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(1)

Bridging

Bridging

Bridging

Studies

Studies

- A Genomic Approach

- A Genomic Approach

Bridging

Studies

Studies

- A Genomic Approach

- A Genomic Approach

By

Jen-pei Liu

,

Ph.D., Professor 劉仁沛教授

Division of Biometry, Department of Agronomy

National Taiwan University

Division of Biostatistics and Bioinformatics , National Health Research Institutes

By

Jen-pei Liu

,

Ph.D., Professor

劉仁沛教授

Division of Biometry, Department of Agronomy National Taiwan University

Division of Biostatistics and Bioinformatics , National Health Research Institutes

at

The 34 Training Course on Clinical Trials

Foundation of Medical Professionals Alliance in Taiwan

October 14, 2005

The views expressed in this paper are professional opinions of the presenter and may not necessarily represent the position of the National Taiwan University and National Health Research Institutes, Taiwan.

(2)

Acknowledgements and Thanks

Acknowledgements and Thanks

Herng-Der Chen, MD, PhD, Center for

Drug Evaluation

 Mey Wang, PhD, Center for Drug

Evaluation

 Chin-Fu Hsiao, PhD, National Health

Research Institutes

Herng-Der Chen, MD, PhD, Center for

Drug Evaluation

 Mey Wang, PhD, Center for Drug

Evaluation

 Chin-Fu Hsiao, PhD, National Health

Research Institutes

(3)

Outline

Outline

I. Statistical Interpretation of ICH E5

II. Implementation of Bridging Studies

III. Examples of Bridging Studies

IV. Current Statistical Approaches

V. A Statistical Genomic Approach

VI. Summary

I. Statistical Interpretation of ICH E5

II. Implementation of Bridging Studies

III. Examples of Bridging Studies

IV. Current Statistical Approaches

V. A Statistical Genomic Approach

VI. Summary

(4)

Statistical Interpretation of ICH E5

Statistical Interpretation of ICH E5

ICH E5

ICH Harmonised Tripartite Guideline (Feb. 5, 1998)

Ethnic Factors in the Acceptability of

Foreign Clinical Data

(5)

Statistical Interpretation of ICH E5

Statistical Interpretation of ICH E5

ICH E5

Ethnic Factors in the Acceptability of Foreign

Clinical Data

The purpose of this guidance is to facilitate the registration of

medicines among ICH regions by recommending a framework

for evaluating the impact of

ethnic factors

upon a medicine’s

effect, i.e., its efficacy and safety at a particular

dosage

and

(6)

Statistical Interpretation of ICH E5

Statistical Interpretation of ICH E5

Objectives of ICH E5 (Section 1.1)

To describe the characteristics of foreign clinical data that will

facilitate their extrapolation to different population and support

their acceptance as a basis for registration of a medicine in a

new region

.

To describe regulatory strategies that minimize duplication of

clinical data and facilitate acceptance of foreign clinical data

in the new region.

To describe the use of bridging study, when necessary, to

allow extrapolation of foreign clinical data to a new region.

To describe development strategies capable of characterizing

(7)

Statistical Interpretation of ICH E5

Statistical Interpretation of ICH E5

ICH E5 Ethnic Factors in the Acceptability of Foreign Data

BRIDGING DATA PACKAGE (Section 3.2)

A bridging data package consists of

1) selected information from the Complete Data Clinical Package

that is relevant to the population of the new region, including pharmacokinetic data, and any preliminary pharmacodynamic and dose-response data,

and

2) if needed, a bridging study to extrapolate the foreign efficacy and/or safety data to the new region.

