This document discusses Bayesian decision making in clinical research as compared to conventional statistics. It begins with definitions of key Bayesian concepts. It then analyzes 3 case studies: [1] A clinical trial comparing treatments A and B, where both conventional and Bayesian analysis find A superior; [2] Whether high cancer rates near power lines are caused by them, where conventional analysis finds an effect but Bayesian does not; [3] Whether certain contraceptives increase blood clots, where Bayesian analysis changes conclusions versus conventional. The document concludes that Bayesian statistics provides probabilities of hypotheses given data, while conventional statistics does not directly address hypothesis probabilities.
Statistical Methods for Removing Selection Bias In Observational StudiesNathan Taback
The slide deck is from a talk I delivered at a Dana Farber / Harvard Cancer Center outcomes seminar. It presents an overview of currently available statistical methods to remove bias in observational studies.
Homeopathy in the treatment of fibromyalgia A comprehensive literature-review...home
Given the low number and included trials and the lowmethodological quality, any conclusion based on the resultsof this review have to be regarded as preliminary. However,as single case studies and clinical trials indicate a positiveeffect, homeopathy could be considered a complementarytreatment for patients with fibromyalgia
A Summary Look at Studies of Cranial Electrotherapy Stimulation by Ray B. Smith, Ph.D. The mechanism of action, research... Cranial Electrotherapy Stimulation provides small pulses of electric current across the head of patients for the FDA recognized treatment of depression, anxiety and insomnia. CES has been in clinical use in the U.S.A. since 1963 and in Europe since 1953. Hundreds of thousands of patients have been treated with CES over the years, and thousands presently use these prescription devices in their homes.
Statistical Methods for Removing Selection Bias In Observational StudiesNathan Taback
The slide deck is from a talk I delivered at a Dana Farber / Harvard Cancer Center outcomes seminar. It presents an overview of currently available statistical methods to remove bias in observational studies.
Homeopathy in the treatment of fibromyalgia A comprehensive literature-review...home
Given the low number and included trials and the lowmethodological quality, any conclusion based on the resultsof this review have to be regarded as preliminary. However,as single case studies and clinical trials indicate a positiveeffect, homeopathy could be considered a complementarytreatment for patients with fibromyalgia
A Summary Look at Studies of Cranial Electrotherapy Stimulation by Ray B. Smith, Ph.D. The mechanism of action, research... Cranial Electrotherapy Stimulation provides small pulses of electric current across the head of patients for the FDA recognized treatment of depression, anxiety and insomnia. CES has been in clinical use in the U.S.A. since 1963 and in Europe since 1953. Hundreds of thousands of patients have been treated with CES over the years, and thousands presently use these prescription devices in their homes.
Quantitative Statistical Analysis Work Sample From StatsworkStats Statswork
Quantitative Data Collection perhaps the most widely used method for primary data collection. A variety of different collection methods of research, including mail surveys and face to face interviews.
EBM Journal Club - Intro and Review of Home BP Monitoring Articletjkinsey
This presentation is an introduction to the EBM Journal Club at MXC and a review of "Effectiveness of Home Blood Pressure
Monitoring, Web Communication, and
Pharmacist Care on Hypertension Control:
A Randomized Controlled Trial.”
Green B, Cook AJ, Ralston JD, et. al.
JAMA. 2008; 299(24): 2857-2867
A Bifactor and Itam Response Theory Analysis of the Eating Disorder Inventory-3David Garner
The Eating Disorder Inventory-3 (EDI-3; Garner, 2004) is a 91-item, self-report measure scored on 12 scales (three Eating
Disorder Risk scales, nine Psychological scales) and six composites. A sample of 1206 female eating disorder patients was
divided randomly into calibration (n = 607) and cross-validation (n = 599) samples for confirmatory factor analyses. A bifactor
model best fit the data in both samples, but a model with second-order factors corresponding to the risk and psychological scales
approached the fit of the bifactor model.
Avoid overfitting in precision medicine: How to use cross-validation to relia...Nicole Krämer
The identification of patient subgroups who may derive benefit from a treatment is of crucial importance in precision medicine. Many different algorithms have been proposed and studied in the literature.
We illustrate that many of these algorithms overfit in the sense that the treatment benefit for the identified patients is substantially overestimated. Further, we show that with cross-validation, it is possible to obtain more realistic estimates.
