Statistical Methods for Biotechnology Products II－Design and Classification of Clinical Trials

(1)

Statistical Methods for

Biotechnology Products II

Design and Classification of Clinical Trials

Instructor: Jen-pei Liu, Ph.D.

Division of Biometry

Department of Agronomy

National Taiwan University, and

Division of Biostatistics and Bioinformatics

National Health Research Institutes

(2)

Statistical Designs



Parallel Group Designs

The patients are randomized to one of two or more groups,

each group being allocated to a different treatment.  Advantages

 Simple and easy to implement.

 Less complicated analysis and interpretation.

 Drawbacks

(3)

(4)

Parallel Group Design



A parallel group design is a completely

randomized design (CRD)



Group comparison designs



Matched pairs parallel design

 Each patient within the pairs is matched with

some important prognostic factors

 One patient in the pair is assigned to the test

drug and other patient is assigned to placebo

(5)

Parallel Group Design

ij i ij i ij k i i i i 1 ij

The basic model for paralle group design

is the fixed-effects model for the one-way ANOVA Y

= + +

is the overall mean,

is the fixed effect of treatment i, 0,

is                 



2 ij ij

random (experimental) error with X , N(0, ) i 1,..., k; j 1,..., n

 

 

(6)

Parallel Group Design



Run-in period

 A period of placebo, no active treatment, dietary

control, or active maintenance therapy prior to randomization

 A washout period to remove effects of previous therapy  A period of obtaining baseline, a training period for

patients, investigator and staff

 A period of identifying placebo responders and

non-compliant

(7)

Example

 Haahtela, et al (NEJM 1991;325:388-392 and NEJM 1994;331:700-5)

 PhaseⅠ ： 2 years

Treatments: inhaled budesonide (600 ug, bid) inhaled terbutaline (375 ug, bid) Design: two parallel groups

 Pre-treatment period

2-week run-in period+4-week baseline period

 Randomized double-blind period:2 years

 PhaseⅡ ： 1 year

Budesonide group from phaseⅠ

4-week run-in period into two parallel groups: inhaled budesonide (200 ug, bid) and placebo

Terbutaline group from phaseⅠ

(8)

Parallel Group Design



Example Dornan, et al.

_{(1991, Diabete care)}



Design: Two-group parallel design: metfor

min vs. placebo in NIDDM



Stratified randomization wrt to HbA1C



Double-blinded



Duration: one month of run-in and 8 mont

hs of treatment

(9)

Crossover Design

Each subject is randomized to a sequence of

two or more treatments

Each subject receives two or more treatments

in a study



Advantages



Subjects act their own control



Reduction of variability

(10)

Crossover Design



Drawbacks



More difficult to implement



For stable and chronic diseases only



Biased inference due to carryover effects



More complicated analysis and

(11)

(12)

Crossover Designs



Example: Chan et al.

_{(1991, Diabete care)}



Design: two-sequence and two-period cros

sover design



Targeted patients: normotensive NIMMD



Treatments: metformin vs. Glibenclamide



2-week run-in of dietary treatment alone



2 periods of 4 weeks of active treatment wi

(13)

Crossover Designs

Optimal crossover designs for 2 formulations

Design A (Balaam’s design)

Period

Sequence

I

II

1 T

T

2 R R

3 R T

4 T R

(14)

Designs of Bioavailability Studies

Design B

Period

Sequence

I

II III

1 T R R

2 R T R

(15)

Designs of Bioavailability Studies

Design C

Period

Sequence

I

II III IV

1 T T R R

2 R R T T

3 T R R T

4 R T T R

(16)

Crossover Designs

Complete crossover design:

each sequence contains all formulations

A g x p crossover design:

There are g sequences of formulations

administered at p different time periods.

Washout period:

Rest period between two treatment periods for

which the effect of one formulation administered

at one treatment period does not carry over to

(17)

Crossover Designs

Direct drug effect:

The effect that a drug product has during the

period in which the drug is administered.

Carryover effect:

The effect that persists after the end of the dosing

period.

C-order carryover effect:

The carryover effects last up to c treatment

periods.

