Statistical Aspects of Disease Progression Modeling

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Statistical Aspects of Disease Progression
Modeling

• Jonathan L. French, ScD
• Clinical Pharmacology Statistics, Pharmacometrics
• Pfizer Global Research Development

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MODELEURS SANS FRONTIERES
MODELERS WITHOUT BORDERS
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Outline

• Introduction
• Statistical issues in disease progression
  modeling
• Methods for handling missing data
• Issues to consider when pooling studies
• Disease progression model for FEV1
• Summary

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Introduction

• Disease progression models are longitudinal
  models that describe the progression of disease
  over time
• Typically we postulate the form of an individual
  response over time
• start with the normal disease progression
  (e.g., without treatment or with placebo)
• Add the effects of treatment/intervention
• Many examples in the literature
• Holford et al (2006) review
• Chan Holford (2001) review
• Holford and Peace (1992) tacrine/Alzheimers
• Mould et al. (2002) topotecan/solid tumors

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General statistical model for disease progression

• Disease progression models are constructed as
  hierarchical models
• Level 1 describes individual disease progression
• Level 2 describes the inter-individual
  variability in disease progression

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Statistical issues

• Many of the statistical aspects of DP modeling
  are the same as those with pop PK and PK/PD
  modeling
• Distributional assumptions about residuals
• Distributional assumptions about inter-individual
  random effects
• Focus on two that are of particular concern in
  disease progression modeling
• Missing data
• Pooling multiple studies
• A third area thats important is starting out
  with well-defined and documented objectives ?
  analysis plan

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Missing data concepts

• Imagine there is a drop-out process time to
  discontinuation (T)
• Conceptually, statisticians categorize the
  drop-out process into three groups (Little and
  Rubin, 1987)
• Drop-out processes that dont depend on observed
  or unobserved outcomes
• called Missing Completely at Random (MCAR)
• E.g., relocation randomized to continue or not
• Drop-out processes that depend only on observed
  data
• called Missing at Random (MAR)
• E.g., observed lack of effectiveness over time
• Drop-out processes that depend on unobserved data
• called Missing Not at Random (MNAR) (aka
  informative dropout)
• E.g., d/c due to (unmeasured) change in disease
  progress

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Missing data what to do?

• Ad-hoc methods
• For example,
• Analyze only the subjects with complete data
• Simple imputation (e.g., LOCF, mean imputation)
• Generally dont provide valid estimates when data
  are not MCAR
• Multiple imputation
• Imputes multiple values for the missing data
• Fit model multiple times and summarize the fits
• Provides valid estimates when data are MCAR or
  MAR (assuming you have the right model)
• Likelihood-based estimation
• Estimate model based on observed data
• Standard approaches to fitting mixed effects
  models fall here
• Provides valid estimates when data are MCAR or
  MAR (assuming you have the right model)

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Missing data the good, bad and ugly

• The good
• MI and Likelihood-based estimation are fairly
  robust to the drop-out process (MCAR or MAR)
• Can identify MCAR vs. MAR/MNAR (e.g., Carpenter
  et al. 2002)
• The bad
• No way to definitively distinguish between MAR or
  MNAR!
• The ugly
• May be important to conduct sensitivity analyses
  to understand the impact of modeling the drop-out
  process
• Selection models (e.g., Diggle and Kenward, 1994)
• Pattern-mixture models (e.g., Little 1993, 1994)
• Selection models applied to disease progression
  modeling see Hu and Sale (2003)

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Informative Missingness

• Not all definitions of informative missingness
  are the same
• DK
• HS
• This has implications for estimation and
  description
• Need to simulate to get correct marginal
  distribution of outcome
• In any case, both selection models and
  pattern-mixture models depend on un-testable
  assumptions (e.g., Kenward 1998)

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Pooling studies

• The studies typically have
• different patient populations
• different study designs with respect to
• Duration of study
• Timing of observations
• Sensitivity of assay
• Differences with respect to when studies are
  conducted
• Changes in standard of care over time?
• Should consider the implications when building
  disease progression models

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Pooling studies (2)

• Typically we attempt to adjust for many of these
  effects by including covariates in the model
• Need to make some assumptions about the
  relationship between study populations (e.g.,
  treatment of metastatic disease vs. adjunct
  treatment)
• Assumptions can be explicit or implicit
• Covariate adjustment can frequently account for
  differences in patient population
• May need to consider study-specific effects if
  covariates cant be found
• Covariates and structural model changes may be
  able to account for differences in assay
  sensitivity and/or changes in standard of care
  over time
• If substantial differences remain or assumptions
  arent tenable, may need to reassess the
  pool-ability of studies

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Disease Progression Model for FEV1