Performance Analysis of Data Mining Methods for Sexually Transmitted Disease ...IJECEIAES
According to health reports of Malang city, many people are exposed to sexually transmitted diseases and most sufferers are not aware of the symptoms. Malang city being known as a city of education so that every year the population number increases, it is at risk of increasing the spread of sexually transmitted diseases virus. This problem is important to be solved to treat earlier sufferers sexually transmitted diseases virus in order to reduce the burden of patient spending. In this research, authors conduct data mining methods to classifying sexually transmitted diseases. From the experiment result shows that K-NN is the best method for solve this problem with 90% accuracy.
Biostatistics Roles and Responsibilities in Clinical Research | PubricaPubrica
This Presentation explains the Roles and Responsibilities of Biostatistics in clinical research
Biostatistics helps to find answer for research question in Biology, Medicine and Public health
- How a new drug works
- What causes cancer
- what is the reason for many diseases
- How long could a person survive with a particular disease?
Learn More: http://pubrica.com/services/research-services/biostatistics-and-statistical-programming-services/
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Addressing the unpredictability issues in cancer vaccine trialsBhaswat Chakraborty
Determining the financial and decisional risks associated with the early phase trials
Understanding the best study designs and selection of controls to eliminate candidates
Understanding the end point selection for Cancer clinical trials
Comparing progress free and overall survival in Intend To Treat (ITT) and per protocol (PP) populations
Critically analysing the decision to proceed to Phase III or to terminate the trial
Case study: Discussing the best practice strategies on ‘Phase II clinical trials of vaccines – to go or not to go to Phase III
Quantitative Statistical Analysis Work Sample From StatsworkStats Statswork
Quantitative Data Collection perhaps the most widely used method for primary data collection. A variety of different collection methods of research, including mail surveys and face to face interviews.
EBM Journal Club - Intro and Review of Home BP Monitoring Articletjkinsey
This presentation is an introduction to the EBM Journal Club at MXC and a review of "Effectiveness of Home Blood Pressure
Monitoring, Web Communication, and
Pharmacist Care on Hypertension Control:
A Randomized Controlled Trial.”
Green B, Cook AJ, Ralston JD, et. al.
JAMA. 2008; 299(24): 2857-2867
A Bifactor and Itam Response Theory Analysis of the Eating Disorder Inventory-3David Garner
The Eating Disorder Inventory-3 (EDI-3; Garner, 2004) is a 91-item, self-report measure scored on 12 scales (three Eating
Disorder Risk scales, nine Psychological scales) and six composites. A sample of 1206 female eating disorder patients was
divided randomly into calibration (n = 607) and cross-validation (n = 599) samples for confirmatory factor analyses. A bifactor
model best fit the data in both samples, but a model with second-order factors corresponding to the risk and psychological scales
approached the fit of the bifactor model.
Avoid overfitting in precision medicine: How to use cross-validation to relia...Nicole Krämer
The identification of patient subgroups who may derive benefit from a treatment is of crucial importance in precision medicine. Many different algorithms have been proposed and studied in the literature.
We illustrate that many of these algorithms overfit in the sense that the treatment benefit for the identified patients is substantially overestimated. Further, we show that with cross-validation, it is possible to obtain more realistic estimates.
Performance Analysis of Data Mining Methods for Sexually Transmitted Disease ...IJECEIAES
According to health reports of Malang city, many people are exposed to sexually transmitted diseases and most sufferers are not aware of the symptoms. Malang city being known as a city of education so that every year the population number increases, it is at risk of increasing the spread of sexually transmitted diseases virus. This problem is important to be solved to treat earlier sufferers sexually transmitted diseases virus in order to reduce the burden of patient spending. In this research, authors conduct data mining methods to classifying sexually transmitted diseases. From the experiment result shows that K-NN is the best method for solve this problem with 90% accuracy.
Biostatistics Roles and Responsibilities in Clinical Research | PubricaPubrica
This Presentation explains the Roles and Responsibilities of Biostatistics in clinical research
Biostatistics helps to find answer for research question in Biology, Medicine and Public health
- How a new drug works
- What causes cancer
- what is the reason for many diseases
- How long could a person survive with a particular disease?
Learn More: http://pubrica.com/services/research-services/biostatistics-and-statistical-programming-services/
Contact:
Web: www.pubrica.com
Email: sales@pubrica.com
WhatsApp : +91 9884350006
United kingdom : +44-1143520021
Addressing the unpredictability issues in cancer vaccine trialsBhaswat Chakraborty
Determining the financial and decisional risks associated with the early phase trials
Understanding the best study designs and selection of controls to eliminate candidates
Understanding the end point selection for Cancer clinical trials
Comparing progress free and overall survival in Intend To Treat (ITT) and per protocol (PP) populations
Critically analysing the decision to proceed to Phase III or to terminate the trial
Case study: Discussing the best practice strategies on ‘Phase II clinical trials of vaccines – to go or not to go to Phase III
Most current highly active antiretroviral therapy (HAART) regimens for HIV-positive patients contain two nucleoside reverse transcriptase inhibitors (NRTIs) with either a Protease inhibitor (PIs) or a non-nucleoside reverse transcriptase inhibitors (NNRTI). Notwithstanding the regulatory guidelines recommending therapeutic drug monitoring (TDM) for these drugs, therapeutic failure is a very serious concern implying drug induced toxicity and more importantly viral rebound and viral resistance.
Single dose, steady state and dose ranging studies have all more or less demonstrated that there is a positive correlation between plasma concentrations and therapeutic effects of anti-retrovirals (ARVs). However, one of the main challenges still seems to be the target concentrations for these drugs and their relevant inhibitory quotient. In this talk, we are going to examine these issues along with bioanalytical challenges, drug-effect and drug –toxicity relationships and finally drug-drug interactions within different HAART regimes.
Common Statistical Concerns in Clinical TrialsClin Plus
Statistics are a major part of clinical trials. This article breaks down how they are used, and things that people think about when recording statistical data.
Bayesian theory in population pharmacokinetics--
1) INTRODUCTION TO BAYESIAN THEORY
2)BAYESIAN PROBABILITY TO DOSING OF DRUGS
3)APPLICATIONS AND USES OF BAYESIAN THEORY IN APPLIED PHARMACOKINETICS:
therapeutic drug monitoring and clinical pharmacokinetics-fifth pharm d notes
Effective strategies to monitor clinical risks using biostatistics - Pubrica.pdfPubrica
In clinical science, biostatistics services are essential for data collection, analysis, presentation, and interpretation. Epidemiology, clinical trials, population genetics, systems biology, and other disciplines all benefit from it. It aids in the evaluation of a drug's effectiveness and safety in clinical trials.
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Biostatistics are widely used in clinical trials to collect and organize and describe and interpret these result and then give to us proves to take appropriate clinical decisions
Observational research designs are those in which the researcher/investigator merely observes and does not carry out any interventions/actions.
to change the result. The three most common types of observational studies are cross-sectional studies, case-control studies, and cohort (or longitudinal) studies.
In cross-sectional studies, exposure/risk factors and outcomes are determined at a single point in time. You can bid
information on disease prevalence and an overview of likely relationships that can be used to form a hypothesis. Control cases In
studies, participants are selected based on the presence/absence of an outcome and risk factors are identified during the study.
after enrollment of study participants.The relationship between exposure and outcome is reported as an odds ratio. This research; However,
carries a high risk of bias, which should be taken into account when designing the study. Cohort studies are prospective and include participants
were selected based on presence/absence of exposure and results were obtained at the end of the study. This research can deliver The incidence/impact of the disease and the relationship between exposure and outcome are presented as relative risks. They are useful
establish causality.A problem that arises in these studies could be the high fluctuation and dropout of study participants.
Descriptive studies generally describe the magnitude of a problem and characteristics of the population/individuals.
The various types of such studies include
case reports
case series or surveys.
A case report generally describes a patient presenting with an unusual disease, or simultaneous occurrence of more than one condition, or uncommon clinical features in a known disease.
A case series is a collection of similar cases. Such studies, other than providing some advancement to knowledge of a disease, are of limited value. Another method often used in epidemiological health care research is conducting surveys.
Surveys are done during a defined time-period and information on several variables of interest is collected from the target population. They provide estimates of prevalence of the various variables of interest, and their distribution. Such studies could also provide insight into individual opinions and practices. Advantages include ease of conduct and cost efficiency. The disadvantages include low response rates and a variety of biases.
An analytical study tests a hypothesis to determine an association between two or more variables, like causation, risk, or effect. Such studies have two or more study groups for comparison.
The primary focus of this article will be the three most common types of analytical observational studies –
cross-sectional,
case control (also known as retrospective) and
cohort (or longitudinal, also known as prospective) studies.
It may be pertinent to note that the primary objective of most clinical studies is to determine one of the following - burden of disease (prevalence
This paper studies an identification problem that arises when clinicians seek to personalize patient care by predicting health outcomes conditional on observed patient covariates. Let y be an outcome of interest and let (x = k, w = j) be observed patient covariates. Suppose a clinician wants to choose a care option that maximizes a patient's expected utility conditional on the observed covariates. To accomplish this, the clinician needs to know the conditional probability distribution P(y|x = k, w = j). It is common to have a trustworthy evidence-based risk assessment that predicts y conditional on a subset of the observed covariates, say x, but not conditional on (x, w). Then the clinician knows P(y|x = k) but not P(y|x = k, w = j). Research on the ecological inference problem studies partial identification of P(y∣x, w) given knowledge of P(y|x) and P(w|x). Combining this knowledge with structural assumptions yields tighter conclusions. A psychological literature comparing actuarial predictions and clinical judgments has concluded that clinicians should not attempt to subjectively predict patient outcomes conditional on covariates that are not utilized in evidence-based risk assessments. I argue that formalizing clinical judgment through analysis of the identification problem can improve risk assessments and care decisions.
Root cause Analysis (RCA) & Corrective and Preventive action (CAPA) in MRCT d...Bhaswat Chakraborty
This presentation describes Identification & differentiation of Protocol deviation & violation; Different methods of RCA & best suitable method for Multiregional Clinical Trial; CAPA management and CAPA application to other trial sites/CRO/SMO/ Country that is involved in same trial (Strategic Management and application of CAPA in MRCT)
This presentation gives effective solutions to outliers issue in bioequivalence trials. It described what would be acceptable to Regulatory agencies as well as some new approaches.
Equivalence approches for complex generics DIA 11 april 2019 Bhaswat Chakraborty
This is a workshop that i gave a few days ago on bioequivalence of complex generics like peptides, polymers, liposomes, colloids, ophthamic and topical produtcts.
Clinical trials that are needed for efficacy & safety evidence of Medical devices include feasibility (pilot) and Pivotal trials. An extended battery of preclinical trials are also needed for high risk devices.
Writing Science papers for for publication requires something more thatn creativity. Target journals, content organization, wrting style, elegance and referencing are equally important.
Multidisc review of NDAs and BLAs nipicon 2018 Dr. ChakrabortyBhaswat Chakraborty
NDAS and BLAs cannot be authoritatively reviewed these days until experts from different disciplines act together like a team. This presentation give some foundational points and an illustrative example in that regard.
Teaching by stories, anecdotes and historical facts sept 25 2018Bhaswat Chakraborty
Many difficult principles in science and humanities can be taught best by a story (of its discovery), by an anecdote or some historical facts about them.
Orientation and Adaptation for Post-Graduate Pharmacy ProgramsBhaswat Chakraborty
PG Pharmacy programs are more focused and professionally oriented than the undergraduate counterpart. Many soft skills are required along with the curricular competence for excellence at the PG level.
Scientific integrity calls for some basic originality. Plagiarism can destroy this original creativity and ideation. This presentation defines plagiarism (stealing from others' works) and some of the creative and systematic remedies.
Best Practices to Risk Based Data Integrity at Data Integrity Conference, Lon...Bhaswat Chakraborty
Data integrity can be implemented using several approaches. One of the most effective ways to implement DI is a risk based approach. The speaker elaborates this.
There are several dimensions in Pharmaceutical ethics -- Practice-, research- and community oriented. This presentation mainly deals with Clinical research oriented Ethics.
Young pharmaceutical scientists are and can get involved in all aspects of new drug discovery and development. They have to be appropriately qualified, trained and experienced though,
This presentation mainly deals with clinical development of biosimilar products. It also gives enough on non-clinical development so that the audience is well oriented.
High variability in PK can be a characteristic of certain drug products which require different from ordinary strategies and study designs for establishing bioequivalence.
High variability in PK can be a characteristic of certain drug products which require different from ordinary strategies and study designs for establishing bioequivalence.
