### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Research Methods BINF 702

Mason

GPA 3.64

### View Full Document

## 13

## 0

## Popular in Course

## Popular in BioInformatics

This 50 page Class Notes was uploaded by Nathanael Schowalter on Monday September 28, 2015. The Class Notes belongs to BINF 702 at George Mason University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/215259/binf-702-george-mason-university in BioInformatics at George Mason University.

## Similar to BINF 702 at Mason

## Reviews for Research Methods

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/28/15

e BINF702 Fall 2008 Chapter 3 Probability BINF702 FALL2008 Chapter 3 Probability 31 Introduction An Example to Hang OurHat On Example 31 Cancer One theory concerning the etiology of breast cancer states that women in a given age group who give birth to their first child relatively late in life after 30 are at greater risk for eventually developing breast cancer over some time period tthan are women who give birth to their first child early in life before 20 Because women in the upper social classes tend to have children later this theory has been used to explain why these women have a higher risk of developing breast cancer than women in the lower social classes To test this hypothesis we might identify 2000 women from a particular census tract who are currently ages 45 54 and have never had breast cancer of whom 1000 had their first child before the age of 20 call this group A and 1000 after the age of 30 group B These 2000 women might be followed for 5 years to assess if they developed breast cancer during this period Suppose there are 4 new cases of breast cancer in group A and 5 new cases in group B BINF702 FALL2008 Chapter 3 Probability g 32 Definition of Probability Def 31 The sample space is the set of all possible outcomes In referring to probabilities of events and event is any set of outcomes of interest The probability of an event is the relative frequency of this set of outcomes over a an indefinitely large or infinite number of trials Ex Toss a fair coin and observe the uppermost side Since we expect that heads is as likely to come up as tails we conclude that the empirical probability distribution is PH 12 PT 12 Can you provide another example BINF702 FALL2008 Chapter 3 Probability Section 32 Definition of Probability 1 The probability of an event E denoted by PrE always satisfies 0 s PrE s 1 2 If outcomes A and Bare two events that cannot both happen at the same time then PrA or 3 occurs PrA Pr8 Can you provide an example of two events that can t happen at the same time BINF702 FALL2008 Chapter 3 Probability Section 32 Definition of g Probability Def 3 2 Two e ven 7quot539 A and B are mu fuely exclusive if fhey can70139 b0 fh happen af fhe same fl39me fax gm 4 A U B muTually exclusive A U B not muTually exclusive BINF702 FALL2008 Chapter 3 Probability Section 33 Some Useful g Probabilistic Notation Def 33 The symbol is used as shorthand for the event Def 34 A U B is the event that either A or B occurs or they both occur Def 35 AmB is the event that both A and B occurs simultaneously Can you provide an example of two events and their intersection AmB BINF702 FALL2008 Chapter 3 Probability Section 33 Some Useful Probabilistic Notation Def 36 The complement of A is denoted A We note Can you provide an PI A 1 PYA example of an event and its complement EA 2 QQV BINF702 FALL2008 Chapter 3 Probability Section 34 The Multiplicative g Law of Probability Hypertension Genetics Suppose we are conducting a hypertension screening program in the home Consider all possible pairs of DBF measurements of the mother and father within a given family assuming that the mother and father are not genetically related This sample space consists of all pairs of numbers of the form C Y where X gt O Y gt 0 Certain specific events might be of interest in this context In particular we might be interested in whether the mother or father is hypertensive which is described respectively by events A mother39s DBF gt 95 B father39s DBF gt 95 These events are diagrammed in Figure 34Suppose we know that PrA 1 PrB 2 What can we say about PrA n B Prmother39s DBF gt 95 and father39s DBF gt 95 Prboth mother and father are hypertensive We can say nothing unless we are willing to make certain assumptions BINF702 FALL2008 Chapter 3 Probability Mia mhbmmuaun monument Mkmmmrmncthmlw u 95 Mother s map E event A Immhnr s mm 95 g even a mm rs 0131 2 951 evem A n B bath DBP 2 951 Section 34 The Multiplicative g Law of Probability Def 37 Two events A and B are called independent events if PI A m Pr Pr Can you provide an example of two independent events Def 38 Two events A B are dependent if Pr A n i Pr Pr 1lou provide an example of two dependent events Eq 32 Multiplication Law of Probabilitv If A1 Ak are mutually exclusive events then P1Al1 AZ n AkPrA1PrA2PrAk BINF702 FALL2008 Chapter 3 Probability Section 35 The Addition Law 5 of Probability Eq 33 Addition Law of Probability If A and B are any events then PI AUB PrAPrB PrArB Figure 35 Diagrammatic representation of the addition law of probability What happens if A and B are mutually exclusive BINF702 FALL2008 Chapter 3 Probability Section 35 The Addition Law of Probability Eq 34 Addition Law of Probability for Independent Events If two events A and B are independent then PrAUB PrAPrB1 PrA Figure 36 Di aaaaaa atic repr sentation of the addition law of robability forinde enden even 5 p p t t How does this come about r k we A VA 395 rquot