/*______________________________________________________________________________ PAPER: "PRACTICAL STRATEGIES FOR HANDLING NUMERICAL DIFFICULTIES WITH MULTIPLE IMPUTATION ALGORITHMS" Authors: C. Nguyen, J. Carlin, K. Lee This file provides Stata code for analyses of data from the Longitudinal Study of Australian Children (LSAC) Nb. The dataset "LSAC_Kcohort.dta" cannot be provided by authors, but access to LSAC data can be requested at https://dataverse.ada.edu.au/dataverse/ncld // THE ANALYSIS MODEL USES THE FOLLOWING VARIABLES: EXPOSURE: bmiz: BMI z-score (exposure variable) COVARIATES: male: gender (0=female, 1=male) age: child's age (months) indig: child's indigenous status (0=no, 1=yes) sdq: child mental health (SDQ total score, range 0-35) mat_edu: mother completed high school (0=no, 1=yes) mat_lang: Mother's main language (0=English, 1=not English) mat_k6: Mother's emotional distress (Kessler-6 score, range 0-24) mat_work: mother's work status (0=not working, 1=working) seifa: neighbourhood disadvantage (Socio-Economic Indexes for Areas, mean~1000, SD~100) OUTCOME VARIABLE: hrqol_w3_1 to hrqol_w3_23: 23 items from PedsQL (Health related quality of life [HRQol]) scale measured at wave 3 (range from 1 to 5) hrqol_w3_bin: Binary HRQoL outcome variable measured at wave 3 (derived from the 23-item PedsQL scale) (0=no problems, 1=HRQoL problems). Nb. In order to derive the binary outcome, the individual items are reverse scored ( 1=100, 2=75, 3=50, 4=25, 5=0) and averaged to produce a total score (range 0-100), which is dichotomised (at 1 standard deviation above the population mean) to produce a binary variable // THE IMPUTATION MODEL INCLUDES: - All variables in the analysis model - The auxiliary variable is HRQoL measured at wave 1, included either as individual items (hrqol_w1_1 to hrqol_w1_21) or as a binary variable at the total score level (hrqol_w1_bin) _______________________________________________________________________________*/ capture log close version 15 set more off log using "an_impute.log", replace *_______________________________________________________________________________ * DEFINING MACROS * Optional - using macros as a convenient way to refer to items in the HRQoL scales * Define global macro "hrqol_items_w3" representing all of the HRQoL items at wave 3 (i.e. items that make up the outcome variable) global hrqol_items_w3 hrqol_w3_1 hrqol_w3_2 hrqol_w3_3 hrqol_w3_4 hrqol_w3_5 hrqol_w3_6 hrqol_w3_7 hrqol_w3_8 // hrqol_w3_9 hrqol_w3_10 hrqol_w3_11 hrqol_w3_12 hrqol_w3_13 hrqol_w3_14 hrqol_w3_15 hrqol_w3_16 // hrqol_w3_17 hrqol_w3_18 hrqol_w3_19 hrqol_w3_20 hrqol_w3_21 hrqol_w3_22 hrqol_w3_23 * Define global macro "hrqol_items_w1" for all of the HRQoL items at wave 1 (i.e. auxiliary variables) global hrqol_items_w1 hrqol_w3_1 hrqol_w1_2 hrqol_w1_3 hrqol_w1_4 hrqol_w1_5 hrqol_w1_6 hrqol_w1_7 hrqol_w1_8 // hrqol_w1_9 hrqol_w1_10 hrqol_w1_11 hrqol_w1_12 hrqol_w1_13 hrqol_w1_14 hrqol_w1_15 hrqol_w1_16 // hrqol_w1_17 hrqol_w1_18 hrqol_w1_19 hrqol_w1_20 hrqol_w1_21 hrqol_w1_22 hrqol_w1_23 *_______________________________________________________________________________ * COMPLETE CASE ANALYSIS use "LSAC_Kcohort.dta", clear logistic hrqol_w3_bin bmiz male age indig sdq mat_edu mat_lang mat_k6 mat_work seifa /******************************************************************************* MULTIPLE IMPUTATION ANALYSES *******************************************************************************/ /*______________________________________________________________________________ ORIGINAL MODEL - MICE imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) at the item level using ordinal logistic regression - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level using ordinal logistic regression _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work (ologit) $hrqol_items_w3 $hrqol_items_w1 /// = male seifa , add(30) rseed(3032189) // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 1 - As original model, but using the "augment" option _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work (ologit) $hrqol_items_w3 $hrqol_items_w1 /// = male seifa , add(30) augment rseed(7269388) // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 2 - MICE imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) at the item level using linear regression - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level using linear regression _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 $hrqol_items_w3 $hrqol_items_w1 /// (logit) indig mat_edu mat_lang mat_work /// = male seifa , add(30) rseed(338711189) * PedsQL (HRQoL) items are transformed to 0-100 scale foreach var of varlist $hrqol_items_w3 { quietly { mi passive: gen `var'_100_imp = (125 -25*`var') } } * Generate HRQoL total score egen hrqol_total_imp= rowmean(hrqol*100_imp) * Dichotomise HRQoL total score mi passive: gen hrqol_w3_bin_imp =1 if hrqol_total_imp<65.42 mi passive: replace hrqol_w3_bin_imp =0 if hrqol_total_imp>=65.42 & hrqol_total_imp <. * Run the analysis model mi estimate: logistic hrqol_w3_bin_imp bmiz male age indig sdq mat_edu mat_lang mat_k6 mat_work seifa /*______________________________________________________________________________ STRATEGY 3 - MICE imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) at the item level using predictive mean matching (PMM) - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level using predictive mean matching (PMM) _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work (pmm, knn(5)) $hrqol_items_w3 $hrqol_items_w1 /// = male seifa , add(30) rseed(871686) * PedsQL (HRQoL) items are transformed to 0-100 scale foreach var of varlist $hrqol_items_w3 { quietly { mi passive: gen `var'_100_imp = (125 -25*`var') } } * Generate HRQoL total score egen hrqol_total_imp= rowmean(hrqol*100_imp) * Dichotomise HRQoL total score mi passive: gen hrqol_w3_bin_imp =1 if hrqol_total_imp<65.42 mi passive: replace hrqol_w3_bin_imp =0 if hrqol_total_imp>=65.42 & hrqol_total_imp <. * Run the analysis model mi estimate: logistic hrqol_w3_bin_imp bmiz male age indig sdq mat_edu mat_lang mat_k6 mat_work seifa /*______________________________________________________________________________ STRATEGY 4 - MICE imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) using ordinal logistic regression - Impute auxiliary HRQoL (wave 1) at the total score level using logistic regression _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 hrqol_w1_bin bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work hrqol_w1_bin (ologit) $hrqol_items_w3 /// = male seifa , add(30) rseed(6834368) // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 5 - MICE imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) using ordinal logistic regression - Impute auxiliary HRQoL (wave 1) at the total score level using logistic regression - Imputation model uses the “augment” option _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 hrqol_w1_bin bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work hrqol_w1_bin (ologit) $hrqol_items_w3 /// = male seifa , add(30) augment rseed(9847809) // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 6 - MICE imputation - Impute HRQoL outcome (wave 3) at total score level using logistic regression - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level using ordinal logistic regression _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed hrqol_w3_bin $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work hrqol_w3_bin (ologit) $hrqol_items_w1 /// = male seifa , add(30) rseed(7321735) // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 7 - MICE imputation - Impute HRQoL outcome (wave 3) at total score level using logistic regression - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level using ordinal logistic regression - Imputation model uses the “augment” option _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed hrqol_w3_bin $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work hrqol_w3_bin (ologit) $hrqol_items_w1 /// = male seifa , add(30) rseed(398717) augment // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 8 - MICE imputation - Impute HRQoL outcome (wave 3) at total score level using logistic regression - Impute auxiliary HRQoL (wave 1) at total score level using logistic regression _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed hrqol_w3_bin hrqol_w1_bin bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute chained (regress) bmiz age sdq mat_k6 /// (logit) indig mat_edu mat_lang mat_work hrqol_w3_bin hrqol_w1_bin /// = male seifa , add(30) rseed(5485577) * Run the analysis model mi estimate: logistic hrqol_w3_bin bmiz male age indig sdq mat_edu mat_lang mat_k6 mat_work seifa /*______________________________________________________________________________ STRATEGY 9 - MVN imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) at the item level using MVNI - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level using MVNI _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed $hrqol_items_w3 $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute mvn $hrqol_items_w3 $hrqol_items_w1 bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work /// = male seifa , add(30) rseed(6938711) * PedsQL (HRQoL) items are transformed to 0-100 scale foreach var of varlist $hrqol_items_w3 { quietly { mi passive: gen `var'_100_imp = (125 -25*`var') } } * Generate PEDSQL total score egen hrqol_total_imp= rowmean(hrqol*100_imp) * Dichotomise PEDSQL total score mi passive: gen hrqol_w3_bin_imp =1 if hrqol_total_imp<65.42 mi passive: replace hrqol_w3_bin_imp =0 if hrqol_total_imp>=65.42 & hrqol_total_imp <. * Run the analysis model mi estimate: logistic hrqol_w3_bin_imp bmiz male age indig sdq mat_edu mat_lang mat_k6 mat_work seifa /*______________________________________________________________________________ STRATEGY 10 - MVN imputation - Impute HRQoL items at wave 3 (i.e. items used to derive the outcome variable) at the item level as indicator variables using MVNI - Impute HRQoL items at wave 1 (i.e. auxiliary variables) at the item level as indicator variables using MVNI - To obtain ordinal values for HRQoL items, the HRQoL items are imputed as indicator variables followed by projected-distance based rounding to obtain ordinal values ( Galati et al. 2014. Journal of Statistical Computation and Simulation, 84:4, 798-811, DOI: 10.1080/00949655.2012.727815 ) _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Create indicator variables for each HRQoL item foreach var of varlist $hrqol_items_w3 $hrqol_items_w1 { xi i.`var' rename _I`var'_2 `var'_2 rename _I`var'_3 `var'_3 rename _I`var'_4 `var'_4 rename _I`var'_5 `var'_5 } * Create global macros for all of the indicator variables at wave 3 and wave 1 (for convenience - to avoid repeating variable names) global hrqol_items_w3_ind hrqol_w3_1_2 hrqol_w3_1_3 hrqol_w3_1_4 hrqol_w3_1_5 /// hrqol_w3_2_2 hrqol_w3_2_3 hrqol_w3_2_4 hrqol_w3_2_5 /// hrqol_w3_3_2 hrqol_w3_3_3 hrqol_w3_3_4 hrqol_w3_3_5 /// hrqol_w3_4_2 hrqol_w3_4_3 hrqol_w3_4_4 hrqol_w3_4_5 /// hrqol_w3_5_2 hrqol_w3_5_3 hrqol_w3_5_4 hrqol_w3_5_5 /// hrqol_w3_6_2 hrqol_w3_6_3 hrqol_w3_6_4 hrqol_w3_6_5 /// hrqol_w3_7_2 hrqol_w3_7_3 hrqol_w3_7_4 hrqol_w3_7_5 /// hrqol_w3_8_2 hrqol_w3_8_3 hrqol_w3_8_4 hrqol_w3_8_5 /// hrqol_w3_9_2 hrqol_w3_9_3 hrqol_w3_9_4 hrqol_w3_9_5 /// hrqol_w3_10_2 hrqol_w3_10_3 hrqol_w3_10_4 