My supervisor suggests that I impute the missing data in my dataset through various methods (namely complete cases, KNN, LOCF and MICE with predictive mean matching) and compare the derived estimates to chose the most appropriate one. Does it make sense to do so if I'm not doing a simulation study for method comparison or is it an overkill? Is it more common to just go for an algorithm with an established performance such as MICE?

(Chances are, he just wants me to practice but I wonder what a common way of doing it is when the focus is on the actual research question)

My supervisor suggests that I impute the missing data in my dataset through various methods (namely complete cases, k-nearest neighbors, last observation carried forward and multiple imputation with predictive mean matching) and compare the derived estimates to choose the most appropriate one. Does it make sense to do so if I'm not doing a simulation study for method comparison or is it an overkill? Is it more common to just go for an algorithm with an established performance such as MICE?

(Chances are, he just wants me to practice but I wonder what a common way of doing it is when the focus is on the actual research question)