I have an longitudinal data with measurements of hand grip strength measured in kg by a hand-held dynamometer, using a maximum of three measurements taken with the strongest hand in an old population. Number of missing participants is due to drop-out, death, invalid measure (if there was a difference of 20 kg or more between two measures on one hand) or no measure. Now, I want to explain that my missingness is at random. I need to also mention that I have not done any imputation (multiple imputation, ...) for hand grip strength in my analysis. I read in paper (DOI: 10.1146/annurev.publhealth.21.1.121) that "Missing at random holds if missingness does not depend on the missing values after conditioning on the values observed in the data set". How can I explain this in my case and prove that I have MAR? Also, what are good reasons for not imputing in my case as I did not? thank you for you inputs.
There is no "proof" for MAR. There are statistical tests for the more restrictive "missing completely at random" (MCAR) mechanism but not for MAR (and the utility of the tests is questionable anyway). What is usually done is an analysis of correlates of missing scores by relating other variables in the data set to one or more missing data indicator variables. That way you can find out which variables may be related to dropout.
Since you have age as a variable in your data set (and perhaps other variables related to mortality and other potential dropout reasons), you could include those in your analysis as auxiliary variables to make it more likely that you will at least approximate the MAR condition. It is typically not a good idea to use listwise deletion because that approach is based on the more restrictive MCAR mechanism and often leads to reduced power relative to other methods for handling missing data. It would likely be better for you to use multiple imputation or full information maximum likelihood estimation with missing data and auxiliary variables included. See
Enders, C. K. (2022). Applied missing data analysis. Guilford Publications.