Recently I got a global longitudinal data from several countries, and each county has one outcome variable and two predictors from 1995 to 2008. I found one of the predictors is always missing in each country in 1995, 1997, 1999, and 2001 because that variable was collected every two years before 2001. This situation seriously affects another complete predictor when using a complete case analysis because too many useful information is lost in that four years. Also, it obviously affects the fitting of a time smoothing function.
I am pretty wondering whether this situation is appropriate to use the multiple imputation method to generate data. As I know, this case is not a missing at random mechanism, so the multiple imputation may not be a perfect way to deal with my case. I am looking for any advice here to find out a solution to deal with those missing data. Any suggestion is appreciated.