*****************************************************************************************
* Linear Mixed Models with Multiple Imputation for Repeated Measures Trials\cb1.        *
*****************************************************************************************
*** STEP 1: Prepare data in "long-format"
*** STEP 2: Set data structure for multiple imputation
mi set mlong
*** STEP 3: Reshape data from long to wide format
* Assumes outcome is the repeated measure (e.g., VAS, ODI, ROM)
mi reshape wide outcome, i(id) j(time)
*** STEP 4: Register variables for imputation
* All relevant variables (with or without missing)should be registered
mi register imputed ///
    outcome0 outcome1 outcome2 /// repeated outcomes
    Group arm gender /// grouping variables
    Height Weight BMI /// anthropometric variables
    Sex Dominant Smoking /// demographic/lifestyle
    Occupation Education Duration3 /// socioeconomic/clinical
*** STEP 5: Impute missing values using chained equations
mi impute chained ///
    (logit) Group Sex Smoking Dominant ///
    (ologit) Occupation Education ///
    (regress) outcome1 outcome2 Height Weight BMI Duration ///
    = outcome0, add(10) rseed(1234)
*** STEP 6: Reshape data back to long format before executing mixed model
mi reshape long outcome, i(id) j(time)
*** STEP 7: Fit Linear Mixed Model with Random Effects
mi estimate: xtreg outcome i.arm##i.time i.gender, i(id) re
* Note: Post-estimation commands are not supported after `mi estimate`
* Thus, analysis continues with manually separated datasets
*** STEP 8: Exit MI environment and save each combined dataset
mi unset
* Repeat for each imputed dataset (m = 1 to 10)
* Example for m=1:
keep if mi_m == 0 | mi_m == 1
drop if mi_miss == 1
save dataset_0_1, replace
*** STEP 9: In each dataset, run LMM and post-estimations
xtset id time
xtreg outcome i.arm##i.time i.gender, re
* Estimate marginal means and contrasts (main outcomes)
contrast arm@time, effects
* Adjust for multiple comparisons using Bonferroni
contrast arm@time, effects mcomp(bon)
*** STEP 10: Pool marginal differences (MD) and standard errors (SE)
* Use Rubin's Rules (1987) via Excel or meta-analysis script
* Input 10 MDs and 10 SEs to compute pooled effect size
**************************************************************************
*                       END of Analysis Protocol                         *
**************************************************************************