Death and Missing Data in Longitudinal Studies: Quality of Life at the End of Life Paula Diehr Maximising return from cohort studies: prevention of attrition

Death and Missing Data Death and Missing Data in Longitudinal Studies: in Longitudinal Studies:

Quality of Life at the End Quality of Life at the End

of Lifeof LifePaula DiehrPaula Diehr

Maximising return from cohort Maximising return from cohort studies: prevention of attrition studies: prevention of attrition and efficient analysis London 6-and efficient analysis London 6-

25-200625-2006

2

ChargeCharge

““The use of imputation to deal with The use of imputation to deal with attrition in cohort studies”attrition in cohort studies”

I will concentrate primarily on what to I will concentrate primarily on what to do about death in longitudinal studiesdo about death in longitudinal studies In In mymy cohorts of older or sicker adults cohorts of older or sicker adults

more than half the missing values are more than half the missing values are missing due to deathmissing due to death

Taking care of the deaths first often helps Taking care of the deaths first often helps deal with the other missing data deal with the other missing data

3

My MOMy MO First step: create a meaningful graphFirst step: create a meaningful graph Organize the dataOrganize the data

A place for every observation that could A place for every observation that could have been made (if the person hadn’t have been made (if the person hadn’t died)died)

Do something about the deaths Do something about the deaths assign a valid valueassign a valid value

Impute the (remaining) missing dataImpute the (remaining) missing data GraphGraph AnalyzeAnalyze

4

OutlineOutline

ADHC example (very simple)ADHC example (very simple) C3 example (more issues)C3 example (more issues) DeathDeath OrganizationOrganization Missing dataMissing data AnalysisAnalysis

Example 1: ADHCExample 1: ADHC

Diehr and Johnson. Accounting for Diehr and Johnson. Accounting for missing data in end-of-life research. missing data in end-of-life research.

Palliative Care 2005; 8:S50-S57.Palliative Care 2005; 8:S50-S57.

6

Example: ADHCExample: ADHC

Adult Day Health Care studyAdult Day Health Care study RCT (ADHC vs Usual Care)RCT (ADHC vs Usual Care) 939 Frail Veterans939 Frail Veterans

At risk of nursing home placementAt risk of nursing home placement 1 year study: data at 0, 6, 12 months1 year study: data at 0, 6, 12 months Findings: ADHC expensive, ineffectiveFindings: ADHC expensive, ineffective Frail veterans didn’t failFrail veterans didn’t fail

Why?Why?

7

Health VariableHealth Variable

Utility (sort-of)Utility (sort-of) 0 to 1000 to 100 100 is perfect health100 is perfect health (0 is dead, but will let dead be (0 is dead, but will let dead be

missing at first)missing at first)

8

24626 134626 279626N =

Raw Data (phf)

adhc07.sps 11-17-2004

Missing Pattern

Some MissingComplete Case

95

% C

I60.0

50.0

40.0

30.0

20.0

10.0

0.0

baseline

6 mos

12 mos

9

AccountingAccounting

939 persons939 persons 3*939=2817 observations if 3*939=2817 observations if

completecomplete 502 observations were missing502 observations were missing

302 missing because of death302 missing because of death 200 missing for other reasons200 missing for other reasons

60% of missing were due to death60% of missing were due to death

10

53785 89785 120785N =

Deaths set to Zero (phf)

adhc07.sps 11-17-2004

Missing Pattern

Some MissingComplete Case

95

% C

I60.0

50.0

40.0

30.0

20.0

10.0

0.0

baseline

6 mos

12 mos

11

939939939N =

Death=0 and Impute if 1 Known (phf)

adhc07.sps 11-17-2004

Missing Pattern

Complete Case

95

% C

I60.0

50.0

40.0

30.0

20.0

10.0

0.0

baseline

6 mos

12 mos

12

In ADHC Example:In ADHC Example:

Complete case data too optimistic – Complete case data too optimistic – significant improvement (65% significant improvement (65% complete)complete)

Available data even more optimisticAvailable data even more optimistic Accounting for the deaths showed Accounting for the deaths showed

significant decline (84% complete)significant decline (84% complete) Imputing remaining missing values Imputing remaining missing values

showed significant decline (100% showed significant decline (100% complete) (ITT)complete) (ITT)

Example 2: C3 Example 2: C3 StudyStudy

Complementary Comfort Complementary Comfort CareCare

Bill Lafferty, P.I.Bill Lafferty, P.I.

