When the Independent Variable is Missing

The within-subject imputation methods just described tend to be more useful when there is a lot of 

If the data are collected at fixed time intervals then one trick to generate imputed values that would account for within-subject correlations is to transform the data into a columnar format with one row of data per subject. So if the data were collected at Visits 2, 3, and 4, then three new variables would be generated. Variable 1 would correspond to Visit 2, Variable 2 to Visit 3, etc. In this manner then each row of data would correspond to a single individual. Now any of the imputation techniques introduced in the chapter on Linear Regression and Modeling could be used to impute the missing data based on the new variables. Once the data are imputed, the data set can be reformatted to multiple rows per subject and the analysis proceeds with the imputed data. This approach assumes that all samples are collected at the same time interval for all subjects, i.e., assumes that all samples were assumed at Visits 1-4 in this case. 

Under this model are four possible outcomes 

0] is the reference value or typical value for a subject with no missing data having x = 0.02 is the proportional multiplier for subjects with no missing data having x = 1 and 03 is the proportional multiplier for any subject with missing data. A similar model was used by Pitsiu et al. (2004) to model apparent oral clearance in an analysis where some subjects did not have creatinine clearance (CLcR) values 

subjects with missing data (MISS = 1) have the model 

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