Modeling Quality of Life Data with Missing Values

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Modeling Quality of Life Datawith Missing Values

• Andrea B. Troxel, Sc.D.
• Assistant Professor of Biostatistics
• Center for Clinical Epidemiology and
  Biostatistics
• University 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
• Subjects 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 Week Week Week
0 6 11 21
n 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 Patternsand Reasons
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Submission Rates

• Restrict analysis to subjects who survived for 21
  weeks
• N227

Week Week Week Week
0 6 11 21
N 227 197 187 172
100 87 82 76
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Missing Data Patterns
Time Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Pattern ( 1submitted, 0missing) Total
0 1 1 1 1 1 1 1 1 227
6 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.

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Results - SDS
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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

• SDSgt24 ? 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
• 95CI (0.28, 0.92)
• Significant random subject effect (p lt .0001)

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Models Hand/Foot Sensitivity

• 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)
• N154 (arms 1-5, alive for 21 weeks)

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Results Hand/Foot Sensitivity
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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