(8)

Statistical Interpretation of ICH E5

Statistical Interpretation of ICH E5

Complete Clinical Data Package (CCDP)

A clinical data package intended for registration

containing clinical data that fulfills regulatory

requirements of the new region and

pharmacokinetic

data

relevant to the population in the new region

(9)

Statistical Interpretation of ICH E5

Statistical Interpretation of ICH E5

Bridging Study

A bridging study is defined as a study performed in

the new region to provide

pharmacodynamic or

clinical

data on efficacy, safety, dosage and dose

regimen in the new region that will allow

extrapolation

of the foreign clinical data to the

population in the new region

(10)

Extrapolation and Similarity

Extrapolation and Similarity

ICH E5 Ethnic Factors in the Acceptability of Foreign Data

If the bridging study shows that dose response, safety and efficacy in the new region are similar, then the study is readily interpreted as capable of "bridging" the foreign data

If a bridging study, properly executed, indicates that a different dose in the new region results in a safety and efficacy profile that is not substantially different from that derived in the original region, it will often be possible to extrapolate the foreign data to the new region, with appropriate dose adjustment, if this can be adequately justified (e.g., by pharmacokinetic and/or pharmacodynamic data).

(11)

Ethnic Factors

Intrinsic Ethnic Factors

are more genetic and

physiologic in nature

e.g., genetic polymorphism, age, gender, height,

weight, lean body mass, body composition, and

disease conditions, etc.

 Extrinsic Ethnic Factors

are more social and

cultural in nature

e.g., environment, culture, medical practice, health

insurance, practices in clinical trials or conduct

(12)

An approved report of a local clinical trial study

is

required for the new drug application in Taiwan—July 7.

1993: Double 7 Announcement

Disadvantages

:

A minimal sample size of 40 as required could be

difficult to provide conclusive and substantial evidence of

efficacy and safety

The study design of the local trial usually only

repeated a study that has been done in the foreign

countries but in a smaller sample size;The study

has not been designed based on the medical

Taiwan’s Strategy to

(13)

Taiwan’s Strategy to

Implement Bridging Study

Smoothly convert compulsory Local Clinical Trials (LCT) to

meaningful bridging studies

Gradually, stepwise announce waived local clinical trials

Create an environment: (1) meet international regulations, ICH

(2) require optimized dosage for

Taiwanese patients

Communicate with local and international pharmaceutical industry

Announce new regulations according to the international norm and

the consensus from communications

Create an international platform “APEC – Taipei”

Implement Double Twelve Announcement – Bridging Study

(14)

Stepwise Implementation

Two years after the 1998 announcement, switch from LCT to

bridging study

Many communications and negotiations with local and

international pharmaceutical industry

Dec. 12,

2000: (Double Twelve Announcement) – public

announcement of the bridging study regulations

1998: Five announcements of LCT wavier

A two-year transition period: both LCT and bridging studies

concurrently acceptable from 2000 ~ 2002

Many international conferences held in Taipei and other Asian

countries, regarding BS, through the APEC platform

Consult with CDE to complete the practical issues related to

implementation of BS

(15)

Products Requiring No

Verification of Ethnic

Insensitivity

Products Requiring No

Verification of Ethnic

Insensitivity

Drugs for treatment of AIDS

Drugs for organ transplantation

Topical agents

Nutrition supplements

Cathartics prior to surgery

Radio-labelled diagnostic pharmaceuticals

The drug is the only choice of treatment for a given

severe disease

Drugs for life-threatening disease have demonstrated a

breakthrough efficacy

Lacking adequate trial subjects for any drug used for

rare disease

(16)

Products Requiring Verification

of Ethnic Insensitivity

Products Requiring Verification

of Ethnic Insensitivity

Anticancer drugs

Drugs with breakthrough efficacy

Drugs of single use

Drugs with different salt of the same composition and the same administered route have been approved internal

Drugs for chronic psychological or immunological diseases and conducting clinical trails internal difficultly

Each compounds of new combination drug have been proved internal, and the efficacy is the same as the single compound

Drugs with the mechanism, administered route, efficacy and adverse effect, similar to the approved drugs

New combination composed of single compound of approved combination or compounds of approved combination has the same efficacy as approved combination

(17)

•Bridging Data Package •Summary for the

Consideration of Bridging Study Accept submission Checking List Technical Review (Designate reviewer) Review meeting Sponsor meeting Supplement Clinical Review

Committee Review report and Recommendation: 1. No Bridging study required 2. Bridging study is required – Type of Bridging study Result of Evaluation:

1. No Bridging study required 2. Bridging study is required –

Type of Bridging study

Notification

Sponsor BoPA CDE

CDE acceptance verification Expert Consultants (Statistical, Clinical, Pharmacokinetics reviewers) Schedule Sponsor meeting

(18)
(19)
(20)

Examples

Examples

Example I

Drug A is a fixed combination of two anti-platelet agents

with indication for secondary prevention of thromboembolic

stroke

After the standard process of BSE, we decided to request a

bridging study due to an ethnic difference in medical

practice (much lower dose for one of the components in

Taiwan) and higher headache-associated dropout rate in

previous Philippine study

(21)

Examples

Examples

Case I

Fixed combination 200mg dipyridamole/25mg aspirin 1bid for prevention of recurrent stroke

Headache drop out rate: Phillipino > Caucasian  Local Bridging Study Result : first 4 weeks

Reduced Dose 2wk Full Dose

Placebo Full Dose 2wk 4wk

Headache 8.7% 6.7% 16.3%

(22)

Examples

Examples

Case II

Drug B is a new potent lipid-lowering agent

The PK study in Japanese shows that Cmax of

Japanese is 1.9~2.5 times of that for Caucasian

while AUC is 2~2.5 times of that for Caucasian

Although the mean interracial difference is not

substantial, Taiwan approved the drug with reduced

maximal dosage due to the dose-dependent,

drug-related rare SAE of rhabdomyolysis

(23)

Examples

Examples

Case II

The decision was further echoed by US FDA

After reviewing the results of a Phase IV PK

study in Asian-Americans, FDA urged the

physicians to reduce the starting dose and

prescribe high dose with caution for Asians in

Labeling in March, 2005

(24)

Current Statistical

Approaches

Current Statistical

Approaches

“Similarity”

• Positive Rx effect

• Equivalence

• Non-inferiority

(25)

Extrapolation and Similarity

Positive treatment effect (better than control)

The efficacy or safety of the test drug is better than

control in the new region

H

o

: 

NT

- 

NC

 0 vs. H

a

: 

NT

- 

NC

> 0

Current Statistical

(26)

Current Statistical

Approaches

Positive Rx Effect

Current Statistical

Approaches

Positive Rx Effect

0

O

N

(27)

Current Statistical Approaches

Current Statistical Approaches

Similarity (No substantial difference)

Two-sided equivalence

The relative efficacy or safety (test - control) of the new region

is within some clinically acceptance limit of that of the original

region

Let

 = (

NT

-

NC

) - (

OT

-

OC

)

H

o

:

  - or   

vs.

H

a

: -

 <  < 

(28)

Current Statistical

Approaches

Equivalence

Current Statistical

Approaches

Equivalence

0

N

(29)

Current Statistical Approaches

Current Statistical Approaches

Similarity (No substantial difference)

One-sided non-inferiority

The relative efficacy or safety (test - control) of the new region

is not inferior to the original region by some clinically

acceptance limit

.

(30)

Current Statistical

Approaches

Non-inferiority

Current Statistical

Approaches

Non-inferiority

0

N

O

(31)

Current Statistical

Approaches

Current Statistical

Approaches

Between-study Analysis:

Equivalence or non-inferiority

Hierarchical Model

(Liu, Hsueh, and Chen 2002, Biometrical J.)

Step 1: From the complete clinical data package, under the

hierarchical model, use the clinical data from the original region to obtain the estimate of relative efficacy and its estimated standard error.

Step 2: From the data of the bridging study, obtain the estimate of

relative efficacy and its estimated standard error in the new region.

Step 3: Based on the estimated relative efficacy and its standard

error from both the new and original regions and equivalence limit , perform the usual two one-sided tests procedure or one-sided non-inferiority test procedure (or confidence interval).

(32)

Empirical Bayesian Approach

Bridging studies

 Small sample size

 Need to borrow “strength” from CCDP of original region.

 Information on dose response, efficacy and safety of the

original region can and should be incorporated in a

statistically sound manner to evaluate bridging evidence

by the bridging studies in the new region

.

