# Accuracy of Multi-Morbidity Index

• Sensitivity, specificity, and area under the curve PubMed►

# Learning Material

1. Predicting outcomes Slides► Basic Ideas for Predicting► Walk through SQL►
2. Product of values of data in one column Slides► Video►
3. Accuracy of Predictive Models (use instructor's last name as password) Read►
4. Constructing Receiver Operating Curves Slides► Video►
5. Calculate Area under the Receiver Operating Curve Slides with Code►

# Assignment

Instruction for Submission of Assignments: Assignments should be submitted directly on Blackboard.  In rare situations assignments can be sent directly by email to the instructor. Submission should follow these rules:

• Nolan's guide on how to insert a plot in Jupyter YouTube►
2. Submit you Jupyter file in Blackboard.

Task 1: Using the attached sensitivity and specificity estimates for Charlson and MM Index, create two receiver operating curve on the same chart.  Label the X-axis and Y-axis.  Provide a legend inside the plot area.  Calculate area under the curve for each curve.  Which index is more accurate?

 Charlson MM Index Sensitivity Specificity Sensitivity Specificity 0 1 0 1 0.017 1.000 0.001 1.000 0.038 1.000 0.061 0.994 0.099 1.000 0.204 0.975 0.232 0.997 0.487 0.920 0.435 0.971 0.867 0.739 0.748 0.801 0.938 0.620 0.818 0.653 0.988 0.366 0.818 0.653 0.998 0.110 0.818 0.653 1.000 0.006 0.818 0.653 1.000 0.001 0.818 0.653 1 0 1 0 1 0

Task 2: Test the accuracy of the Multimorbidity index in predicting mortality of patients in 6-months. Score the Multimorbidity index using ontological adjustments for rare diagnosis with less than 30 cases. Then calculate the sensitivity and specificity of the index in predicting mortality.  Finally, calculate the area under the receiver operating curve for the Multi-Morbidity index.

Task 3: Test the accuracy of the Multimorbidity index in predicting mortality of patients in 6-months. Score the Multimorbidity index using the worst disease in the body systems. Then calculate the sensitivity and specificity of the index in predicting mortality.  Finally, calculate the area under the receiver operating curve for the Multimorbidity index.

Sample Code

The following is a modified sample code from Grace Buck:

USE HAP464

-- Assign null values for LR and Age at Death

SELECT a.*, iif (ISNUMERIC(LR)=1,convert(float, LR), 1.0) as LR

, left(a.icd9, 4) AS body

, iif(Ageatdeath is null, 0.0, iif(AgeatDeath - AgeofDx<.5,1.0,0.0)) AS actual

INTO #data FROM  dbo.clean a LEFT JOIN dbo.adjustedLR b ON a.icd9 = b.icd9

--(17431402 rows affected)

-- selecting codes into categories for each body system

SELECT *

, iif(body in ('I001', 'I002', 'I003', 'I004', 'I005', 'I006', 'I007', 'I008', 'I009', 'I010', 'I011', 'I012', 'I013', 'I014', 'I015', 'I016', 'I017', 'I018', 'I019', 'I020'

, 'I021', 'I022', 'I023', 'I024', 'I025', 'I026', 'I027', 'I028', 'I029', 'I030', 'I031', 'I032', 'I033', 'I034', 'I035', 'I036', 'I037', 'I038', 'I039', 'I040', 'I041', 'I042'

, 'I043', 'I044', 'I045', 'I046', 'I047', 'I048', 'I049', 'I050', 'I051', 'I052', 'I053', 'I054', 'I055', 'I056', 'I057', 'I058', 'I059', 'I060', 'I061', 'I062', 'I063', 'I064'

, 'I065', 'I066', 'I067', 'I068', 'I069', 'I070', 'I071', 'I072', 'I073', 'I074', 'I075', 'I076', 'I077', 'I078', 'I079', 'I080', 'I081', 'I082', 'I083', 'I084', 'I085', 'I086'

