Can I use restricted cubic splines to model non-linear relationships if the underlying variable is not normally distributed? I am estimating the association between an exposure ("time in therapeutic range", possible values from 0% to 100%)) and time to a binary outcome ("chronic kidney disease"). I would like to assess potential non-linear relationships between the exposure and outcome.
The exposure is not normally distributed with many participants having a value of 0% or 100%. Is it still valid to model non-linear associations for this type of variable distribution using restricted cubic splines? I feel like the 0% and 100% participants are exerting outsized influence on the results. Additionally, the 0% and 100% categories don't provide the most clinically relevant information because it is obvious that 0% is bad and 100% is good.
Here are the splines with and without the 0%/100% patients. 4 knots minimized the AIC if 0%/100% participants were included. The relationship between the exposure (time in therapeutic range) and outcome was not non-linear after excluding the 0%/100% participants.
Your help is much appreciated.


 A: In general, the question is whether the spline modeling accurately represents the association of the continuous but range-limited predictor with outcome. Unless there is reason to believe that there is some discontinuity in that relationship associated with the 0% or 100% groups then it doesn't matter.
Note, however, that with restricted cubic splines the association is forced to be linear beyond the outer knots. I suppose that you could devise a model that handles the 0% and 100% groups separately while modeling the intermediate groups continuously. You can already see the difference that would make. For example, with a predictor value of 10%, such separate modeling would predict a value just below 4 per 1000 person-years; continuous modeling including the endpoints would predict a value just above 4. Does that make a substantive difference? Alternatively, you could force the outer knots to be closer to the edges by manually choosing their positions instead of accepting the defaults.
In this specific context, however, I'm more worried about the nature of the predictor: "time in therapeutic range." For a time-to-event study, that sounds like it has a risk of introducing survivorship bias. You don't want your "predictor" of good outcome to be essentially a measure of how long time someone has gone without an event. Think carefully about that possibility, based on your knowledge of the subject matter.