NCINCI

14

Study DesignStudy Design

RCTRCT Effect of massage or meditation on Effect of massage or meditation on

QOL and Sx in patients at the end of QOL and Sx in patients at the end of lifelife

QOL and Sx assessed ~ QOL and Sx assessed ~ every week every week until deathuntil death

In progressIn progress 3 years of data collection 3 years of data collection First 100 cases (DSMB ok)First 100 cases (DSMB ok)

15

Outcome VariablesOutcome Variables

Quality of Life (QOL)Quality of Life (QOL) Symptoms (SX)Symptoms (SX) Health Rating (Hlthrat)Health Rating (Hlthrat)

16

QOL (pqol)QOL (pqol)How would you rate your overall quality How would you rate your overall quality

of life during the past 7 days?of life during the past 7 days?

0 is NO QUALITY OF LIFE 0 is NO QUALITY OF LIFE toto10 is PERFECT QUALITY OF LIFE10 is PERFECT QUALITY OF LIFE

Note: if 0 had been “dead”, this would be Note: if 0 had been “dead”, this would be a “preference-rated / utility / rating scale” a “preference-rated / utility / rating scale” variable and dead would have the value variable and dead would have the value zero. Missed opportunity.zero. Missed opportunity.

17

Health rating (Hlthrat)Health rating (Hlthrat)

0=worst possible health you can 0=worst possible health you can imagine and still be aliveimagine and still be alive

10 = as near perfect health as you 10 = as near perfect health as you can imaginecan imagine

Baseline onlyBaseline only

2-Death2-Death

Everyone is expected to die Everyone is expected to die in C3.in C3.

19

Approaches to Handle Approaches to Handle DeathDeath

IgnoreIgnore Set death to a “low” value, perform Set death to a “low” value, perform

sensitivity analysis to see if final sensitivity analysis to see if final results change (arbitrary) results change (arbitrary)

Impute the values after death as if Impute the values after death as if person was still alive (immortal cohort)person was still alive (immortal cohort)

Joint modeling of survival and healthJoint modeling of survival and health Health conditional on being aliveHealth conditional on being alive Transformation approachTransformation approach

20

Transformation Transformation ApproachApproach

Transform the outcome variable that Transform the outcome variable that has no value for death to another has no value for death to another variable that does have a variable that does have a natural natural valuevalue for death. for death.

Dichotomize, assign deaths to “low” Dichotomize, assign deaths to “low” category.category.

Transform to a probability Transform to a probability Probability of being healthyProbability of being healthy Dead have probability 0Dead have probability 0

21

Probability Probability TransformationsTransformations

Probability (QOL Probability (QOL >> 7 now | QOL now) 7 now | QOL now) Dichotomize (good QOL Dichotomize (good QOL >> 7 or bad QOL <7 7 or bad QOL <7

now)now) Probability (QOL Probability (QOL >> 7 7 next weeknext week | QOL | QOL

now)now) Probability (Hlthrat Probability (Hlthrat >> 7 now | QOL now) 7 now | QOL now)

Diehr et al, J Clin Epidemiology, 2005Diehr et al, J Clin Epidemiology, 2005

22

QOLQOL QOLQOL>>7 now7 now

P(QOLP(QOL>>7) 7) next next weekweek

P(HlthrP(Hlthratat>>7) 7) now *now *

1010

99

88

77

66

55

44

33

22

11

00

deaddead

OrdinalOrdinal OK if dead is worst OK if dead is worst

QOLQOL State worse than State worse than

deathdeath OK if OK if

nonparametric nonparametric analysis (ordinal)analysis (ordinal)

