An introduction to logistic regression for physicians, public health students and other health workers. Logistic regression is a way to look at effect of a numeric independent variable on a binary (yes-no) dependent variable. For example, you can analyze or model the effect of birth weight on survival.
Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.In this presentation a brief introduction about SLR and MLR and their codes in R are described
It introduces the reader to the basic concepts behind regression - a key advanced analytics theory. It describes simple and multiple linear regression in detail. It also talks about some limitations of linear regression as well. Logistic regression is just touched upon, but not delved deeper into this presentation.
Binary Logistic Regression Classification makes use of one or more predictor variables that may be either continuous or categorical to predict target variable classes. This technique identifies important factors impacting the target variable and also the nature of the relationship between each of these factors and the dependent variable. It is useful in the analysis of multiple factors influencing an outcome, or other classification where there two possible outcomes.
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
This presentation guide you through Logistic Regression, Assumptions of Logistic Regression, Types of Logistic Regression, Binary Logistic Regression, Multinomial Logistic Regression and Ordinal Logistic Regression.
For more topic stay tuned with Learnbay.
1. continuous probability distribution
2. Normal Distribution
3. Application of Normal Dist
4. Characteristics of normal distribution
5.Standard Normal Distribution
Logistic Regression: Predicting The Chances Of Coronary Heart DiseaseMichael Lieberman
Logistic Regression - Predicting the Chances of Coronary Heart Disease weighs risks factors for heart disease and calculates the odds of contracting the disease within the next ten years.
A gentle introduction to 2 classification techniques, as presented by Kriti Puniyani to the NYC Predictive Analytics group (April 14, 2011). To download the file please go here: http://www.meetup.com/NYC-Predictive-Analytics/files/
Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.In this presentation a brief introduction about SLR and MLR and their codes in R are described
It introduces the reader to the basic concepts behind regression - a key advanced analytics theory. It describes simple and multiple linear regression in detail. It also talks about some limitations of linear regression as well. Logistic regression is just touched upon, but not delved deeper into this presentation.
Binary Logistic Regression Classification makes use of one or more predictor variables that may be either continuous or categorical to predict target variable classes. This technique identifies important factors impacting the target variable and also the nature of the relationship between each of these factors and the dependent variable. It is useful in the analysis of multiple factors influencing an outcome, or other classification where there two possible outcomes.
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
This presentation guide you through Logistic Regression, Assumptions of Logistic Regression, Types of Logistic Regression, Binary Logistic Regression, Multinomial Logistic Regression and Ordinal Logistic Regression.
For more topic stay tuned with Learnbay.
1. continuous probability distribution
2. Normal Distribution
3. Application of Normal Dist
4. Characteristics of normal distribution
5.Standard Normal Distribution
Logistic Regression: Predicting The Chances Of Coronary Heart DiseaseMichael Lieberman
Logistic Regression - Predicting the Chances of Coronary Heart Disease weighs risks factors for heart disease and calculates the odds of contracting the disease within the next ten years.
A gentle introduction to 2 classification techniques, as presented by Kriti Puniyani to the NYC Predictive Analytics group (April 14, 2011). To download the file please go here: http://www.meetup.com/NYC-Predictive-Analytics/files/
Data Science - Part XV - MARS, Logistic Regression, & Survival AnalysisDerek Kane
This lecture provides an overview on extending the regression concepts brought forth in previous lectures. We will start off by going through a broad overview of the Multivariate Adaptive Regression Splines Algorithm, Logistic Regression, and then explore the Survival Analysis. The presentation will culminate with a real world example on how these techniques can be used in the US criminal justice system.
Eduard Ponarin- Higher School of Economics, Russia
Veronica Kostenko- The National Research University
ERF Training Workshop on Opinion Poll Data Analysis Using Multilevel Models
Beirut, Lebanon August 22-23, 2016
www.erf.org.eg
This is a presentation made for our Intro to Machine Learning class. As a result it focuses more on the use of logit regression as a classifier as opposed to statistical applications. Many of the slides are based on Stanford's Open Course in machine learning.
Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
Data Science training certifies you with ‘in demand’ Big Data Technologies to help you grab the top paying Data Science job title with Big Data skills and expertise in R programming, Machine Learning and Hadoop framework.
In this talk, I am going to discuss logistic regression, a topic that has been (and still is) quite heavily used as a solution to many supervised learning problems, in several different domains.
I will be focussing on three fundamental and general aspects related to any supervised learning problem: i) the model, ii) the error measure (or cost function), and iii) the learning algorithm. Then, I will cast each of those aspects into the specific case of logistic regression.
