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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 and efficient analysis London 6-25-2006

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2 Charge “The use of imputation to deal with attrition in cohort studies” “The use of imputation to deal with attrition in cohort studies” I will concentrate primarily on what to do about death in longitudinal studies I will concentrate primarily on what to do about death in longitudinal studies In my cohorts of older or sicker adults more than half the missing values are missing due to death In my cohorts of older or sicker adults more than half the missing values are missing due to death Taking care of the deaths first often helps deal with the other missing data Taking care of the deaths first often helps deal with the other missing data

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3 My MO First step: create a meaningful graph First step: create a meaningful graph Organize the data Organize the data A place for every observation that could have been made (if the person hadn’t died) A place for every observation that could have been made (if the person hadn’t died) Do something about the deaths Do something about the deaths assign a valid value assign a valid value Impute the (remaining) missing data Impute the (remaining) missing data Graph Graph Analyze Analyze

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4 Outline ADHC example (very simple) ADHC example (very simple) C3 example (more issues) C3 example (more issues) Death Death Organization Organization Missing data Missing data Analysis Analysis

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Example 1: ADHC Diehr and Johnson. Accounting for missing data in end-of-life research. Palliative Care 2005; 8:S50-S57.

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6 Example: ADHC Adult Day Health Care study Adult Day Health Care study RCT (ADHC vs Usual Care) RCT (ADHC vs Usual Care) 939 Frail Veterans 939 Frail Veterans At risk of nursing home placement At risk of nursing home placement 1 year study: data at 0, 6, 12 months 1 year study: data at 0, 6, 12 months Findings: ADHC expensive, ineffective Findings: ADHC expensive, ineffective Frail veterans didn’t fail Frail veterans didn’t fail Why? Why?

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7 Health Variable Utility (sort-of) Utility (sort-of) 0 to 100 0 to 100 100 is perfect health 100 is perfect health (0 is dead, but will let dead be missing at first) (0 is dead, but will let dead be missing at first)

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9 Accounting 939 persons 939 persons 3*939=2817 observations if complete 3*939=2817 observations if complete 502 observations were missing 502 observations were missing 302 missing because of death 302 missing because of death 200 missing for other reasons 200 missing for other reasons 60% of missing were due to death 60% of missing were due to death

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12 In ADHC Example: Complete case data too optimistic – significant improvement (65% complete) Complete case data too optimistic – significant improvement (65% complete) Available data even more optimistic Available data even more optimistic Accounting for the deaths showed significant decline (84% complete) Accounting for the deaths showed significant decline (84% complete) Imputing remaining missing values showed significant decline (100% complete) (ITT) Imputing remaining missing values showed significant decline (100% complete) (ITT)

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Example 2: C3 Study Complementary Comfort Care Bill Lafferty, P.I. NCI

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14 Study Design RCT RCT Effect of massage or meditation on QOL and Sx in patients at the end of life Effect of massage or meditation on QOL and Sx in patients at the end of life QOL and Sx assessed ~ every week until death QOL and Sx assessed ~ every week until death In progress In progress 3 years of data collection 3 years of data collection First 100 cases (DSMB ok) First 100 cases (DSMB ok)

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15 Outcome Variables Quality of Life (QOL) Quality of Life (QOL) Symptoms (SX) Symptoms (SX) Health Rating (Hlthrat) Health Rating (Hlthrat)

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16 QOL (pqol) How would you rate your overall quality of life during the past 7 days? 0 is NO QUALITY OF LIFE to 10 is PERFECT QUALITY OF LIFE Note: if 0 had been “dead”, this would be a “preference-rated / utility / rating scale” variable and dead would have the value zero. Missed opportunity. Note: if 0 had been “dead”, this would be a “preference-rated / utility / rating scale” variable and dead would have the value zero. Missed opportunity.

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17 Health rating (Hlthrat) 0=worst possible health you can imagine and still be alive 0=worst possible health you can imagine and still be alive 10 = as near perfect health as you can imagine 10 = as near perfect health as you can imagine Baseline only Baseline only

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2-Death Everyone is expected to die in C3.