(18)

Crossover Designs

A linear model for response of subject i in at perio

d j sequence k:

Y

ijk

=  + S

ik

+ P

j

+ F

j,k

+ C

(j-1,k)

+ e

ijk

S

ik

iid ~ N(0, 

S2

)

e

ijk

iid~ N(0, 

t2

), t=1,…,t

(19)

Crossover Designs

Observed means for period j in sequence k



Y

_.jk

= (1/n

_k

)Y

ijk

All fixed effects can be estimated based on

gp sequence-by-period means

(gp – 1) = (g-1) + (p-1) + (g-1)(p-1)

overall = seq + period + seq*period

(20)

Crossover Designs

Within-subject linear contrasts



L =

c

1

Y

.1k

+ c

2

Y

.2k

+ …+ c

p

Y

.pk

where c

j

= 0.

Two linear contrasts

l

1

and

l

2

, are indepen

(21)

Crossover Designs

Complete crossover design:

each sequence contains all formulations

A g x p crossover design:

There are g sequences of formulations

administered at p different time periods.

Washout period:

Rest period between two treatment periods for

which the effect of one formulation administered

at one treatment period does not carry over to

the next.

(22)

Crossover Designs

Direct drug effect:

The effect that a drug product has during the

period in which the drug is administered.

Carryover effect:

The effect that persists after the end of the dosing

period.

C-order carryover effect:

The carryover effects last up to c treatment

periods.

(23)

Crossover Designs

A linear model for response of subject i in at perio

d j sequence k:

Y

ijk

=  + S

ik

+ P

j

+ F

j,k

+ C

(j-1,k)

+ e

ijk

S

ik

iid ~ N(0, 

S2

)

e

ijk

iid~ N(0, 

t2

), t=1,…,t

(24)

Crossover Designs

Observed means for period j in sequence k



Y

_.jk

= (1/n

_k

)Y

ijk

All fixed effects can be estimated based on

gp sequence-by-period means

(gp – 1) = (g-1) + (p-1) + (g-1)(p-1)

overall = seq + period + seq*period

(25)

Designs of Bioavailability Studies

Within-subject linear contrasts



L =

c

1

Y

.1k

+ c

2

Y

.2k

+ …+ c

p

Y

.pk

where c

j

= 0.

Two linear contrasts

l

1

and

l

2

, are indepen

(26)

Designs of Bioavailability Studies

The standard 2x2 crossover design

Y

ik

=(Y

i1k

, Y

i2k

)’

Mean and covariance matrix

Sequence 1

 + P1 + F1 12 + s2 s2

E(Y_ik) =

[

], 

₁

=

[

]

 + P2 + F2 + C1 s2 22 + s2

(27)

Designs of Bioavailability Studies

Sequence 2  + P1 + F2 22 + s2 s2 E(Yik) =

[

], 

2

=

[

]

 + P2 + F1 + C2 s2 12 + s2 If 12 = 22 = e2, e2 + s2 s2



₁

= 

₂

= 

= [ ]

s2 e2 + s2

(28)

Inferences for the 2x2 Design

Data Structure

Sequence Period I Period II

1 (RT) Reference Test

Data: Y

i11

Data:Y

i21

2 (TR) Test

Reference

(29)

Inferences for the 2x2 Design

The general model for the standard 2x2 c

rossover design

Y

ijk

=  + S

ik

+ P

j

+ F

(j,k)

+ C

(j-1,k)

+ e

ijk

where i(subject) = 1,…,n

k

, j(period) = 1

(30)

Inferences for the 2x2 Design

F

_R

, if k=j

F

(j,k)

=

{

k=1,2; j=1,2

F

T

, if kj

C

R

, if k=1, j=2

C

(j-1,k)

=

{

C

T

, if k=2, j=1

(31)

Inferences for the 2x2 Design

Fixed effects

Sequence Period I Period II 1 (RT) 11=  +P1+FR 21 =  +P2+FT+CR

2 (TR) 12=  +P1+FT 22=  +P2+FR+CT

(32)

