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. MedicationTricyclics (Impramine, Amitriptyline)

SSRI’s (Prozac, Zoloft, Paxil)

Others (Wellbutrin)

2. TherapyCognitive 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, andu is the endpoint of the trial.

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Six Week Trial of Fluoxetine vs Fluoxetine + Pindolol in Major Depressive Disorder

One Hundred Eleven Randomized Patients

Twice Weekly Visits for First Three Weeks, WeeklyVisits Thereafter

Response: 50% or greater reduction in HAMD 17 itemfrom baseline

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Unconditional Time to Response Curves

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Conditional Time to Response Curves

Why not look at H(t)? Time to response for all patients

Antidepressant A: 50% response rateEveryone responds at exactly two

weeks

Antidepressant B: 90% response rateEveryone 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

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Conditional Time to Response Curves

A Two-Sample Cramer-von Mises Test Statistic:

S is a weighted pooled estimate of S from S1 and S2.

Tamura, Faries & Feng, 2000

W2 = -(n1p1) (n2p2) / (n1p1 + n2p2)S1(t) - S2(t)]2 dS (t)^ ^ ^ ^ ^ ^ ^

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Bootstrap for Cramer von Mises statistic

From the sample data, construct C1, C2, p1, p2, S

where C1 and C2 are the Kaplan-Meier estimatesof the censoring distributions for Groups 1 and 2

Bootstrap for Cramer von Mises statistic

1. Generate Z, a Bernoulli random variable (pi).

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 Ci.

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 abootstrap test statistic value W2*.

Use the empirical distribution of W2* to determine p-valuesfor the observed value of W2.

Fluoxetine / Pindolol Case Study

• Cramer-von Mises Statistic W2 = .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: 50 - 100 per group

Response Rates: 0.6 - 0.9 (equal and unequal across groups)

Censoring Rates: 0 - 50%

Proportional Hazards: S2(t) =S1(t)}

S1 chosen as Weibull (median time to response 17 days)

1000 realizations, each realization uses 1000 bootstrap repetitions

Simulation Results for n1 = n2 = 75 Nominal = 0.05

p1 p2 CensoringRejection Rate

.6 .6 None 1 .049

.6 .6 Moderate (35%) 1 .048

.6 .6 Heavy (52%) 1 .073

.6 .6 None 1.5 .322

.6 .6 Moderate 1.5 .279

.6 .6 Heavy 1.5 .195

.6 .6 None 2 .764

.6 .6 Moderate 2 .710

.6 .6 Heavy 2 .533

.6 .6 None 2.5 .938

.6 .6 Moderate 2.5 .904

.6 .6 Heavy 2.5 .805

NOTE:= 2.5 corresponds to shift in median time to responsefrom 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) = (S0(t))exp(z')

Kuk and Chen, 1992Sy and Taylor, 2000

Proportional hazards cure model

• Estimate b, , and S0(t) using maximum likelihood. Inference about parameters b and based on observed information matrix.

• Constraining S0(t) to zero after the last observed response time leads to better estimation.

Sy and Taylor, 2000

PH Cure Model - Pindolol Case Study

Parameter Estimate S.E. pIncidence

Treatment 1.01 0.45 .026

LatencyTreatment -0.01 0.27 .968

PH Cure Model - Pindolol Case StudyBaseline covariates: melancholia diagnosis (yes/no) and HAMD 17 score.

Parameter Estimate S.E. p

Incidence

Treatment 0.97 0.46 .035

Melancholia Diagnosis 0.30 0.60 .671

HAMD 17 Score -0.09 0.07 .203

Latency

Treatment -0.08 0.28 .772

Melancholia Diagnosis -0.19 0.37 .602

HAMD 17 Score -0.03 0.05 .540

Comments on PH Cure Model

1. Attractive to be able to adjust for covariates.

2. Computationally intensive. Can't ignore S0(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: 1223-1234.

• 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: 2169-2184.

• Kuk, AYC, Chen, CH. A mixture model combining logistic regression with proportional hazards regression. Biometrika 1992; 79: 531-541.

• Sy, JP, Taylor, JMG. Estimation in a Cox proportional hazards cure model. Biometrics 2000; 56: 227-236.