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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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Missing Data - Definitions

• Missing completely at random

• Missing at random

• Nonignorable

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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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Results - SDS

12

14

16

18

20

22

24

0 6 11 21

Time (weeks)

SD

S s

core

NI

Wtd MAR

MAR

CC

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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)

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Conclusions

• Missing data is a pervasive problem• Standard approaches can lead

to misleading inferences• Sensitivity analysis is a key

component• Certain comparisons are more

susceptible than others