Mean is Mean is meaninglessmeaningless Without deaths?Without deaths? With deathsWith deaths

Mean Difference Mean Difference or change or AUC or change or AUC is meaninglessis meaningless

23

QOQOLL

QOLQOL>>7 now7 now

P(QOLP(QOL>>77) next ) next weekweek


1010 100100

99 100100

88 100100

77 100100

66 00

55 00

44 00

33 00

22 00

11 00

00 00

deadeadd

00

Dichotomize to Good Dichotomize to Good QOL yes/noQOL yes/no

Dead = 0Dead = 0 OK if death is not OK if death is not

good QOLgood QOL Mean interpretable, Mean interpretable,

any analysis OKany analysis OK AUC=weeks with AUC=weeks with

good QOLgood QOL Change meaningfulChange meaningful

Loses information?Loses information? Bad cutpoint?Bad cutpoint? Assume death is bad Assume death is bad

QOLQOL

24

QOLQOL QOLQOL>>7 7 nownow

P(QOLP(QOL>>7) next 7) next weekweek


1010 100100 9494

99 100100 8888

88 100100 7676

77 100100 5959

66 00 3939

55 00 2222

44 00 1111

33 00 55

22 00 22

11 00 11

00 00 .5.5

deaddead 00 00

Pr (Good QOL 1 week Pr (Good QOL 1 week later|QOL now) later|QOL now)

Estimated from Estimated from transition pairstransition pairs

Dead have 0 Dead have 0 probability of high probability of high QOL 1 week laterQOL 1 week later

Mean interpretable, Mean interpretable, any analysis OKany analysis OK AUC = # good QOL AUC = # good QOL

weeks starting 1 week weeks starting 1 week after b/l after b/l

change, differencechange, difference Assume is death part Assume is death part

of the of the QOLQOL construct construct (dead people have (dead people have bad QOL). Probably bad QOL). Probably ok.ok.

25

QOQOLL

QOLQOL>>7 7 nownow

P(QOLP(QOL>>7) next 7) next weekweek

P(HlthratP(Hlthrat>>7) now 7) now

* QOLt* QOLt

1010 100100 9494 7575

99 100100 8888 6666

88 100100 7676 5555

77 100100 5959 4444

66 00 3939 3434

55 00 2222 2525

44 00 1111 1717

33 00 55 1212

22 00 22 88

11 00 11 55

00 00 .5.5 33

deadeadd

00 00 00

QOLt = Pr (Good QOLt = Pr (Good health now |QOL health now |QOL now)now)

Dead have 0 Dead have 0 probability of being probability of being healthy now.healthy now.

Mean interpretable, Mean interpretable, any analysis OKany analysis OK AUC = Healthy weeks AUC = Healthy weeks

starting at B/L starting at B/L change, difference OKchange, difference OK

Assume death part of Assume death part of the the healthhealth construct. construct. (Dead people not (Dead people not healthy). This seems healthy). This seems obviousobvious

Dead vs. 0Dead vs. 0

26

Transformation Transformation modifies relative modifies relative

spacingspacing

QOLQOL QOLQOL>>7 now7 now

P(QOLP(QOL>>7) one 7) one week week laterlater

P(HlthrP(Hlthratat>>7) 7) nownow

*QOLt*QOLt

1010 100100 9494 7575

99 100100 8888 6666

88 100100 7676 5555

77 100100 5959 4444

66 00 3939 3434

55 00 2222 2525

44 00 1111 1717

33 00 55 1212

22 00 22 88

11 00 11 55

00 00 <1<1 <5<5

deaddead 00 00 00

QOL, all distances QOL, all distances are the sameare the same 10-9 = 110-9 = 1 2-1 = 12-1 = 1

QOLt differentQOLt different 75-66=975-66=9 8-5 = 38-5 = 3

Break between 6 Break between 6 and 7=1, 100, 20, and 7=1, 100, 20, 1010

Use QOLtUse QOLt for this for this analysisanalysis

27

Transform to Transform to prob(healthy)prob(healthy)