• Exubera (INH) is insulin powder for oral
  inhalation with a specially designed pulmonary
  inhaler
• The extensive development program
• confirmed the effectiveness of inhaled insulin
  and
• assessed the unique consequences of pulmonary
  delivery
• The impact of INH on lung function over time is
  an important aspect of its safety profile
• One measure of lung function is FEV1 (forced
  expiratory volume in one second) FEV1 is a
  robust measure of airway function

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Background

• Previous analyses of lung function data across
  the Exubera development program showed that
  there are small decreases in FEV1 associated with
  INH treatment
• In particular, FEV1 declines associated with INH
  occurred within the first two weeks of treatment
  and were
• small,
• non-progressive after 2 weeks, and
• reversible upon discontinuation of INH treatment

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Objectives of FEV1 analysis

• Modeling was used to provide an integrated
  analysis of the pooled data
• Objectives of modeling
• Is there an acceleration of decline in pulmonary
  function?
• Is the decline in pulmonary function reversible
  after (prolonged) use of inhaled insulin?

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Patient Population Study design

• Patient population
• 3766 adult subjects with Type 1 or Type 2
  diabetes
• Duration of time-on-study ranged from 1 week to
  7 years
• Pooled across 17 phase 2/3 studies which differed
  with respect to
• patient population for example,
• Type 1 vs. Type 2 diabetes
• Healthy, asthma and COPD patients
• Study design for example,
• Controlled (parent) and uncontrolled (extension)
  studies
• Dense and sparse PFT assessments
• Discontinuation phase vs. no d/c phase
• Standard/concomitant treatment
• Standardized vs. non-standardized PFT protocol

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Exposure measure

• Exposure was measured as a dichotomous variable
  at each time point in the study
• exposed to INH,
• not exposed to INH
• When subjects were not exposed to INH, they were
  receiving the standard of care (COMP)
• Five potential treatment patterns

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Disease Progression Model for FEV1
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Results of modeling
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Effects of INH occur early and are small,
non-progressive and reversible
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Model Evaluation Population predicted values vs
Time by Group
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Posterior predictive checks

• Quantile-quantile plots of simulated vs.
  observed values suggest the model provides a
  reasonably good fit.

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Results (2)

• Factors that affected baseline FEV1 were
  consistent with those reported in the literature
• Height, age, sex, smoking status, asthma/COPD,
  BMIgt30
• Enhanced understanding of natural longitudinal
  changes in lung function in diabetic patients
• Older patients decline more rapidly
• After adjusting for other covariates, diabetes
  type was not an important covariate
• Enhanced understanding of the impact of Exubera
• Estimates of rates of onset and recovery
• Estimate of magnitude of symptomatic effect

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Pooling studies in FEV1 analysis

• Pooling multiple studies with
• differing patient populations (e.g., Type 1 vs.
  Type 2 diabetes)
• differing study designs (e.g., sparse vs. dense
  PFT assessments standardized vs.
  Non-standardized PFT assessments)
• Controlled (parent) and uncontrolled (extension)
  studies
• Discontinuation data on a subset of subjects (but
  we have some)
• We attempted to adjust for differences in patient
  population and study design by including
  covariates in the model
• Final FEV1 model included covariates for age,
  height, sex, smoking status, etc.
• Also included different residual error variances
  for protocols with standardized and
  non-standardized PFTs

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Example of pooling in FEV1 analysis

• Impact of adding covariates and changing
  structural model should be considered

Separate residual variance terms leads to more
weight given to studies with smaller variance.
.
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Missing data in FEV1 analysis

• Discontinuation rates ranged between 0 and 18
  in any treatment group across the controlled
  studies
• Pooling many studies of different durations
• view data after any discontinuation (including
  end-of-study) as missing
• In the analysis of FEV1 data, we likely have a
  mixture of missing data processes

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Missing data (2)

• Studies were planned to be of different
  durations,
• Long-term data for subjects who stopped at the
  end of their (parent) study may be MCAR
• Subjects choose whether or not to enter extension
  study
• Possible that subjects with poor FEV1 decide not
  to continue
• Since weve observed their FEV1 to that point,
  the long-term data would be MAR
• Drop-outs prior to the planned end of a (parent)
  study may be informative (MNAR)
• Possible that subjects with a steep drop in lung
  function may drop out early without a
  corresponding PFT

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Analysis Plan for FEV1

• Defined the objectives of modeling
• Is there an acceleration of decline in pulmonary
  function?
• Is the decline in pulmonary function reversible
  after (prolonged) use of inhaled insulin?
• Communicate with the project team about
  objectives, assumptions, and uses of the model
• Discussed statistical issues we knew that we
  would face
• Defined the summary statistics to use for model
  evaluation

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Analysis Plans are they worth it?

