# Stratified Covariate Balancing is easy ... - Open Online Courses

Stratified Covariate Balancing Farrokh Alemi, Ph.D. HEALTH INFORMATICS PROGRAM H I .G M U. E D U Purpose of Stratified Covariate Balancing Propensity Scoring Stratified Covariate Balancing EHR Ready Statistical May Not Work Focusses on Main Effects H E A LT H I N F O R M AT I C S P R O G R A M Analytical Guaranteed Focusses on Interactions GEORGE MASON UNIVERSITY Propensity Scoring

Stratified Covariate Balancing EHR Ready Statistical May Not Work Focusses on Main Effects H E A LT H I N F O R M AT I C S P R O G R A M Analytical Guaranteed Focusses on Interactions GEORGE MASON UNIVERSITY Propensity Scoring Stratified Covariate Balancing EHR Ready Statistical May Not Work Focusses on Main Effects H E A LT H I N F O R M AT I C S P R O G R A M Analytical Guaranteed

Focusses on Interactions GEORGE MASON UNIVERSITY R Package Steps in Stratified Covariate Balancing 1. Divide Data into Strata H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 1. Divide Into Cases -- Cases describe residents who are unable to eat SELECT COUNT(distinct [ID]) AS nCases -- Number of residents unable to eat , Sum(IIF([Dead6M] = 1, 1., 0.)) AS a -- Number unable to eat and dead in 6 months , SUM(IIF([Dead6M] = 0, 1., 0.)) AS b Number unable to eat and alive , [Gender], [OlderThanAvg] , [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] INTO #Cases -- Save in temporary file called Cases FROM [dbo].[Data] -Name of your table may be different Select Cases WHERE [uEat] = 1 -- Select only residents who were unable to eat GROUP BY -- Create strata from gender, age, and disabilities. Age is matched coarsely [Gender], [OlderThanAvg], [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] H E A LT H I N F O R M AT I C S P R O G R A M

GEORGE MASON UNIVERSITY 1. Divide Into Cases -- Cases describe residents who are unable to eat SELECT COUNT(distinct [ID]) AS nCases -- Number of residents unable to eat , Sum(IIF([Dead6M] = 1, 1., 0.)) AS a -- Number unable to eat and dead in 6 months , SUM(IIF([Dead6M] = 0, 1., 0.)) AS b Number unable to eat and alive , [Gender], [OlderThanAvg] , [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] INTO #Cases -- Save in temporary a file called Cases t a r FROM [dbo].[Data] -- Name ofSt your table may be different WHERE [uEat] = 1 -- Select only residents who were unable to eat GROUP BY -- Create strata from gender, age, and disabilities. Age is matched coarsely [Gender], [OlderThanAvg], [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 1. Divide Into Cases e m o utc O nt to eat u -- Cases describe residents who are unable

o C SELECT COUNT(distinct [ID]) AS nCases -- Number of residents unable to eat , Sum(IIF([Dead6M] = 1, 1., 0.)) AS a -- Number unable to eat and dead in 6 months , SUM(IIF([Dead6M] = 0, 1., 0.)) AS b Number unable to eat and alive , [Gender], [OlderThanAvg] , [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] INTO #Cases -- Save in temporary file called Cases FROM [dbo].[Data] -- Name of your table may be different WHERE [uEat] = 1 -- Select only residents who were unable to eat GROUP BY -- Create strata from gender, age, and disabilities. Age is matched coarsely [Gender], [OlderThanAvg], [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 1. Divide Into Controls -- Controls describe residents who are able to eat SELECT COUNT(distinct [ID]) AS nControls -- Number of residents unable to eat , Sum(IIF([Dead6M] = 1, 1., 0.)) AS c -- Number able to eat and dead in 6 months , SUM(IIF([Dead6M] = 0, 1., 0.)) AS d Number able to eat and alive in 6 months Select Controls , [Gender], [OlderThanAvg] , [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] INTO #Controls -- Save in temporary file called Cases FROM [dbo].[Data] WHERE [uEat] = 0 -- Select only residents who were able to eat GROUP BY -- Create strata from gender, age, and disabilities. Age is matched coarsely [Gender], [OlderThanAvg], [uWalk], [uToilet], [uGroom], [uBathe], [uDress],

[uBowel], [uUrine], [uSit] H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 1. Divide Into Controls -- Controls describe residents who are able to eat SELECT COUNT(distinct [ID]) AS nControls -- Number of residents unable to eat , Sum(IIF([Dead6M] = 1, 1., 0.)) AS c -- Number able to eat and dead in 6 months , SUM(IIF([Dead6M] = 0, 1., 0.)) AS d Number able to eat and alive in 6 months to , [Gender], [OlderThanAvg] n i p rou ata , [uWalk], [uToilet], G[uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] r t S temporary file called Cases INTO #Controls -- Save in FROM [dbo].[Data] WHERE [uEat] = 0 -- Select only residents who were able to eat GROUP BY -- Create strata from gender, age, and disabilities. Age is matched coarsely [Gender], [OlderThanAvg], [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 1. Divide Into Controls -- Controls describe residents who are able to eat

