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Summarizing Quality of Life in the Presence of Limited Survival Gerhardt Pohl, Li Li Eli Lilly and Company

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Objectives In this talk we focus on a special case of informative missing data, patients who cease to provide longitudinal patient reported outcomes (PRO’s) due to death. We compare various commonly used methods for analyzing such data and propose an approach based on the proportion of patients at various levels.

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Overview Problem Statement Limitations of Current Methods (Brief Aside on Plotting Individual Patient Profiles) Proposal Summary and Discussion of Future Directions

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Problem Statement Consider QoL or other PRO’s collected over time. We desire to summarize the mean profile of the scores at the various time points. However, patients often fail to complete all assessments due to early death. Further complicating the situation is informative censoring. Patient’s scores decline as they approach death, but they also often fail to report scores as they decline.

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Non-Informative vs. Informative Censoring Solid lines indicate observed data; and dotted, missing data. Non-InformativeInformative

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Commonly Used Methods Mixed Model Repeated Measures (MMRM) Area Under the Curve (AUC) Survival Methods Latent Effects Models

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Limitations of MMRM Consider the model with unique mean and between-patient variability at each time point with possible within-patient correlation in the scores over the time. Underlying assumption is that patients share same trajectory of score over time with some patients only contributing a portion of the profile. Variability is modeled only in outcome and not in time of observation which is assumed fixed with common mean outcome at each observation time. However, in reality, patients are experiencing accelerated time to failure with informative censoring.

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MMRM Unbiased in the Non- Informative Setting Solid lines indicate observed data; and dotted, missing data. Non-InformativeInformative

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Complex Profile of Real-Life PRO’s in Oncology Burden Time Untreated Treated Chemotherapy

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Complex Profile Befuddles Time to Worsening Analyses Time to event analysis appears ideal for handling right-censored data. However, of worsening in treated occurs immediately at outset of cytotoxic chemotherapy.

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Causal Diagram Treatment PROAE Disease Cycle 1 Treatment PROAE Disease Cycle 2 Etc. Disease Measure AE Measure Disease Measure AE Measure

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Plotting Individual Patient Profiles: Spaghetti Plots Symptom scores (discrete 0-4) for 300 patients versus time.

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Plotting Individual Patient Profiles: Lasagna Plots Bruce J. Swihart, Brian Caffo, Bryan D. James, Matthew Strand, Brian S. Schwartz, and Naresh M. Punjab. “Lasagna Plots: A Saucy Alternative to Spaghetti Plots”. Epidemiology, Vol. 21, Number 5, Sept Remap intensity of score from vertical axis to a color and use the location on vertical axis to denote individual patient.

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Each Row is a Patient Week 1Week 2Week 3Week 4Week 5Week 6Week 7

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Each Row is a Patient Week 1Week 2Week 3Week 4Week 5Week 6Week 7 Hint of early tolerability burden

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Sorted by Treatment Group Week 1Week 2Week 3Week 4Week 5Week 6Week 7 Control Treated

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Sorted by Treatment Group and Duration of Follow-Up Week 1Week 2Week 3Week 4Week 5Week 6Week 7DurationWeek 1Week 2Week 3Week 4Week 5Week 6Week 7Duration

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Sorted by Treatment Group and Duration of Follow-Up Week 1Week 2Week 3Week 4Week 5Week 6Week 7DurationWeek 1Week 2Week 3Week 4Week 5Week 6Week 7Duration Poorer scores near termination

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Additional Features Sorting by characteristics of plotted data and/or by external characteristics Annotation of discrete events and events with duration. Filtering rows to subsets of patients Automated aggregation of patients with similar profiles to allow more than one patient per horizontal band. Side panels showing related data, e.g., Kaplan- Meier plots, proportion of data plotted. Special thanks to Wei Wang, Eli Lilly and Co., Advanced Analytics Visualization.

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Limitations of AUC Methods Two AUC-Equivalent Patients An approach to compensate for varying lengths of survival is to calculate area under the curve or score time values (cf. QALY). Note that death is mapped to zero score. AUC yields a complete ordering of score and survival. Exchangeability of quality and time is questionable. Induces linearity in PRO scale that may not be realistic.

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Probability-Based Methods Rather than average scores, summarize as proportion of patients at various levels at each time point. n = vs.

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Incorporating Survival Death can be appended to low end of score. n = vs. n =

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Summaries of Categorical Probabilities Cumulative Proportion of Time in Category –One can “integrate” over time to obtain the cumulative proportion of time the group spends in each PRO level.

