Classification of clinical trials

Chapter 7 Reading instructions

• 7.1 Introduction• 7.2 Multicenter Trials: Read + extra material• 7.3 Superiority Trials: Read• 7.4 Equivalence/Non-inferiority Trials: Read• 7.5 Dose Response Trials: Read• 7.6 Combination Trials: Read• 7.7 Bridging Trials: Skip• 7.8 Vaccine Trails: Skip• 7.9 Discussion

Multicenter trials

All large studies are conducted at multiple centers.

Center=clinic=study site

Issues: • Treatment by center interaction*• Estimation of treatment effect.• Randomization

*) partly Covered in the lecture on basic statistical concepts

Multi center trials: interactionExample:

Treatment by center interaction

Treatment difference in diastolic blood pressure

-25

-20

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30

Ordered center number

mm

Hg

Average treatment effect: -4.39 [-6.3, -2.4] mmHg

Treatment by center: p=0.01

What can be said about the treatment effect?

Multicenter trials: interaction

Center1 2

Treatment A

Treatment B

No interaction

Center1 2

Treatment A

Treatment B

Quantitative interaction

Center1 2

Treatment A

Treatment B

Quantitative interaction

Center1 2

Treatment A

Treatment B

Qualitative interaction

• Is to be expected but difficult to detect

• Quantitative (i.e., same direction only magnitude differs) very common• Qualitative (i.e., treatment shows benefit in some centers , Placebo shows benefit in

others) less common• Qualitative interaction is of concern but not found very often and hard to establish

Multi center trials: interaction

ICH E9:• Test main effect first , if significant:• Test interaction as an exploratory analysis• If there are a large number of centers, it is less

important to consider interaction.

Sometimes poeple suggest to pool small centers.

Easy to see why (more patients/center) but what does it mean??

Multicanter trial: statistical model

ijkijjiijky

Obsijk=grand mean + centeri+treatmentj+(center*treatment)ij+errorijk

,0~ Nijk

Alternatives:• Fixed: Center and treatment*center interaction are fixed effects• Random: Center and treatment*center interaction are random effects

Fixed:• Gives a precise answer to a fairly well

defined question, does the drug work for patients at these centers?

• The only option for a single center study

• Centers are carefully chosen, not randomly

• The definition of center is arbitrary

Random:• We want to say something about patients in

general and this is the best shot at this difficult question

• Wider confidence interval reflects the true uncertainty of centers are really different.

• Allows prediction of the effect in one specific center using information from all centers.

Multicenter trialsEstimation of treatment effect

Model: effect=center + treatment + center*treatment + error

Sum of squares:

Type I Type IIIType IIVaration due to each specific factor beyond those already inthe model according to orderof specification.

Varation due to each specific factor beyond what can be explained by all other specified factors including interactions

Varation due to each specific factor beyond what can be explained by the others, excluding interactions with this specific factor

Multicenter trials

Assume k centers withTrue treatment effect:

Estimated treatment effect:

Variance of estimated treatment effect:

ii

2i

Overall treatment effect estimated by

k

iiiw

1

k

iiw

1

1where

Type III estimator: kwi 1

Treatment effects averaged over center with equal weight for all centers

Type II estimator:

k

ii

iiw

1

2

2

/1

/1

Treatment effects averaged over center weighted according to precision (think ni).

Multicenter trialsThe effect of center imbalance on type III estimates and test

0

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80

0 10 20 30 40 50 60

Percentage of patients on the smallest of two centers

Sta

ndard

err

or

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pow

erStandard error of

estimated treatment effect

Power of treatmentcomparison

200 patients split on 2 centers, placebo response N(50,25) and on treatment N(80,25), no true center effect or interaction between center and treatment.

Model including treatment, center and treatment*center, simulated 1000 times.

Multi center trial-randomization

Central randomization• One central randomization

list• Potentially large anounts of

drug wasted• Near perfectly balanced

treatemnt groups over all• Potentially large inbalance

between treatment group in individual center

• Block size can be open

For large studies with many small centers the imbalance is often ”small”,and can be estimated using a normal approximation see Anisimov 2011

Stratified randomization• One randomization list per

center• Small amount of drugs wasted• Treatment groups can be

inbalanced over all*• Close to balanced treatment

groups within centers• Block size should be sectret

ExampleThe Jupiter study includes 17802 patients recruited from 1348 centers. If the recruitment rate is modeled as a Poisson process with a intensity that follows a Gamma distribution the parameter of that gamma distribution is estimated to be scale=18.05, shape=0.73.

Upper limit of the imbalance between treatment groups for a study similar to Jupiter with center stratified randomization and block size=4

Number of patients Number of centers 95% Imbalance limit17000 1307 14318000 1384 14819000 1461 154

The 95% upper limit for the imbalance in the number of randomized patients between the two treatment groups of a study like Jupiter with almost 18000 patients and 1348 centers is 148 patients.’