SELECT COUNT(distinct [ID]) AS nControls -- Number of residents unable to eat , Sum(IIF([Dead6M] = 1, 1., 0.)) AS c -- Number able to eat and dead in 6 Count outcome months , SUM(IIF([Dead6M] = 0, 1., 0.)) AS d Number able to eat and alive in 6 months , [Gender], [OlderThanAvg] , [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] INTO #Controls -- Save in temporary file called Cases FROM [dbo].[Data] WHERE [uEat] = 0 -- Select only residents who were able to eat GROUP BY -- Create strata from gender, age, and disabilities. Age is matched coarsely [Gender], [OlderThanAvg], [uWalk], [uToilet], [uGroom], [uBathe], [uDress], [uBowel], [uUrine], [uSit] H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 2. Match Cases & Controls H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 2. Match Cases & Controls -- Match cases with controls and calculate common odds ratio SELECT sum(a*d/(a+b+c+d))/sum(b*c/(a+b+c+d)) As [Common Odds Ratio] FROM #Cases inner join #Controls ON #Cases.[Gender] =#Controls.[Gender] and #Cases.[OlderThanAvg] = #Controls.[OlderThanAvg] and #Cases.[uWalk]= #Controls.[uWalk]

and #Cases.[uToilet]= #Controls.[uToilet] and #Cases.[uGroom]= #Controls.[uGroom] and #Cases.[uBathe]= #Controls.[uBathe] and #Cases.[uDress]= #Controls.[uDress] and #Cases.[uBowel]= #Controls.[uBowel] and #Cases.[uUrine]= #Controls.[uUrine] and #Cases.[uSit]= #Controls.[uSit] H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 2. Match Cases & Controls Patients' Characteristics Same n Covariates for Cases and Controls H E A LT H I N F O R M AT I C S P R O G R A M Cases (T = 1) Controls (T = 0) Outcome Outcome y=1 y=0 ai bi ci di

GEORGE MASON UNIVERSITY 2. Match Cases & Controls Patients' Characteristics Same n Covariates for Cases and Controls H E A LT H I N F O R M AT I C S P R O G R A M Cases (T = 1) Controls (T = 0) Outcome Outcome y=1 y=0 ai bi ci di GEORGE MASON UNIVERSITY 2. Match Cases & Controls Patients' Characteristics Same n Covariates for Cases and Controls

H E A LT H I N F O R M AT I C S P R O G R A M Cases (T = 1) Controls (T = 0) Outcome Outcome y=1 y=0 ai bi ci di GEORGE MASON UNIVERSITY 2. Match Cases & Controls Cases Unable to Eat, X = 1 k 1 2 3 4 5 6 7 8 Age Male 6585 M

4065 M 6585 M 85+ M 4065 M 6585 M 6585 M 4065 M H E A LT H I N F O R M AT I C S P R O G R A M Disabilities SGTBWDL SGTBWDL SGTBWD SGTBWDL SGTBWD GTBWD GTBWDL GTBWD Total, 36,677 19,317 14,494 11,336 10,987 6,386 5,101 4,592

Number Dead, 12,831 9,787 3,118 3,951 3,263 3,275 2,192 982 Matched Controls Able to Eat, X = 0 Total, 17,862 10,739 7,456 22,220 6,318 3,032 9,524 7,283 Number Dead, 4,253 3,512 1,153 5,436 1,358 1,121 2,544 1,226 Weight,

wi0 2.053 1.79 1.944 0.51 1.739 2.106 0.536 0.631 GEORGE MASON UNIVERSITY 2. Match Cases & Controls Cases Unable to Eat, X = 1 k 1 2 3 4 5 6 7 8 Age Male 6585 M 4065 M 6585 M 85+ M 4065 M

6585 M 6585 M 4065 M H E A LT H I N F O R M AT I C S P R O G R A M Disabilities SGTBWDL SGTBWDL SGTBWD SGTBWDL SGTBWD GTBWD GTBWDL GTBWD Total, 36,677 19,317 14,494 11,336 10,987 6,386 5,101 4,592 Number Dead, 12,831 9,787 3,118 3,951 3,263

3,275 2,192 982 Matched Controls Able to Eat, X = 0 Total, 17,862 10,739 7,456 22,220 6,318 3,032 9,524 7,283 Number Dead, 4,253 3,512 1,153 5,436 1,358 1,121 2,544 1,226 Weight, wi0 2.053 1.79 1.944 0.51 1.739 2.106 0.536

0.631 GEORGE MASON UNIVERSITY 2. Match Cases & Controls Cases Unable to Eat, X = 1 k 1 2 3 4 5 6 7 8 Age Male 6585 M 4065 M 6585 M 85+ M 4065 M 6585 M 6585 M 4065 M H E A LT H I N F O R M AT I C S P R O G R A M