, 'I087', 'I088', 'I089', 'I090', 'I091', 'I092', 'I093', 'I094', 'I095', 'I096', 'I097', 'I098', 'I099', 'I100', 'I101', 'I102', 'I103', 'I104', 'I105', 'I106', 'I107', 'I108'

, 'I109', 'I110', 'I111', 'I112', 'I113', 'I114', 'I115', 'I116', 'I117', 'I118', 'I119', 'I120', 'I121', 'I122', 'I123', 'I124', 'I125', 'I126', 'I127', 'I128', 'I129', 'I130'

, 'I131', 'I132', 'I133', 'I134', 'I135', 'I136', 'I137', 'I138', 'I139'),LR,1) AS Infectious

, iif(body in ('I140', 'I141', 'I142', 'I143', 'I144', 'I145', 'I146', 'I147', 'I148', 'I149', 'I150', 'I151', 'I152', 'I153', 'I154', 'I155', 'I156', 'I157', 'I158', 'I159', 'I160', 'I161'

, 'I162', 'I163', 'I164', 'I165', 'I166', 'I167', 'I168', 'I169', 'I170', 'I171', 'I172', 'I173', 'I174', 'I175', 'I176', 'I177', 'I178', 'I179', 'I180', 'I181', 'I182', 'I183', 'I184', 'I185'

, 'I186', 'I187', 'I188', 'I189', 'I190', 'I191', 'I192', 'I193', 'I194', 'I195', 'I196', 'I197', 'I198', 'I199', 'I200', 'I201', 'I202', 'I203', 'I204', 'I205', 'I206', 'I207', 'I208', 'I209'

, 'I210', 'I211', 'I212', 'I213', 'I214', 'I215', 'I216', 'I217', 'I218', 'I219', 'I220', 'I221', 'I222', 'I223', 'I224', 'I225', 'I226', 'I227', 'I228', 'I229', 'I230', 'I231', 'I232', 'I233'

, 'I234', 'I235', 'I236', 'I237', 'I238', 'I239'),LR,1) AS Neoplasms

, iif(body in ('I240', 'I241', 'I242', 'I243', 'I244', 'I245', 'I246', 'I247', 'I248', 'I249', 'I250', 'I251', 'I252', 'I253', 'I254', 'I255', 'I256', 'I257', 'I258', 'I259', 'I260', 'I261'

, 'I262', 'I263', 'I264', 'I265', 'I266', 'I267', 'I268', 'I269', 'I270', 'I271', 'I272', 'I273', 'I274', 'I275', 'I276', 'I277', 'I278', 'I279'),LR,1) AS EndocrineDiseases

, iif(body in ('I280', 'I281', 'I282', 'I283', 'I284', 'I285', 'I286', 'I287', 'I288', 'I289'),LR,1) AS BloodDiseases

, iif(body in ('I290', 'I291', 'I292', 'I293', 'I294', 'I295', 'I296', 'I297', 'I298', 'I299', 'I300', 'I301', 'I302', 'I303', 'I304', 'I305', 'I306', 'I307', 'I308', 'I309', 'I310', 'I311', 'I312', 'I313'

, 'I314', 'I315', 'I316', 'I317', 'I318', 'I319'),LR,1) AS MentalDisorders

, iif(body in ('I320', 'I321', 'I322', 'I323', 'I324', 'I325', 'I326', 'I327', 'I328', 'I329', 'I330', 'I331', 'I332', 'I333', 'I334', 'I335', 'I336', 'I337', 'I338', 'I339', 'I340'

, 'I341', 'I342', 'I343', 'I344', 'I345', 'I346', 'I347', 'I348', 'I349', 'I350', 'I351', 'I352', 'I353', 'I354', 'I355', 'I356', 'I357', 'I358', 'I359'),LR,1) AS NervousDiseases

, iif(body in ('I360', 'I361', 'I362', 'I363', 'I364', 'I365', 'I366', 'I367', 'I368', 'I369', 'I370', 'I371', 'I372', 'I373', 'I374', 'I375', 'I376', 'I377', 'I378', 'I379'