Inferences for the 2x2 Design

Assumptions

S

ik

iid ~ N(0, 

S2

)

e

ijk

iid ~ N(0, 

e2

)

(33)

Inferences for the 2x2 Design

The Carryover Effects

Subject totals: U

_ik

= Y

_i1k

+ Y

_i2k

2 + C

R,

if sequence 1

E(U

ik

) =

{

2 + C

T

, if sequence 2

V(U

ik

) = 2(

e2

+ 2

s2

)

=



u2

{

U

₁₁

…,U

_n11

} and

{

U

₁₂

…,U

_n22

} are independent

(34)

Inferences for the 2x2 Design

Define C = C

_T -

C

_R

H

o

: C = 0 vs. H

a

: C  0

_

U

_.k

= (1/n

_k

)U

ik

, k=1,2.

The MVUE OF C is given as

__{    }

(35)

Inferences for the 2x2 Design

V(c) = 

u2

[(1/n

1

) + (1/n

2

)]

v(c) = s

_u2

[(1/n

₁

) + (1/n

₂

)],

where

_

s

_u2

=  (U

ik

- U

.k

)

2

/(n

1

+n

2

–2)

T

_c

= c/v(c)

(36)

Inferences for the 2x2 Design

Reject Ho if

Tc > t(/2, n1+n2 –2) Confidence interval

c  t(/2, n1+n2 –2)v(c)

The carryover effect is confounded with the sequence effect (homewo rk)

(37)

Inferences for the 2x2 Design

The Direct Drug Effect

Period differences d_ik = (Y_i2k – Y_i1k)/2 [(P2 - P1) + (FT - FR) + CR]/2, if sequence = 1 E(d_ik) =

{

[(P2 - P1) + (FR - FT) + CT]/2, if sequence = 2 V (d_ik) = _d2 = _e2/2

(38)

Inferences for the 2x2 Design

{d

11

…,d

n11

} and {d

12

…,d

n22

} are independent

samples with the same variance 

d2

Sample means of period differences



d

_.k

= (1/n

_k

)d

ik

, k=1,2

Define F = F

T

- F

R

_{ }

(39)

Inferences for the 2x2 Design

Unless C = 0, no unbiased estimator for F based on the data from both period exists

      f = d.1 – d.2 = (Y.21 - Y.11) - (Y.22 - Y.12) _{   } = (Y.21+ Y.12) - (Y.11+ Y.12) _{ } = Y.T - Y.R

f is a linear combination of the sequence-by-period means and the least squares estimator of F

(40)

Inferences for the 2x2 Design

V(f) = 

d2

[(1/n

1

) + (1/n

2

)]

v(f) = s

d2

[(1/n

1

) + (1/n

2

)],

where

_

s

d2

=  (d

ik

- d

.k

)

2

/(n

1

+n

2

–2)

H

o

: F = 0 vs. H

a

: F  0

Test Statistic T

d

= f/v(f)

(41)

Inferences for the 2x2 Design

Under the assumption of C=0

Reject H

_o

if

T

_F

 > t(/2, n

₁

+n

₂

–2)

Confidence interval

(42)

Inferences for the 2x2 Design

When C  0, f is not unbiased for F.

However, unbiased estimator can be obtained as

the difference of sample means of the first

period between the two sequences:

 

f C = Y

.11

- Y

.12

V(f C) = (

e2

+ 

s2

) [(1/n

1

) + (1/n

2

)]

(43)

Inferences for the 2x2 Design

The Period Effect

Crossover difference

d

ik

, if sequence = 1

O

_ik

=

{

(44)

Inferences for the 2x2 Design

[(P₂- P₁) + (F_T - F_R) + C_R]/2, if sequence = 1 E(Oik) = { [(P₁– P₂) + (F_T - F_R) - C_T]/2, if sequence = 2 V (Oik) = d2 = e2/2

{O11…,On11} and {O12…,On22} are independent samples with

the same variance d2.

The inference for the period effect can be performed as th at for the carryover effects and direct effect. (homework)

(45)

Inferences for the 2x2 Design

The Analysis of Variance

_

SS

total

=  (Y

ijk

- Y

…

)

2

_

=  (Y

ijk

- Y

i.k

+

Y

i.k

- Y

...

