This document describes techniques for selecting explanatory variables in regression modeling to avoid overfitting or underfitting. It discusses stepwise regression, which starts with no variables or all variables and iteratively adds or removes variables. Too few variables leads to underfitting while too many leads to overfitting by including noise. The document demonstrates this using simulated quadratic data, showing a linear fit underfits while a high-degree polynomial overfits. It outlines the stepwise algorithm and provides an example application.
Here different concepts you come across in the research methodology are discussed. It is applicable to social sciences to a large extent. The definitions are explained in a way that will be understood by social scientists.
Types of "T-Test" - Research Methodology, Hypothesis Testing
Hypothesis (अनुमानम्) is a predictive statement, capable of being tested by scientific methods, that relates an independent variable to some dependent variable.
The t-test compares the actual difference between two means in relation to the variation in the data (expressed as the standard deviation of the difference between the means).
Here different concepts you come across in the research methodology are discussed. It is applicable to social sciences to a large extent. The definitions are explained in a way that will be understood by social scientists.
Types of "T-Test" - Research Methodology, Hypothesis Testing
Hypothesis (अनुमानम्) is a predictive statement, capable of being tested by scientific methods, that relates an independent variable to some dependent variable.
The t-test compares the actual difference between two means in relation to the variation in the data (expressed as the standard deviation of the difference between the means).
SPSS does not have Z test for proportions, So, we use Chi-Square test for proportion tests. Test for single proportion and Test for proportions of two samples
Basics of Hypothesis testing for PharmacyParag Shah
This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
Non-parametric Statistical tests for Hypotheses testingSundar B N
A complete guidelines for Non-parametric Statistical tests for Hypotheses testing with relevant examples which covers Meaning of non-parametric test, Types of non-parametric test, Sign test, Rank sum test, Chi-square test, Wilcoxon signed-ranks test, Mc Nemer test, Spearman’s rank correlation, statistics,
Subscribe to Vision Academy for Video assistance
https://www.youtube.com/channel/UCjzpit_cXjdnzER_165mIiw
The DNP must have a basic understanding of statistical measureme.docxtodd701
The DNP must have a basic understanding of statistical measurements and how they apply within the parameters of data management and analytics. In this assignment, you will demonstrate understanding of basic statistical tests and how to perform the appropriate test for the project using SPSS or other statistical programs.
General Requirements:
Use the following information to ensure successful completion of the assignment:
Refer to "Setting Up My SPSS," "SPSS Database," and "Comparison Table of the Variable's Level of Measurement," located in the DNP 830 folder of the DC Network Practice Immersion workspace.
Doctoral learners are required to use APA style for their writing assignments. The APA Style Guide is located in the Student Success Center.
This assignment uses a rubric. Review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.
You are required to submit this assignment to LopesWrite. Refer to the
LopesWrite Technical Support articles
for assistance.
Directions:
Set up your IBM SPSS account and run several statistical outputs based on the "SPSS Database" Use "Setting Up My SPSS" to set up your SPSS program on your computer or device. You may also use programs such as Laerd Statistics or Intellectus, if you subscribe to them.
The patient outcome or dependent variables and the level of measurement must be displayed in a comparison table which you will provide as an Appendix to the paper. Refer to the "Comparison Table of the Variable's Level of Measurement."
Submit a 1,000-1,250 word data analysis paper outlining the procedures used to analyze the parametric and non-parametric variables in the mock data, the statistics reported, and a conclusion of the results.
Provide a conclusive result of the data analyses based on the guidelines below for statistical significance.
PAIRED SAMPLE T-TEST:
Identify the variables
BaselineWeight
and
InterventionWeight
. Using the Analysis menu in SPSS, go to Compare Means, Go to the Paired Sample
t
-test. Add the
BaselineWeight
and
InterventionWeight
in the Pair 1 fields. Click OK. Report the mean weights, standard deviations,
t-statistic,
degrees of freedom, and p level. Report as
t(df)=value, p = value.
Report the
p
level out three digits.
INDEPENDENT SAMPLE T-TEST:
Identify the variables
InterventionGroups
and
PatientWeight
. Go to the Analysis Menu, go to Compare Means, Go to Independent Samples
t
T-test. Add
InterventionGroups
to the Grouping Factor. Define the groups according to codings in the variable view (1=Intervention, 2 =Baseline). Add
PatientWeight
to the test variable field. Click OK. Report the mean weights, standard deviations,
t-statistic,
degrees of freedom, and p level. Report
t(df)=value, p = value.