x quota I M H k n 3 a a BINF702 FALL2008 Chapter 3 Probability Section 36 Conditional g Probability Def 39 The conditional probability of B given A written PrBA is defined as PrA B PrA AOBBFA PrBA 1 If A and B are independent events then PrB I A PrB PrB I Z 2 If two events A B are dependent then PrBA PrB PrBI26md PrAmB PrAPrB BINF702 FALL2008 Chapter 3 Probability Section 36 Conditional g Probability Def 310 The relative risk RR of B given A is given by PrB A PrB Z N B A and B independent implies RR is 1 The larger the dependence of the two events the further the relative risk is different from 1 RRBA BINF702 FALL2008 Chapter 3 Probability Section 36 Conditional g Probability Eq 36 Total Probability rule For any events A and B PrB PrB I APrAPrB I ZPrZ N B This is a very useful rule Def 311 A set of events A1 Ak is exhaustive if at least one of the events must occur Eq 37 Total Probability Rule Let A1 Akbe mutually exclusive and exhaustive events The unconditional probability of B PrB can be written as a weighted average of the conditional probabilities of Bgiven A PBAJ as fol0 W5 k PrB ZPrB AlPrAl i1 BINF702 FALL2008 Chapter 3 Probability Section 36 Conditional Probability Eq 38 Generalized Multiplicative Law of Probabilitv If A1 4k are an arbitrary set of events then PrA1 mAZ mnAkPrAlPrA2 IAIP1A3 IA2 mAlPrAkAk1 mnmAZ mAl BINF702 FALL2008 Chapter 3 Probability Section 37 Bayes Rule and Screening Tests Def 312 The predictive value positive PV of a screening test is the probability that a person has a disease given that the test is positive Prdiseaseltest The predictive value negative PV of a screening test is the probability that a person does not have a disease given that the test is negative Prno diseasetest BINF702 FALL2008 Chapter 3 Probability Section 37 Bayes Rule and Screening Tests Def 313 The sensitivity of a symptom or set of symptoms or screening test is the probability that the symptom is present given that the person has a disease Def 314 The specificity of a symptom or set of symptoms or screening test is the probability that the symptom is not present given that the person does not have a disease Def 315 A false negative is defined as a person who tests out as negative but who is actually positive A false positive is defined as a person who tests out as positive but who is actually nega ve BINF702 FALL2008 Chapter 3 Probability Section 37 Bayes Rule and Screening Tests g 39 Bayes Rule Let A symptom and B disease PrAIBPrB PrAIBPrBPrA PrE PVPrBA In words we can write this as PV sensmVlty sen51t1V1ty x 1 spe01flclty 1K where X PrB prevalence of disease in the reference population Similarly specificity l x speci city 1 x 1 sensitivityx Section 37 Bayes Rule and g Screening Tests Eq 310 Generalized Bayes Rule Let BI 52 Bk be a set of mutually exclusive and exhaustive disease states that is at lease one disease state must occur and no two disease states can occur at the same time Let A represent the presence of a symptom or set of symptoms Then PrA BlPrBl PrAlBjPrBj PrBl IA 2 BINF702 FALL2008 Chapter 3 Probability Section 38 Bayesian Inference Def 316 The prior probability of an event is the best guess by the observer of an event s probability in the absence of data This prior probability may be a single number or it may be a range of likely values for the probability perhaps with weights attached to each possible value Def 317 The posterior probability of an event is the probability of an event after collecting some empirical data It is obtained by integrating information from the prior probability with additional data related to the event in question BINF702 FALL2008 Chapter 3 Probability g Section 39 ROC Curves Def A receiver operating characteristic ROC curve is a plot of the sensitivity versus 1 specificity of a screening test where the different points on the curve correspond to different cutoff points used to designate test positive BINF702 FALL2008 Chapter 3 Probability Section 310 Prevalence and Incidence De 319 The prevalence of a disease is the probability of currently having the disease regardless of the duration of time one has had the diseaseIt is obtained by dividing the number of people who currently have the disease by the number of people in the study population Def 320 The cumulative incidence of a disease is the probability that a person with no prior disease will develop a new case of the disease over some specified period BINF702 FALL2008 Chapter 3 Probability Occupational Health Ex 329 pg 69 g Occupational Health I EX BINF702 FALL2008 Chapter 3 Probability BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease 353 BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease 360 BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability V Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease I EX BINF702 FALL2008 Chapter 3 Probability Pulmonary Disease EX 374 Hypertension I EX BINF702 FALL2008 Chapter 3 Probability BINF702 FALL2008 Chapter 3 Probability Hypertension I EX BINF702 FALL2008 Chapter 3 Probability Hypertension I EX BINF702 FALL2008 Chapter 3 Probability Hypertension I EX BINF702 FALL2008 Chapter 3 Probability Orthopedics I EX BINF702 FALL2008 Chapter 3 Probability Orthopedics I EX BINF702 FALL2008 Chapter 3 Probability Orthopedics I EX BINF702 FALL2008 Chapter 3 Probability Orthopedics I EX Can you produce R code to produce a ROC curve from this data BINF702 FALL2008 Chapter 3 Probability Orthopedics I EX BINF702 FALL2008 Chapter 3 Probability

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.