)

2



=  (Y

ijk

- Y

i.k

)

2

+ (Y

i.k

- Y

...

)

2

(46)

Inferences for the 2x2 Design

SS

between

= SS

carry

+ SS

inter



 

SS

carry

= [2n

1

n

2

/(n

1

+n

2

)][(Y

.12

+ Y

.22

) - (Y

.11

+ Y

.21

)]

2

df = 1

SS

inter

= Y

2i.k

/2 - Y

2..k

/

2n

k

, df = n

1

+n

2

-2

E(MS

carry

) = [2n

1

n

2

/(n

1

+n

2

)](C

T

- C

R

)

2

+ 

e2

+ 2

s2

(47)

Inferences for the 2x2 Design

SS

within

= SS

drug

+ SS

period

+ SS

intra



 

SS

drug

= [2n

1

n

2

/(n

1

+n

2

)][(Y

.21

- Y

.11

) - (Y

.22

+ Y

.12

)]

2

df =1



 

SS

period

= [2n

1

n

2

/(n

1

+n

2

)][(Y

.21

- Y

.11

) - (Y

.12

+ Y

.22

)]

2

df = 1

SS

inter

= Y

2ijk

- Y

2i.k

/2 - Y

2.jk

/n

k

- Y

2..k

/2n

k

,

(48)

Inferences for the 2x2 Design

E(MS

drug

)=[2n

1

n

2

/(n

1

+n

2

)][(F

T

- F

R

)+(C

T

- C

R

)]

2

+

e2

E(MS

period

) = [2n

1

n

2

/(n

1

+n

2

)](P

2

– P

1

)

2

+ 

e2

(49)

Inferences for the 2x2 Design

Carryover effect: F

_c

=

MS

carry

/MS

inter

Direct Drug Effect:

F

_d

=

MS

drug

/MS

intra

Period Effect : F

_P

=

MS

period

/MS

intra

Intersubject variability

F

v

=

MS

inter

/MS

intra

(50)

Factorial Designs

Two or more treatments are evaluated

simultaneously in the same sets of patients

via various of combinations of two

(51)

Factorial Designs



Factors: Drugs



Levels: Doses



Treatments: Combinations of drugs and

doses



Design: parallel, crossover, or a

(52)

Example

FACET International Study Group(NEJM 1997;337:1405-11)

 Effect of inhaled formoterol and budesonide on exacerbatio

n of asthma

 Double-blind, randomized, parallel group

 4-week run-in period with budesonide with 800 ug bid follo

wed by 12-month DB, randomized treatments Treatment Budesonide (A) Formoterol (B) Ⅰ _{100 ug bid Placebo}

Ⅱ _{100 ug bid 12 ug bid} Ⅲ _{400 ug bid Placebo}

(53)

(54)

Example



Parallel group design: a comparison bet

ween dietary treatment

(Mediterranean-type diet) and habitual diet



Crossover design: a comparison betwee

n simvastatin (a cholesterol lowering ag

ent) and placebo

(55)

Example



Advantages

 can efficiently use patients for evaluation of efficacy of

both treatments

 can investigate the joint treatment effects

 can establish dose-response relationship of a combination

drug product



Drawbacks

 Difficult to implement because of large number of

treatment groups

(56)

Factorial Design

ijk i j ij ijk

i j

Factorial design in parallel group design

Model for a two-way classification

Y =μ+τ+β+(τβ) +ε

is the fixed effect of level i of treatment A,

is the fixed effect of level j of treatment B,

(β







_ij _i _j

ijk

) is the interaction between of τ and β,

is the random error in observing Y

ijk

(57)

Factorial Design

a 2 i.. ... i=1 b 2 .i. ... j=1 a b 2 ij. i.. .j. ... i=1 j a b n 2 ijk ij. i=1 j=1 k

SSA = bn

(Y -Y ) ,df=a-1

SSB = an

(Y -Y ) ,df=b-1

SSAB = n

(Y -Y -Y +Y ) ,df=(a-1)(b-1)