This presentation describes the application of regression analysis in research, testing assumptions involved in it and understanding the outputs generated in the analysis.
Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest.
Slides from the presentation "Probably, Definitely, Maybe" delivered at Deovxx 2014. See Parleys.com for the full video https://www.parleys.com/speaker/5148920c0364bc17fc5697a5
very detailed illustration of Log of Odds, Logit/ logistic regression and their types from binary logit, ordered logit to multinomial logit and also with their assumptions.
Thanks, for your time, if you enjoyed this short article there are tons of topics in advanced analytics, data science, and machine learning available in my medium repo. https://medium.com/@bobrupakroy
Linear regression is an approach for modeling the relationship between one dependent variable and one or more independent variables.
Algorithms to minimize the error are
OLS (Ordinary Least Square)
Gradient Descent and much more.
Let me know if anything is required. Ping me at google #bobrupakroy
- Video recording of this lecture in English language: https://youtu.be/kqbnxVAZs-0
- Video recording of this lecture in Arabic language: https://youtu.be/SINlygW1Mpc
- 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
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
Basavarajeeyam is a Sreshta Sangraha grantha (Compiled book ), written by Neelkanta kotturu Basavaraja Virachita. It contains 25 Prakaranas, First 24 Chapters related to Rogas& 25th to Rasadravyas.
Title: Sense of Taste
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the structure and function of taste buds.
Describe the relationship between the taste threshold and taste index of common substances.
Explain the chemical basis and signal transduction of taste perception for each type of primary taste sensation.
Recognize different abnormalities of taste perception and their causes.
Key Topics:
Significance of Taste Sensation:
Differentiation between pleasant and harmful food
Influence on behavior
Selection of food based on metabolic needs
Receptors of Taste:
Taste buds on the tongue
Influence of sense of smell, texture of food, and pain stimulation (e.g., by pepper)
Primary and Secondary Taste Sensations:
Primary taste sensations: Sweet, Sour, Salty, Bitter, Umami
Chemical basis and signal transduction mechanisms for each taste
Taste Threshold and Index:
Taste threshold values for Sweet (sucrose), Salty (NaCl), Sour (HCl), and Bitter (Quinine)
Taste index relationship: Inversely proportional to taste threshold
Taste Blindness:
Inability to taste certain substances, particularly thiourea compounds
Example: Phenylthiocarbamide
Structure and Function of Taste Buds:
Composition: Epithelial cells, Sustentacular/Supporting cells, Taste cells, Basal cells
Features: Taste pores, Taste hairs/microvilli, and Taste nerve fibers
Location of Taste Buds:
Found in papillae of the tongue (Fungiform, Circumvallate, Foliate)
Also present on the palate, tonsillar pillars, epiglottis, and proximal esophagus
Mechanism of Taste Stimulation:
Interaction of taste substances with receptors on microvilli
Signal transduction pathways for Umami, Sweet, Bitter, Sour, and Salty tastes
Taste Sensitivity and Adaptation:
Decrease in sensitivity with age
Rapid adaptation of taste sensation
Role of Saliva in Taste:
Dissolution of tastants to reach receptors
Washing away the stimulus
Taste Preferences and Aversions:
Mechanisms behind taste preference and aversion
Influence of receptors and neural pathways
Impact of Sensory Nerve Damage:
Degeneration of taste buds if the sensory nerve fiber is cut
Abnormalities of Taste Detection:
Conditions: Ageusia, Hypogeusia, Dysgeusia (parageusia)
Causes: Nerve damage, neurological disorders, infections, poor oral hygiene, adverse drug effects, deficiencies, aging, tobacco use, altered neurotransmitter levels
Neurotransmitters and Taste Threshold:
Effects of serotonin (5-HT) and norepinephrine (NE) on taste sensitivity
Supertasters:
25% of the population with heightened sensitivity to taste, especially bitterness
Increased number of fungiform papillae
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.
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.
Follow us on: Pinterest
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
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.
Flu Vaccine Alert in Bangalore Karnatakaaddon Scans
As flu season approaches, health officials in Bangalore, Karnataka, are urging residents to get their flu vaccinations. The seasonal flu, while common, can lead to severe health complications, particularly for vulnerable populations such as young children, the elderly, and those with underlying health conditions.
Dr. Vidisha Kumari, a leading epidemiologist in Bangalore, emphasizes the importance of getting vaccinated. "The flu vaccine is our best defense against the influenza virus. It not only protects individuals but also helps prevent the spread of the virus in our communities," he says.
