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Evaluating Change in Hazard in Clinical Trials With Time-to-Event Safety Endpoints Rafia Bhore, PhD Statistical Scientist, Novartis Email: rafia.bhore@novartis.com Midwest Biopharmaceutical Statistics Workshop Muncie, Indiana May 21, 2013

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Outline Motivation Metrics of risk Time-dependency of adverse events Change-point methodology | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop2

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Motivation | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop3

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US FDA Regulations FDA regulations created from these laws Federal Food and Drug Cosmetic (FD&C) Act (1938) submit evidence of safety to the FDA Kefauver-Harris Amendments (1962) Strengthened rules for drug safety In addition to safety, effectiveness of drug needs to be demonstrated Food and Drug Administration Amendments Act (FDAAA) (2007) Enhanced authority on monitoring safety FDA Safety and Innovation Act (FDASIA) (2012) Better adapt to truly global supply chain (Chinese and Indian drug suppliers) Safety – an older/consistent regulatory requirement | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop4

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Why quantitative methods for evaluation of safety? Safety evaluation required by regulators Extensive collection of safety data E.g., extensive safety data collected in new application (NDA/BLA/PMA) packages comprising several clinical trials Abundance of descriptive safety analyses Surprises in post-hoc review of safety data Descriptive analyses not adequate. No planned inferential analyses. Top reason why new applications for drugs/biologics/devices go to FDA Advisory Panels Understand risk of “major” events | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop5

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Metrics of risk | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop6

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Metrics of Risk 1. Crude rates 2. Exposure-adjusted rates a.Occurrences (events) per unit time of exposure (aka exposure- adjusted event rate) b.Incidences (subjects) per unit time of exposure (aka exposure- adjusted incidence rate) 3. Cumulative rates -Life table method or Kaplan-Meier method 4. Hazard rates and functions -Instantaneous measure of risk -Similar to cumulative rates -constant, decreasing, or increasing 7| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

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Type of metricDistributionAssumptions 1.Crude rateProportion (%)Binomial / Beta-binomial Appropriate when risk is relatively constant, shorter duration of exposure, or rare 2.Exposure- adjusted incidence rate Count per person- time Poisson / Neg. Binomial Appropriate when risk is relatively constant 3.Exposure- adjusted event rate Count per person- time Poisson / Neg. Binomial Appropriate when risk is relatively constant 4.Cumulative rate Based on time-to- event (%) Parametric or Non-parametric Risk can vary over time. 5.Hazard rateBased on time-to- event (count per person-time) Parametric or Non-parametric Risk can vary over time. | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop8 Different Metrics of Risk An overview

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Time-dependency of adverse events | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop9

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10 Drug Exposure vs. Adverse Event Rates Three patterns of AEs – O’Neill, 1988 CUMULATIVE

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Time-to-event Endpoints Time-to-event endpoint is a measure of time for an event from start of treatment until time that event occurs Safety Outcomes -Invasive breast cancer in Women’s Health Study -CV Thrombotic Events in a large clinical trial -Safety Signals detected through biochemical markers, Change in grade of Liver Function Tests Abnormalities in serum creatinine and phosphorus Abnormal elevations in other lab tests Efficacy Outcomes -Time-to-Relapse, Overall survival (SCLC), Cessation of Pain (Post- herpetic neuralgia) | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop11

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop12 Increased risk of Invasive Breast Cancer? Women’s Health Initiative Study on Estrogen Plus Progestin (JAMA 2002)

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop13 Increased risk of Cardiovascular Thrombotic events? FDA Advisory Committee Meeting – Li, 2001 New England Journal of Medicine – Lagakos, 2006 Study 1Study 2

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Change-Point Methodology | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop14 A tool to test and estimate for change in risk

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Risk abruptly changes over time Define risk using time-to-event outcome Is there a change in hazard? Is this statistically significant? What is the estimated time of change? (aka CHANGE- POINT) Change-point is defined as the time point at which an abrupt change occurs in the risk/benefit due to a treatment Definition of the Problem 15 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

