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Recent Statistical Techniques

in Clinical Research


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iii

Recent Statistical

Techniques In Clinical

Research

Dr Basavarajaiah D M

EDUCREATION PUBLISHING (Since 2011)

www.educreation.in


iv


v

TO

PARENTS AND WIFE

WITH LOVE


vi

PREFACE

Statistical methods play an essential role in all stages of a

quantitative health care and clinical research from design analysis

and interpretation of real life data sets. The clinical trial is “ the

most definitive tool for evaluation of the applicability of clinical

research” It represents “a key research activity with the potential

to improve the quality of health care and management through

careful comparison of alternative treatments” It has been called on

many occasions “the gold standard” against which all other

clinical research is measured. Although many clinical trial are of

high quality, a careful reader of the medical literature will notice

that a large number have deficiencies in design, conduct, analysis,

presentation, and /or interpretation of results. Improvements have

occurred over the past few decades, but too many trials are still

conducted without adequate attention to its fundamental principles.

Certainly, numerous studies could have been upgraded if the

authors had a better understanding of the fundamentals. This book

covers the essential principles and methods required for clinical

research. The underlying concepts of statistical analysis including

basic and some more advanced analysis techniques are also

covered. This book is an attempt to present the recent statistical

techniques and tools with suitable examples from real life data

sets, which the clinical researchers and academicians need. A

considerable part of the book is devoted therefore to the design of

experiments in phase I, II and III clinical trials. The reader will be

able to follow the sequence of ideas in the latter part of the book. It

is probably desirable to list these topics explicitly because of the

tendency of uncritical readers to regard either the whole of a book

as new, or none of it. The specific topics, most of which have been

dealt with formulation of the model and its applications in the

context of clinical trials or medical research. The book have been

framed with seven chapters, chapter -I describes the clinical

research design and statistical methods, it covers brief concept of

clinical study, research design, different phases of clinical trials,

drug development process, statistical issues and methods etc.,


vii

Chapter –II describes the different experimental design approach

to clinical research; basic elements of experimental design, CRD,

RCBD and LSD with mathematical models. Chapter-III covers

the recent simulation models viz., sensor –noise estimation by snap

shot techniques, which covers the pharmacokinetic model,

formulation of epidemiological probability model, Sensor fusion

with normally distributed simulation model by real life animal

science data sets and also we discuss the practical utility of the

sensor fusion model in medical science. Chapter –IV covers the

statistical methods for clinical research. Chapter -V briefly covers

the survival analysis, hazard rate, censored data, parametric –

weibull distribution, KPM, Gompertzmakeham distribution

models. Chapter –VI deals with the different statistical models

approach to life threatened diseases -an Indian perspective viz.,

neural network modeling, application of neural network modeling

in medical research etc. Chapter-VII covers the image processing

modeling on radiographic features; analog, digital image

processing, different stages of digital image processing, signal,

artificial intelligence (AIs) etc. Chapter-VIII describes an

introduction to the database management in clinical research,

model structures, different types of model, Data base management

system flow,security,sequences,statistical modeling on DBMS,data

base environment etc.Finally, the Chapter IX deals with the

ethical issues and perspective of clinical research.

There are many fascinating problems that remain and we

would have liked to have solved these. However, the solution

might suggest themselves in the forthcoming days. Some problems

are discussed briefly for all chapters. My basis debt with regard to

whole book is to all scientific and academic community. I am

indebted to our University officers, Karnataka Veterinary Animal

and Fisheries Sciences University, Bidar, India for moral support

and permission to entitled of this publication.

*****


viii

ACKNOWLEDGEMENTS

„Recent statistical techniques in clinical research’ text book is the

product of shared network. We would like to give special thanks to

our university KVAFSU (B) officers who helped to build it. We

would like to express our gratitude to Dr.B.Parabhakar former

Professor and head, Department of Medicine, Bengaluru Medical

College and Research Institute, Fort Road, Bengaluru. Thanks to

our parents, wife and kids for their love and support.