Disabilities SGTBWDL SGTBWDL SGTBWD SGTBWDL SGTBWD GTBWD GTBWDL GTBWD Total, 36,677 19,317 14,494 11,336 10,987 6,386 5,101 4,592 Number Dead, 12,831 9,787 3,118 3,951 3,263 3,275 2,192 982 Matched Controls Able to Eat, X = 0 Total, 17,862

10,739 7,456 22,220 6,318 3,032 9,524 7,283 Number Dead, 4,253 3,512 1,153 5,436 1,358 1,121 2,544 1,226 Weight, wi0 2.053 1.79 1.944 0.51 1.739 2.106 0.536 0.631 GEORGE MASON UNIVERSITY 2. Match Cases & Controls Cases Unable to Eat, X = 1 k

1 2 3 4 5 6 7 8 Age Male 6585 M 4065 M 6585 M 85+ M 4065 M 6585 M 6585 M 4065 M H E A LT H I N F O R M AT I C S P R O G R A M Disabilities SGTBWDL SGTBWDL SGTBWD SGTBWDL SGTBWD GTBWD

GTBWDL GTBWD Total, 36,677 19,317 14,494 11,336 10,987 6,386 5,101 4,592 Number Dead, 12,831 9,787 3,118 3,951 3,263 3,275 2,192 982 Matched Controls Able to Eat, X = 0 Total, 17,862 10,739 7,456 22,220 6,318 3,032 9,524 7,283

Number Dead, 4,253 3,512 1,153 5,436 1,358 1,121 2,544 1,226 Weight, wi0 2.053 1.79 1.944 0.51 1.739 2.106 0.536 0.631 GEORGE MASON UNIVERSITY 3. Calculate Impact H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Calculate Impact: Common Odds Ratio ^ = /

i / i H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Calculate Impact: Weighted Data + = +(1 ) + H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Calculate Impact: Weighted Data + = +(1 ) + 1 1 0 H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Calculate Impact: Weighted Data +

= +(1 ) + 0 0 1 H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Unconfounded Impact: Weighted Data + = +(1 ) + 0 0 1 H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Calculate Impact: Weighted Data Combination of Covariates Balanced H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY 3. Calculate Impact: Switch Distributions k

1k 1 2 2 3 3 4 5 4 6 5 7 6 8 7 8 Age Male Age Male 6585 M 6585 M 4065 M 4065 M 6585 M 6585 M 85+ 4065 M 85+ M

6585 M 4065 M 6585 M 6585 M 4065 M 6585 M 4065 M H E A LT H I N F O R M AT I C S P R O G R A M Disabilities Disabilities SGTBWDL SGTBWDL SGTBWDL SGTBWDL SGTBWD SGTBWD SGTBWDL SGTBWD SGTBWDL GTBWD SGTBWD GTBWDL GTBWD GTBWD GTBWDL GTBWD

Cases Cases Unable Unable to to Eat, Eat, X X == 1 1 Number Total, Dead, 36,677 12,831 36,677 12,831 19,317 9,787 19,317 9,787 14,494 3,118 14,494 3,118 11,336 3,951 10,987 3,263 11,336 3,951 6,386 3,275 10,987 3,263 5,101 2,192 6,386

3,275 4,592 982 5,101 2,192 4,592 982 Matched Matched Controls Controls Able to Eat, Able to Eat, X X == 0 0 Weight, Number Weight, wi0 Total, Dead, wi0 17,862 4,253 2.053 17,862 4,253 2.053 10,739 3,512 1.79 10,739 3,512 1.79

7,456 1,153 1.944 7,456 1,153 1.944 22,220 5,436 0.51 6,318 1.739 22,220 5,436 0.51 11,336 1,358 3,032 1,121 2.106 6,318 1,358 1.739 9,524 2,544 0.536 3,032 1,121 2.106 7,283 1,226 0.631 9,524 2,544 0.536 7,283 1,226 0.631

GEORGE MASON UNIVERSITY Odds in Cases & Controls 10.00 Odds 1.00 0.10 65 85 40 65 e e g g A A e Ag + 85 es l a M a Un e bl

to a Tr n er f s l b a Un e to Gr m o o Un Original Sample H E A LT H I N F O R M AT I C S P R O G R A M le b a

to T t le i o b a Un le to he t Ba ab n U le to W k al le b a n

U to ss e Dr ab n U le to w o B Un el le b a to U te a rin Weighted Sample

GEORGE MASON UNIVERSITY Percent Error Accuracy 80% 70% 60% 50% 40% 30% 20% 10% 0% Propensity Scoring with 2-way Interaction Stratified Covariate Balancing Type & Number of Interaction Terms H E A LT H I N F O R M AT I C S P R O G R A M GEORGE MASON UNIVERSITY STRATIFIED COVARIATE BALANCING IS EASY TO IMPLEMENT, REQUIRES NO STATISTICAL ANALYSIS, AND IS MORE ACCURATE THAN PROPENSITY SCORING

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