This year, the flu season is expected to coincide with a potential increase in other respiratory illnesses. The Karnataka Health Department has launched an awareness campaign highlighting the significance of flu vaccinations. They have set up multiple vaccination centers across Bangalore, making it convenient for residents to receive their shots.
To encourage widespread vaccination, the government is also collaborating with local schools, workplaces, and community centers to facilitate vaccination drives. Special attention is being given to ensuring that the vaccine is accessible to all, including marginalized communities who may have limited access to healthcare.
Residents are reminded that the flu vaccine is safe and effective. Common side effects are mild and may include soreness at the injection site, mild fever, or muscle aches. These side effects are generally short-lived and far less severe than the flu itself.
Healthcare providers are also stressing the importance of continuing COVID-19 precautions. Wearing masks, practicing good hand hygiene, and maintaining social distancing are still crucial, especially in crowded places.
Protect yourself and your loved ones by getting vaccinated. Together, we can help keep Bangalore healthy and safe this flu season. For more information on vaccination centers and schedules, residents can visit the Karnataka Health Department’s official website or follow their social media pages.
Stay informed, stay safe, and get your flu shot today!
micro teaching on communication m.sc nursing.pdfAnurag Sharma
Microteaching is a unique model of practice teaching. It is a viable instrument for the. desired change in the teaching behavior or the behavior potential which, in specified types of real. classroom situations, tends to facilitate the achievement of specified types of objectives.
2. Logistic RegressionLogistic Regression
A way to look at effect ofA way to look at effect of
– ““Numeric” (interval or ratio) independentNumeric” (interval or ratio) independent
variablevariable
OnOn
– BinaryBinary (yes-no) dependent variable(yes-no) dependent variable
3. Dependent variable is continuousDependent variable is continuous intervalinterval oror
ratioratio (numeric)(numeric)
Independent variables are also interval orIndependent variables are also interval or
ratioratio
ExamplesExamples
– Effect of weight on blood pressureEffect of weight on blood pressure
– Effect of drug dose on reticulocyte countEffect of drug dose on reticulocyte count
Review Linear RegressionReview Linear Regression
6. Logistic RegressionLogistic Regression
Dependent variable is binary (yes/no) outcome.Dependent variable is binary (yes/no) outcome.
Independent variables are continuous intervalIndependent variables are continuous interval
Examples:Examples:
– Relation of weight and BP to 10 year risk of deathRelation of weight and BP to 10 year risk of death
– Relation of CD4 count to 1 year risk of AIDS diagnosisRelation of CD4 count to 1 year risk of AIDS diagnosis
7. Why do we need it?Why do we need it?
Could use categorical analysis such as frequency tableCould use categorical analysis such as frequency table
AIDSAIDS No AIDSNo AIDS
CD4 > 350CD4 > 350 8080 2020
150 < CD4 < 350150 < CD4 < 350 5050 5050
CD4 < 150CD4 < 150 2020 8080
• Problems
a) some information is lost when we collapse the
numeric data into categories. This leads to loss
of power.
b) no estimate of magnitude of relation
8. Odds RatioOdds Ratio
Probability:Probability:
p = probability of eventp = probability of event
1 - p = probabilty of1 - p = probabilty of notnot the event (also called q)the event (also called q)
p varies from 0 to 1p varies from 0 to 1
OddsOdds
– Ratio of probability of event to probability of notRatio of probability of event to probability of not
having the event: Odds = p/(1 - p)having the event: Odds = p/(1 - p)
– When p = 0.5, odds = 1 (or “1:1 odds”)When p = 0.5, odds = 1 (or “1:1 odds”)
– When p = 0.1, odds = 0.1/0.9 = 0.11When p = 0.1, odds = 0.1/0.9 = 0.11
9. Log Odds RatioLog Odds Ratio
The log odds ratio (also called “logit”) is simply the naturalThe log odds ratio (also called “logit”) is simply the natural
logarithm of the odds ratio:logarithm of the odds ratio:
¤ logitlogit = ln(odds ratio)= ln(odds ratio)
= ln(p/(1-p))= ln(p/(1-p))
= ln(p) – ln(1-p)= ln(p) – ln(1-p)
ln (1) = 0, so logit is 0 when odds are 1:1, orln (1) = 0, so logit is 0 when odds are 1:1, or
probability = 50%probability = 50%
The logit for event of probability p is the opposite of the logitThe logit for event of probability p is the opposite of the logit
for the probability of not having the event.for the probability of not having the event.