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19 Approaches to Handle Death Ignore Ignore Set death to a “low” value, perform sensitivity analysis to see if final results change (arbitrary) Set death to a “low” value, perform sensitivity analysis to see if final results change (arbitrary) Impute the values after death as if person was still alive (immortal cohort) Impute the values after death as if person was still alive (immortal cohort) Joint modeling of survival and health Joint modeling of survival and health Health conditional on being alive Health conditional on being alive Transformation approach Transformation approach

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20 Transformation Approach Transform the outcome variable that has no value for death to another variable that does have a natural value for death. Transform the outcome variable that has no value for death to another variable that does have a natural value for death. Dichotomize, assign deaths to “low” category. Dichotomize, assign deaths to “low” category. Transform to a probability Transform to a probability Probability of being healthy Probability of being healthy Dead have probability 0 Dead have probability 0

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21 Probability Transformations Probability (QOL > 7 now | QOL now) Probability (QOL > 7 now | QOL now) Dichotomize (good QOL > 7 or bad QOL 7 or bad QOL <7 now) Probability (QOL > 7 next week | QOL now) Probability (QOL > 7 next week | QOL now) Probability (Hlthrat > 7 now | QOL now) Probability (Hlthrat > 7 now | QOL now) Diehr et al, J Clin Epidemiology, 2005 Diehr et al, J Clin Epidemiology, 2005

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22 QOL QOL>7 now P(QOL >7) next week P(Hlthrat >7) now * 10 9 8 7 6 5 4 3 2 1 0 dead Ordinal OK if dead is worst QOL State worse than death OK if nonparametric analysis (ordinal) Mean is meaningless Without deaths? With deaths Mean Difference or change or AUC is meaningless

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23 QOL QOL> 7 now P(QOL>7) next week P(Hlthrat >7) now * 10100 9100 8100 7100 60 50 40 30 20 10 00 dead0 Dichotomize to Good QOL yes/no Dead = 0 OK if death is not good QOL Mean interpretable, any analysis OK AUC=weeks with good QOL Change meaningful Loses information? Bad cutpoint? Assume death is bad QOL

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24 QOL QOL> 7 now P(QOL>7) next week P(Hlthrat >7) now * 1010094 910088 810076 710059 6039 5022 4011 305 202 101 00.5 dead00 Pr (Good QOL 1 week later|QOL now) Estimated from transition pairs Dead have 0 probability of high QOL 1 week later Mean interpretable, any analysis OK AUC = # good QOL weeks starting 1 week after b/l change, difference Assume is death part of the QOL construct (dead people have bad QOL). Probably ok.

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25 QOL QOL> 7 now P(QOL>7) next week P(Hlthrat>7) now * QOLt 101009475 91008866 81007655 71005944 603934 502225 401117 30512 2028 1015 00.53 dead000 QOLt = Pr (Good health now |QOL now) Dead have 0 probability of being healthy now. Mean interpretable, any analysis OK AUC = Healthy weeks starting at B/L change, difference OK Assume death part of the health construct. (Dead people not healthy). This seems obvious Dead vs. 0

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26 Transformation modifies relative spacing QOL QOL> 7 now P(QOL>7) one week later P(Hlthrat >7) now *QOLt 101009475 91008866 81007655 71005944 603934 502225 401117 30512 2028 1015 00<1<5 dead000 QOL, all distances are the same 10-9 = 1 2-1 = 1 QOLt different 75-66=9 8-5 = 3 Break between 6 and 7=1, 100, 20, 10 Use QOLt for this analysis

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27 Transform to prob(healthy) “Healthy” = Hlthrat score of 7 or more “Healthy” = Hlthrat score of 7 or more Logit(healthy) = Logit(healthy 0 ) = -3.323 +.442* QOL 0 QOL = original coding QOL = original coding QOLt = transformed to Prob(healthy) QOLt = transformed to Prob(healthy) QOLtd = QOLt with deaths set to zero QOLtd = QOLt with deaths set to zero QOLtdi = QOLtd with missing imputed QOLtdi = QOLtd with missing imputed

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28 SX Memorial Symptom Assessment Scale (MSAS) Memorial Symptom Assessment Scale (MSAS) In the past week did you have: In the past week did you have: Difficulty concentrating, Pain, Lack of energy, Cough, Changes in skin, Dry mouth, Nausea, Feeling drowsy, Numbness/tingling in hands and feet, Difficulty sleeping, Feeling bloated, Problems with urination, Vomiting, Shortness of breath, Diarrhea, sweats, mouth sores, problems with sexual interest, itching, lack of appetite, dizziness, difficulty swallowing, change in the way food tastes, weight loss, hair loss, constipation, swelling of arms or legs, “I don’t look like myself”, other (!) Difficulty concentrating, Pain, Lack of energy, Cough, Changes in skin, Dry mouth, Nausea, Feeling drowsy, Numbness/tingling in hands and feet, Difficulty sleeping, Feeling bloated, Problems with urination, Vomiting, Shortness of breath, Diarrhea, sweats, mouth sores, problems with sexual interest, itching, lack of appetite, dizziness, difficulty swallowing, change in the way food tastes, weight loss, hair loss, constipation, swelling of arms or legs, “I don’t look like myself”, other (!) Feeling sad, worrying, feeling irritable, feeling nervous Feeling sad, worrying, feeling irritable, feeling nervous