, 'I380', 'I381', 'I382', 'I383', 'I384', 'I385', 'I386', 'I387', 'I388', 'I389'),LR,1) AS SenseOrganDiseases

, iif(body in ('I390', 'I391', 'I392', 'I393', 'I394', 'I395', 'I396', 'I397', 'I398', 'I399', 'I400', 'I401', 'I402', 'I403', 'I404', 'I405', 'I406', 'I407', 'I408', 'I409', 'I410', 'I411'

, 'I412', 'I413', 'I414', 'I415', 'I416', 'I417', 'I418', 'I419', 'I420', 'I421', 'I422', 'I423', 'I424', 'I425', 'I426', 'I427', 'I428', 'I429', 'I430', 'I431', 'I432', 'I433', 'I434', 'I435'

, 'I436', 'I437', 'I438', 'I439', 'I440', 'I441', 'I442', 'I443', 'I444', 'I445', 'I446', 'I447', 'I448', 'I449', 'I450', 'I451', 'I452', 'I453', 'I454', 'I455', 'I456', 'I457', 'I458', 'I459'),LR,1) AS CirculatoryDiseases

, iif(body in ('I460', 'I461', 'I462', 'I463', 'I464', 'I465', 'I466', 'I467', 'I468', 'I469', 'I470', 'I471', 'I472', 'I473', 'I474', 'I475', 'I476', 'I477', 'I478', 'I479', 'I480', 'I481',

'I482', 'I483', 'I484', 'I485', 'I486', 'I487', 'I488', 'I489', 'I490', 'I491', 'I492', 'I493', 'I494', 'I495', 'I496', 'I497', 'I498', 'I499', 'I500', 'I501', 'I502', 'I503', 'I504', 'I505',

'I506', 'I507', 'I508', 'I509', 'I510', 'I511', 'I512', 'I513', 'I514', 'I515', 'I516', 'I517', 'I518', 'I519'),LR,1) AS RespiratoryDiseases

, iif(body in ('I520', 'I521', 'I522', 'I523', 'I524', 'I525', 'I526', 'I527', 'I528', 'I529', 'I530', 'I531', 'I532', 'I533', 'I534', 'I535', 'I536', 'I537', 'I538', 'I539', 'I540', 'I541', 'I542', 'I543'

, 'I544', 'I545', 'I546', 'I547', 'I548', 'I549', 'I550', 'I551', 'I552', 'I553', 'I554', 'I555', 'I556', 'I557', 'I558', 'I559', 'I560', 'I561', 'I562', 'I563', 'I564', 'I565', 'I566', 'I567', 'I568', 'I569'

, 'I570', 'I571', 'I572', 'I573', 'I574', 'I575', 'I576', 'I577', 'I578', 'I579'),LR,1) AS DigestiveDiseases

, iif(body in ('I580', 'I581', 'I582', 'I583', 'I584', 'I585', 'I586', 'I587', 'I588', 'I589', 'I590', 'I591', 'I592', 'I593', 'I594', 'I595', 'I596', 'I597', 'I598', 'I599', 'I600', 'I601', 'I602', 'I603'

, 'I604', 'I605', 'I606', 'I607', 'I608', 'I609', 'I610', 'I611', 'I612', 'I613', 'I614', 'I615', 'I616', 'I617', 'I618', 'I619', 'I620', 'I621', 'I622', 'I623', 'I624', 'I625', 'I626', 'I627', 'I628', 'I629'),LR,1) AS GenitourinaryDiseases

, iif(body in ('I630', 'I631', 'I632', 'I633', 'I634', 'I635', 'I636', 'I637', 'I638', 'I639', 'I640', 'I641', 'I642', 'I643', 'I644', 'I645', 'I646', 'I647', 'I648', 'I649', 'I650', 'I651'