hrqol_w3_10_5 /// hrqol_w3_11_2 hrqol_w3_11_3 hrqol_w3_11_4 hrqol_w3_11_5 /// hrqol_w3_12_2 hrqol_w3_12_3 hrqol_w3_12_4 hrqol_w3_12_5 /// hrqol_w3_13_2 hrqol_w3_13_3 hrqol_w3_13_4 hrqol_w3_13_5 /// hrqol_w3_14_2 hrqol_w3_14_3 hrqol_w3_14_4 hrqol_w3_14_5 /// hrqol_w3_15_2 hrqol_w3_15_3 hrqol_w3_15_4 hrqol_w3_15_5 /// hrqol_w3_16_2 hrqol_w3_16_3 hrqol_w3_16_4 hrqol_w3_16_5 /// hrqol_w3_17_2 hrqol_w3_17_3 hrqol_w3_17_4 hrqol_w3_17_5 /// hrqol_w3_18_2 hrqol_w3_18_3 hrqol_w3_18_4 hrqol_w3_18_5 /// hrqol_w3_19_2 hrqol_w3_19_3 hrqol_w3_19_4 hrqol_w3_19_5 /// hrqol_w3_20_2 hrqol_w3_20_3 hrqol_w3_20_4 hrqol_w3_20_5 /// hrqol_w3_21_2 hrqol_w3_21_3 hrqol_w3_21_4 hrqol_w3_21_5 /// hrqol_w3_22_2 hrqol_w3_22_3 hrqol_w3_22_4 hrqol_w3_22_5 /// hrqol_w3_23_2 hrqol_w3_23_3 hrqol_w3_23_4 hrqol_w3_23_5 global hrqol_items_w1_ind hrqol_w1_1_2 hrqol_w1_1_3 hrqol_w1_1_4 hrqol_w1_1_5 /// hrqol_w1_2_2 hrqol_w1_2_3 hrqol_w1_2_4 hrqol_w1_2_5 /// hrqol_w1_3_2 hrqol_w1_3_3 hrqol_w1_3_4 hrqol_w1_3_5 /// hrqol_w1_4_2 hrqol_w1_4_3 hrqol_w1_4_4 hrqol_w1_4_5 /// hrqol_w1_5_2 hrqol_w1_5_3 hrqol_w1_5_4 hrqol_w1_5_5 /// hrqol_w1_6_2 hrqol_w1_6_3 hrqol_w1_6_4 hrqol_w1_6_5 /// hrqol_w1_7_2 hrqol_w1_7_3 hrqol_w1_7_4 hrqol_w1_7_5 /// hrqol_w1_8_2 hrqol_w1_8_3 hrqol_w1_8_4 hrqol_w1_8_5 /// hrqol_w1_9_2 hrqol_w1_9_3 hrqol_w1_9_4 hrqol_w1_9_5 /// hrqol_w1_10_2 hrqol_w1_10_3 hrqol_w1_10_4 hrqol_w1_10_5 /// hrqol_w1_11_2 hrqol_w1_11_3 hrqol_w1_11_4 hrqol_w1_11_5 /// hrqol_w1_12_2 hrqol_w1_12_3 hrqol_w1_12_4 hrqol_w1_12_5 /// hrqol_w1_13_2 hrqol_w1_13_3 hrqol_w1_13_4 hrqol_w1_13_5 /// hrqol_w1_14_2 hrqol_w1_14_3 hrqol_w1_14_4 hrqol_w1_14_5 /// hrqol_w1_15_2 hrqol_w1_15_3 hrqol_w1_15_4 hrqol_w1_15_5 /// hrqol_w1_16_2 hrqol_w1_16_3 hrqol_w1_16_4 hrqol_w1_16_5 /// hrqol_w1_17_2 hrqol_w1_17_3 hrqol_w1_17_4 hrqol_w1_17_5 /// hrqol_w1_18_2 hrqol_w1_18_3 hrqol_w1_18_4 hrqol_w1_18_5 /// hrqol_w1_19_2 hrqol_w1_19_3 hrqol_w1_19_4 hrqol_w1_19_5 /// hrqol_w1_20_2 hrqol_w1_20_3 hrqol_w1_20_4 hrqol_w1_20_5 /// hrqol_w1_21_2 hrqol_w1_21_3 hrqol_w1_21_4 hrqol_w1_21_5 * Multiple imputation mi set flong mi register imputed $hrqol_items_w3_ind $hrqol_items_w1_ind bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute mvn $hrqol_items_w3_ind $hrqol_items_w1_ind bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work /// = male seifa , add(30) rseed(5204175) // No imputations generated because model did not run /*______________________________________________________________________________ STRATEGY 11 - MVN imputation - Impute HRQoL outcome (wave 3) at total score level - Impute auxiliary HRQoL (wave 1) at total score level - Adapting rounding performed after imputation to obtain the binary outcome variable for the analysis (Bernaards CA, Belin TR, Schafer JL. Robustness of a multivariate normal approximation for imputation of incomplete binary data. Statistics in Medicine 2007; 26:1368–1382.) _______________________________________________________________________________*/ use "LSAC_Kcohort.dta", clear * Multiple imputation mi set flong mi register imputed hrqol_w3_bin hrqol_w1_bin bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work mi impute mvn hrqol_w3_bin hrqol_w1_bin bmiz age sdq mat_k6 indig mat_edu mat_lang mat_work /// = male seifa , add(30) rseed(7906128) * Adaptive rounding of hrqol_w3_bin cap prog drop adround_mvn program define adround_mvn args var qui sum `var' if _mi_m==0 local omegabar = `r(mean)' di "omegabar = `omegabar'" local threshold = `omegabar' - invnorm(`omegabar') * sqrt(`omegabar'*(1 - `omegabar')) replace `var' = 0 if `var' < `threshold' & _mi_m != 0 replace `var' = 1 if `var' > `threshold' & _mi_m != 0 end adround_mvn hrqol_w3_bin * Run the analysis model mi estimate: logistic hrqol_w3_bin bmiz male age indig sdq mat_edu mat_lang mat_k6 mat_work seifa log close