Finally, we would like to thank our readers. We hope you

enjoy reading this book and find it useful. We wish all our readers

all the very best in their future endeavour .We would love to hear

your comments and suggestions .You can send your mails to

[email protected]

*****


ix

CONTENTS AT A GLANCE

S. No. Content Page

1

Clinical Research Design And Statistical

Methods

1

1.1 Introduction

1.2 Statistical historical perspectives of clinical

trial

1.3 Brief concept of study design

1.3.1 Cross sectional study

1.3.2 Longitudinal study

1.3.3 Prospective study

1.3.4 Retrospective study: Case control

1.4 Different phases of clinical trial

1.5 Drug development process

1.6 Study population

1.7 Statistical issues and methods

1.8 Application of multinomial distribution in

clinical trial

1.8.1 Gehans‟s two stage design

1.8.2 Two stage Simon‟s experimental design

1.9 Random variable

1.9.1 Conditional expectation

1.9.2 Conditional variance

1.10 Randomized clinical trial (RCT)

1.10.0 Simple randomization

1.10.1 Block randomization

1.10.2 Minimization method stratification

1.10.3 Stratified randomization method

2 Different Experimental Design Approach

To Clinical Research

27

2.10 Experimental design


x

2.11 Replication

2.12 Randomization

2.13 Control of error

2.13.1 Blocking

2.13.2 Proper experimental techniques

2.13.3 Data analysis

2.14 Design on single factor clinical experiments

2.15 Complete randomized design

2.15.1 Randomization

2.16 Analytical method

2.17 Analysis of variance (ANOVA)

2.18 Randomized complete block design (RCBD)

2.19 Randomization and lay out

2.20 Analytical method

2.21 Analysis of variance-ANOVA RCBD

2.22 Latin square designs-LSD

2.23 Randomization and lay out

2.24 Analytical method-ANOVA LSD

2.25 Cross over design –Switch back design

2.26 Bio-equilancy trial

2.27 Design approach to human genetics

2.28 Multinomial distribution in clinical trial

2.29 Moment generating function of crosses between

males and females genotypes (MGF)

2.30 Simulation-Monte Carlo method (SMCM)

2.31 Expected values

2.32 Discrete series: Expected

2.33 Continuous series: Expected

2.34 Effect of genetic inheritance on new drug trail

2.35 Genetic correlation

2.36 Formulation of the model-genetics

2.36.1 Assumption of the model

2.37 Analytical procedure or methods

2.38 Genetic correlation


xi

2.38.1 ANOVA and co variances of cd4 count

and RNA viral load

2.39 Estimation of heritability

2.40

2.41

Method of analysis of clinical research -non

orthogonal life data sets

Model formulation of non-orthogonal clinical

data

3 Sensor Fusion -Noise Estimation By

Snapshots Techniques

60

3.10 Introduction

3.11 Model formulation: diseases/infection

susceptible model

3.12 Pharmacokinetic model for FMD

3.12.1 Model formulation

3.13 Formulation of epidemiological probability

model

3.14 Sensor fusion with normally distributed

3.15 Practical utility of the sensor fusion model in

animal science

4 Statistical Methods For Clinical Research 73

4.10 Bio equilancy trial

4.11 Equivalence testing- a new gold standard

4.12 Comparing two response rates

4.13 Characteristics of normal distribution

4.14 Log normal distribution

5 Survival Analysis 86

5.10 Introduction

5.11 Model description

5.12 Survival analysis

5.13 Survival function

5.14 Concept of the model

5.14.1 Survival function

5.14.2 Estimation of s(t):

5.14.3 Probability density function:


xii

5.15 Hazard Function(Hz)

5.16 Hazard rate

5.17 Exponential distribution

5.18 Gompertz –Makeham distribution model

5.19 Censoring and life table methods

5.20 Kaplan Meir analysis

5.21 Estimation with censored data

5.22 Non informative censoring

5.23 Mantel-haenszel test

5.24 K-Sample Mantel-Haenszel test

6 Statistical Models Approach To Life

Threatened Diseases -An Indian Perspective

111

6.10 Introduction

6.11 Demographic features of HIV infected women

6.12 Model description

Table 6.13.1 Probabilities of transmitting HIV,

at of before birth by ASSA model.

