Comparing the Time to Response in Antidepressant Clinical Trials Roy N. Tamura, Ph.D. Eli Lilly and Company Indianapolis, Indiana 2001 Purdue University Department of Statistics Seminar

Comparing the Time to Response in Antidepressant Clinical Trials I. Background on Depression and Depression Clinical Trials II. Cure Model for Time to Response III. Test of Latency for Cure Model IV. Proportional Hazards Cure Model

Major Depression Lifetime risk: Women: 10-25% Men: 5-12% Average age at onset: mid-20s Course of illness: –50-60% of patients will have a 2nd episode

Cost of Depression Estimated Annual Costs to Business in the US: >40 billion dollars –Absenteeism –Lost Productivity –Suicides –Treatment/Rehabilitation MIT Sloan School of Management Study

Treatment Options for Depression 1. Medication Tricyclics (Impramine, Amitriptyline) SSRI’s (Prozac, Zoloft, Paxil) Others (Wellbutrin) 2. Therapy Cognitive Behavioral Interpersonal 3. Electroshock

Clinical Trials Patients meeting diagnostic criteria for depression are randomly assigned to treatment groups Patients are scheduled for visits to a psychiatrist at prespecified visit intervals up to some time point (usually 6-8 weeks) At each visit, severity of depression is assessed using a structured interview and depression rating scale

Important Efficacy Components of an Antidepressant 1. Response Rate 2. Time to Response Response usually defined by change in a rating scale like CGI or Hamilton Depression Scale.

Cure Model: H(t) = p S(t) + (1-p) H(t) is the probability that time to response > t p is the probability of response S(t) is the probability that time to response > t among patients who respond

Cure Model Terminology Proportion of responders (p): incidence Time to response for responders (S(t)): latency

Nonparametric Generalized Maximum Likelihood Estimates: p = 1 - H(u) S(t) = (H(t) - (1 - p )) / p where H is the Kaplan-Meier product limit estimator, and u is the endpoint of the trial. ^ ^ ^ ^ ^ ^ ^

Six Week Trial of Fluoxetine vs Fluoxetine + Pindolol in Major Depressive Disorder One Hundred Eleven Randomized Patients Twice Weekly Visits for First Three Weeks, Weekly Visits Thereafter Response: 50% or greater reduction in HAMD 17 item from baseline

Unconditional Time to Response Curves

Conditional Time to Response Curves

Why not look at H(t)? Time to response for all patients Antidepressant A:50% response rate Everyone responds at exactly two weeks Antidepressant B:90% response rate Everyone responds at exactly two weeks Antidepressant B is more effective than Antidepressant A but does not exhibit faster onset of action.

Suppose we want to compare incidence and latency between 2 drugs in a clinical trial Incidence: several tests available (Laska and Meisner, 1992) Latency: few tests in the literature until this past year

Conditional Time to Response Curves

A Two-Sample Cramer-von Mises Test Statistic: S is a weighted pooled estimate of S from S 1 and S 2. Tamura, Faries & Feng, 2000 W 2 = -(n 1 p 1 ) (n 2 p 2 ) / (n 1 p 1 + n 2 p 2 )  S 1 (t) - S 2 (t)] 2 dS (t)   ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Bootstrap for Cramer von Mises statistic From the sample data, construct C 1, C 2, p 1, p 2, S where C 1 and C 2 are the Kaplan-Meier estimates of the censoring distributions for Groups 1 and 2       

Bootstrap for Cramer von Mises statistic 1. Generate Z, a Bernoulli random variable (p i ). 2. If Z = 1, then generate response time T* from S. If Z = 0, then set T* arbitrarily large. 3. Generate censoring time U* from C i. 4. Construct the pair (y*, *) where y* is the minimum of u* and t*, and * is the indicator variable taking the value 1 if t* is less than u*. Repeat Steps 1-4 for sample sizes of the trial and construct a bootstrap test statistic value W 2 *. Use the empirical distribution of W 2 * to determine p-values for the observed value of W 2.    

Fluoxetine / Pindolol Case Study Cramer-von Mises Statistic W 2 =.247, bootstrap p =.204 Proportions Test of Equality of Incidence Z=2.33, p =.020

Simulation Study of CvM/bootstrap procedure: Seven Scheduled Visits Sample Sizes: per group Response Rates: (equal and unequal across groups) Censoring Rates: % Proportional Hazards: S 2 (t) =  S 1 (t)}  S 1 chosen as Weibull (median time to response  17 days) 1000 realizations, each realization uses 1000 bootstrap repetitions

Simulation Results forn 1 = n 2 = 75Nominal = 0.05 p 1 p 2 Censoring  Rejection Rate.6.6None Moderate (35%) Heavy (52%) None Moderate Heavy None Moderate Heavy None Moderate Heavy NOTE:  = 2.5 corresponds to shift in median time to response from 17 days to 11 days.

Comments 1. Active comparator antidepressant trials usually have low drop-out rates. 2. Simulations of weekly assessments versus instantaneous observation of response suggest little effect on level or power of Cramer-von Mises test. 3. Typical antidepressant clinical trials have power to detect a 5-7 day shift in median time to response.

A proportional hazards cure model H(t)=p(x) S(t) + (1-p(x)) where p(x) = Pr(Response; x) = exp(x'b) / (1+ exp(x'b)) and S(t) = (S 0 (t)) exp(z'  ) Kuk and Chen, 1992 Sy and Taylor, 2000

Proportional hazards cure model Estimate b, , and S 0 (t) using maximum likelihood. Inference about parameters b and  based on observed information matrix. Constraining S 0 (t) to zero after the last observed response time leads to better estimation. Sy and Taylor, 2000

PH Cure Model - Pindolol Case Study

Baseline covariates: melancholia diagnosis (yes/no) and HAMD 17 score.

Comments on PH Cure Model 1. Attractive to be able to adjust for covariates. 2. Computationally intensive. Can't ignore S 0 (t) 3. Increased Type I error for latency parameter  in presence of heavy censoring.

Summary 1.Examining time to response increasing in importance in tests of new antidepressants. 2.Cure model is a simple way to separate incidence from latency. 3.Tests of latency possible using CvM statistic or cure model PH analyses. 4.Both CvM and PH analyses of latency need low censoring to preserve nominal level.

References Laska, EM, Meisner, MJ. Nonparametric estimation and testing in a cure model. Biometrics 1992; 48: Tamura, RN, Faries, DE, Feng, J. Comparing time to onset of response in antidepressant clinical trials using the cure model and the Cramer-von Mises test. Statistics in Medicine 2000; 19: Kuk, AYC, Chen, CH. A mixture model combining logistic regression with proportional hazards regression. Biometrika 1992; 79: Sy, JP, Taylor, JMG. Estimation in a Cox proportional hazards cure model. Biometrics 2000; 56: