Comparing the Time to Response in Antidepressant Clinical Trials

1
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

2
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

3
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

4
Cost of Depression

• Estimated Annual Costs to Business in the US
  gt40 billion dollars
• Absenteeism
• Lost Productivity
• Suicides
• Treatment/Rehabilitation
• MIT Sloan School of Management Study

5
Treatment Options for Depression

• 1. Medication
• Tricyclics (Impramine, Amitriptyline)
• SSRIs (Prozac, Zoloft, Paxil)
• Others (Wellbutrin)
• 2. Therapy
• Cognitive Behavioral
• Interpersonal
• 3. Electroshock

6
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

7
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.
8
Cure Model H(t) p S(t) (1-p)
H(t) is the probability that time to response gt
t p is the probability of response S(t) is the
probability that time to response gt t among
patients who respond
9
Cure Model Terminology

• Proportion of responders (p) incidence
• Time to response for responders (S(t)) latency
  
  

10
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.
11
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
12
Unconditional Time to Response Curves
13
Conditional Time to Response Curves
14
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.
15
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

16
Conditional Time to Response Curves
17
A Two-Sample Cramer-von Mises Test Statistic
ó







W2 -(n1p1) (n2p2) / (n1p1 n2p2) S1(t) -
S2(t)2 dS (t)
õ



18
Bootstrap for Cramer von Mises statistic
?
?
?
?
?
From the sample data, construct C1, C2, p1, p2,
S where C1 and C2 are the Kaplan-Meier
estimates of the censoring distributions for
Groups 1 and 2
?
?
19
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
a bootstrap test statistic value W2. Use the
empirical distribution of W2 to determine
p-values for the observed value of W2.
?
d
d
20
Fluoxetine / Pindolol Case Study

• Cramer-von Mises Statistic W2 .247, bootstrap
  p .204
• Proportions Test of Equality of Incidence
  Z2.33, p .020

21
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)b S1 chosen as Weibull
(median time to response ? 17 days) 1000
realizations, each realization uses 1000
bootstrap repetitions
22
Simulation Results for
n1 n2 75 Nominal 0.05
p1 p2 Censoring b Rejection 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 b 2.5 corresponds to shift in
median time to response from 17 days to 11
days.
23
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.

24
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, 1992 Sy and Taylor, 2000
25
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
26
PH Cure Model - Pindolol Case Study
27
PH Cure Model - Pindolol Case Study
Baseline covariates melancholia diagnosis
(yes/no) and HAMD 17 score.
28
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.
29
Summary
1. Examining time to response increasing in
importance in tests of new antidepressants. 2. Cur
e 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.
30
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.