SSE =

(Y -Y ) ,df=ab(n-1)







(58)

Factorial Design

a 2 2 i i=1 b 2 2 j j=1 a 2 2 ij i=1

E(MSA)=E[SSA/(a-1)]=σ+(bnτ)/(a-1)

E(MSB)=E[SSB/(b-1)]=σ+(anβ)/(b-1)

E(MSAB)=E[SSAB/(a-1)(b-1]

=σ+[n

(τβ) ]/[(a-1)(b-1)]



(59)

Factorial Design

Magnitude 8-group parallel design

Frequency P d1 d2 d3 QID BID Combination Trial Drug A Drug B O d1 d2 d3

0 Dose response of design A alone

16-group parallel design J. Hung

d1 d2 d3

Dose-response of design B alone chemotherapy, antibiotic, antihypertensive Randomized Concentration Control Trials (Sanathanan & Peck, 1991 Controlled Clinical Trial)

(60)

Williams’s Designs for Combination Therapy Period

Sequence Ⅰ Ⅱ Ⅲ Ⅳ

Panel A: 2 × 2 Factorial Without Concurrent Placebo Control

1 A B A + B 2 B A + B A 3 A + B A B 4 A A + B B 5 B A A + B 6 A + B B B

Panel A: 2 × 2 Factorial With Concurrent Placebo Control

1 Placebo A + B A B

(61)

Designs for Two-Drug Combined Therapy With a

Fixed Dose of One Component

Group Drug A Drug B

Panel A: The Same Fixed Dose For One Component

1 Active dose 1 Placebo

2 Active dose 1 Active dose 1

b + 1 Active dose 1 Active dose b

Panel B: Titration of The Dose Level of One Component to The Maximum Tolerable Dose

1 Titrated to MTD Placebo

2 Titrated to MTD Active dose 1

(62)

Maximum Tolerable Doses of Single Agents

for Treatment of Advance Ovarian Cancer

Drug Maximum Tolerable _{Dose (mg/m}₂_/week) Organ System of Dose-_{Limiting Toxicity}

Cisplatin 35 Renal

Carboplatin 100 Bone marrow

Cyclophosphamide 400 Bladder, Bone marrow Hexamethylmelamine 2200 Gastrointestinal

Dozorubicin 30 Bone marrow

(63)

Combinations Used in the Eradication of H. Pylori

combinations Dose Duration Eradication Rate (%) Overall Adverse Events (%) Bismuth 564 mg/ 4 times/ day 14-15 days 89 % 32 %

Metronidazole 0.6-1.5 g/ day 14-15 days Tetracycline 500 mg/ 4 times/ day 14-15 days

Bismuth 564 mg/ 4 times/ day 10-14 days 84 % 31 % Metronidazole 1.0-1.5 g/ day 10-14 days

Amoxicillin 1.5-2.0 g/ day 10-14 days

Metronidazole 500 mg 3 times/ day 12 days 89 % 13 % Amoxicillin 750 mg 3 times/ day 12 days

Ranitidine 300 mg at bed time 6 weeks

Clarithromycin 500 mg 3 times/ day 10 days 86 % 34 % Amoxicillin 750 mg 3 times/ day 10 days

Ranitidine 300 mg at bed time 6 weeks

Metronidazole 400 mg 3 times/ day 14 days 90 % 13 % Amoxicillin 750 mg 3 times/ day 14 days

Omeprazole 40 mg / day 6 weeks

Metronidazole 500 mg 2 times/ day 14 days 88 % 18 % Clarithromycin 250 mg 2 times/ day 14 days

(64)

Dose Titration Designs



A set of pre-determined dose levels



A set of pre-specified criteria of responders



Initiation with a placebo washout period



Titration up according to the pre-specified



Advantages



Simulate real clinical practices



Require fewer patients

(65)

(66)

Dose Titration Designs



Drawbacks

 Unable to blind the dose levels

 Treatment effects are confounded with time

 Unable to separate and estimate carryover effects  Should include a concurrent parallel placebo group  Overestimation of the necessary dose

