which survival should be measured. Is the actual study-entry time the correct setting for time = 0 for each "bag"? Or is some earlier time (e.g., the date that the "bag" was "manufactured") more appropriate? In that situation you might need to treat some cases as having left-truncated times (if there are no observations between manufacture date and study entry date). Again, use you knowledge of the subject matter to resolve those issues.