Best Ayurvedic medicine for Gas and IndigestionSwastikAyurveda
Here is the updated list of Top Best Ayurvedic medicine for Gas and Indigestion and those are Gas-O-Go Syp for Dyspepsia | Lavizyme Syrup for Acidity | Yumzyme Hepatoprotective Capsules etc
- Video recording of this lecture in English language: https://youtu.be/lK81BzxMqdo
- Video recording of this lecture in Arabic language: https://youtu.be/Ve4P0COk9OI
- Link to download the book free: https://nephrotube.blogspot.com/p/nephrotube-nephrology-books.html
- Link to NephroTube website: www.NephroTube.com
- Link to NephroTube social media accounts: https://nephrotube.blogspot.com/p/join-nephrotube-on-social-media.html
NVBDCP.pptx Nation vector borne disease control programSapna Thakur
NVBDCP was launched in 2003-2004 . Vector-Borne Disease: Disease that results from an infection transmitted to humans and other animals by blood-feeding arthropods, such as mosquitoes, ticks, and fleas. Examples of vector-borne diseases include Dengue fever, West Nile Virus, Lyme disease, and malaria.
The Gram stain is a fundamental technique in microbiology used to classify bacteria based on their cell wall structure. It provides a quick and simple method to distinguish between Gram-positive and Gram-negative bacteria, which have different susceptibilities to antibiotics
Knee anatomy and clinical tests 2024.pdfvimalpl1234
This includes all relevant anatomy and clinical tests compiled from standard textbooks, Campbell,netter etc..It is comprehensive and best suited for orthopaedicians and orthopaedic residents.
Muktapishti is a traditional Ayurvedic preparation made from Shoditha Mukta (Purified Pearl), is believed to help regulate thyroid function and reduce symptoms of hyperthyroidism due to its cooling and balancing properties. Clinical evidence on its efficacy remains limited, necessitating further research to validate its therapeutic benefits.
These lecture slides, by Dr Sidra Arshad, offer a quick overview of the physiological basis of a normal electrocardiogram.
Learning objectives:
1. Define an electrocardiogram (ECG) and electrocardiography
2. Describe how dipoles generated by the heart produce the waveforms of the ECG
3. Describe the components of a normal electrocardiogram of a typical bipolar lead (limb II)
4. Differentiate between intervals and segments
5. Enlist some common indications for obtaining an ECG
6. Describe the flow of current around the heart during the cardiac cycle
7. Discuss the placement and polarity of the leads of electrocardiograph
8. Describe the normal electrocardiograms recorded from the limb leads and explain the physiological basis of the different records that are obtained
9. Define mean electrical vector (axis) of the heart and give the normal range
10. Define the mean QRS vector
11. Describe the axes of leads (hexagonal reference system)
12. Comprehend the vectorial analysis of the normal ECG
13. Determine the mean electrical axis of the ventricular QRS and appreciate the mean axis deviation
14. Explain the concepts of current of injury, J point, and their significance
Study Resources:
1. Chapter 11, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 9, Human Physiology - From Cells to Systems, Lauralee Sherwood, 9th edition
3. Chapter 29, Ganong’s Review of Medical Physiology, 26th edition
4. Electrocardiogram, StatPearls - https://www.ncbi.nlm.nih.gov/books/NBK549803/
5. ECG in Medical Practice by ABM Abdullah, 4th edition
6. Chapter 3, Cardiology Explained, https://www.ncbi.nlm.nih.gov/books/NBK2214/
7. ECG Basics, http://www.nataliescasebook.com/tag/e-c-g-basics
Adv. biopharm. APPLICATION OF PHARMACOKINETICS : TARGETED DRUG DELIVERY SYSTEMSAkankshaAshtankar
MIP 201T & MPH 202T
ADVANCED BIOPHARMACEUTICS & PHARMACOKINETICS : UNIT 5
APPLICATION OF PHARMACOKINETICS : TARGETED DRUG DELIVERY SYSTEMS By - AKANKSHA ASHTANKAR
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journey
Bayesian ijupls
1. International Standard Serial Number (ISSN): 2249-6793
International Journal of Universal Pharmacy and Life Sciences 2(1): January-February 2012
INTERNATIONAL JOURNAL OF UNIVERSAL
PHARMACY AND LIFE SCIENCES
Pharmaceutical Sciences Original Article……!!!
Received: 02-01-2012; Accepted: 08-01-2012
BAYESIAN DECISION MAKING IN CLINICAL RESEARCH: A PRIMER FOR NON-
STATISTICIANS
Bhaswat S. Chakraborty*
Cadila Pharmaceuticals, Ahmedabad, Gujarat 387810, India.