 Formal statistical procedures are yet to be developed

except for binary data

(67)

Titration Design with a parallel Placebo Concurrent

Control with Diastolic Blood Pressure (mm Hg)

Dose Level 0 mg 25 mg 50 mg 100 mg 150 mg Captopril Observed DBP 110 100 99 96 94 Change from 0 -10 -11 -14 -16 Placebo Observed DBP 110 104 104 103 101 Change from 0 -6 -6 -7 -9 Difference in Change from 0 -4 -5 -7 -6

(68)

Forced Dose-Escalation Designs



Drugs have undesirable but reversible safety concerns



Drugs are not efficacious at lower dose levels



Criteria for escalation of dose levels are some safety

limiting factors



A significant number of dropouts is expected



All patients with no pre-defined safety problems are

(69)

Example

Farlow, et al (JAMA 1992;268: 2523-2529) Knapp, et al (JAMA 1992;271: 985-991)

 Tacrine for th treatment of patients with mild to moderate dementia

of probable Alzheimer’s disease

 Induction of elevation of alanine aminotransferase (ALT) in 43%-5

4% of patient over the upper limit of the normal range and in 28% of patients over three times the upper limits

 The two-adequate well-controlled studies generated the substantial

evidence for approval of tacrine employed the forced dose-escalatio n design

 Randomized, DB, placebo-controlled

(70)

Forced Dose-Escalation Design for 12-Week Tria

l of Tacrine in Alzheimer’s Disease

Randomized

Sequences Double-Blind Phase Ⅰ_{Week 1 to 6} Double-Blind Phase Ⅱ_{Week 7 to 12 Open Label}

1 Placebo Placebo

2 Placebo Tacrine 20 mg/d

3 Tacrine 20 mg/d Tacrine 20 mg/d 4 Tacrine 20 mg/d Tacrine 40 mg/d 5 Tacrine 40 mg/d Tacrine 40 mg/d

(71)

Forced Dose-Escalation Design for 30-Week Tria

l of Tacrine in Alzheimer’s Disease

Randomized Groups

Week

0-6 7-12 13-18 19-30

1 Placebo Placebo Placebo Placebo 2 40 mg/d 80 mg/d 80 mg/d 80 mg/d 3 40 mg/d 80 mg/d 120 mg/d 120 mg/d 4 40 mg/d 80 mg/d 120 mg/d 160 mg/d

(72)

Flexible Dose-Escalation Design

(NEJM 1998 338: 1397-1404)

Example: Viagra

V P 25 mg 2% 0% 50 mg 38% 5% 100 mg 74% 95% R 4 wk run-in 0 2 4 8 12 placebo Open-Label (v) 32 wk 225 (68.3%)

(73)

Targeted Clinical Trials



Therapeutic agents are molecularly target

ed to protein products of genes that are di

sregulated in the patients with the disease

.



Identify the candidates in whom the agent

s is likely to be beneficial in the early phas

e of the study



This early phase is called the Enrichment

(74)

Targeted Clinical Trials



The identified candidates are then evaluated by

the standard design for adequate

well-controlled studies



Enrichment Designs consist of two phases

 Enrichment phase

 Randomized, double-blind, placebo-controlled phase



Predictability of short-term response for

(75)

Targeted Clinical Trials

 Imatinib mesylate (Gleevec) for Chronic Myelogenous

Leukemia (CML) and gastrointesitnal stromal tumors (GIST)

 Philadelphia (Ph+) chromosome from reciprocal trans

location of long arms of 9 and 22 in 90% of patients with CML

 Formation of BCR-ABL fusion gene BCR-ABL tyrosin

e kinase  CML

 KIT proto-oncogene  transmembrane receptor KIT

 GIGS

(76)

 Other examples

 HER2 gene in metastatic breast cancer - Herceptin - r

equirement of screening the patients with over-expre ssed HER2 level (Slamon, 2001).

 Estrogen receptor ploymorphism - Estrogen Replace

ment Atherosclerosis trial (ERA, Herrington, et al, 20 02): a total of 9 SNPs were identified and interaction between treatment of HRT and some of SNPs in elev ation of lipid levels is suggested

 Sample size determination: Fijal, et al. (2000) and Ma

itournam and Simon (2005).