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29 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 much 4.0 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 constantly 4 almost constantly Total score is average value (high is bad, 4 is max) Total score is average value (high is bad, 4 is max) “Continuous”, low value is good “Continuous”, low value is good

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30 SX (selected values) **SXt P(Hlthrat>7) given SX.0383.2575.566 143 1.522 210 2.5 3 dead 0 Transform SX to SXt Transformation can be done for continuous variables

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3-organization

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32 Longitudinal Data-- Ideal Rectangular File Rectangular File Spread sheet Spread sheet A QOL value in every cell A QOL value in every cell ADHC ADHC 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) C3 C3 300 rows (1 row for each person) 300 rows (1 row for each person) 3*52 = 156 columns, (1 column for each week) 3*52 = 156 columns, (1 column for each week)

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33 ADHC was not ideal We set dead to zero We set dead to zero We imputed the missing We imputed the missing Complete 3 x 937 array Complete 3 x 937 array

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34 C3 not ideal Deaths Deaths Missing data Missing data Unscheduled weeks Unscheduled weeks Recruited over time Recruited over time persons will have unequal number of weeks persons will have unequal number of weeks Each person has a different schedule Each person has a different schedule When did the missing interviews “not happen”? When did the missing interviews “not happen”?

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35 Tidy Dataset Person’s potential f/u = weeks from enrollment to end of data collection Person’s potential f/u = weeks from enrollment to end of data collection Bin (cell, column) for each week of potential f/u Bin (cell, column) for each week of potential f/u First enrollee will have 52*3 bins First enrollee will have 52*3 bins Enrollee 2.5 years later will have 52/2=26 bins Enrollee 2.5 years later will have 52/2=26 bins Deaths: Set value in bins from death to the end of this person’s potential follow-up to zero Deaths: Set value in bins from death to the end of this person’s potential follow-up to zero

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36 Person 34 50-year old man 50-year old man Referred from Hospice Referred from Hospice Dying of cancer, frequent severe pain Dying of cancer, frequent severe pain QOLbase = 10 QOLbase = 10 SXbase =.75 SXbase =.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)

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37 Person 34 QOL (original coding)

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38 Person 34 QOLt (transformed)

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39 Person 34 QOLtd (set dead to zero)

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4- missing data and imputation

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41 Influence of the deaths Complete case analysis gives no weight to deaths Complete case analysis gives no weight to deaths Transforming and setting deaths to 0 may give too much weight to deaths, because after death a person has no missing data Transforming and setting deaths to 0 may give too much weight to deaths, because after death a person has no missing data May need to impute other missing data as well May need to impute other missing data as well Can remove later as sensitivity analysis Can remove later as sensitivity analysis Only during potential follow-up Only during potential follow-up

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42 Missing All methods are based on untestable assumptions All methods are based on untestable assumptions Multiple imputation for cross-sectional missing Multiple imputation for cross-sectional missing Software Software Longitudinal, jury’s still out Longitudinal, jury’s still out No software No software C3 data surely not MAR C3 data surely not MAR (unless accounting for death makes them MAR?) (unless accounting for death makes them MAR?) Gain some intuition Gain some intuition

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43 CHS Subjects who return from being missing Y 0 Y 1 __(Y 4 ) _ Y 6 Y 7 Y 0 Y 1 __(Y 4 ) _ Y 6 Y 7 Y 4 is “like” a missing value Y 4 is “like” a missing value 10 times as likely to be missing as Y 1 or Y 7 10 times as likely to be missing as Y 1 or Y 7 This person had other missing data This person had other missing data Like healthier subset of missing? Like healthier subset of missing? Impute Y 4 in various simple ways Impute Y 4 in various simple ways Compare observed to imputed value of Y 4 Compare observed to imputed value of Y 4 Engels and Diehr. Journal of Clinical Epidemiology 2003; 56:968-976. Engels and Diehr. Journal of Clinical Epidemiology 2003; 56:968-976.