Report the
p
level out three digits
CHI-SQUARE (Independent):
Identify the variables
BaselineReadmission
and
InterventionReadmission
. Go to the Analysis Menu, go to Descripti.
SPSS does not have Z test for proportions, So, we use Chi-Square test for proportion tests. Test for single proportion and Test for proportions of two samples
Basics of Hypothesis testing for PharmacyParag Shah
This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
Non-parametric Statistical tests for Hypotheses testingSundar B N
A complete guidelines for Non-parametric Statistical tests for Hypotheses testing with relevant examples which covers Meaning of non-parametric test, Types of non-parametric test, Sign test, Rank sum test, Chi-square test, Wilcoxon signed-ranks test, Mc Nemer test, Spearman’s rank correlation, statistics,
Subscribe to Vision Academy for Video assistance
https://www.youtube.com/channel/UCjzpit_cXjdnzER_165mIiw
The DNP must have a basic understanding of statistical measureme.docxtodd701
The DNP must have a basic understanding of statistical measurements and how they apply within the parameters of data management and analytics. In this assignment, you will demonstrate understanding of basic statistical tests and how to perform the appropriate test for the project using SPSS or other statistical programs.
General Requirements:
Use the following information to ensure successful completion of the assignment:
Refer to "Setting Up My SPSS," "SPSS Database," and "Comparison Table of the Variable's Level of Measurement," located in the DNP 830 folder of the DC Network Practice Immersion workspace.
Doctoral learners are required to use APA style for their writing assignments. The APA Style Guide is located in the Student Success Center.
This assignment uses a rubric. Review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.
You are required to submit this assignment to LopesWrite. Refer to the
LopesWrite Technical Support articles
for assistance.
Directions:
Set up your IBM SPSS account and run several statistical outputs based on the "SPSS Database" Use "Setting Up My SPSS" to set up your SPSS program on your computer or device. You may also use programs such as Laerd Statistics or Intellectus, if you subscribe to them.
The patient outcome or dependent variables and the level of measurement must be displayed in a comparison table which you will provide as an Appendix to the paper. Refer to the "Comparison Table of the Variable's Level of Measurement."
Submit a 1,000-1,250 word data analysis paper outlining the procedures used to analyze the parametric and non-parametric variables in the mock data, the statistics reported, and a conclusion of the results.
Provide a conclusive result of the data analyses based on the guidelines below for statistical significance.
PAIRED SAMPLE T-TEST:
Identify the variables
BaselineWeight
and
InterventionWeight
. Using the Analysis menu in SPSS, go to Compare Means, Go to the Paired Sample
t
-test. Add the
BaselineWeight
and
InterventionWeight
in the Pair 1 fields. Click OK. Report the mean weights, standard deviations,
t-statistic,
degrees of freedom, and p level. Report as
t(df)=value, p = value.
Report the
p
level out three digits.
INDEPENDENT SAMPLE T-TEST:
Identify the variables
InterventionGroups
and
PatientWeight
. Go to the Analysis Menu, go to Compare Means, Go to Independent Samples
t
T-test. Add
InterventionGroups
to the Grouping Factor. Define the groups according to codings in the variable view (1=Intervention, 2 =Baseline). Add
PatientWeight
to the test variable field. Click OK. Report the mean weights, standard deviations,
t-statistic,
degrees of freedom, and p level. Report
t(df)=value, p = value.
Report the
p
level out three digits
CHI-SQUARE (Independent):
Identify the variables
BaselineReadmission
and
InterventionReadmission
. Go to the Analysis Menu, go to Descripti.
univariate and bivariate analysis in spss Subodh Khanal
this slide will help to perform various tests in spss targeting univariate and bivariate analysis along with the way of entering and analyzing multiple responses.
DirectionsSet up your IBM SPSS account and run several statisti.docxjakeomoore75037
Directions:
Set up your IBM SPSS account and run several statistical outputs based on the "SPSS Database" Use "Setting Up My SPSS" to set up your SPSS program on your computer or device. You may also use programs such as Laerd Statistics or Intellectus, if you subscribe to them.
The patient outcome or dependent variables and the level of measurement must be displayed in a comparison table which you will provide as an Appendix to the paper. Refer to the "Comparison Table of the Variable's Level of Measurement."