ABSTRACT
Keywords: The objective of this article is to demonstrate a few fundamental applications
of Bayesian statistics in evaluating evidence from clinical and epidemiological
Conventional (Frequentist) research and understanding their implications in conclusions of clinical trials,
statistics – Bayesian medical practice, guidelines and policies. The methodology mainly compares
statistics – posterior and contrasts the conventional (Frequentist) and Bayesian theories of
probabilities through examples. First, inference of the results of a clinical trial
(conditioned) probability – comparing treatments A and B was considered. Conventional analysis
clinical trial – inference concluded that treatment A is superior because there is a low probability that
such a significant difference would have been observed when the treatments
For Correspondence: were in fact equal. Bayesian analysis on the other hand looked at the observed
difference and induced the likelihood of treatment A being superior to B. Two
Dr. Bhaswat S. Chakraborty additional case studies (case study 2 concerning that their high cancer rate
could be due to two nearby high voltage transmission lines and case study 3
Senior Vice President, concerning third generation contraceptive pills containing desogestral and
Research & Development, gestodene causing venous thromboembolism) were also analyzed using
Bayes’ rule. In all cases, relative merits of the two approaches were analyzed
Cadila Pharmaceuticals
for medical practice, guidelines and policies. As results of the case study 1, the
Limited, 1389, Trasad Road, conventional analysis showed a p value for the difference between treatments
Dholka 387810, Ahmedabad, A and B is 0.001, which is highly significant at α = 0.05. This means that the
Gujarat, India chance of observing this difference when A and B are in fact equal is 1 in a
1000. The Bayesian conditioned probability of A being superior to B was
E-mail: 0.999. Although the same conclusion was reached here, the next two case
drb.chakraborty@cadilapharma.co.in studies (case study 2: whether cancer can be induced by proximity to high-
voltage transmission lines and case study3: an increased risk of venous
thrombosis with third generation oral contraceptives) showed very different
results leading to different conclusions. It is concluded that conclusions from
both conventional and Bayesian inferences can be similar but the key
difference between conventional and Bayesian reasoning is that the Bayesian
believes that truth is subjective and naturally conditioned by the evidence.
Almost all areas of clinical research and medicine now have applications of
Bayesian statistics, one of the earliest being diagnostic medicine. From the
results of the case studies, we shall also see the application of Bayesian
methods clinical trials and epidemiology.
48 Full Text Available On www.ijupls.com
2. International Standard Serial Number (ISSN): 2249-6793
INTRODUCTION
Rev. Thomas Bayes (1702 – 1761) noted that sometimes the probability of a statistical
hypothesis is given before event or evidence is observed (Prior). He showed how to compute the
probability of the hypothesis after some observations are made (Posterior).
Before Rev. Bayes, no one knew how to measure the probability of statistical hypotheses in the
light of data. Only it was known as to how to reject a statistical hypothesis in the light of data.
In order to understand what the preceding paragraph means, let us define certain probabilities in
clear ordinary language. Let us say that if two events are mutually exclusive if they have no
sample points in common. An example of such events would be probability of positive diagnosis
of a disease by a kit and the probability of actually developing that disease in a person. Then, let
us define that the probability that event A occurs, given that event B has occurred, is called a
conditional probability. The conditional probability of A, given B, is denoted in statistics by the
symbol P(A|B). Similarly, the probability of event A not occurring is given by P(A'). Further, if
events A and B come from the same sample space, the probability that both A and B occur is the
probability of event A occurring multiplied with the probability of event B occuring, given A has
occurred.
P(A ∩ B) = P(A) * P(B|A)
And finally, probability that either A has occurred or B has occurred or both have occurred is
given by:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Bayes' Theorem
Let X1, X2, ... , Xn be a set of mutually exclusive events that form a sample space S. Let Y be any
event from a same sample space, such that P(Y) > 0. Then,
Since P( Xk ∩ Y ) = P( Xk )*P( Y | Xk ), Bayes’ theorem can also be expressed as
49 Full Text Available On www.ijupls.com
3. International Standard Serial Number (ISSN): 2249-6793
CASE STUDIES
Case Study 1 – A Superiority Trial
Conventional Statistics
In the first case study, let us consider a randomized clinical trial (RCT) in which a new
therapeutic intervention A is being tested for superiority of its effectiveness over that of B in an
appropriate patient population. Let the null (H0) and alternate (H1) hypotheses be as follows:
H0: μA – μB ≤ and H1: μA – μB > ….Eq. 3
These hypotheses were tested at level of significance, α = 0.05. Once the trial was over, the
experimental data showed that the mean outcome measure of A was higher in magnitude than
that of B and conventional statistical analysis computed a p = 0.001 i.e., the probability of
observing this difference by chance is 1 in 1000. Consequently, the null hypothesis was rejected
and it was concluded that the alternate is true – A is superior to B.