““Healthy” = Hlthrat score of 7 or moreHealthy” = Hlthrat score of 7 or more Logit(healthyLogit(healthy0) = ) = -3.323 + .442* QOL0

QOL QOL = original coding= original coding QOLt QOLt = transformed to = transformed to

Prob(healthy)Prob(healthy) QOLtd QOLtd = QOLt with deaths set to zero= QOLt with deaths set to zero QOLtdi QOLtdi = QOLtd with missing imputed= QOLtd with missing imputed

28

SXSX Memorial Symptom Assessment Scale Memorial Symptom Assessment Scale

(MSAS)(MSAS) In the past week did you have:In the past week did you have: Difficulty concentrating, Pain, Lack of energy, Difficulty concentrating, Pain, Lack of energy,

Cough, Changes in skin, Dry mouth, Nausea, Cough, Changes in skin, Dry mouth, Nausea, Feeling drowsy, Numbness/tingling in hands and Feeling drowsy, Numbness/tingling in hands and feet, Difficulty sleeping, Feeling bloated, feet, Difficulty sleeping, Feeling bloated, Problems with urination, Vomiting, Shortness of Problems with urination, Vomiting, Shortness of breath, Diarrhea, sweats, mouth sores, problems breath, Diarrhea, sweats, mouth sores, problems with sexual interest, with sexual interest, itchingitching, lack of appetite, , lack of appetite, dizziness, difficulty swallowing, change in the dizziness, difficulty swallowing, change in the way food tastes, weight loss, hair loss, way food tastes, weight loss, hair loss, constipation, swelling of arms or legs, “I don’t constipation, swelling of arms or legs, “I don’t look like myself”, other (!)look like myself”, other (!)

Feeling sad, worrying, feeling irritable, feeling Feeling sad, worrying, feeling irritable, feeling nervousnervous

29

Sx Scoring (MSAS)Sx Scoring (MSAS) First 22: First 22:

0 did not occur; 0 did not occur; 1.6 a little bit, 1.6 a little bit, 2.4 somewhat, 2.4 somewhat, 3.2 a lot, 3.2 a lot, 3.8, occurred but did not bother me at all, 3.8, occurred but did not bother me at all, 4.0 bothered me very much4.0 bothered me very much

Last 4: Last 4: 0 did not occur, 0 did not occur, 1 occurred rarely, 1 occurred rarely, 2 occasionally, 2 occasionally, 3 frequently, 3 frequently, 4 almost constantly4 almost constantly

Total score is average value (high is bad, 4 is Total score is average value (high is bad, 4 is max)max)

““Continuous”, low value is goodContinuous”, low value is good

30

SX SX

(selected (selected values)values)

**SXt**SXt

P(HlthratP(Hlthrat>>77) given SX ) given SX

.03.03 8383

.25.25 7575

.5.5 6666

11 4343

1.51.5 2222

22 1010

2.52.5 33

deaddead 00

Transform SX to Transform SX to SXtSXt

Transformation Transformation can be done for can be done for continuous continuous variablesvariables

3-organization3-organization

32

Longitudinal Data-- IdealLongitudinal Data-- Ideal

Rectangular FileRectangular File Spread sheetSpread sheet

A QOL value in every cellA QOL value in every cell ADHCADHC

939 rows (1 row for each person)939 rows (1 row for each person) 3 columns (0, 6, 12 months)3 columns (0, 6, 12 months)

C3C3 300 rows (1 row for each person)300 rows (1 row for each person) 3*52 = 156 columns, (1 column for each 3*52 = 156 columns, (1 column for each

week)week)

33

ADHC was not idealADHC was not ideal

We set dead to zeroWe set dead to zero We imputed the missingWe imputed the missing Complete 3 x 937 arrayComplete 3 x 937 array

34

C3 not idealC3 not ideal

DeathsDeaths Missing dataMissing data Unscheduled weeksUnscheduled weeks Recruited over timeRecruited over time

persons will have unequal number of persons will have unequal number of weeksweeks

Each person has a different scheduleEach person has a different schedule When did the missing interviews “not When did the missing interviews “not

happen”?happen”?