, 'I652', 'I653', 'I654', 'I655', 'I656', 'I657', 'I658', 'I659', 'I660', 'I661', 'I662', 'I663', 'I664', 'I665', 'I666', 'I667', 'I668', 'I669', 'I670', 'I671', 'I672', 'I673', 'I674', 'I675', 'I676'),LR,1) AS PregnancyComplication

, iif(body in ('I680', 'I681', 'I682', 'I683', 'I684', 'I685', 'I686', 'I687', 'I688', 'I689', 'I690', 'I691', 'I692', 'I693', 'I694', 'I695', 'I696', 'I697', 'I698', 'I699', 'I700', 'I701'

, 'I702', 'I703', 'I704', 'I705', 'I706', 'I707', 'I708', 'I709'),LR,1) AS SkinDiseases

, iif(body in ('I710', 'I711', 'I712', 'I713', 'I714', 'I715', 'I716', 'I717', 'I718', 'I719', 'I720', 'I721', 'I722', 'I723', 'I724', 'I725', 'I726', 'I727', 'I728', 'I729', 'I730', 'I731', 'I732', 'I733'

, 'I734', 'I735', 'I736', 'I737', 'I738', 'I739'),LR,1) AS MusculoskeletalDiseases

, iif(body in ('I740', 'I741', 'I742', 'I743', 'I744', 'I745', 'I746', 'I747', 'I748', 'I749', 'I750', 'I751', 'I752', 'I753', 'I754', 'I755', 'I756', 'I757', 'I758', 'I759'),LR,1) AS CongenitalAnomalies

, iif(body in ('I760', 'I761', 'I762', 'I763', 'I764', 'I765', 'I766', 'I767', 'I768', 'I769', 'I770', 'I771', 'I772', 'I773', 'I774', 'I775', 'I776', 'I777', 'I778', 'I779'),LR,1) AS PerinatalConditions

, iif(body in ('I780', 'I781', 'I782', 'I783', 'I784', 'I785', 'I786', 'I787', 'I788', 'I789', 'I790', 'I791', 'I792', 'I793', 'I794', 'I795', 'I796', 'I797', 'I798', 'I799'),LR,1) AS illDefined

, iif(body in ('I800', 'I801', 'I802', 'I803', 'I804', 'I805', 'I806', 'I807', 'I808', 'I809', 'I810', 'I811', 'I812', 'I813', 'I814', 'I815', 'I816', 'I817', 'I818', 'I819', 'I820', 'I821', 'I822'

, 'I823', 'I824', 'I825', 'I826', 'I827', 'I828', 'I829', 'I830', 'I831', 'I832', 'I833', 'I834', 'I835', 'I836', 'I837', 'I838', 'I839', 'I840', 'I841', 'I842', 'I843', 'I844', 'I845', 'I846', 'I847', 'I848'

, 'I849', 'I850', 'I851', 'I852', 'I853', 'I854', 'I855', 'I856', 'I857', 'I858', 'I859', 'I860', 'I861', 'I862', 'I863', 'I864', 'I865', 'I866', 'I867', 'I868', 'I869', 'I870', 'I871', 'I872', 'I873', 'I874'

, 'I875', 'I876', 'I877', 'I878', 'I879', 'I880', 'I881', 'I882', 'I883', 'I884', 'I885', 'I886', 'I887', 'I888', 'I889', 'I890', 'I891', 'I892', 'I893', 'I894', 'I895', 'I896', 'I897', 'I898', 'I899', 'I900'

, 'I901', 'I902', 'I903', 'I904', 'I905', 'I906', 'I907', 'I908', 'I909', 'I910', 'I911', 'I912', 'I913', 'I914', 'I915', 'I916', 'I917', 'I918', 'I919', 'I920', 'I921', 'I922', 'I923', 'I924', 'I925', 'I926'

, 'I927', 'I928', 'I929', 'I930', 'I931', 'I932', 'I933', 'I934', 'I935', 'I936', 'I937', 'I938', 'I939', 'I940', 'I941', 'I942', 'I943', 'I944', 'I945', 'I946', 'I947', 'I948', 'I949', 'I950', 'I951', 'I952'