Bayesian Statistics
We shall understand the basic propositions of Bayesian analysis in Case 1 and not repeat these
for the other two case studies. Let us say that the prior probability of treatment A being superior
to treatment B, P( XA ) is 80% or 0.8. Therefore, as stated above, the prior probability of
treatment A not being superior to Treatment B, P( XB ) = 1 – 0.8 = 0.2. Let the probability of
experimental evidence from the RCT, of concluding A is superior to B, when A is indeed
superior, P(Y | XA) is 95% or 0.95 and, therefore, experimental probability of concluding A not
being superior to B, when A is indeed superior, P(Y | XB) = 1 – 0.95 = 0.05.
What we would like to know is whether the posterior or conditional probability of A indeed
being superior to B when the experimental evidence is superiority of A following Eq. 2. Thus:
50 Full Text Available On www.ijupls.com
4. International Standard Serial Number (ISSN): 2249-6793
Therefore, the Bayesian conclusion, in this case, is that there is a 99% probability of the
hypothesis that treatment effect of A is Superior to the treatment effect of B. This is same as the
one concluded from the conventional analysis by rejecting its null hypothesis.
Case Study 2 – Effect (Cancer) to Cause (High Voltage) Analysis
One of the salient characteristics of Bayesian statistics is, of course, its ability to compute the
probability of hypothesis being true. This allows investigation of effect to cause. In the second
case study, the statistical problem is that an elementary school staff is concerned that their high
cancer rate among the ex- and current employees could be due to two nearby high voltage
transmission lines.[1] The data in support of such suspicion include the fact that there have been
8 cases of invasive cancer over a long time among 145 women staff members whose average age
was between 40 and 44. The national average of incidence of this cancer is 3% in women aged
40-45. Therefore, based on the national cancer rate among woman this age, the expected number
of cancers in this school staff would be 4.2.
What we are assuming in this case study that the staff members developed cancer independently
of each other and the rate of developing cancer, , was the same for each woman staff member.
Therefore, the number of cancers, X, which follows a binomial distribution can be given as
follows:
X ~ bin (145, ) …. Eq. 4
Where could be 0.03 (national cancer rate) or more, i.e., 0.04, 0.05, 0.06 which we’ll define as
theories A, B, C, and D, respectively. For each hypothesized, we can use the elementary results
of the binomial distribution to calculate the probabilities:
P(X=8 | θ) = θ8 (1 – θ)(145-8) …. Eq. 5
Thus, theory A gives P(X=8 | θ=0.03 ) = 0.036; theory B: P(X=8 | θ=0.04 ) = 0.096; theory C:
P(X=8 | θ=0.05 ) = 0.134; and theory D: P(X=8 | θ=0.06 ) = 0.136. This is a ratio of
approximately 1:3:4:4. It is obvious that theory B explains the data about 3 times as well as
theory A. Here, first let us look at the likelihood principle. Initially, P(X | θ) is a function of two
variables: X and θ. But once X = 8 has been observed, then P(X | θ) describes how well each
theory, or value of θ explains the data. No other value of X is relevant and we should treat Pr(X |
) simply as Pr( X = X | ).[2]
Conventional Statistics:
Once again, let us state the null (H0) and alternate (H1) hypotheses as follows:
H0: θ = 0.03 and H1: θ ≠ 0.03 …. Eq. 6
And p = P(X = 8 | θ = 0.03)+ P(X = 9 | θ = 0.03) + +…+ P(X = 145 | θ = 0.03)
0.07
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5. International Standard Serial Number (ISSN): 2249-6793
Therefore, at the given level of significance, α = 0.10, the null hypothesis is rejected and and it is
concluded that the high voltage has a significant effect on the cancer rate among the women staff
at the school.
Bayesian Statistics:
For Bayesian analysis, we can look at the probabilities of getting 8 cancers given incidence rates
of θ = 0.03 or more (define as theories A, B, C, and D).
Thus, P(A | X = 8) = 0.23;
P(B | X = 8) = 0.21;
P(C | X = 8) = 0.28; and
P(D | X = 8) = 0.28
If we add the probabilities of X = 8 given = 0.04, = 0.05 and = 0.06, we get 0.77. Thus, the
Bayesian P( > 0.03) = 0.77, which would not be sufficient to reject the null hypothesis. This is
in contrast with the conclusion from the conventional analysis.