35

Tidy DatasetTidy Dataset

Person’s potential f/u = weeks from Person’s potential f/u = weeks from enrollment to end of data collectionenrollment to end of data collection

Bin (cell, column) for each week of Bin (cell, column) for each week of potentialpotential f/u f/u

First enrollee will have 52*3 binsFirst enrollee will have 52*3 bins Enrollee 2.5 years later will have 52/2=26 Enrollee 2.5 years later will have 52/2=26

binsbins Deaths: Set value in bins from death to the Deaths: Set value in bins from death to the

end of this person’s end of this person’s potential follow-uppotential follow-up to to zerozero

36

Person 34Person 34 50-year old man50-year old man Referred from HospiceReferred from Hospice Dying of cancer, frequent severe painDying of cancer, frequent severe pain QOLbase = 10QOLbase = 10 SXbase = .75SXbase = .75 Lived 135 days (19 weeks)Lived 135 days (19 weeks) Potential f/u 463 days (66 weeks)Potential f/u 463 days (66 weeks)

(from his enrollment to end of data collection)(from his enrollment to end of data collection) 328 days dead (47 weeks)328 days dead (47 weeks)

37

Person 34 QOL (original Person 34 QOL (original coding)coding)

pattern for person 34 (original coding)

QOLt, QOLtd, QOLtdi

laff nice_graphs01.sps 2-20-2006 (new )

after days after enroll

5004003002001000

QO

L

10.0

9.0

8.0

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6.0

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Person 34 QOLt Person 34 QOLt (transformed)(transformed)

pattern for person 34 QOLt

QOLt, QOLtd, QOLtdi


after days after enroll

5004003002001000

QO

LT

80.0

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Person 34 QOLtd (set dead Person 34 QOLtd (set dead to zero)to zero)

pattern for person 34, QOLt, QOLtd

QOLt, QOLtd, QOLtdi


5004003002001000

80.0

60.0

40.0

20.0

0.0

QOLTD

after days after enr

QOLT


4- missing data 4- missing data and imputationand imputation

41

Influence of the deathsInfluence of the deaths

Complete case analysis gives no weight to Complete case analysis gives no weight to deathsdeaths

Transforming and setting deaths to 0 may Transforming and setting deaths to 0 may give too much weight to deaths, because give too much weight to deaths, because after death a person has no missing dataafter death a person has no missing data

May need to impute other missing data as May need to impute other missing data as wellwell Can remove later as sensitivity analysisCan remove later as sensitivity analysis

Only during potential follow-upOnly during potential follow-up

42

MissingMissing All methods are based on untestable All methods are based on untestable

assumptionsassumptions Multiple imputation for cross-sectional Multiple imputation for cross-sectional

missingmissing Software Software

Longitudinal, jury’s still outLongitudinal, jury’s still out No softwareNo software

C3 data surely not MARC3 data surely not MAR (unless accounting for death makes them (unless accounting for death makes them

MAR?)MAR?) Gain some intuitionGain some intuition

43

CHS Subjects who return from CHS Subjects who return from being missingbeing missing

YY00 YY11 __ __ (Y(Y44) _ Y) _ Y6 6 YY77

YY4 4 is “like” a missing value is “like” a missing value 10 times as likely to be missing as Y10 times as likely to be missing as Y1 1 or Yor Y77 This person had other missing dataThis person had other missing data Like healthier subset of missing?Like healthier subset of missing?

Impute YImpute Y4 4 in various simple ways in various simple ways Compare observed to imputed value of YCompare observed to imputed value of Y44

Engels and Diehr. Journal of Clinical Engels and Diehr. Journal of Clinical Epidemiology 2003; 56:968-976.Epidemiology 2003; 56:968-976.