10. Relation between probability p and logit
0.000
0.250
0.500
0.750
1.000
-8 -6 -4 -2 0 2 4 6 8
logit = ln[p/(1-p)]
11. Logistic regression modelLogistic regression model
The linear regression model with one variableThe linear regression model with one variable
isis
y = a + bx + ey = a + bx + e
The logistic regression model with oneThe logistic regression model with one
variable isvariable is
logit = a + bx + elogit = a + bx + e
wherewhere
logit = ln(p/(1-p))logit = ln(p/(1-p))
12. The logistic regression model with oneThe logistic regression model with one
variable isvariable is
logit = a + bxlogit = a + bx where logit = ln(p/(1-p))where logit = ln(p/(1-p))
In other words, the model says the odds of the eventIn other words, the model says the odds of the event
happening arehappening are
– A constant factor (a)A constant factor (a)
– Some other constant (b)Some other constant (b)
– times a numeric risk factor (x) (for example, SBP)times a numeric risk factor (x) (for example, SBP)
Logistic regression modelLogistic regression model
13. Logistic regression modelLogistic regression model
Given value of the independent variables, theGiven value of the independent variables, the
regression equation predicts theregression equation predicts the
Log Odds RatioLog Odds Ratio
14. Logistic regression modelLogistic regression model
The statistics program calculates theThe statistics program calculates the
coefficient bcoefficient b
TheThe coefficient bcoefficient b shows how much the oddsshows how much the odds
ratio changes with a change in theratio changes with a change in the
independent variableindependent variable
Positive bPositive b higher risk with higher valueshigher risk with higher values
Negative bNegative b lower risk with higher valueslower risk with higher values
15. Logistic regression modelLogistic regression model
Hypothetical example given above examining relation of BP toHypothetical example given above examining relation of BP to
risk of stroke/death. The model predicts:risk of stroke/death. The model predicts:
ln(odds ratio) = constant + bln(odds ratio) = constant + b ∙ SBPSBP
ee(lnoddsratio)(lnoddsratio)
= e= e(c+b(c+b∙ SBP)SBP)
Odds RatioOdds Ratio == ee(c+b(c+b∙SBP)SBP)
== eecc
∙ ee(b(b∙SBP)SBP)
16. Logistic regression modelLogistic regression model
The coefficient b shows how much the odds ratioThe coefficient b shows how much the odds ratio
changes with a change in the independent variablechanges with a change in the independent variable
Odds RatioOdds Ratio == eecc
∙ ee(bx)(bx)
In other words,In other words,
Odds RatioOdds Ratio == somethingsomething ∙ (e(ebb
))(x)(x)
17. Logistic regression modelLogistic regression model
Odds RatioOdds Ratio = constant= constant ∙ ((eebb
))(x)(x)
SoSo eebb
is the factor indicating effect of x on theis the factor indicating effect of x on the
event.event.
Each one unit change in x will multiply the oddsEach one unit change in x will multiply the odds
ratio by a factor of eratio by a factor of ebb
..
18. Logistic regression modelLogistic regression model
Odds RatioOdds Ratio = constant= constant ∙ ((eebb
))(x)(x)
– Suppose b = 0.693 so eSuppose b = 0.693 so ebb
= 2= 2
– A one-unit change in x willA one-unit change in x will doubledouble the odds ratiothe odds ratio
– Suppose b = -0.693 so eSuppose b = -0.693 so ebb
= 0.5= 0.5
– A one-unit change in x willA one-unit change in x will halvehalve the odds ratio.the odds ratio.
– If b = 0, eIf b = 0, ebb
= 1, and x has no effect on OR= 1, and x has no effect on OR
19. Logistic regression modelLogistic regression model
For the hypothetical example above, the report isFor the hypothetical example above, the report is
given by Epi Info asgiven by Epi Info as
TermTerm OddsOdds
RatioRatio
95% CI95% CI CoeffCoeff S. E.S. E. ZZ PP
BPBP 1.05971.0597 1.0221.022 1.0981.098 0.05790.0579 0.01850.0185 3.1313.131 0.00170.0017
ConstConst ** ** ** -7.201-7.201 2.29942.2994 3.1313.131 0.00170.0017
20. Logistic regression modelLogistic regression model
TermTerm Odds RatioOdds Ratio 95% CI95% CI CoefficientCoefficient S. E.S. E. ZZ P-valueP-value
BPBP 1.05971.0597 1.0221.022 1.0981.098 0.05790.0579 0.0180.018 3.1313.131 0.00170.0017
ConstantConstant ** ** ** -7.2014-7.2014 2.2992.299 3.1313.131 0.00170.0017
Coefficient, or beta, or b, is the slope or magnitude
of the effect.