Submit a 1,000-1,250 word data analysis paper outlining the procedures used to analyze the parametric and non-parametric variables in the mock data, the statistics reported, and a conclusion of the results.
Provide a conclusive result of the data analyses based on the guidelines below for statistical significance.
PAIRED SAMPLE T-TEST: Identify the variables BaselineWeight and InterventionWeight. Using the Analysis menu in SPSS, go to Compare Means, Go to the Paired Sample t-test. Add the BaselineWeight and InterventionWeight in the Pair 1 fields. Click OK. Report the mean weights, standard deviations, t-statistic, degrees of freedom, and p level. Report as t(df)=value, p = value. Report the p level out three digits.
INDEPENDENT SAMPLE T-TEST: Identify the variables InterventionGroups and PatientWeight. Go to the Analysis Menu, go to Compare Means, Go to Independent Samples tT-test. Add InterventionGroups to the Grouping Factor. Define the groups according to codings in the variable view (1=Intervention, 2 =Baseline). Add PatientWeight to the test variable field. Click OK. Report the mean weights, standard deviations, t-statistic, degrees of freedom, and p level. Report t(df)=value, p = value. Report the p level out three digits
CHI-SQUARE (Independent): Identify the variables BaselineReadmission and InterventionReadmission. Go to the Analysis Menu, go to Descriptive Statistics, go to Crosstabs. Add BaselineReadmission to the row and InterventionReadmission to the column. Click the Statistics button and choose Chi-Square. Select eta to report the Effect Size. Click suppress tables. Click OK. Report the frequencies of the total events, the chi-square statistic, degrees of freedom, and p level. Report ꭓ2 (df) =value, p =value. Report the p level out three digits.
MCNEMAR (Paired): Identify the variables BaselineCompliance and InterventionCompliance. Go to the Analysis Menu, go to Descriptive Statistics, go to Crosstabs. Add BaselineCompliance to the row and InterventionCompliance to the column. Click the Statistics button and choose Chi-Square and McNemars. Select eta to report the Effect Size. Click suppress tables. Click OK. Report the frequencies of the events, the Chi-square, and the McNemar’s p level. Report (p =value). Report the p level out three digits.
MANN WHITNEY U: Identify the variables InterventionGroups and PatientSatisfaction. Using the Analysis Menu, go to Non-parametric Statistics, go to LegacyDialogs, go to 2 I.
Psyc 355 Effective Communication - tutorialrank.comBartholomew88
For more course tutorials visit
www.tutorialrank.com
Exam 1 Psych 355
3. A p level of 0.05 corresponds to a confidence level of __________%
4. In a within-groups design where one group is measured twice over time, the appropriate hypothesis test is an:
7. Why do we divide by N-1 rather than by N when estimating a population standard deviation from the
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Ve...kevinkariuki227
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Verified Chapters 1 - 19, Complete Newest Version.pdf
TEST BANK for Operations Management, 14th Edition by William J. Stevenson, Verified Chapters 1 - 19, Complete Newest Version.pdf
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
Lung Cancer: Artificial Intelligence, Synergetics, Complex System Analysis, S...Oleg Kshivets
RESULTS: Overall life span (LS) was 2252.1±1742.5 days and cumulative 5-year survival (5YS) reached 73.2%, 10 years – 64.8%, 20 years – 42.5%. 513 LCP lived more than 5 years (LS=3124.6±1525.6 days), 148 LCP – more than 10 years (LS=5054.4±1504.1 days).199 LCP died because of LC (LS=562.7±374.5 days). 5YS of LCP after bi/lobectomies was significantly superior in comparison with LCP after pneumonectomies (78.1% vs.63.7%, P=0.00001 by log-rank test). AT significantly improved 5YS (66.3% vs. 34.8%) (P=0.00000 by log-rank test) only for LCP with N1-2. Cox modeling displayed that 5YS of LCP significantly depended on: phase transition (PT) early-invasive LC in terms of synergetics, PT N0—N12, cell ratio factors (ratio between cancer cells- CC and blood cells subpopulations), G1-3, histology, glucose, AT, blood cell circuit, prothrombin index, heparin tolerance, recalcification time (P=0.000-0.038). Neural networks, genetic algorithm selection and bootstrap simulation revealed relationships between 5YS and PT early-invasive LC (rank=1), PT N0—N12 (rank=2), thrombocytes/CC (3), erythrocytes/CC (4), eosinophils/CC (5), healthy cells/CC (6), lymphocytes/CC (7), segmented neutrophils/CC (8), stick neutrophils/CC (9), monocytes/CC (10); leucocytes/CC (11). Correct prediction of 5YS was 100% by neural networks computing (area under ROC curve=1.0; error=0.0).