 Positive treatment effect:

(Liu, Hsiao, and Hsueh, 2002, JBS)

 Noninferiority approach:

(Liu, Hsueh, and Hsiao 2004, JBS)

(33)

Between-study Analysis:

Bayesian Approach

(Liu, Hsiao, and Hsueh, 2002)

 Use the estimate of treatment effect from the

original region formulated as a normal prior

 Compute the posterior treatment effect with the

data from the new region

Compute the posterior probability of similarity, P

sp

as the

posterior probability of a positive treatment effect

 Conclude the results of the foreign region can be extrapolated

to the new region if

P

sp

is

sufficiently large.

 Sample size might be determined based on the

difference between the posterior and prior treatment

effect

Current Statistical

Approaches

(34)

Current Statistical Approaches

Current Statistical Approaches

For a positive treatment effect

The model

(Liu, Hsiao, and Hsueh, 2002)

Y

i

= P(1-X

i

) + {

N

z

i

+ 

O

(1-Z

i

)}X

i

+ 

i

, 

I

~ N(0, 

2

), where

P: control effect

N

: treatment effect of the new region

O

: treatment effect of the original region

X = 1(0) treatment (control) group

Z = 1(0) new (original region)

(35)

Current Statistical

Approaches

Current Statistical

Approaches

For a positive treatment effect

Empirical Bayesian Approach

(Liu, Hsiao, and Hsueh, 2002)

 Given P,

N

, the estimates of

P,

N

, say p and a

N

follows a

bivariate normal distribution with mean vector (

P,

N

)’ and the

diagonal covariance matrix diag(V

P

, V

N

).

In addition, the prior distribution of (

P,

N

, 

O

)’ follows a trivariate

normal distribution with mean vector (

p

, 

N

, 

O

) and

diagonal covariance matrix diag(

2

p

, 

2N

, 

2O

).

Conclude a positive treatment effect if posterior probability of

similarity

(36)

Current Statistical

Approaches

Current Statistical

Approaches

For a positive treatment effect

Empirical Bayesian Approach

(Liu, Hsiao, Hsueh, 2002)

Under assumption that 

N

= 

O

,

for P(

N

- P > 0data and prior) > 1 - ,

the following equation must be satisfied

(

O

- 

p

)/

2

O

+

2p

= 

-1

(1-q),

where 

-1

(1-q) represents the evidence for positive

(37)

Current Statistical

Approaches

Current Statistical

Approaches

Results from Original Region

Change from baseline in sitting DBP at week 12

Region Statistics

Test

Placebo

I

n

138

132

Mean

-18

-3

SD

11

12

II

n

185

179

Mean

-17

-2

SD

10

11

III

n

141

143

Mean

-15

-5

SD

13

14

(38)

Current Statistical

Approaches

Current Statistical

Approaches

Results from New Region:

Change from baseline in Sitting DBP at week 12

Region Statistics

Test

Placebo

New

n

64

65

Mean

-4.5

-3.8

SD

11

11

(39)

Current Statistical

Approaches

Current Statistical

Approaches

 Original region: Efficacy of the test drug is

superior to the placebo.

 New Region: Reduction of sitting BP of the test

drug is same as that of the placebo.

 Conclusion: The results of the original region

can be extrapolated to the new region despite of

inconsistent results between original and new

regions.

Evaluation of bridging studies is overwhelmingly

by the results of original region due to imbalance

of information provided by the two regions.

(40)

Current Statistical

Approaches

Current Statistical

Approaches

A Mixture Prior Bayesian Approach

(Hsiao, Hsu and Liu, 2005)

Define 

N

=

NT

- 

NC

A mixture

prior model:

(

N

)

=



1

(

N

) +(1 -

)

2

(

N

)

1

(

N

) is a noninformative prior and is set to be 1.

2

(

N

) is a normal prior that summarizes the results of original

region

 is a weighing factor; 0   1

 = 0: the same prior used in Liu, Hsueh and Hsiao (2002)

 = 1: no results of original region is used

(41)

Current Statistical

Approaches

Current Statistical

Approaches

Posterior Probability of Similarity

SP

N

N

N

0

ˆ

P

(

|

)

1

,

0

0.5.

d

 

 

 

(42)

Current Statistical Approaches

Current Statistical Approaches

Marginal Distribution

.