21. Logistic regression modelLogistic regression model
TermTerm OddsOdds
RatioRatio
95% CI95% CI CoefficientCoefficient S. E.S. E. ZZ P-valueP-value
BPBP 1.05971.0597 1.02201.0220 1.09871.0987 0.05790.0579 0.01850.0185 3.13193.1319 0.00170.0017
ConstantConstant ** ** ** -7.2014-7.2014 2.29942.2994 3.13193.1319 0.00170.0017
Odds ratio for one unit change in the
independent variable (e.g. BP). This is the
calculated eb
eb
A one unit change in BP multiplies the odds ratio by
1.0597.
22. Logistic regression modelLogistic regression model
TermTerm Odds RatioOdds Ratio 95% CI95% CI CoeffCoeff S. E.S. E. ZZ P-valueP-value
BPBP 1.05971.0597 1.0221.022 1.0981.098 0.05790.0579 0.01850.0185 3.13193.1319 0.00170.0017
ConstantConstant ** ** ** -7.2014-7.2014 2.29942.2994 3.13193.1319 0.00170.0017
95% confidence interval for that odds ratio.
The confidence interval does not include 1, so the
effect is statistically significant
23. Using more than one independentUsing more than one independent
variablevariable
Single variable:Single variable:
logit = c + bxlogit = c + bx
OR = c’ ∙ (eOR = c’ ∙ (ebb
))xx
Multiple variables:Multiple variables:
logit = c + blogit = c + b11xx11 + b+ b22xx22 + … + b+ … + bnnxxnn
OR = c’ ∙ (eOR = c’ ∙ (eb1b1
))x1x1
∙ (e∙ (eb2b2
))x2x2
∙ … ∙ (e∙ … ∙ (ebnbn
))xnxn
Note that the termsNote that the terms multiplymultiply their effect ontheir effect on
odds ratio.odds ratio.
24. Using more than one independentUsing more than one independent
variablevariable
Analysis reports a b coefficient for eachAnalysis reports a b coefficient for each
independent variable.independent variable.
That coefficient is the effect of the givenThat coefficient is the effect of the given
independent variable, separated from theindependent variable, separated from the
effects of all the other independent variables.effects of all the other independent variables.
25. Real Life ExampleReal Life Example
Prospective cohort study of causes ofProspective cohort study of causes of
cardiac disease: Evans County Study 1965cardiac disease: Evans County Study 1965
Independent variables = age, gender,Independent variables = age, gender,
race, social index, SBP, diabetes, smoking,race, social index, SBP, diabetes, smoking,
cholesterol, and an obesity indexcholesterol, and an obesity index
Dependent variable = risk of dying duringDependent variable = risk of dying during
10 year period10 year period
26. VariableVariable RangeRange b coeffb coeff SESE pp
ConstantConstant -6.376-6.376 1.6341.634 <0.001<0.001
AgeAge 40-69 y40-69 y 0.0860.086 0.1150.115 <0.001<0.001
GenderGender 0=m, 1=f0=m, 1=f 1.5001.500 0.9670.967 0.1210.121
Age x genderAge x gender -0.043-0.043 0.0170.017 0.0110.011
Social indexSocial index 20-8420-84 -0.056-0.056 0.0400.040 0.1600.160
(Soc ind)(Soc ind)22
400-7056400-7056 0.00060.0006 0.00030.0003 0.0820.082
SBPSBP 88-31088-310 0.0190.019 0.0020.002 <0.001<0.001
DiabetesDiabetes 0=n, 1=y0=n, 1=y 1.1231.123 0.2610.261 <0.001<0.001
SmokingSmoking 0=n, 1=y0=n, 1=y 0.3170.317 0.1570.157 0.0430.043
CholesterolCholesterol 94-54694-546 0.00310.0031 0.00150.0015 0.0410.041
QuartletQuartlet 2.11-8.762.11-8.76 -1.064-1.064 0.4320.432 0.0140.014
(Quartlet)(Quartlet)22
4.44-76.84.44-76.8 0.1120.112 0.0490.049 0.0220.022
Cited in Kelsey et al., Methods in Observational Epidemiology, 1986
28. Statistical SignificanceStatistical Significance
The p value indicates statistical significanceThe p value indicates statistical significance
Age is positively correlated with risk of deathAge is positively correlated with risk of death
Gender has positive b coefficient, but the p valueGender has positive b coefficient, but the p value
is 0.12, indicating that we cannot say that there isis 0.12, indicating that we cannot say that there is
a significant relationship.a significant relationship.
