Bayesian considerations for non-inferiority clinical trials with ...2015/10/02 · Non-inferiority (NI) Trial What NI trials seek to show is that any difference between the two treatments

Bayesian considerations for non-

inferiority clinical trials with case

example

Fanni Natanegara, PhD

Eli Lilly and Company

Duke Industry-Statistics Symposium

October 23, 2015

Acknowledgement

♦ Pengfei Li (Eli Lilly)

♦ Margaret Gamalo-Siebers (FDA) , Aijun Gao (Inventiv

Health Clinical), Mani Lakshminarayanan (Pfizer),

Guanghan Liu (Merck), Fanni Natanegara (Eli Lilly),

Radha Railkar (Merck), Heinz Schmidli (Novartis),

Guochen Song (Quintile)

• Bayesian Methods for the Design and Analysis of Non-

Inferiority. JBS, 2015

10/27/2015 Company Confidential © 2015 Eli Lilly and Company 2

Motivations

♦ Compare efficacy in one ethnic group to another

group for an approved drug

♦ Compare a new formulation (SC) to an existing

one (IV)

♦ Compare a drug in development to standard of

care


Non-inferiority (NI) Trial

♦ What NI trials seek to show is that any difference

between the two treatments is small enough to

allow a conclusion that the new drug (T) has at

least some effect or, in many cases, an effect

that is not too much smaller than the active

control (C).


Source: FDA2010 draft guidance for NI trials, lines 70-72

ABC of NI trial (Julious 2011)

♦ Assay sensitivity: C had its expected effect in

the NI study

♦ Bias: to be minimized by ensuring that patient

population and endpoint are similar between

past placebo-controlled and current NI studies

♦ Constancy assumption of effect: similarity of C

effect vs P in studies

• Placebo creep

• Shift in patient population


Practical consideration: NI Margin


♦ FDA CDER and CBER 2010 NI draft guidance: “single

greatest challenge in the design, conduct and interpretation of

NI trials”

♦ M1 margin: entire effect of C relative to Placebo (P) in the NI

study

• An assumed value since P is not observed

• Show that T had effect > 0 or superior to P

♦ M2 margin: largest clinically relevant difference of T vs C

• smaller than M1 (20-50% of M1)

♦ HESDE: Historical Evidence of Sensitivity to Drug Effect (ICH

E-10)

• Past trials showing a consistent estimate of a drug’s treatment

effect compared to P

NI Study Interpretations

TC

Negative direction: smaller is better

0 M

1. NI and superiority of T

2. NI only

3. NI but C is superior to T

4. NI not demonstrated

CT

Positive direction: bigger is better

NI Study Interpretations

TC

Positive direction

0 M

1. NI not demonstrated

2. NI but C is superior to T

3. NI only

4. NI and superiority of T

CT

Negative direction

Practical consideration: Fixed

margin method


♦ Pre-specified M from past studies then uses CI to reject the H0 of inferiority by M

♦ Hypothesis testing

H0: T C <M vs H1: T C M

where T and C are treatment response for T and C, respectively

♦ Fixed margin M = f*(C P) = f*CP where P is treatment response of P, CP is treatment effect of C over P, and f is between 0 and 1

• Conservative estimate of CP is to use lower bound of CI

♦ H0 is rejected if

Practical consideration: Synthesis

method


♦ Combines estimate of T vs C in NI study with estimates of C from past placebo

controlled studies

• Use variability from current and past studies to yield a CI for testing NI

hypothesis that the treatment effect rules out a loss of pre-specified fixed fraction

of the C effect

♦ Hypothesis testing

H0: TC <f* CP vs H1: TC f* CP

♦ H0 is rejected if

♦ The synthesis approach is always more efficient than the fixed margin test.

• Fixed margin method controls a Type I error rate within the NI study for a pre-

specied M

• Synthesis method controls an unconditional error rate for H0 provided that data

from the historical studies for C were treated similarly as in the current NI study.

Bayesian motivation to NI trials

♦ NI trials provides 2 comparisons,

• Direct comparison of T vs C

• Indirect comparison of T vs P

♦ Existing past trials on C vs P and the essential need to incorporate those data

• frequentist’s methods are not well suited for such situation

♦ Hypotheses of interests can be based on posterior distribution, which in turn can provide direct probability statements

♦ Increase in power and reduction in sample size, with appropriate assumptions


Bayesian approach: Meta-analytic-predictive

♦ Indirect comparison to P using historical data

♦ Note that T P = (T C) + (C P)

current NI trial historical trial(s)


• Strict constancy assumption: C P = (1C

1P) = …= (m

C m

P) = CP

• Likelihood: Xj ~ N(j , 2

j) where j(T, C)

• Prior: Meta-analysis of historical trials, XH, can provide posterior

distribution P(CP |XH), which can be used for prior on C P

• Posterior distribution on P(T P| XT, XC, XH)

♦ Alternative model: allow between trial variability

(C P), (1C

1P), …, (m

C m

P) ~ N(CP,2)

Bayesian approach: Hierarchical

priors ♦ Likelihood: Xij ~ N(j ,

2j) where j(T, C)

♦ Information on active control(s) incorporated into model as

informative priors

• T and C have informative priors obtained from historical data

e.g. meta-analysis

♦ Posterior distribution on T C

♦ Decision rule for concluding NI

where p is pre-specified and can be used to control Type I error rate

♦ How much borrowing is needed from the historical trials?

