Post on 17-Dec-2015
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Modeling Quality of Life Datawith Missing Values
Andrea B. Troxel, Sc.D.Assistant Professor of
BiostatisticsCenter for Clinical Epidemiology
and BiostatisticsUniversity of Pennsylvania
School of Medicine
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Outline
• Why measure QOL in oncology?
• Types of missing data
• Possible modeling approaches
• Example: SWOG study of QOL in colorectal cancer
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QOL in Oncology
• Potentially debilitating effects of treatment
• Tradeoff between quantity and quality of life
• An increasingly chronic disease
• Important focus on survivorship
• Longitudinal measurements
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Missing Data - Examples
• Subject moves out of town• Researcher forgets to administer
questionnaire• Subject returns incomplete
questionnaire• Subject’s family refuses questionnaire• Subject is too sick to fill out
questionnaire• Subject dies
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Modeling Approaches
• Complete case approaches• Models for MAR data• Models for NI data• Sensitivity analyses• Extensions of failure-time
models• Imputation methods
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Models for MAR data
• Generalized linear models
• Generalized estimating equations
• Weighted methods
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Models for NI data
• Fully parametric models–Directly model the missingness
mechanism
–Estimate a nonignorability parameter
–Computationally difficult
–Untestable assumptions
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Sensitivity Analyses
• Vary aspects of model and determine effects on inference
• Local sensitivity analysis– ISNI (Troxel, Ma, and Heitjan, 2005)
–Assess sensitivity in the neighborhood of the MAR assumption
–Easy to compute and interpret
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Failure-time Models
• Take advantage of bivariate survival methods• Integrate clinical and QOL
data• Avoid primacy of one outcome
over the other• Partially handle missing data
due to death
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Multiple Imputation
• Use an appropriate method to create a series of “complete” data sets
• Use any appropriate method of analysis on each data set
• Combine the analyses to achieve one reportable result
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SWOG 9045
• Companion study to SWOG 8905– 599 subjects with advanced colorectal
cancer
–Seven arms (!) assessing effectiveness of 5-FU
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SWOG 8905
• Variations in–Route of administration
» Bolus injection (arms 1-3)
» Protracted 28-day continuous infusion (arms 4-5)
» Four weekly 24-hour infusions (arms 6-7)
–Biochemical modulation» None (arms 1, 4, 6)
» Low dose leucovorin (arms 2, 5)
» High dose leucovorin (arm 3)
» PALA (arm 7)
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SWOG 9045
• Five primary outcomes–Mouth pain–Diarrhea–Hand/foot sensitivity–Emotional functioning (SF-36)–Physical functioning (SF-36)
• Secondary outcome–Symptom distress scale (high scores = more distress)
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SWOG 9045
• 4 assessments–Randomization– 6 weeks– 11 weeks– 21 weeks
• 287 patients registered• 272 (95%) submitted baseline
questionnaire
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QOL Submission Rates
Week
0 6 11 21n 272 230 207 182
% of total 95 80 72 63
% of 272 100 83 76 65
% of alive 100 85 79 78
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Missing Data Patterns
and Reasons
11
16
21
26
0 6 11 21
Assessment Time (weeks)
SD
S
lost - death
lost - illness
lost - other
completefollow-up
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Submission Rates
• Restrict analysis to subjects who survived for 21 weeks
• N=227
Week
0 6 11 21
N 227 197 187 172% 100 87 82 76
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Missing Data Patterns
Time Pattern ( 1=submitted, 0=missing) Total
0 1 1 1 1 1 1 1 1 2276 1 1 1 1 0 0 0 0 197
11 1 1 0 0 1 1 0 0 187
21 1 0 1 0 1 0 1 0 172
n 150 26 8 13 9 2 5 14 227
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Models - SDS
• Normal GLM–Complete cases
–All available data, unweighted
–All available data, weighted
• NI model–Normal component for SDS data
– Logistic model for missingness probs.
0 1logit 0 1, 2,3it t t itP R Y t
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Sensitivity Analysis
• Assess sensitivity to nonignorability in the neighborhood of the MAR model
• Sensitivity of parameters depends on how the model is parameterized
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Sensitivity - SDS
Estimate SE ISNI*
T0(single) 17.0 .51 14.29
T6(single) 17.4 .53 1.24
T11(single) 17.3 .56 0.87
T21(single) 18.1 .59 0.73
T0(comb) 18.5 .57 4.26
T6(comb) 19.0 .60 1.10
T11(comb) 18.8 .62 1.21
T21(comb) 19.6 .64 1.02
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Frailty Model - SDS
• SDS>24 SDS “event”• Jointly assess survival and
SDS events• Estimate correlation• Estimate covariate effects• No special programming
required
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Frailty Model – SDS
• No significant effect of combination therapy
• Frailty variance estimated to be 0.54
• 95%CI (0.28, 0.92)
• Significant random subject effect (p < .0001)
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Models – Hand/Foot Sensitivity
0 1 2 3 4logit 6 11 21it iE Y I t I t I t X
• Yit is a binary indicator of bothersome or worse symptoms
• Xi is an indicator of continuous infusion vs bolus injection (arms 4,5 vs arms 1-3)
• N=154 (arms 1-5, alive for 21 weeks)
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Results – Hand/Foot Sensitivity
0
5
10
15
20
25
30
0 6 11 21
Time (weeks)
Est
imat
ed %
CC
Unwtd GEE
Wtd GEE
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Models – Hand/Foot Sensitivity
• Treatment effect OR estimates–CC: 3.1 (1.4 – 7.0)
–MAR: 2.5 (1.2 – 5.3)
–Wtd MAR: 2.5 (1.2 – 4.8)