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Underlying Nature of Data PatientTime in Category 1(1.0, 2.0, 1.0, 1.0, 0.0) 2(0.0, 0.0, 1.0, 4.0, 0.0) 3(0.0, 1.0, 1.0, 3.0, 0.0) 4(0.0, 0.0, 1.0, 1.0, 3.0) Group-Level(1.0, 3.0, 4.0, 9.0, 3.0) Proportion of time-person spent in each Category Group-Level(1/20, 3/20, 4/20, 9/20, 3/20) Treatment ( p ) (p 1, p 2, p 3, p 4, p 5 ) Control ( q ) (q 1, q 2, q 3, q 4, q 5 )

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Need an Ordering Metric for Ranking which Summary Vectors are “Better” 3 possible methods, each has pros and cons.

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1. Majorization Order

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2. Utility or Cost function

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3. Pseudo Increasing Convex Order (P-ICX order)

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A 3-state example 3 health statesGoodBadDeath Proportion of time spent in each state Treatment (p)P1P1 P2P2 P3P3 Control (q)q1q1 q2q2 q3q3 Difference (d=p-q)d1d1 d2d3d3

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Connecting each approach with d.

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3 health states GoodBadDeath Propo rtion of time spent in each state Trt (p) P 1 (0.29) P 2 (0.71) P 3 (0.0) Con (q) q 1 (0.30) q 2 (0.5) q 3 (0.5) Diff. (d=p-q) d 1 (-0.01) d2 (0.21) d 3 (-0.5) Majorization: reject that treatment is better than control P-ICX: accept that treatment is better than control at c=2

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3 health states GoodBadDeath Propo rtion of time spent in each state Trt (p) P 1 (0.49) P 2 (0) P 3 (0.51) Con (q) q 1 (0.0) q 2 (0.97) q 3 (0.03) Diff. (d=p-q) d 1 (0.49) d2 (-0.97) d 3 (0.48) P-ICX: Reject that treatment is better than control at c=2 trol Cost Function: Accept that treatment is better at c=2an

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P-ICX order is in the middle of majorization and Cost function method regarding acceptance of good PRO performance. Both majorization order and P-ICX order consider survival benefit.

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Example Simulated Data –Two arms: treatment vs. control (1:1) –Sample size: 300. –Survival: treatment arm has longer survival rate than control (To show contrast, treatment arm survival rate ~ 1). –Planned visits: 6 bi-monthly visit. Follow PRO until death or completion of visits, follow patients until death or completion of study (720 days).

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Survival curve

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Simulated Data (continued) –Longitudinal categorical QoL scores True trend: –Treatment arm has worse QoL score than control at the first 2-3 cycles, decreased to more tolerable score than control with time going on. –Control arm has an increasing trend over time –Health status declines faster (PRO score increases) as they approach death. Observed trend (Average of Available Data): –Missing due to death or inability to conduct survey due to approaching death.

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True Curve

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Method 1: Naïve Estimator Average of score at each visit among available patients. Observed curve gives impression that control arm is better than treatment arm.

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Method 2: MMRM –Treat score as continuous dependent. –Model separate means at each visit (treatment by visit interaction) with exchangeable covariance within-patient and independent between-patient. –Profile is similar to naïve estimator.

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Method 3: AUC method Area under curve up to 14 months. [Conclusion] x1NMeanStd DevStd Err Pr > |t| Control Treatment <.0001 P-value: two-sample t-test

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Proposed Method Select a time period of interest– e.g., 14 months. Collapse 5 categories (raw categories: 0-4) to 2 categories (0 or category for scores of 1-4). Incorporate death as the worst PRO level. Integrate over time to obtain the proportion of time the group spends in each PRO level. Adopt P-ICX order to compare PRO and select weight of treatment effect in each level: weight (2,1)->state (0, 1-4).

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Results Proportion of time spent in each level during 12 months Weight for raw states: (5,4,3,2,1)

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d=(-0.06, 0.20) Quality of Life Status Arms 01-4Death Treatment Control Difference

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Summary and Discussion: Proposed probability based method to compare PRO between treatments may avoid need for weighting scores in some cases (majorization). 3 possible ranking methods for comparing vectors. –Majorization: strongest condition –Cost function: simple concept –P-ICX order: cost function+ improved survival requirement Future research: How to choose weight? P-ICX share the same question with cost function.

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A formal definition of ICX

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