• Power prior (Ibrahim and Chen, 2000)

• Review paper of historical borrowing (Viele, 2014)


Case example: background

♦ We consider a mock diabetes NI trial, comparing

T and C in their effects in lowering the HbA1c of

Type 1 diabetes patients

♦ In diabetes NI trial, a fixed margin of 0.3% or

0.4% is usually used

• “%” is a unit in the measurement of HbA1c


Case example: model and decision rule

♦ We assume a simple Normal-based ANCOVA

model for the observed changed from baseline

in HbA1c in ith subject and jth treatment group

Yij ~ N (ij , )

ij = α0 *baselineij + αT * I[T]i + αC* (1 I[T]i ),

αT and αC are changes in HbA1c for T and C, respectively,

and I[T] is an indicator variable for T

♦ Decision rule: upper bound of 95% Credible

Interval of (T C) < 0.4%


Case example: Bayesian hierarchical

prior model

♦ Likelihood

• “Current trial” : two arms (T and C), N=150 per arm

• Sample size assumption: no treatment difference,

common sd=1.2%, NI margin=0.4%, 80% of power

♦ Prior information

• Historical studies for the C group


Historical

study

N Baseline

(sd)

Change

(sd)

S1 30 8.47 (1.6) -0.03 (1)

S2 66 7.3 (0.74) 0.06 (0.56)

S3 60 7.44 (0.86) 0.9 (0.56)


prior model

♦ Prior information

• Prior 1: non-informative prior on regression

coefficients ie α ~ N(0, sd=100), ~ U(0,100) • Prior 2: informative prior on effects on C and

baseline based on 3 historical studies in a hierarchical fashion

– Power prior (Chen, 2000) was used to generate the priors for the “current trial” by controlling the amount of historical data used via power parameter a (0=no borrowing, 1=full borrowing)

– Prior 2A: full borrowing of historical data a=1

– Prior 2B: S1 used a=1; S2 and S3 used a=0.5



prior model

♦ Frequentist analyses on the “current trial” was

conducted in SAS PROC MIXED; 95% CI for the

LSM difference of (TC) will be used for making

NI conclusion

♦ Bayesian inference was conducted in SAS

PROC MCMC with 5K burn-in, 50K posterior

samples and thin=5. Posterior mean for T and C

was reported. Upper tail of 95% posterior equal-

tail intervals for TC was used for making NI

conclusion.


Case example: analyses results


Methods

Estimate for

coefficient of

Baseline

Estimate C

(adj mean)

Estimate T

(adj mean) Estimate T-C (95% interval)

NI

conclusion

(margin 0.4)

Frequentist -0.0099 0.1521

(0.0677)

0.1574

(0.0731)

0.0054

(-0.2679, 0.2786) NI met

Non-informative

prior -0.0097

0.1519

(0.0688)

0.1544

(0.0714)

0.0025

(-0.2826, 0.2774) NI met

Informative prior

S1(1), S2(1), S3

(1)

-0.0275 0.3915

(0.1566)

0.3055

(0.0706)

-0.0860

(-0.3040, 0.1322) NI met

Informative prior

S1(1), S2(0.5),

S3 (0.5)

-0.0208 0.2780

(0.1004)

0.2505

(0.0728)

-0.0276

(-0.2634, 0.2107) NI met

Conclusions

♦ Fixed margin approach is well utilized in recent

literature whether Bayesian or not

♦ Bayesian approach to NI trials provides

advantages

• straightforward probabilistic statements

• takes into account uncertainty

• utilizes all relevant data to inform future studies

♦ Simulation work to understand sensitivity around

inclusion of historical data and operating

characteristics of NI study design

Questions?

Abstract

♦ The gold standard for evaluating treatment efficacy of a pharmaceutical product is a placebo controlled study. However, when a placebo controlled study is considered to be unethical or impractical to conduct, a viable alternative is a non-inferiority (NI) study in which an experimental treatment is compared to an active control treatment. The objective of such study is to determine whether the experimental treatment is not inferior to the active control by a pre-specified NI margin. The availability of historical studies in designing and analyzing NI study makes these types of studies conducive to the use of the Bayesian approach. In this presentation, we will highlight case examples for utilizing Bayesian methods in NI study and provide recommendations.


Documents

Bayesian considerations for non-inferiority clinical trials with ...2015/10/02 · Non-inferiority (NI) Trial What NI trials seek to show is that any difference between the two treatments