44

FindingsFindings

Most imputed values were biased too Most imputed values were biased too healthyhealthy Best were: (before+after)/2, LOCF, NOCB, Best were: (before+after)/2, LOCF, NOCB,

regression on baseline dataregression on baseline data Most imputed values were under-Most imputed values were under-

disperseddispersed Best were: NOCB, LOCFBest were: NOCB, LOCF

Conclusion: use the person’s own Conclusion: use the person’s own longitudinal data to impute missing datalongitudinal data to impute missing data

45

IImputation of Missingmputation of Missing

Everyone has a favorite methodEveryone has a favorite method I prefer imputation by a simple I prefer imputation by a simple

method, using the person’s own method, using the person’s own longitudinal datalongitudinal data

Knowing person died helpsKnowing person died helps Scatterplot of QOLtd by several Scatterplot of QOLtd by several

f(time) for each person who died f(time) for each person who died Log of “time until death” looked Log of “time until death” looked

the best for all subjects.the best for all subjects.

46

47

Person 34, QOLtd by log(days from death)

nicegraphs_02.sps, 6-15-2006

6.05.95.85.75.65.5

80.0

60.0

40.0

20.0

0.0

-20.0

QOLTD

ln(400 - # of days u

QOLT


48

IImputation of Missing Datamputation of Missing Data(weeks with no entry)(weeks with no entry)

Separate regression for each person.Separate regression for each person. Set QOLtdi = a + b* ln(days before Set QOLtdi = a + b* ln(days before

death) if QOLtd is missingdeath) if QOLtd is missing

Other approachesOther approaches ModelingModeling Multiple imputationMultiple imputation

49

Person 34 QOLtdi (impute Person 34 QOLtdi (impute missing)missing)

pattern for person 34

QOLt, QOLtd, QOLtdi


5004003002001000

80.0

60.0

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QOLTD


QOLT


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Different NInterpretation

51

52

Person 34, SXtd by log(days from death)

nicegraphs_02.sps, 6-15-2006

6.05.95.85.75.65.5

80.0

60.0

40.0

20.0

0.0

-20.0

SXTD


SXT


53

Person 34 SX, deaths and Person 34 SX, deaths and missingmissing

MI,Locf,

Missing=“5”


SXt, SXtd, SXtdi


5004003002001000

80.0

60.0

40.0

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0.0

-20.0

SXTDI


SXTD


SXT


pain

Average QOLtdi Average QOLtdi and SXtdi in the and SXtdi in the first 6 monthsfirst 6 months

(estimated) % healthy (estimated) % healthy conditional on either QOL or conditional on either QOL or

SXSX

55

Standardized at baselineQOL < SX

AUC (to date)7.8 wk, 9.9 wk, t=3.8

QOLtdi and SXtdi in first 6 months

nice_graphs04.sps 3-25-2006 (new )

WEEK

25

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an

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QOLTDI

SXTDI

5-analysis5-analysis

57

Possible Outcome Possible Outcome VariablesVariables

QOL, QOLtQOL, QOLt If death, missing rates low (or MCAR)If death, missing rates low (or MCAR)

QOLtdQOLtd For analytic methods that (implicitly) impute For analytic methods that (implicitly) impute

missing (GEE, AUC, growth curve, multi-level)missing (GEE, AUC, growth curve, multi-level) QOLtdi QOLtdi

For graphs, population meansFor graphs, population means QOLtdi | aliveQOLtdi | alive

Imputed values improve estimatesImputed values improve estimates f f -1-1 (QOLtdi) (QOLtdi)

Original scale, death is its own categoryOriginal scale, death is its own category

58

Survival Function

Survival in Days (as of 2-15-2006)

6005004003002001000

Cu

m S

urv

iva

l1.0

.8

.6

.4

.2

0.0

Survival Function

Censored

Healthy volunteer effect

59At least 26 weeks potential f/u, Back-transform, original coding (QOL)