Jupiter is an outcome study with low event rates and the imbalance of 148 patients corresponds to an imbalance of one event

Superiority, equivalence and non-inferiority

Experimental treatment with true mean effect:

Control treatment with true mean effect:

T

C

Superiority: The experimental treatment is better than the control treatment.

Equivalence: The experimental treatment and the control treatment are similar.

Non-inferiority: The experimental treatment is not that much worse than the control treatment.

CTH :0

CTH :1

dH CT :0

dH CT :0

dH CT :1

dH CT :1

Superiority

Superiority: The experimental treatment is better than the control treatment.

CTH :0

CTH :1

CT 0

The experimental treatment is not better than the control treatment

CTH :0

CTH :1

The experimental treatment is better than the control treatment

CT 0 CT ˆˆ

CT 0 CT ˆˆ

REJECTED

95% conf. Int.

Equivalence

dH CT :0

CT 0

The experimental treatment and the control treatment differ at least d

dH CT :0

The experimental treatment and the control treatment differs less than d

The combined null hypothesis H0 can be tested at level by testing each of the two disjunct components also at level .

-d d

dH CT :0

CT 0 dH CT :0-d d

CT

REJECTED REJECTED

90% conf. Int.

What is similarity?

Example:

We have developed a new formulation (tablet) for our old best selling drug. How do we prove that the new formulation has the same effect as the old one without new big studies?

Due credit to Chris Miller AstraZeneca biostatistics USA

BioequivalenceFDA definition:

Pharmaceutical equivalents whose rate and extent of absorption are not statistically different when administered to patients or subjects at the same molar dose under similar experimental conditions

Operationalized as:

Compared exposure in terms of AUC and Cmax of the plasma concentration vs time curve and conclude bioequivalence if the confidence for the ration between the formulations lies between 0.8 and 1.25 for both AUC and Cmax.

Crash pharmacokinetics

Time (h)

Conce

ntr

ati

on (

nm

ol/L)

Time of dose=0 Absorbtion:

Distribution:

Elimination:

The drug is distributed to the various sub compartments of the body.

The drug leaves the circulation by metabolism or excretion at an exponential rate.

The drug is absorbed from the cite of administration leading to increased concentration in the blood (plasma).

AUC=Area Under Curve Cmax=maximal concetrationTmax=time to Cmax

ExampleA phase I, open, randomized, four-way cross-over, single-centre study to estimate the pharmacokinetics and tolerability of single oral doses of 100 mg AR-H044277XX given as two different mesylate salt tablets, a base form tablet and an oral solution in healthy male subjects.

The primary objectives of this study are to estimate and compare the pharmacokinetics of two different mesylate salt tablets, a base form tablet and an oral solution given as single oral doses of 100 mg AR-H044277XX in healthy male subjects by assessment of AUC and Cmax.

A BB D

CA

DC

C AD C

DB

BA

Design: Model:Mixed effect ANOVA

ijktjkiiijkY )(

Example cont.

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8

0 4 8 12 16 20 24 28 32 36

Time af ter dos e (h)

Mea

n pl

asm

a co

ncen

tratio

n (µ

mol

/L)

x

micr base form

mesylate salt

micr mesylate salt

oral solution

Table 1 Geometric mean of the ratio between XX/sol, AW/sol and AW micr/sol of AUC, AUCt and Cmax (n=13)

Parameter Ratio Estimate 90% CI lower upper AUC XX/sol 0.95 0.85 1.07 AW/sol 1.08 0.90 1.32 AW micr/sol 1.08 0.96 1.22 Cmax XX/sol 0.97 0.84 1.13 AW/sol 1.04 0.90 1.20 AW micr/sol 1.04 0.78 1.39

XX and sol are bioequivalent by not AW and sol or AWmicr and sol.

Compare 3 new formulations to a solution

Non inferiority

dH CT :0

CT 0

The experimental treatment and the control treatment differ at least d

The experimental treatment and the control treatment differes less than d

-d

CT 0 CT ˆˆ -ddH CT :0

REJECTED

95% conf. Int.

Why Non inferiority?

To claim that the effect of the test drug is at least not to a relevant degree worse than the comparator.

Often combined with superiority on other variable e.g. non inferior effect and superior safety.

To claim that the effect of the test drug is better than placebo when placebo not considered ethical.

Intrinsic non-inferiority:

Indirect superiority:

Challenges in Non-inferiority

• The choice of delta:– How much worse (i.e. Δ) can we be but still claim ”no

worse than…”)– Work with Key Opinion Leaders on this to get a global

agreement

• Assay sensitivity:– Is a property of a clinical trial defined as the ability to

distinguish an effective treatment from a less effective or ineffective treatment

• We need to know that if placebo was included – we whould have been superior

– Similar designs as previously used including length of treatment, entry criteria etc.

