I am analysing the effect of an intervention to reduce length of hospital stay (LOHS) after surgery. The main outcome is LOHS and the intervention is the main exposure. Death while in hospital is an event competing with discharge from hospital and I am therefore considering using a competing risk regression model (using Stata's stcrreg command) in addition to normal Cox regression. However, there were very few deaths in comparison to participants (~2%). In other regression models I would be concerned that this small group would result in inaccurate estimation of regression coefficients. Considering the small number of deaths is it still appropriate to consider death a competing risk or should I explore the effect of these truncated outcomes through alternative means?
This paper includes the following statement:
Of importance, when ...the competing risk is low, the difference between traditional survival analysis and competing risk approach may not be substantial. Thus, it may not always be necessary to apply a competing risks approach even in the presence of a competing risk. However, when the proportion of subjects experiencing a competing risk is equal or greater to the proportion of subjects experiencing the primary outcome, ...a failure to consider competing risks can lead to biased results.
This suggests that the main consideration is whether results will be biased by not accounting for the competing risk of death. If the bias is expected to be low then it should be appropriate to ignore the competing risk.