Table 6.13.2 Probabilities of transmitting HIV

of African infants infected at 4-6 weeks, after

birth to mothers on HAART

6.13 Intrauterine and intrapartum transmission

6.14 Transmission probability at or before birth, in

the absence of ARV-prophylaxis.

6.15 Neural network modeling in HIV/AIDS

6.16 Application of neural network in medical

science

6.17 Equation of survival analysis –model constructs

6.18 Neural network model –corollary

6.19 Hierarchical neural nets for survival analysis

6.20 Nonhierarchical neural nets for survival analysis

6.21 Salient findings of neural net work model fitting

6.22 Application of the neural network in HIV or

medical research

6.23 Modeling on assessment of quality of life of


xiii

patients

6.24 Quality life domain model

6.25 Model formulation

6.26 Model structure

6.27 Principle component analysis

6.28 Model discussion

7 Image Processing Modeling On

Radiographic Features

154

7.10 Introduction

7.11 Analog image processing

7.12 Digital image processing

7.13 Application of digital image processing

7.14 Different stages of digital image processing

7.15 Signal

7.16 Relationship

7.17 How a digital image is formed

7.18 Overlapping fields-Machine computer vision

7.19 Computer graphics

7.20 Artificial intelligence

7.21 Signal processing

7.22 Signals

7.23 Analog signal

7.24 Human voice

7.25 Digital signal

7.26 System

7.27 Sampling

7.28 Quantization

7.29 Application of digital image processing

7.30 Image sharpening and restoration

7.31 UV imaging

7.32 Transmission and encoding

7.33 Machine /Robot vision

7.34 Hurdle detection

7.35 Line follower robot


xiv

7.36 Color processing

7.37 Pattern recognition

7.38 Video processing

7.39 Modeling on image processing

7.40 Camera pixels

7.41 Oversampling.

7.42 Zooming

7.43 Pixel

7.44 Resolution

7.45 Megapixels: We can calculate mega pixels of a

camera using pixel resolution

7.46 Advantage

7.47 Kernel regression model for image processing

7.48 Advanced model of image processing

8 Data Base Management In Clinical Research 181

8.10 Introduction

8.11 Data collection and documentation

8.12 Database management system (DBMS) and its

Applications

8.13 Database management system models (DBMS)

8.14 Hierarchical model

8.15 Network model

8.16 Object oriented model

8.17 DBMS-Architecture

8.18 Data types and diversity of clinical research

8.19 Structured and unstructured Sequences

8.20 Diagrammatic expression (graphs)

8.21 High-Dimensional Data sets

8.22 Data dimension

8.23 Data- temporal

8.24 Scalar and Vector Fields

8.25 Statistical and mathematical Models

8.26 Constraints

8.27 Data Provenance


xv

8.28 Workflow Management

8.29 Data Integration

8.30 Data ware housing

8.31 Time variant

8.32 Major components

8.33 Minor components-Schematic diagram of ware

housing

8.34 Data base security

8.35 Data base environment

8.36 Data security risks

8.37 Clinical data tempering

8.38 Falsifying user identies

8.39 Password related threats

8.40 Unauthorized access to data matrix

8.41 Different dimension of clinical data base

security

8.42 Requirement of data security

8.43 Masking or blinding data sets

9 Ethical Issues And Perspective On Clinical

Research

205

9.10 Introduction

Experimental unit

Treatment

9.11 Evaluation

9.12 Principles of good clinical practices (GCD)

9.13 Basic consideration of clinical research-

objective of trial:

9.14 Target population and patient selection

9.15 Eligibility criteria for anti-infective agents

Inclusion criteria

Exclusion criteria

9.16 Design –basic consideration of clinical research

Selection of control

Statistical consideration


xvi

Other consideration

9.17 Different design of trails: parallel group design:

9.18 Cross overdesign

9.19 Different design of trails: parallel group design:

9.20 Factorial design

9.21 Randomization

9.22 Merits of randomization

9.23 Blinding or masking

9.24 Ethical issues and perspectives on clinical

research Milestones

9.25 Ethical issues

9.26 Flow diagram of informed consent

9.27 Indian scenario

9.28 Ethical issues


xvii

TABLE AND FIGURES CONTENTS

Index Contents

TABLES

2.39.1 Genetic correlation matrix of CD4 count

follow up of infected mother who are

transfer HIV infection to her child

2.39.2 Genetic correlation matrix of RNA Plasma

viral load of infected mother who are

transfer HIV infection to her child

5.16.18 Survivability of different CD4 category

with HAART duration

5.22.2 Means and Medians for Survival Time

5.22.4 Area under the Curve (AUC) on different

mortality associated parameters.

6.13.1 Probabilities of transmitting HIV, at of

before birth by ASSA model.

6.13.2 Probabilities of transmitting HIV of

African infants infected at 4-6 weeks, after

birth to mothers on HAART

6.18 .1 Table 6.18(f) Confidence interval of Mean

survivability with gender wise and

different age class

6.28.2 Total scores of different domains of QOL

(Transformed scale)

6.28.3 Total scores of different domains of QOL

(Transformed scale)

6.28.4 Correlation matrix of categorical variables

of PLHIV Table 6.28(e) Strong correlation

of categorical variables of HIV patients.

6.28.5 Associated parameters in PLHIV.

6.28.6 Principle component analysis of

associated parameters in PLHIV.

6.28.7 Component transformation matrix of


xviii

associated parameters in PLHIVs

5.16.2 Kaplan-Meier survival curve and its 95%

confidence interval for patients initiating

therapy from different CD4 category

5.22.1 Mortality in relation to the low birth

weight (kgs)

5.22.3 ROC curve depicted for weight of the baby

and defined parameters with respect to

mortality

6.15.1 Probability plot for base line CD4 count at

the time of HAART Initiation of pregnant

women

1.15.2 Probability plot for CD4 count at the time

of pregnancy

6.18.1 Descriptive statistics of PLHA five year

Cohort

FIGURES

6.18.2 Survivability at Five years

6.18.3 Survivability function at Five years

6.18.4 Log survival function and Hazard function

6.18.5 Cohort Survivability and survival function

among PLHA with different age class

6.18.6 Log survival function and Hazard function

with different age class

6.18.7 Multilayer Neural net work Output and

hidden layer

6.18.9 Radial basis function neural net work

Output and hidden layer

6.18.10 Gender wise relation with Survivability

6.18.11 Mean scores of QOL


Recent Statistical Techniques in Clinical Research

19

1

Clinical Research Design

And Statistical Methods ______________________________________________________

1.1 Introduction

Statistical methods are backbone of clinical research and will infer

the sound knowledge on formulation and randomization of clinical

trials. The statistical tools are very important for clinicians and

policymakers for the implementation of new RCT-guidelines and

hands-on training programme for clinicians, specialists and young

researchers. Many clinicians and researchers will fail to use the

advanced statistical tools in their research work, due to non

availability of statistical literatures and reference books. In this

section we discussed the different statistical tools, study designs

and advanced statistical methods for formulating the clinical trials.

The clinical trial is a study in human subjects, in which

treatment (intervention) is initiated specially for therapy

evaluation. Practically, we define a clinical trial as a type of study

for comparing the effect and value of intervention against a control

in human beings (Lind et al., 1996). It is an experiment involving

testing medical treatment in human subjects (Zhang et al., 2005).