)

/

2

(

2

)

ˆ

(

exp

)

ˆ

(

2

1

)

1

(

)

ˆ

(

N 2 2 0 2 0 N 2 2 0 N





n

m

(43)

Current Statistical

Approaches

Current Statistical

Approaches

Posterior Distribution

2 N N N N 2 2 N N N 2 2 N 0 N N 2 2 2 0 N N 0

ˆ

(

)

1

1

ˆ

(

|

)

exp

ˆ

4

/

(

)

2 (2

/

)

ˆ

(

)

(

)

1

(1

)

exp

.

2

4

/

2 (2

/

)

n

m

n

n

n

 

 

  

  



 

  



(44)

Current Statistical

Approaches

Current Statistical

Approaches

Find the smallest n

N

that

SP

N

N

N

0

ˆ

P

(

|

)

1

,

d

is satisfied

 

(45)

Current Statistical

Approaches

Current Statistical

Approaches

Group Sequential Method

(Hsiao, Xu, Liu, 2003)

A Two-stage Design

(Hsiao, Xu, Liu, 2005)

Reason:

Under the hierarchical model or Bayesian approach,

evaluation of similarity or non-inferiority based on the

difference of relative efficacy might still require large

sample size for the bridging study in the new region.

These are between-study analysis without internal

validity and may provide biased inference

Criterion for similarity

(46)

Current Statistical

Approaches

Current Statistical

Approaches

Step 1: When designing the adequate and well-controlled

studies for submission to the original region, include the patients in the new region as part of recruitment for the whole study (The bridging study is a sub-study).

Step 2: The study should have a structure of group sequential

design. Use the region as group sequence to enroll the patients from the original region first and then to enroll patients from the new region subsequently.

Step 3: Pre-specify the boundaries in the protocol, say

spending function. Because the primary objective of the trial is for submission to the original region, most of type I error rate should be spent for the interim analysis based on the results from the original region.

(47)

Current Statistical

Approaches

Current Statistical

Approaches

Step 4: When the recruitment of patients in the original region is

completed, perform the interim analysis up to results of the original region.

Step 5: Enroll the patients in the new region. After the

recruitment of the patients is completed, perform the final analysis with additional data from the new region and

adjustment of the interim analysis. If similar results (i.e., similar significance level to meet requirement of crossing

boundary) are obtained for the final analysis, then the results of the new region can be declared similarity to the original region

.

(48)

Targeted Clinical Trials

HER2 (the human epidermal growth factor receptor 2) gene

in metastatic breast cancer - Herceptin - requirement of

screening the patients with over-expressed HER2 level

(Slamon, 2001).

Estrogen receptor polymorphism - Estrogen Replacement

Atherosclerosis trial (ERA, Herrington, et al, 2002): a total of

9 SNPs were identified and interaction between treatment of

HRT and some of SNPs in elevation of lipid levels is

suggested

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

A Statistical Genomic

Approach

(49)

Targeted Clinical Trials and EGFR

Iressa (gefitnib) and Tarceva (Erlotinib) are targted

at the 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)

A Statistical Genomic

Approach

(50)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A Statistical Genomic

Approach

A Statistical Genomic

Approach

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% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 —— IRESSA® --- Placebo P at ie n ts s u rv iv in g ( % )

(51)

110/07/16 51

From: Tsao, et al (2005, NEJM)

(52)

From: Tsao, et al (2005, NEJM)

From: Tsao, et al (2005, NEJM)

(53)

From: Tsao, et al (2005, NEJM)

From: Tsao, et al (2005, NEJM)

(54)

From: Tsao, et al (2005, NEJM)

From: Tsao, et al (2005, NEJM)

A Statistical Genomic

Approach

(55)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

Current statistical methods for bridging studies do not

really take ethnic factors into considerations

After Human Genome Project, the availability of

genomic data can provide the necessary quantitative

information for intrinsic ethnic factor

Genomic information should be incorporated into

evaluation of bridging studies

Bridging studies may be considered as one type of

targeted clinical trials with genomic data as the

bio-targets for intrinsic ethnic factors

(56)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

Stratified Approach

Original Region

Genetic

Polymorphism Proportion Test Control

1 P

O1

1T

1C

2 P

O2

2T

2C . . . . . . . .