, 'I953', 'I954', 'I955', 'I956', 'I957', 'I958', 'I959', 'I960', 'I961', 'I962', 'I963', 'I964', 'I965', 'I966', 'I967', 'I968', 'I969', 'I970', 'I971', 'I972', 'I973', 'I974', 'I975', 'I976', 'I977', 'I978'

, 'I979', 'I980', 'I981', 'I982', 'I983', 'I984', 'I985', 'I986', 'I987', 'I988', 'I989', 'I990', 'I991', 'I992', 'I993', 'I994', 'I995', 'I996', 'I997', 'I998', 'I999'),LR,1) AS Injury

, iif(body like '%E%', LR, 1) AS Ecodes

, iif(body like '%V%', LR, 1) AS Vcodes

INTO  #bodysystem FROM  #data

---(17431402 rows affected)

--- taking max value for each body system

SELECT id, actual,

max(Infectious) * max(Neoplasms) * max(EndocrineDiseases) * max(BloodDiseases) * max(MentalDisorders) * max(NervousDiseases) * max(SenseOrganDiseases)

* max(CirculatoryDiseases) * max(RespiratoryDiseases) * max(DigestiveDiseases) * max(GenitourinaryDiseases) * max(PregnancyComplications) * max(SkinDiseases)

* max(MusculoskeletalDiseases) * max(CongenitalAnomalies) * max(PerinatalConditions) * max(illDefined) * max(Injury) * max(Ecodes) * max(Vcodes) AS score

INTO  #temp2 FROM #bodysystem GROUP BY  id, actual

---- (897324 rows affected)

-- Assign values to null

SELECT id, SUM(iif (score is null, 1.0, score)) AS predicted

, MAX(actual) AS actual

INTO #temp3 from #temp2 GROUP BY  id ORDER BY actual desc

--- (829625 rows affected)

-- DROP TABLE #cutoff

CREATE TABLE #cutoff (cutoff float);

INSERT INTO  #cutoff (cutoff)

values (0.0), (0.0001), (0.001), (0.01), (0.1), (0.2), (0.5), (1.0), (2.0), (5.0), (10.0), (100.0), (1000.0), (10000.0), (7000000.0);

--- (15 rows affected)

-- DROP TABLE  #ordereddata

SELECT ROW_NUMBER() OVER (ORDER BY predicted) AS Row

, predicted AS prob

, actual

INTO #OrderedData FROM #temp3 ORDER BY predicted

--- (829625 rows affected)

-- Classify predicted scores by comparing it to cutoff values

--- DROP TABLE #temp1

SELECT cutoff

, iif (a.predicted > b.cutoff, 1.,0) as predicted

, actual

INTO #Temp1 FROM  #temp3 a CROSS JOIN #cutoff b

--- (12444375 rows affected)

-- calculate sensitivity and specificity

SELECT Cutoff

,  SUM(CAST(Actual AS FLOAT)*CAST(Predicted AS FLOAT)) / SUM(CAST(Actual AS FLOAT)) AS Sensitivity

,  SUM((1-Predicted)*(1-Actual)) / SUM(1-Actual) AS Specificity

, ROW_NUMBER() OVER(ORDER BY Cutoff DESC) AS rnum

INTO #sensspec FROM #Temp1 GROUP BY Cutoff

-- (15 rows affected)

SELECT * FROM  #sensspec

/*The receiver operating curve is plotted in Excel as below:

*/

SELECT SUM(ABS(a.specificity - c.specificity)

* (a.[sensitivity] + c.[sensitivity])/2) AS Area

FROM #sensspec AS a INNER JOIN #sensspec AS c ON a.rNum = C.rNUm - 1;

--- The Area under the Receiver Operating Curve is >0.8

 Copyright © 2021 Farrokh Alemi, Ph.D. Most recent revision 04/26/2021.  This page is part of the course on Electronic Health Record Configuration and Data Analysis.