VariableVariable RangeRange b coeffb coeff SESE pp
AgeAge 40-69 y40-69 y 0.0860.086 0.1150.115 <0.001<0.001
GenderGender 0=m, 1=f0=m, 1=f 1.5001.500 0.9670.967 0.1210.121
29. Dichotomous (yes-no) variablesDichotomous (yes-no) variables
Gender is coded as 0 for male, 1 for femaleGender is coded as 0 for male, 1 for female
eebb
[e[e1.51.5
= 4.48] is change in OR for 1 unit change in gender,= 4.48] is change in OR for 1 unit change in gender,
i.e. OR for females relative to malesi.e. OR for females relative to males
eebb
for any dummy variable (coded 0-1) is the adjustedfor any dummy variable (coded 0-1) is the adjusted
OR for that risk factor, since “1 unit of change” =OR for that risk factor, since “1 unit of change” =
presence vs. absence of risk factorpresence vs. absence of risk factor
VariableVariable RangeRange b coeffb coeff SESE pp
ConstantConstant -6.376-6.376 1.6341.634 <0.001<0.001
AgeAge 40-69 y40-69 y 0.0860.086 0.1150.115 <0.001<0.001
GenderGender 0=m, 1=f0=m, 1=f 1.5001.500 0.9670.967 0.1210.121
30. Squared termsSquared terms
Social index squared is included as well asSocial index squared is included as well as
social index itself.social index itself.
Squared terms allow for curvilinearSquared terms allow for curvilinear
relationships, just as in ordinaryrelationships, just as in ordinary
regressionregression
VariableVariable RangeRange b coeffb coeff SESE pp
Age x genderAge x gender -0.043-0.043 0.0170.017 0.0110.011
Social indexSocial index 20-8420-84 -0.056-0.056 0.0400.040 0.1600.160
(Soc ind)(Soc ind)22
400-7056400-7056 0.00060.0006 0.00030.0003 0.0820.082
31. Interaction termsInteraction terms
Age and gender are entered into model asAge and gender are entered into model as
separate termsseparate terms
Age x gender included to see whether ageAge x gender included to see whether age
has different effect in males than inhas different effect in males than in
females.females.
VariableVariable RangeRange b coeffb coeff SESE pp
AgeAge 40-69 y40-69 y 0.0860.086 0.1150.115 <0.001<0.001
GenderGender 0=m, 1=f0=m, 1=f 1.5001.500 0.9670.967 0.1210.121
Age x genderAge x gender M: 0-0M: 0-0
F: 40-69F: 40-69
-0.043-0.043 0.0170.017 0.0110.011
32. InterpretationInterpretation
With binary, dummy variables, eWith binary, dummy variables, ebb
is the odds ratio.is the odds ratio.
You can compare the strength (slope) of the effectYou can compare the strength (slope) of the effect
by comparing b.by comparing b.
With numeric variables, b is not a direct measure ofWith numeric variables, b is not a direct measure of
strength of effect.strength of effect.
– Example: b is quite small in effect of BP on mortality,Example: b is quite small in effect of BP on mortality,
because it is the effect of onlybecause it is the effect of only one mmHgone mmHg change in BP. BPchange in BP. BP
is still an important factor in mortality because there is ais still an important factor in mortality because there is a
widewide rangerange in the BP.in the BP.
33. InterpretationInterpretation
In a prospective cohort study we can useIn a prospective cohort study we can use
logistic regression model to predictlogistic regression model to predict probabilityprobability
of the event given the independent variables.of the event given the independent variables.
Also can derive relative risk.Also can derive relative risk.
In a cross sectional study we only have theIn a cross sectional study we only have the
odds ratio.odds ratio.
34. Selection of variablesSelection of variables
Same principle as with ordinary regressionSame principle as with ordinary regression
Forward selection: add one variable at a timeForward selection: add one variable at a time
until there are no more that make a significantuntil there are no more that make a significant
differencedifference
Backward selection: start with all, remove oneBackward selection: start with all, remove one
at a time to see if they made a significantat a time to see if they made a significant
contributioncontribution
EPI Info has suggestions on how to do thisEPI Info has suggestions on how to do this