(77)

 Other examples

 The epidermal growth factor receptor (EGFR) inhibitor fo

r the non-small cell lung cancer.

 Iressa (gefitnib) and Tarceva (Erlotinib) are targted at th

e EGFR pathway.

 Efficacy is correlated to

race

number of gene copies protein expression EGFR mutation

Gappuzzo et al. (JNCI, 2005), Tsao, et al (NEJM, 2005)

(78)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Survival by Ethnic Origin

Asian (n = 342) HR = 0.66 (0.48, 0.91), P = .011 RR = 12.0% Non-Asian (n = 1350) HR = 0.93 (0.81, 1.08), P = .364 RR = 6.5% 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 —— IRESSA® --- Placebo P at ie n ts s u rv iv in g ( % )

(79)

(80)

(81)

From: Tsao, et al (2005, NEJM)

(82)

(83)

Targeted Clinical Trials

All subjects All subjects diagnosed but results not used for randomization

®

Test Group Control Group

(84)

Targeted Clinical Trials

(2)

All subjects All diagnosed at randomization Diagnosis is Diagnosis is ® Control Group Test Group Control Group ® Test Group

(85)

Targeted Clinical Trials

(3)

All subjects All diagnosed at randomization Diagnosis is

Diagnosis is

Control Group ® Test Group

(86)

Targeted Clinical Trials

Control Group ® Test Group All subjects No Diagnosed

Control Group ® Test Group Subset Diagnosed

Diagnosis

(87)

Multicenter Trials

A multicenter study is a single study conducted un

der a common protocol, involving several centers

(e.g., clinics, practices, hospitals) where the data c

ollected are intended to be analyzed as whole (as o

pposed to a post-hoc decision to combine data or r

esults from separate studies).

(88)

Multicenter Trials



Goals

 To accrue patients efficiently

 To provide a basis for generalization of its findings



Centers

 Single investigator at a single hospital

 Single investigator at more than one hospital  A team of clinicians at one hospital

(89)

Examples



FACET International Study Group (NEJM 19

97; 337: 1405-11)

A multinational and multicenter trial



Targeted population: 852 randomized patients



18-70 years old



Asthma >= 6 months



Inhaled glucocorticoid >= 3 monyhs

(90)

Issues



Variations in conduct and evaluation among

centers



A common protocol



Standardization of procedures



Pre-study investigator’s meeting



Training of personnel

(91)

Issues



Variation in the number of patients



Few small centers vs. lots of large centers



Few large centers vs. lots of small centers



All small centers



Heterogeneity of treatment effects

Treatment-by-center interaction



Quantitative



qualitative

(92)

Issues

Center Placebo Low Medium High Total San Diego 16 19 17 18 70 Phoenix 15 17 18 14 64 Houston 15 18 20 16 69 Minneapolis 1 0 2 0 3

(93)

(94)

(95)

Issues



Fixed or random center effects



Recruit a minimal # of patients



Expertise and experience of investigators



Special equipments or facilities required by

the study



Not for comparisons among centers



A classification factor and not a design

(96)

Superiority Trials

The objective of the trial is to establish the

efficacy by demonstrating that the test

treatment is superior to



a concurrent placebo control



a concurrent active treatment control

or

(97)

Superiority Trials

o T C o T C

o

T C

(1) Testing H :μ = μ vs. H :μ μ

at the α significance level

(2) If H is rejected and the estimate of

the difference between μ and μ, then

test drug is concluded to be superior to

the control.

