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Evaluating Change in Hazard in Clinical Trials With Time-to-Event Safety Endpoints Rafia Bhore, PhD Statistical Scientist, Novartis

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Presentation on theme: "Evaluating Change in Hazard in Clinical Trials With Time-to-Event Safety Endpoints Rafia Bhore, PhD Statistical Scientist, Novartis"— Presentation transcript:

1 Evaluating Change in Hazard in Clinical Trials With Time-to-Event Safety Endpoints Rafia Bhore, PhD Statistical Scientist, Novartis Midwest Biopharmaceutical Statistics Workshop Muncie, Indiana May 21, 2013

2 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

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

4 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

5 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

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

7 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

8 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

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

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

11 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

12 | 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)

13 | 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

14 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

15  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

16 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

17 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)

18  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

19  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

20 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

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

22 | 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)

23 | 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

24 | 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

25 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 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

26 | 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 =

27 | 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 =

28 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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