Further the clinical trial may be elucidated in many ways viz., the

comparison of Stavudine fixed dose combination versus placebo

consideration on the length of survival in patients with HIV/ AIDS,

evaluating the effectiveness of a new antifungal medication on

Athlete's foot, and hormonal therapy on the reduction of breast

cancer etc. The clinical trial is more important perspective for



20

clinicians and researchers. Many clinicians obtained evidence

based results and drew the conclusion based on the practical

approach. However, the trial is very easy for anecdotal information

about the benefit of therapy accepted for standard treatment care.

Many literature reported that high concentration of oxygen was

useful for therapy in premature infants until a clinical trial

demonstrated. Tsiatis et al. (2004) reported that, the prolonged use

of hormone replacement therapy for women followed menopause

problem.

1.2 Statistical Historical Perspectives of

Clinical Trial

Scurvy experiment was the first clinical trial conducted during

1747 by James F. Lind, a physician onboard of the “Salisbury“.

From1920onwards,R. A. Fisher introduced randomization as a core

principle in the statistical theory of the design of experiments.

During 1947-1948, Streptomycin was invented by randomized

controlled clinical trial (RCT) for curing tuberculosis and it was

published in the British Medical Journal, 1948.Statisticians, Sir

Austin Bradford Hill et al.(1951) reported that, a total of 1.80

million children participated in the largest trial to assess the

effectiveness of Salk vaccine in preventing paralysis or death from

poliomyelitis. Such large number was needed, because the

incidence rate of polio was about 1/2000 and evidence of treatment

effect was needed as soon as possible so that, the vaccine could be

routinely administered. As per the results, they observed that there

were two components (randomized and non-randomized) of the

trial. For the non-randomized component, one million children in

the first to third grades participated. The second grade was offered

vaccine, where as first and third grades formed the control group.

There was also randomized component where 0.8 million children

were screened in double blind placebo trial. The incidence of polio

in the randomized vaccinated group was less than half that in the

control group and even larger differences were seen in the decline

of paralytic polio.



21

1.3 Brief Concept of Study Design

1.3.1 CROSS SECTIONAL STUDY: In cross sectional study, the

data were obtained from a random sample of the population at one

point of time. This gave a snapshot of the population. Based on

single survey of a specific population or a random sample thereof,

we determined the proportion of individuals with heart disease at

one point of time. This is referred to as the prevalence of disease.

Collection of demographic and other information would allow to

break down the prevalence by age, race, sex, socioeconomic status

and geographical area etc. Important special case, where the

exposure and diseases are dichotomous, the data from a cross

sectional study can be represented by using 2X2 contingency table:

Characteristics Disease No disease Total

Exposed A B (A+B)

Unexposed C D (C+D)

Total (A+C) (B+D) GT

Prevalence of disease (%) = , Probability of exposure = ,

Prevalence of disease among exposed population = ,

Prevalence of diseases among unexposed population = . We

can also assess the association between the exposure and disease

using data from a cross sectional study. One such measure is

relative risk was estimated by:

It is easy to conclude that the relative risk has following

properties:

1 positive association; i.e., the exposed population has

higher disease probability than the unexposed population.

1 no association; i.e., the exposed population has the same

disease probability as the unexposed population.

1 negative association; i.e., the exposed population has

lower disease probability than the unexposed population.



22

1.3.2 LONGITUDINAL STUDY: In a longitudinal study,

subjects are followed over time and single or multiple

measurements of the variables of interest are obtained.

Longitudinal epidemiological studies generally fall into two

categories, prospective (moving forward in time) and retrospective

(going backward in time).

1.3.3 PROSPECTIVE STUDY: In a prospective study, a cohort

of individuals are obtained, who are free of a particular disease

under study and data are collected on certain risk factors i.e.

children were exposed to contaminants with respect to age, sex,

race etc. The individuals are then followed over for some specified

period of time, to determine whether they get the disease or not.

The relationship between the probability of getting disease during

certain time period is called as incidence of the disease.