It is



o T C o T C

equivalent to test

H :μ μ vs. H :μ > μ

at the α/2 significance level



(98)

Examples

Canadian Beclomethasone Dipropoinate Salmethrol Xinafoate Stu dy Group (NEJM, 1997; 337: 1659-65)

 Patient population

241 children, 6-14 years old with stable asthma

 Test treatment

Long-acting β2-adrenergic-recepto agonist Salmethrol Xinafo ate (50 ug twice daily)

Active treatment concurrent control Glucocorticoid

(99)

Concept of Equivalence

 To show that the efficacy of the new treatment is either as effective as

or is no worse than the concurrent active control (standard therapy)

 Therapeutic areas  Oncology  Infectious diseases  Bioequivalence  Reasons  Less toxic  Easier to administer

 Substitution of an invasive procedure  Less expensive (cost-effectiveness)  Better quality of life

(100)

Two-sided equivalence-similarity

 The effect of the test treatments does not differ substantially in

either direction from that of the control

 As compared to the concurrent active control

 The effect of the test treatment is not too low (the effect of the

test treatment is not inferior) and

The effect of the test treatment is not too high (the effect of the test treatment is not superior )

(101)

One-sided equivalence-non-inferiority



Therapeutic equivalence

Because the test treatment offers some

advantages over the control, the question is

whether its effectiveness is within a specific

tolerance of the control



One-sided problem

(102)

Example

COBALT Investigators and Ware and Antman (NEJM

1997;337: 1124-30; 1159-61)



Patient population

7169 patients with myocardial infarction



Objective

To demonstrate that the 30-day mortality of double-bolus alte plase (a bolus of 50 mg over 1-3 minutes followed by 30 mi nutes later by a second bolus of 50 mg) is no worse than tha

(103)

Statistical Formulations of Equivalence

Only consider two treatment groups

μ

_T

: the average effect of the test treatment

μ

_R

: the average effect of the active control

δ

_L

: the allowable lower equivalence limit (-)

δ

_U

: the allowable upper equivalence limit (+)

(104)

The hypothesis of equivalence trial



Null hypothesis

The regular and as needed uses of albuterol are not

equivalent in morning peak flow rate in patients w

ith mild, chronic, stable asthma.



Alternative hypothesis

The regular and as needed uses of albuterol are eq

uivalent in morning peak flow rate in patients wit

h mild, chronic, stable asthma.

(105)

U R T L a U R T L R T

H

vs

or

H



























:

.

:

0

Two one-sided hypothesis

(two-sided equivalence)

U R T aU U R T U L R T aL L R T L

H

vs

H

and

H

vs

H



































:

.

:

.

:

0 0

(106)

One-sided hypothesis

(non-inferiority)

H

_oL

:

_T

–

_R

≦



_L

_{vs. H}

_aL

: 

_T

– 

_R

> 

_L



A statistically significant difference can also be

claimed that the test treatment and control are e

quivalent



The test treatment can be concluded no worse th

an control and also to be superior to control at t

he same time

(107)

Significance level

= Prob (

Type I error

)

= prob (Reject H₀ when H₀ is true)

= Prob (Conclude equivalence when it is not equivalent) Power

= 1- Prob (

Type

II

error

)

= prob (Reject H₀ when H₀ is true)

True state Non-equivalence Equivalence Non-equivalence Correct Type I error

(False positive) Equivalence Type II error

(108)

Issues of equivalence or

non-inferiority trials

 Lack of internal validity without concurrent placebo

control

 Determination of equivalence margins

Largest difference that is clinically acceptable

 Equivalence trials

Both upper and lower margins

 Non-inferiority trials

Only the lower margin

 COBALT

(109)

Issues of Active Control Trials

 Efficacy of a treatment should be established against placebo  Equivalence or non-inferiority of test treatment to the active

control

both superior to placebo both inferior to placebo

 The efficacy of the active control in the relevant indication has

been clearly established and quantified in design and well-documented superiority trials and that can be reliably expected to exhibit similar efficacy in the contemplated active control trial

(110)

Issues of Active Control Trials

 Same design features

 Inclusion / exclusion criteria  Dose

 Primary endpoints

 Objective of equivalence or non-inferiority must be stated in

the protocols with the equivalence limits

 Inclusion of a concurrent placebo control for interval validity  Superiority of active concurrent control to placebo

(111)

Determination of Equivalence Limit

 Largest difference which can be judged as being clinically acceptable

 Smaller than the relative efficacy of active concurrent control compared to placebo established in designed and well-documented superior trial