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Evaluating Change in Hazard in Clinical Trials With Time-to-Event Safety Endpoints

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. Outline. Motivation Metrics of risk

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Evaluating Change in Hazard in Clinical Trials With Time-to-Event Safety Endpoints

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  1. Evaluating Changein 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

  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 Workshop

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

  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 Workshop

  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 Workshop

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

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

  8. Different Metrics of Risk An overview | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

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

  10. Drug Exposure vs. Adverse Event Rates Three patterns of AEs – O’Neill, 1988 CUMULATIVE | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  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 Workshop

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

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

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

  15. Definition of the Problem • 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 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  16. Change-point models for hazard function • Let (Ti , 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 l1,...,lkand (k-1) change points t1,...,tk-1 K-piece Piecewise Exponential Two-piece Piecewise Exponential Exponential Model | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  17. Estimation or Hypothesis Testing? Which comes first? (Chicken or Egg) Two-piece Piecewise Exponential Model • Test hypothesis of no change point, H0 ,vs. H1 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 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  18. Estimation of hazard rates Known change point • 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 Workshop

  19. Estimation of hazard rates Unknown change point • 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 Lwrtt over a restricted interval [ta,tb]. | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  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 Workshop

  21. Simulated example of Change-Point λ2= 5 2.5 Change-point? 1.5 1 λ1 = 1 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  22. 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) | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

  23. Testing of Change Points Likelihood Ratio Test (2-piece PWE) • One would think that LRT statistic has χ2 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 | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

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

  25. Simulation criteria for data True underlying models for change-point Sample size, N = 150 or 40 subjects • 2-piece Piecewise Exponential (15 models) • λ1 = 1 • λ2 = 0.2, 0.5, 1, 2, 5 • Change point,  = 30th, 50th, 70th percentile of λ1 • 3-piece Piecewise Exponential (9 models) • Early:Mid:Late hazard rates = 0.25:1:0.3 or 2:1:2 • Change point,  = 20th:50th, 20th:70th, or 50th:20th percentiles of early and middle hazards • 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 Workshop

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

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

  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) | Change in Hazard | Rafia Bhore | 21 May 2013 | Midwest Biopharmaceutical Statistics Workshop

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