K P

OK

KT

KC

P

Oi

iT

P

Oi

iC

(57)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

Stratified Approach

New Region

Genetic

Polymorphism Proportion Test Control

1 PN1 1T 1C 2 PN2 2T 2C . . . . . . . . K PNK KT KC PNiiT PNiiC

(58)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

P

oi

: the proportion of type i for some genetic polymorphism in the

original region

P

Ni

: the proportion of type i for some genetic polymorphism in the

new region

iT

: the mean response of a patient with type i polymorphism in

treatment group

2C

: the mean response of a patient with type i polymorphism in

control group

OT

=P

Oi

iT

: the mean response of the treatment group in the

original region (mean of a mixture distribution)

OC

=P

Oi

iC

: the mean response of the control group in the

original region

NT

=P

Ni

iT

: the mean response of the treatment group in the new

(59)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

If P

Oi

 P

Ni

, 

OT

- 

OC

 

NT

- 

NC

 Genetic

polymorphism are similar between the two regions

Data on efficacy and safety can be extrapolated from

the original region to the new region  Bridging

studies may not be needed

If P

Oi

 P

Ni

, 

OT

- 

OC

 

NT

- 

NC

 Genetic

polymorphism are not similar between the two regions

Extrapolation of efficacy and safety from the original

region to the new region is in doubt Bridging studies

may be required

(60)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

The hypothesis for the bridging study is the proof of a

positive treatment effect in the new region

H

o

: 

NT

- 

NC

 0 vs. H

a

: 

NT

- 

NC

> 0

Standard design, statistical estimation and testing

procedures can be applied

Selection of different doses in the bridging study if the

information on relation between the response and

polymorphism is provided in CCDP

Sample size will be reduced if it is expected that

(61)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

Requirement of the stratified approach

(1) Diagnostic devices for identification of polymorphism

(2) proportions of types of polymorphisms in both regions

(3) the response in each type of polymorphisms, and

(4) the relationship between the response polymorphism

May be expensive for identification of polymorphism

Complication in recruitment and randomization of subjects

because prevalence rates of different types of polymorphisms

(62)

A Statistical Genomic

Approach

A Statistical Genomic

Approach

Analysis of Covariance (ANCOVA) Approach

The hypothesis for the bridging study is the proof of a positive

treatment effect in the new region

H

o

: 

NT

- 

NC

 0 vs. H

a

: 

NT

- 

NC

> 0

The quantitative genomic information is used as covariates in

the model

Treatment effect is adjusted for the genomic information

Sample size may be reduced if a significant relationship

between the response and genomic covariates

(63)

Summary

Summary

Bridging studies and extrapolation

 Statistical hypothesis

 Taiwan experience with bridging studies

 Overview of current statistical methods

 Proposal on statistical genomic

參考文獻

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This discovery is not only to provide a precious resource for the research of Wenxuan that has a long and excellent tradition in Chinese literature studies, but also to stress

substance) is matter that has distinct properties and a composition that does not vary from sample

• A knock-in option comes into existence if a certain barrier is reached.. • A down-and-in option is a call knock-in option that comes into existence only when the barrier is

• A knock-in option comes into existence if a certain barrier is reached?. • A down-and-in option is a call knock-in option that comes into existence only when the barrier is

First, in the Intel documentation, the encoding of the MOV instruction that moves an immediate word into a register is B8 +rw dw, where +rw indicates that a register code (0-7) is to

• A knock-in option comes into existence if a certain barrier is reached.. • A down-and-in option is a call knock-in option that comes into existence only when the barrier is

• The randomized bipartite perfect matching algorithm is called a Monte Carlo algorithm in the sense that.. – If the algorithm finds that a matching exists, it is always correct