• Advantages
• Can be an effective tool for communicating the
  planned analysis
• Among project teams (PK, Clinicians,
  Statisticians)
• Between researchers and regulators
• Defines the scope of the analysis
• Opportunity to make assumptions and uses of the
  model explicit
• Highlights which aspects to use for model
  evaluation
• Gets you part-way to your final report/paper

• Disadvantages
• Takes time to prepare
• Analyst may feel locked-in to a specific model

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Summary

• Missing data can often be a problem when building
  disease progression models. Important to
• Recognize the potential pitfalls
• Recognize the alternative approaches to handling
  missing data
• Consider sensitivity analyses
• Pooling studies can always be done, but should be
  done with care and understanding about
  implications
• Recommend writing some sort of analysis plan
  prior to starting analysis
• good communication tool and helps solidify
  objectives

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Acknowledgements

• Exubera project team
• Benefited from many conversations with Diane
  Mould, Marc Gastonguay, Ken Kowalski, and Tom
  Tensfeldt

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References

• Carpenter J, Pocock, S, and Lamm CJ (2002).
  Coping with missing data in clinical trials a
  model-based approach applied to asthma trials.
  Statistics in Medicine. 21 1043-1066.
• Chan PLS and Holford NHG (2001). Drug treatment
  effects on disease progression. Annu. Rev.
  Pharmacol. Toxicol. 41 625-659.
• Diggle PJ and Kenward MG (1994). Informative
  drop-out in longitudinal data analysis (with
  discussion). Applied Statistics, 43 49-93.
• Holford NHG, Mould DR, and Peck C (2006). Disease
  Progression Models in Principles of Climical
  Pharmacology 2nd ed. A. Atkinson. New York
  Academic Press.
• Holford NHG and Peace KE (1992). Methodologic
  aspects of a population pharmacodynamic model for
  cognitive effects in Alzheimer patients treated
  with tacrine. Proc. Natl. Acad Sci. 89
  11466-11470.
• Hu C and Sale ME (2003). A Joint Model for
  nonlinear Longitudinal Data with Informative
  Dropout. J. Pharmakokinet Pharmacodyn., 30
  83-103.
• Kenward, MG (1998). Selection models for repeated
  measurements with nonrandom dropout an
  illustration of sensitivity. Statistics in
  Medicine. 17 2723-2732.
• Little RJA. (1993). Pattern-mixture models for
  multivariate incomplete data. J. Amer. Stat.
  Assoc, 88 125-134.
• Little RJA (1994). A class of pattern-mixture
  models for normal incomplete data. Biometrika,
  81 471-483.
• Little RJA and Rubin DB (1987) Statistical
  Analysis with Missing Data. New York John Wiley
  Sons.
• Mould DR, Holford NHG, Schellens JHM, Beijnen JH,
  Hutson PR, Rosing H, ten Bokkel Huinink WW,
  Rowinsky EK, Schiller JH, Russo M, and Ross G
  (2002). Population pharmacokinetic and adverse
  event analysis of topotecan in patients with
  solid tumors. Clin Pharm Ther. 71 334-348

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Backup slides
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Effects on FEV1 are small and non-progressive
Adjusted mean treatment group differences and 95
CI for FEV1 change from baseline (3- and 6-month
controlled PFT Phase 2/3 studies)
Mean Change from baseline FEV1 (? SD) by
time Type 2 subjects in Controlled PFT Phase 2/3
studies
Exubera Inhaled Insulin (INH) Advisory
Committee Briefing Document
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Effects on FEV1 are small, non-progressive
Mean Change from baseline FEV1 (? SD) by time
Type 2 subjects in Controlled PFT Phase 2/3
studies
Exubera Inhaled Insulin (INH) Advisory
Committee Briefing Document
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and reversible upon discontinuation
Mean Change from Baseline and Standard Deviation
in FEV1 (L) by Time in Patients with Type 1 DM
Onset and Withdrawal
Exubera Inhaled Insulin (INH) Advisory
Committee Briefing Document
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Results of modeling

• Is the rate of decline in FEV1 accelerated? ? No
• Natural progression in FEV1 is a loss of 57.3
  mL/year (95 CI -60.6 mL/year, -49.3 mL/year)
• The effect of INH on slope is to slow the
  progression by 1.26 mL/year (95 CI 1.2 mL/year
  faster, 2.9 mL/year slower)
• Is the effect reversible? ? Yes
• Time to recovery of 90 of the maximum offset is
  21 days (95 CI 8 days, 503 days)
• Maximum offset was estimated to be a reduction in
  FEV1 of 68.1 mL (95 CI -88 mL, -59mL)
• Time to onset of 90 of the maximum offset is 51
  days (95 CI 15 days, 390 days)

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Demographics
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Missing data in FEV1 analysis
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Predicted mean trends
Predicted typical trend Reversibility after 2
year dosing
50 year old, male, non-smokers, no ULD, BMIlt30,
HT170 cm
50 year old, female, non-smokers, no ULD, BMIlt30,
HT170 cm
Start INH
Stop INH