Accounts for death and imputed values, Hospice vs Other? - Ordinal analysis

THE Graph

Inverse QOLtdi in First 6 Months

N = 84, 6 mos pot f/u, nice_graphs27.sps 6-25-2006

WEEK

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Co

un

t

100

80

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QOLtdi inv

Dead

0-2

3-6

7-10

60

Hospice effect on QOLtdi Hospice effect on QOLtdi (n=84)(n=84)

AUC = weeks of healthy lifeSimilar baseline

Average QOLtdi per week


WEEK

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DI

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Hospice Referral

Other

Hospice Referral

61

QOL AUC = WHL|QOLQOL AUC = WHL|QOL

62

Regression of QOLtdi on Regression of QOLtdi on TimeTime

Average QOLtdi in Hospice vs. Other


WEEK

3020100

QO

LT

DI

80

60

40

20

0

Hospice Referral

Hospice Referral

Other

63

QOLtdi |AliveQOLtdi |Alive

Different folks each timeImmortal cohort

Average QOLtdi per week (alive only)


WEEK

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Hospice Referral

Other

Hospice Referral

6-Discussion6-Discussion

Transformations/DeathTransformations/Death

ImputationImputation

Tidy datasetTidy dataset

65

Transformation:Transformation: Dichotomizing and QOLtd are the only measures Dichotomizing and QOLtd are the only measures

that combine death and QOL (utility, preferences)that combine death and QOL (utility, preferences) Transformation is not appropriate for every Transformation is not appropriate for every

variable. Death should be part of the construct. variable. Death should be part of the construct. Dichotomizing, OK to put death in “low” categoryDichotomizing, OK to put death in “low” category

Death is bad health (Hlthrat )Death is bad health (Hlthrat ) Death is probably bad QOLDeath is probably bad QOL May we think of death as bad SX?May we think of death as bad SX?

Unclear. Maybe death cures SX. (itching)Unclear. Maybe death cures SX. (itching)

Does using Pr( Hlthrat Does using Pr( Hlthrat >>7 | SX) get around this 7 | SX) get around this problem? Only need to assume that dead not problem? Only need to assume that dead not healthy.healthy.

66

Multiple ImputationMultiple Imputation

vs. sensitivity analysisvs. sensitivity analysis with AUCwith AUC

67

Person 34 SX, multiple Person 34 SX, multiple imputation?imputation?


SXtd, SXtdi


5004003002001000

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SXTD


68

Person 34 SX, deaths and Person 34 SX, deaths and missingmissing


SX: AUC by trapezoidal rule


5004003002001000

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40.0

20.0

0.0

-20.0

SXTDI


SXTD


Is trapezoidalrule imputation?

69

To create a tidy datasetTo create a tidy dataset BBin the data in equal-time bins (1 week), 1 in the data in equal-time bins (1 week), 1

bin for each potential week of f/ubin for each potential week of f/u TTransform QOL to new 0 to 100 scale where ransform QOL to new 0 to 100 scale where

dead=0dead=0 QOLtQOLt

Fill in zeroes for potential weeks when Fill in zeroes for potential weeks when person was person was DDeadead QOLtd QOLtd

IImpute the missing data for potential weeks mpute the missing data for potential weeks when person was alive but data were missing. when person was alive but data were missing. QOLtdiQOLtdi

BTDI --- Be Tidy!BTDI --- Be Tidy!

70

Tidy DatasetTidy Dataset

Necessary to place the imputed, dead Necessary to place the imputed, dead interviewsinterviews

Makes it clear what is known when, Makes it clear what is known when, as everyone has a value at each as everyone has a value at each potential timepotential time

Specifically deals with death and Specifically deals with death and missing data, so assumptions are missing data, so assumptions are clearclear

““Virtual” tidy dataset may be enough Virtual” tidy dataset may be enough in simpler datasets in simpler datasets

Death MattersDeath MattersBe TidyBe Tidy

Documents

Death and Missing Data in Longitudinal Studies: Quality of Life at the End of Life Paula Diehr Maximising return from cohort studies: prevention of attrition