1.3.4 RETROSPECTIVE STUDY: CASE CONTROL:A very

popular design in many epidemiological and RCT studies is the

retrospective cross sectional, case control design. In such a study,

individuals with disease (cases) and the individuals without disease

(controls) were identified. Using records or questionnaires the

investigators go back in time and ascertain the exposure status and

risk factors from their past. Such data are used to estimate relative

risk factors.

Drug

response Cases Controls Total

Responded A B (A+B)

Not

responded C D (C+D)

Total (A+C) (B+D) GT

Sensitivity (%) = , Specificity (%) = , Drug responded

among cases = ,Drug not responded among cases = ,

relative risk was estimated in accordance with the above

mentioned formula.



23

1.4 Different Phases of Clinical Trial

The process of drug development can be broadly classified as

preclinical and clinical. Preclinical refers to experimentation that

occurs before exposure to human subjects, whereas clinical refers

to experimentation after exposure to the human subjects. It will be

assumed that, the drug has already been developed by the chemist

or biologist, tested in the laboratory for biological activity (invivo)

and the new drug or therapy is found to be classified and

sufficiently promising to be introduced into the humans. Within the

paradigm, we can classify the clinical trial into four phases;

Phase I: To explore possible toxic effects of drugs and determine a

tolerated dose for further experimentation. During this phase the

pharmacology of the drug may also be explored.

Phase II:Screening and feasibility study by initial assessment for

therapeutic effects and further assessment of toxicities.

Phase III: Comparison of new intervention (drug or therapy) to

the current standard of treatment; both with respect to efficacy and

toxicity.

Phase IV: Observational study of morbidity/ adverse effects on

human intervention.

1.5 Drug Development Process



24

1.6 Study Population:

Population is an universe. The target population of the study must

be defined in advance with unambiguous inclusion and exclusion

criteria. The impact of these criteria on the study design will be

visualized on the basis of location. Individual population group or

sample should be generalized before the recruitment procedure in

accordance with human ethical guidelines.

1.7 Statistical Issues And Methods

Our goal in clinical trial is to estimate an endpoint related to the

treatment efficacy and sufficient precision to aid the investigations

for determining, whether the proposed treatment to be studied for

further period. The following points highlighted for the recruitment

of the patients during study interventions;

1) The proportion of patients responding to the treatment arm

[response has to be unambiguously defined].

2) The proportion of patients with known side effects.

3) Average decreased level of serological markers over a period

of time.

Many literatures quoted that “the reliable statistical tools

inform sound decisions and better outcomes” incorrect /unethical

use of statistics can produce misleading results, poor advice and

worse choice.

For example, suppose we consider the patients with esophageal

cancer, who were treated with chemotherapy prior to surgical

resection. A complete response is defined as an absence of

macroscopic tumor at that time of surgery; we suspect that this

may occur with 35 per cent probability using a drug under

investigation in phase-II. The 35 per cent is just a guess, possibly

based on similar acting drugs used in the past and the goal is to

estimate the actual response rate with sufficient precision, in this

case we want 95 per cent confidence interval to be within 15 per

cent of the true or positives value.

As researchers, we start by positioning a statistical model; i.e.,

let 'p' denote the complete population response rate. Suppose we



25

conduct an experiment having η patients with known esophageal

cancer treated with the chemotherapy prior to surgical resection.

The data was collected based on the incumbent changes of

serological values and associated casual indicators. The result of

the experiment yields a random variable 'X', the number of patients

in a sample of size 'η' that have a complete response rate. A

popular discrete probability model for this scenario is to assume

that:

, X Binomial (η ,p)

Where, n = number of cancer patients, p = probability of

treatment success, (1-p) = probability of treatment failure and 'x' is

random variable with different time period.