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44 Findings Most imputed values were biased too healthy Most imputed values were biased too healthy Best were: (before+after)/2, LOCF, NOCB, regression on baseline data Best were: (before+after)/2, LOCF, NOCB, regression on baseline data Most imputed values were under-dispersed Most imputed values were under-dispersed Best were: NOCB, LOCF Best were: NOCB, LOCF Conclusion: use the person’s own longitudinal data to impute missing data Conclusion: use the person’s own longitudinal data to impute missing data

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45 Imputation of Missing Everyone has a favorite method Everyone has a favorite method I prefer imputation by a simple method, using the person’s own longitudinal data I prefer imputation by a simple method, using the person’s own longitudinal data Knowing person died helps Knowing person died helps Scatterplot of QOLtd by several f(time) for each person who died Scatterplot of QOLtd by several f(time) for each person who died Log of “time until death” looked the best for all subjects. Log of “time until death” looked the best for all subjects.

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48 Imputation of Missing Data (weeks with no entry) Separate regression for each person. Separate regression for each person. Set QOLtdi = a + b* ln(days before death) if QOLtd is missing Set QOLtdi = a + b* ln(days before death) if QOLtd is missing Other approaches Other approaches Modeling Modeling Multiple imputation Multiple imputation

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49 Person 34 QOLtdi (impute missing)

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50 Different N Interpretation

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53 Person 34 SX, deaths and missing MI, Locf, Missing=“5” pain

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Average QOLtdi and SXtdi in the first 6 months (estimated) % healthy conditional on either QOL or SX

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55 Standardized at baseline QOL < SX AUC (to date) 7.8 wk, 9.9 wk, t=3.8

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5-analysis

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57 Possible Outcome Variables QOL, QOLt QOL, QOLt If death, missing rates low (or MCAR) If death, missing rates low (or MCAR) QOLtd QOLtd For analytic methods that (implicitly) impute missing (GEE, AUC, growth curve, multi-level) For analytic methods that (implicitly) impute missing (GEE, AUC, growth curve, multi-level) QOLtdi QOLtdi For graphs, population means For graphs, population means QOLtdi | alive QOLtdi | alive Imputed values improve estimates Imputed values improve estimates f -1 (QOLtdi) f -1 (QOLtdi) Original scale, death is its own category Original scale, death is its own category

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58 Healthy volunteer effect

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59 At least 26 weeks potential f/u, Back-transform, original coding (QOL) Accounts for death and imputed values, Hospice vs Other? - Ordinal analysis

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60 Hospice effect on QOLtdi (n=84) AUC = weeks of healthy life Similar baseline

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61 QOL AUC = WHL|QOL

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62 Regression of QOLtdi on Time

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63 QOLtdi |Alive Different folks each time Immortal cohort

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6-Discussion Transformations/DeathImputation Tidy dataset

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65 Transformation: Dichotomizing and QOLtd are the only measures that combine death and QOL (utility, preferences) Dichotomizing and QOLtd are the only measures that combine death and QOL (utility, preferences) Transformation is not appropriate for every variable. Death should be part of the construct. Transformation is not appropriate for every variable. Death should be part of the construct. Dichotomizing, OK to put death in “low” category Dichotomizing, OK to put death in “low” category Death is bad health (Hlthrat ) Death is bad health (Hlthrat ) Death is probably bad QOL Death 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 >7 | SX) get around this problem? Only need to assume that dead not healthy. Does using Pr( Hlthrat >7 | SX) get around this problem? Only need to assume that dead not healthy.

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66 Multiple Imputation vs. sensitivity analysis vs. sensitivity analysis with AUC with AUC

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67 Person 34 SX, multiple imputation?

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68 Person 34 SX, deaths and missing Is trapezoidal rule imputation?

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69 To create a tidy dataset To create a tidy dataset Bin the data in equal-time bins (1 week), 1 bin for each potential week of f/u Bin the data in equal-time bins (1 week), 1 bin for each potential week of f/u Transform QOL to new 0 to 100 scale where dead=0 Transform QOL to new 0 to 100 scale where dead=0 QOLt QOLt Fill in zeroes for potential weeks when person was Dead Fill in zeroes for potential weeks when person was Dead QOLtd QOLtd Impute the missing data for potential weeks when person was alive but data were missing. Impute the missing data for potential weeks when person was alive but data were missing. QOLtdi QOLtdi BTDI --- Be Tidy! BTDI --- Be Tidy!

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70 Tidy Dataset Necessary to place the imputed, dead interviews Necessary to place the imputed, dead interviews Makes it clear what is known when, as everyone has a value at each potential time Makes it clear what is known when, as everyone has a value at each potential time Specifically deals with death and missing data, so assumptions are clear Specifically deals with death and missing data, so assumptions are clear “Virtual” tidy dataset may be enough in simpler datasets “Virtual” tidy dataset may be enough in simpler datasets

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Death Matters Be Tidy

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