Dose Response trials objectives

Objectives:• Confirm efficacy• Investigate shape of dose reponse curve• Estimate a appropriate starting dose• Indentify optimal individual dose adjustment strategy • Determination of maximal dose• Safety!

(ICH E9)

Effect

emax

e0

e50

ed50 Dose

Toxic effect

Beneficial effect

Therapeutic window

Dose Concentration(s) Effectsc

Time

E

TimeOne dose results in concentration vs time profiles for the given compound as well as one or several metabolites

Depending on the mechanisms of action we get effect vs time profiles for both wanted and unwanted effects

Effect

Dose

Inter individual variation in dose response

Population average

Dose response trials design

Design optionsParallell groups Cross overForced titration

• Large• Easy to impement• No confounding• Easy to analyse

• Small• Confounding

• Small• Carry over effects

Dose response trials design

Design: Parallell groups with k dose groups and a control.

R

Dose 1

Dose 2

Dose k

Control

N=n1N=n2

N=nkN=nk+1

How are the doses selected?Which sample size(s) should be used?

Placebo?

Dose Response trials models

ded

dEEy

50

max0

Effect: y

Ema

x

E0

E50

ed5

0

Dose

ijiijy 2,0 iid Nij;

Separate means with equal variance Regression model (here an Emax model)

Choice of statistical model

Design criteria?• Power of statistical test

• Pariwise• Trend

• Estimation of model parameter• Optimal design (E, D,…)

• Decision model for choice of dose• Which utility, NPV?

Seriously non trivial!

No placebo but significant linear dose response means efficacy confirmation

Dose 1 Dose 2 Dose 3

Dose 1Dose 2Dose 3Placebo

Significant difference from placebo confirms efficacy

Dose 1Dose 2Dose 3Active

Noninferiority to active control confirms efficacy

Confiriming efficacy

Dose response trials design options

Fixed design: doses and sample sizes are descided upfront and subsequently not changed during the trial.Adaptive design: Initial doses and sample sizes are descided upfront may subsequently be changed during the trial depending on the outcome.

5

6

78

10

911

1

2

3

4

longitudinalmodel predictsfinal outcome

estimation of dose-response

curve

decisionrule

find the optimal dosefor learning about ED95

randomisationto placebo or

“optimal ”dose

dose to vialtranslation

New patient

Continue

Go Pivotal

ongoing /outcome

patient data

Stop

Figure 4

Basic adaptive variants:• Bayesian • Frequentist (D-optimality)

Dose response trial analysis options

Pairwise comparisons: The doses are compared using significance tests often adjusted for multiple comparisons and the aim is to show effect vs the comparator and to separate the doses.

Model based: The effect is assumed to follow a parameteric model with parameters estimated from the data.

• Limited assumptions• Easy to compare doses • Need relatively many observations• No estimate of a dose reponse curve

• More assumptions• Tricky to compare doses • Need relatively few observations• Estimates a dose reponse curve

How to design a dose response trial

Predicting the percentage of time with intragastric pH>4 based on data from C2, C6, C18 and L4

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100

0 20 40 60 80 100 120 140 160

Dose AZDXXXX (mg)

Per

cen

tage

of

tim

e w

ith

pH

>4,

0-2

4h (

%)

Modelled % time with pH>4

Observed % time with pH>4

The design of a dose response trial is based on data from previous studies with the same or similar drugs.

In this example we have plenty of data on the relation between the dose and the effect on a biomarker.

Predicting the 4 week heal ing rate using a log l inear model

y = 20.26Ln(x) + 22.143

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8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Tine with pH>4 (h)

Per

cent

age

heal

ed a

fter

4

wee

ks

E40E20

L30P40

O20

We could also find litterature data relating the effect on the biomarker to clinical effect.

0 20 40 60 80 100 120 140 1600

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Modelled % time with pH>4

Observed % time with pH>4

Modelled % healed at 4 weeks

Dose AZDXXXX (mg)

Per

cen

tage

of

tim

e w

ith

pH

>4,

0-2

4h (

%)

Per

cen

tage

of

pat

ien

ts h

eald

aft

er 4

wee

ks

(%)

Samplesize:

Highest dose to have power 80% against competitor-How does this help us to select the best dose???

backup

Multicenter trials

Type II:

k

ii

k

iiik

ik

i i

i

i

n

nEE

1

1

1

12

2

1

ˆ

ˆ

Assuming (true) within center variance equal in all centers.

k

iin

Var

1

24ˆ

Type III:

k

iik

E1

1ˆ

k

iik

Var1

22

1ˆ