We assumed that, the probability of treatment success is equal

to the probability of failure. The treatment effect should be

dichotomous and the probability of success and failure is always

equal to one, the mean of the probability was 'np' and standard

deviation was „npq‟. If the number of patients increased in

treatment arm, the binomial distribution tends to be poison

distribution. When „n‟ is sufficiently large, the distribution of the

sample proportion is well approximated by a normal

distribution with mean „np‟ and variance p(1-p)/n,

This approximation is useful for inference

regarding the population parameter „np‟. Because of the

approximate normality, the estimator „p‟ will be within 1.96

standard deviations of „np‟, approximately 95 per cent of the time

(Approximation gets better with increasing sample size).

Therefore, the population parameter „np‟ will be within the interval

, with approximately 95 per cent

probability. Since, the value „p‟ is unknown to us, we approximate

using „p‟ to obtain the approximate 95 per cent confidence interval.

Switch back to above mentioned example, where best guess for the

response rate is about 35 per cent, if we want the precision of our

estimator to be such that the 95 per cent confidence interval with in

the 15 per cent of true „p‟, then we need to calculate sample size.



26

= 39 patients (needed for our

experimentation).

If the number of patients increased in phase II and III trial, the

binomial distribution tends to be poison approximation the

probability of success is very small or nearer to zero. Binomial

distribution showed to be poison approximation, the density

function is given by:

, so that the binomial distribution tends to the

Poisson distribution with mean .

It was showed that the expected number of patients of ‟ is

equal to and that variance of x is also . This distribution

tends to the normal distribution as „ gets large in essentially the

same sense as the binomial distribution tends to normality. The

Poisson law is useful in getting quick approximation to binomial

probabilities.

1.8 Application Of Multinomial Distribution In

Clinical Trial

Let us, consider the simple situation of clinical trial conducted in

varied geographical locations and obtaining the data as per the

norms. We assumed „n‟ clinical trials and there were „t‟ possible

results viz., a1, a2, a3,……at with probability that we shall get n1a1‟s

n2a2‟s ..anat. Again the matter was solved by permutation and

combination for any possible arrangements of n1 a1‟s, n2a2

‟s …and

so on, the probability of trial is equal to:

Then, the cumulative probability for pooled trial is calculated

by the following density function

For example, the new-clinical trials were conducted in the

following geographical location, the resulted observations are

mentioned below:



27

1.8.1 GEHAN’S TWO STAGE DESIGN: Unlikely treatment

will achieve some low level of response because due to recursive

changes of clinical and biological parameters, the researcher

favorably should stop the trial as early as possible. For example,

suppose 20 per cent response rate is the lowest i.e., we consider the

acceptable new treatment experimentation. Suppose, no responses

in „n patients and if „n‟ is sufficiently large, then we confident that

the treatment is ineffective. Statistically how „n‟ is drawn from

parent population, so that if there are zero responses among „n‟

patients, we relatively confident that the response rate will not be

achieved 20 per cent or better

if and p≥0.20,

Choose „n‟ so that =0.05 or . This

leads to (rounding up), thus with the patient is unlikely

(≤0.50) that no one could response, if the treatment response rate

was greater than 20 per cent. Thus, zero patients responding among

Sl.

No. Location

No. of

patients

Sample

number

Probability

values

1. Northern

region 14 n1 0.23

2. Southern

region 15 n2 0.22

3. Middle

region 19 n3 0.36

4. Eastern

region 28 n4 0.44

5. Western

region 32 n5 0.52

Total 108



28

15 might be used as evidence to stop the clinical trial and declare

the treatment failure. This was the logic behind Gehan‟s two stage

design and he also suggested the following strategy, if minimal

acceptable response rate is then we choose the first stage with

patients such that:

=0.5;

If there is zero response among the first patients, then stop

and treatment can be declared as failure. Otherwise, continue with

recruiting additional patients that will ensure a certain degrees of

freedom of predetermined accuracy in 95 per cent confidence

interval.

Figure 2: Normal distribution simulated curve from Gehan’s

two stage design with 99 per cent confidence interval

From figure 2, Gehan‟s design was treated 15 patients

initially. If none responded, the treatment would be declared as

failure and the study stopped.



29

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