Case Study 3 – Another Effect (thromboembolism) to Cause (Contraceptive Treatment)
Analysis
This case study has been taken from many articles published in British Medical Journal.[3-7] Four
case-control studies (including one nested in a cohort study) of third generation contraceptive
pills containing desogestral and gestodene were compared with pills containing other
progestagens for the relative risk of venous thromboembolism.[4-7]
Conventional Statistics
The pills we are talking about were all declared “safe and effective” by conventional analysis.
Now, the question arises as to why was not the risk of increased thromboembloism picked up by
conventional analysis? As we illustrated in previous examples, conventional analysis does not
calculate the probability of a hypothesis being true given the data.
Bayesian Statistics
The details of the Bayesian analysis of this case study may not be warranted as the goal of this
paper is to just introduce the latter to non-statistical readership. However, the
Bayesian analysis showed that the posterior distributions are much narrower than the prior
distributions, indicating less doubt about the value of the true relative risk (odds ratio of 2.0).
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6. International Standard Serial Number (ISSN): 2249-6793
The data influenced the posterior distributions more than the prior distributions, such that they
are centred on log(1.69) and log(1.76) respectively, and the probability of the true relative risk
being greater than 1 is more than 0.999 in both cases.
The real scientific question could have been – "what is the probability that the third generation
pills increase the risk when compared to the others; what is the probability that they at least
double the risk – as measured in the case-control study; and what is the 'median estimate' (as
likely to be too small as too large)?"[8]
CONCLUSIONS
Conventional statistics (also known as Frequentist statistics) make no claims about probabilities
although one get misled that one is establishing a probability of something. For example, the
95% confidence interval (CI) of mean does not claim there is a 95% probability the mean is in
that range. What it states is that if the experiment was repeated 100 times, 95 times the estimated
mean would lie that range. Likelihood also does not give you probability of a hypothesis – it
gives only the likelihood of the data given the hypothesis. Maximum likelihood estimation is
thus only a little more reliable than conventional statistics.
Bayesian statistics, on the other hand, does give you the probability of a hypothesis being true
given the data. This is closest to intuition and normal process of decision making. Everyone
would normally want to know if a hypothesis is given some observed data, such as, given an
effect whether the cause is true. The three case studies that have been looked at in this paper
represent three different scenarios, each of which has its own place in clinical research. The first
one shows, if the prior and posterior are equally influenced by data, then the conventional and
Bayesian conclusions are nominally the same. In the second case, however, the conditioned
(posterior) probability, although influenced by the data, did not yet call for a rejection of the
hypothesis. And in the third case, the most complicated and challenging for the decision makers,
the data changed the posterior probability so much that only the conditioned hypothesis was
considered to be true.
REFERENCES
1. Brodeur P, “The Cancer at Slater School”, Annals of radiation, The New Yorker, December
7, 1992, p. 86.
2. http://www.home.uchicago.edu/~grynav/bayes/ABSLec1.ppt, access date 06.03.2009.
3. McPherson K. Third Generation Oral Contraception and Venous Thromboembolism. BMJ,
1995, 312, 68-69.
4. Poulter NR,Chang CL, Farley TMM, Meirik O, Marmot MG. Venous thromboembolic
disease and combined oral contraceptives: results of international multicentre case-control
study. Lancet, 1995, 346, 1575–1582.
5. Farley TMM, Meirik O, Chang CL, Marmot MG, Poulter NR. Effect of different
progestagens in low oestrogen oral contraceptives on venous thromboembolic disease.
Lancet, 1995, 346, 1582–1588.
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6. Jick H, Jick SS, Gurewich V, Myers MW, Vasilakis C. Risk of idiopathic cardiovascular
death and non-fatal venous thromboembolism in women using oral contraceptives with
differing progestagen components. Lancet, 1995, 346, 1589–1593.
7. Bloemenkamp KWM, Rosendaal FR, Helmerhorst FM, Buller HR, Vandenbroucke JP.
Enhancement by factor V Leiden mutation of risk of deep-vein thrombosis associated with
oral contraceptives containing third-generation progestage. Lancet, 1995, 346, 1593–1596.
8. Lilford RJ, Braunholtz D. The Statistical Basis of Public Policy: a Paradigm Shift is
Overdue. BMJ, 1996, 313, pp. 603-607.
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