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Change-point models for hazard function | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop16 Exponential ModelTwo-piece Piecewise Exponential K -piece Piecewise Exponential Let (T i, i ) be the observed data (time & censoring variable) with hazard function h(t) and survival function S(t) Assume hazard is constant piecewise in k intervals of time Total of k hazard rates l 1,..., l k and ( k-1) change points t 1,...,t k-1

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Two-piece Piecewise Exponential Model Test hypothesis of no change point, H 0, vs. H 1 of one change point. We can expand statistical methods to more than one change-point Estimation (Point and 95% Confidence Interval/Region) Estimate where the change point(s) occurs 17 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop Estimation or Hypothesis Testing? Which comes first? (Chicken or Egg)

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Log likelihood functions for exponential and 2-piece PWE Maximum likelihood estimates of hazard rates, l’s, given t Generalized to k (>2) change points (Bhore, Huque 2009) | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop18 Estimation of hazard rates Known change point

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In real clinical data, change points are unknown Consider log likelihood functions for 2-piece PWE Estimate t using a grid search that maximizes profile log likelihood Substitute MLE of hazard rates into log L and maximize log L wrt t over a restricted interval [t a, t b ]. | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop19 Estimation of hazard rates Unknown change point

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Confidence region/interval for change-point, t An approximate confidence region for the change point, t, was given by Loader (1991). Underlying likelihood function is not a smooth function of t. Hence confidence region may be a union of disjoint intervals. Gardner (2007) developed an efficient parametric bootstrap algorithm to estimate the confidence interval. | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop20

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Simulated example of Change-Point | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop21 Change-point? λ 1 = 1 λ 2 = 5 2.5 1.5 1

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop22 Estimation of change-point Simulation example E.g. Result: Change in hazard is estimated to occur at 0.81 units of time (95% CI: 0.64 to 0.99 units of time)

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop23 Testing of Change Points Likelihood Ratio Test (2-piece PWE) One would think that LRT statistic has χ 2 distribution with two degrees of freedom. Not true because of discontinuity at change-point See Bhore, Huque (2009), Gardner (2007) & Loader (1991) for details on computing significance level

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop24 Goodness-of-fit: Selecting correct CP model Hammerstrom, Bhore, Huque (2006 JSM, 2007 ENAR) Consider 6 time-to-event models 1.Exponential (constant hazard) 2.Two-piece PWE with decreasing hazard 3.Two-piece PWE with increasing hazard 4.Three-piece PWE with V shape 5.Three-piece PWE with upside down V shape 6.Weibull

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Sample size, N = 150 or 40 subjects 1.2-piece Piecewise Exponential (15 models) λ 1 = 1 λ 2 = 0.2, 0.5, 1, 2, 5 Change point, = 30 th, 50 th, 70 th percentile of λ 1 2.3-piece Piecewise Exponential (9 models) Early:Mid:Late hazard rates = 0.25:1:0.3 or 2:1:2 Change point, = 20 th :50 th, 20 th :70 th, or 50 th :20 th percentiles of early and middle hazards 3.Weibull (25 models) Shape = 0.25, 0.5, 1, 2, 5 and Scale = 0.5, 2, 3, 3.5, 4 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop25 Simulation criteria for data True underlying models for change-point

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop26 True model: 2-piece Piecewise Exponential (N=150) Pairwise comparison of models 2 =

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| Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop27 True model: 2-piece Piecewise Exponential (N=40) Pairwise comparison of models 2 =

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Concluding Remarks Uncontrolled or open-label Phase II/III clinical trials provide a major source of long-term safety/efficacy data for a single group. Crude incidence rates underestimate the incidence of delayed events Visual check of Kaplan-Meier curves are not sufficient to detect change in hazard Change-point methodology (new in application to clinical trials) can be applied to test whether and estimate where a change in hazard occurs. Piecewise exponential model is robust for modeling change in hazard (Bhore and Huque 2009). Percentile bootstrap preferred for computing CIs (work not shown) 28 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

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