CONCLUSIONS: 5YS of LCP after radical procedures significantly depended on: 1) PT early-invasive cancer; 2) PT N0--N12; 3) cell ratio factors; 4) blood cell circuit; 5) biochemical factors; 6) hemostasis system; 7) AT; 8) LC characteristics; 9) LC cell dynamics; 10) surgery type: lobectomy/pneumonectomy; 11) anthropometric data. Optimal diagnosis and treatment strategies for LC are: 1) screening and early detection of LC; 2) availability of experienced thoracic surgeons because of complexity of radical procedures; 3) aggressive en block surgery and adequate lymph node dissection for completeness; 4) precise prediction; 5) adjuvant chemoimmunoradiotherapy for LCP with unfavorable prognosis.
New Directions in Targeted Therapeutic Approaches for Older Adults With Mantl...i3 Health
i3 Health is pleased to make the speaker slides from this activity available for use as a non-accredited self-study or teaching resource.
This slide deck presented by Dr. Kami Maddocks, Professor-Clinical in the Division of Hematology and
Associate Division Director for Ambulatory Operations
The Ohio State University Comprehensive Cancer Center, will provide insight into new directions in targeted therapeutic approaches for older adults with mantle cell lymphoma.
STATEMENT OF NEED
Mantle cell lymphoma (MCL) is a rare, aggressive B-cell non-Hodgkin lymphoma (NHL) accounting for 5% to 7% of all lymphomas. Its prognosis ranges from indolent disease that does not require treatment for years to very aggressive disease, which is associated with poor survival (Silkenstedt et al, 2021). Typically, MCL is diagnosed at advanced stage and in older patients who cannot tolerate intensive therapy (NCCN, 2022). Although recent advances have slightly increased remission rates, recurrence and relapse remain very common, leading to a median overall survival between 3 and 6 years (LLS, 2021). Though there are several effective options, progress is still needed towards establishing an accepted frontline approach for MCL (Castellino et al, 2022). Treatment selection and management of MCL are complicated by the heterogeneity of prognosis, advanced age and comorbidities of patients, and lack of an established standard approach for treatment, making it vital that clinicians be familiar with the latest research and advances in this area. In this activity chaired by Michael Wang, MD, Professor in the Department of Lymphoma & Myeloma at MD Anderson Cancer Center, expert faculty will discuss prognostic factors informing treatment, the promising results of recent trials in new therapeutic approaches, and the implications of treatment resistance in therapeutic selection for MCL.
Target Audience
Hematology/oncology fellows, attending faculty, and other health care professionals involved in the treatment of patients with mantle cell lymphoma (MCL).
Learning Objectives
1.) Identify clinical and biological prognostic factors that can guide treatment decision making for older adults with MCL
2.) Evaluate emerging data on targeted therapeutic approaches for treatment-naive and relapsed/refractory MCL and their applicability to older adults
3.) Assess mechanisms of resistance to targeted therapies for MCL and their implications for treatment selection
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
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.
These simplified slides by Dr. Sidra Arshad present an overview of the non-respiratory functions of the respiratory tract.
Learning objectives:
1. Enlist the non-respiratory functions of the respiratory tract
2. Briefly explain how these functions are carried out
3. Discuss the significance of dead space
4. Differentiate between minute ventilation and alveolar ventilation
5. Describe the cough and sneeze reflexes
Study Resources:
1. Chapter 39, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 34, Ganong’s Review of Medical Physiology, 26th edition
3. Chapter 17, Human Physiology by Lauralee Sherwood, 9th edition
4. Non-respiratory functions of the lungs https://academic.oup.com/bjaed/article/13/3/98/278874
Recomendações da OMS sobre cuidados maternos e neonatais para uma experiência pós-natal positiva.
Em consonância com os ODS – Objetivos do Desenvolvimento Sustentável e a Estratégia Global para a Saúde das Mulheres, Crianças e Adolescentes, e aplicando uma abordagem baseada nos direitos humanos, os esforços de cuidados pós-natais devem expandir-se para além da cobertura e da simples sobrevivência, de modo a incluir cuidados de qualidade.
Estas diretrizes visam melhorar a qualidade dos cuidados pós-natais essenciais e de rotina prestados às mulheres e aos recém-nascidos, com o objetivo final de melhorar a saúde e o bem-estar materno e neonatal.
Uma “experiência pós-natal positiva” é um resultado importante para todas as mulheres que dão à luz e para os seus recém-nascidos, estabelecendo as bases para a melhoria da saúde e do bem-estar a curto e longo prazo. Uma experiência pós-natal positiva é definida como aquela em que as mulheres, pessoas que gestam, os recém-nascidos, os casais, os pais, os cuidadores e as famílias recebem informação consistente, garantia e apoio de profissionais de saúde motivados; e onde um sistema de saúde flexível e com recursos reconheça as necessidades das mulheres e dos bebês e respeite o seu contexto cultural.
Estas diretrizes consolidadas apresentam algumas recomendações novas e já bem fundamentadas sobre cuidados pós-natais de rotina para mulheres e neonatos que recebem cuidados no pós-parto em unidades de saúde ou na comunidade, independentemente dos recursos disponíveis.
É fornecido um conjunto abrangente de recomendações para cuidados durante o período puerperal, com ênfase nos cuidados essenciais que todas as mulheres e recém-nascidos devem receber, e com a devida atenção à qualidade dos cuidados; isto é, a entrega e a experiência do cuidado recebido. Estas diretrizes atualizam e ampliam as recomendações da OMS de 2014 sobre cuidados pós-natais da mãe e do recém-nascido e complementam as atuais diretrizes da OMS sobre a gestão de complicações pós-natais.
O estabelecimento da amamentação e o manejo das principais intercorrências é contemplada.
Recomendamos muito.
Vamos discutir essas recomendações no nosso curso de pós-graduação em Aleitamento no Instituto Ciclos.
Esta publicação só está disponível em inglês até o momento.
Prof. Marcus Renato de Carvalho
www.agostodourado.com
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Report Back from SGO 2024: What’s the Latest in Cervical Cancer?bkling
Are you curious about what’s new in cervical cancer research or unsure what the findings mean? Join Dr. Emily Ko, a gynecologic oncologist at Penn Medicine, to learn about the latest updates from the Society of Gynecologic Oncology (SGO) 2024 Annual Meeting on Women’s Cancer. Dr. Ko will discuss what the research presented at the conference means for you and answer your questions about the new developments.
1. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Model selection
Tuan V. Nguyen
Professor and NHMRC Senior Research Fellow
Garvan Institute of Medical Research
University of New South Wales
Sydney, Australia
2. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Contents
• To describe some techniques for selecting the
explanatory variables for a regression
• To describe the consequences of making an
incorrect choice
• To apply these techniques to an example
3. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Variable Selection
• Often there are several (perhaps a large number) of
potential explanatory variables available to build a
regression model. Which ones should we use?
• We could, of course, use them all. However, this turns
out to be not such a good idea.
4. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Overfitting
• If we put too many variables in the model, including
some unrelated to the response, we are overfitting.
Consequences are:
– Fitted model is not good for prediction of new data –
prediction error is inflated
– Model is too elaborate, models “noise” that will not be the
same for new data
5. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Underfitting
• If we put too few variables in the model, leaving out
variables that could help explain the response, we
are underfitting. Consequences:
– Fitted model is not good for prediction of new data –
prediction is biased
– Regression coefficients are biased
– Estimate of error variance is too large
6. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Example
• Suppose we have some data which follow a
quadratic model
Y = 1 + 0.5 x + 4 x2 + N(0,1)
where the x’s are uniform on [0,1]
The next slide shows the data, with the true regression
shown as a dotted line.
7. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
7
0.0 0.2 0.4 0.6 0.8 1.0
0
2
4
6
Plot of y vs x, showing true quadratic relationship
x
y
8. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Under-fitting and over-fitting
• Suppose we fit a straight line. This is underfitting,
since we are not fitting the squared term. The fitted
line (in green) is shown on the next slide.
• Alternatively, we could fit a 6-degree polynomial.
This is overfitting, since there are unnecessary
terms in x3, x4, x5 and x6. The fitted polynomial is
shown in blue on the next slide. Fit using
lm(y ~ poly(x,6))
9. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
0.0 0.2 0.4 0.6 0.8 1.0
0
2
4
6
Plot of y vs x, showing true quadratic relationship
x
y
True curve
Degree 1 poly
Degree 6 poly
True curve
Degree 1 poly
Degree 6 poly
Modelling noise!
10. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Points to note
• Straight line is biased: can’t capture the curvature in
the true regression
• 6-degree line: too variable, attracted to the errors
which would be different for a new set of data
• Moral: For good models we need to choose variables
wisely to avoid overfitting and underfitting.
This is called variable selection
11. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Methods for variable selection
• If we have k variables, and assuming a constant term
in each model, there are 2k-1 possible subsets of
variables (not counting the null model with no
variables)
• How do we select a subset for our model?
• Two main approaches: stepwise methods and all
possible regressions (APR)
12. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise Regression Procedure
13. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise regression algorithm
Start
Compute F stat and P-value
for each independent
variable NOT in the model
Any P-value >
alpha (0.15) to
remove?
Compute F stat and P-value
for each independent
variable in the model
Any P-value <
alpha (0.15) to
remove?
STOP
Indep variable with smallest
P-value is entered into the
model
Indep variable
with largest P-
value is removed
from the model
No
Yes
No
Yes
14. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Forward selection algorithm
Start with NO indep variable
in the model
Any P-value <
alpha (0.15) to
remove?
Indep variable with smallest
P-value is entered into the
model
Compute F stat and P-value
for each independent
variable NOT in the model
Yes
No
15. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Backward elemination algorithm
Start with ALL indep
variables in the model
Any P-value <
alpha (0.15) to
remove?
Indep variable with smallest
P-value is entered into the
model
Compute F stat and P-value
for each independent
variable NOT in the model
Yes
No
16. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection procedure
• Specify an Alpha-to-Enter significance level. Many software
packages set this significance level by default to αE = 0.15.
• Specify an Alpha-to-Remove significance level. Again, many software
packages set this significance level by default to αR = 0.15.
• Step #1. Once we've specified the starting significance levels,
then we
– Fit each of the one-predictor models — that is, regress y on x1,
regress y on x2, ..., and regress y on xp-1.
– Of those predictors whose t-test P-value is less than αE = 0.15,
the first predictor put in the stepwise model is the predictor
that has the smallest t-test P-value.
– If no predictor has a t-test P-value less than αE = 0.15, stop.
17. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection procedure
• Step #2. Then:
– Suppose x1 had the smallest t-test P-value below αE = 0.15 and therefore
was deemed the "best" one predictor arising from the the first step.
– Now, fit each of the two-predictor models that include x1 as a predictor —
that is, regress y on x1and x2, regress y on x1 and x3, ..., and regress y on x1
and xp-1.
– Of those predictors whose t-test P-value is less than αE = 0.15, the second
predictor put in the stepwise model is the predictor that has the smallest t-
test P-value.
– If no predictor has a t-test P-value less than αE = 0.15, stop. The model with
the one predictor obtained from the first step is your final model.
– But, suppose instead that x2 was deemed the "best" second predictor and it
is therefore entered into the stepwise model.
– Now, since x1 was the first predictor in the model, step back and see if
entering x2 into the stepwise model somehow affected the significance of
the x1 predictor. That is, check the t-test P-value for testing β1 = 0. If the t-
test P-value for β1 = 0 has become not significant — that is, the P-value is
greater than αR = 0.15 — remove x1 from the stepwise model.
18. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection procedure
• Step #3. Then:
– Suppose both x1 and x2 made it into the two-predictor stepwise model.
– Now, fit each of the three-predictor models that include x1 and x2 as
predictors — that is, regress y on x1, x2, and x3, regress y on x1, x2, and x4, ...,
and regress y on x1, x2, and xp-1.
– Of those predictors whose t-test P-value is less than αE = 0.15, the third
predictor put in the stepwise model is the predictor that has the smallest t-
test P-value.
– If no predictor has a t-test P-value less than αE = 0.15, stop. The model
containing the two predictors obtained from the second step is your final
model.
– But, suppose instead that x3 was deemed the "best" third predictor and it is
therefore entered into the stepwise model.
– Now, since x1 and x2 were the first predictors in the model, step back and see
if entering x3 into the stepwise model somehow affected the significance of
the x1 and x2 predictors. That is, check the t-test P-values for testing β1 = 0
and β2 = 0. If the t-test P-value for either β1 = 0 or β2 = 0 has become not
significant — that is, the P-value is greater than αR = 0.15 — remove the
predictor from the stepwise model.
19. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection procedure
• Stopping the procedure. Continue the steps as
described above until adding an additional predictor
does not yield a t-test P-value below αE = 0.15.
20. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection: example
• To starting our stepwise regression procedure, let's set our Alpha-to-
Enter significance level at αE = 0.15, and let's set our Alpha-to-
Remove significance level at αR = 0.15. Now, regressing y on x1,
regressing y on x2, regressing y on x3, and regressing y on x4, we
obtain:
21. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection: example
• Now, following step #2, we fit each of the two-predictor models that
include x4 as a predictor — that is, we regress y on x4 and x1, regress
y on x4 and x2, and regress y on x4 and x3, obtaining:
22. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection: example
• Now, following step #3, we fit each of the three-predictor models that
include x1 and x4 as predictors — that is, we regress y on x4, x1, and
x2; and we regress y on x4, x1, and x3, obtaining
23. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection: example
• Now, since x1 and x4 were the first predictors in the model, we must
step back and see if entering x2 into the stepwise model affected the
significance of the x1 and x4 predictors. Indeed, it did — the t-test P-
value for testing β4 = 0 is 0.205, greater than αR = 0.15. Therefore,
we remove the predictor x4 from the stepwise model, leaving us with
the predictors x1 and x2 in our stepwise model:
Now, we proceed fitting each of the three-predictor models that include x1 and
x2 as predictors — that is, we regress y on x1, x2, and x3; and we regress y on
x1, x2, and x4, obtaining:
24. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection: example
• Neither of the remaining predictors — x3 and x4 — are eligible for
entry into our stepwise model, because each t-test P-value — 0.209
and 0.205, respectively — is greater than αE = 0.15. That is, we
stop our stepwise regression procedure. Our final regression
model, based on the stepwise procedure contains only the
predictors x1 and x2:
25. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Stepwise selection: example
• Summary of steps:
26. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Be careful!
• The final model is not guaranteed to be optimal in any specified sense.
• The procedure yields a single final model, although there are often
several equally good models.
• Stepwise regression does not take into account a researcher's
knowledge about the predictors. It may be necessary to force the
procedure to include important predictors.
• One should not over-interpret the order in which predictors are
entered into the model.
• One should not jump to the conclusion that all the important predictor
variables for predicting y have been identified, or that all the
unimportant predictor variables have been eliminated. It is, of course,
possible that we may have committed a Type I or Type II error.
• Many t-tests for testing βk = 0 are conducted in a stepwise regression
procedure. The probability is therefore high that we included some
unimportant predictors or excluded some important predictors.
27. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
All Possible Regressions
28. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
All Possible Regressions
• For each subset, define a criterion of “model
goodness” which tries to balance over-fitting (model
too complex) with under-fitting (model doesn’t fit very
well).
• Calculate the criterion for each of the 2k-1 models
• Pick the best one according to the criterion.
• One difficulty: there are several possible criteria, and
they don’t always agree.
29. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Possible criteria: R2
• Since R2 increases as we add more variables,
picking the model with the biggest R2 will always
select the model with all the variables. This will
often result in overfitting.
• However, R2 is OK for choosing between models
with the same number of variables.
• We need to modify R2 to penalize overly
complicated models. One way is to use the
adjusted R2 (p = number of coefficients in model)
)
1
(
)
(
)
1
(
1 2
2
p
p
R
p
n
n
R −
−
−
−
=
30. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Interpretation
• Suppose we have 2 models: model A with p-1 variables
and model B with an additional q variables (we say A is
a submodel of B)
• Then the adjusted R2 is defined so that
where F is the F statistic for testing that model A is
adequate.
1
if
only
and
if
2
2
>
< + F
R
R q
p
p
31. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Residual mean square (RMS)
• Recall the estimate of the error variance s2: estimated
by s2=RSS/(n-p), sometimes called the residual mean
square (RMS)
• Choose model with the minimum RMS
• We can show that this is equivalent to choosing the
model with the biggest adjusted R2
32. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
AIC and BIC
• These are criteria that balance goodness of fit (as measured by
RSS) against model complexity (as measured by the number of
regression coefficients)
• AIC (Akaike Information Criterion) is, up to a constant depending
on n , AIC = n log(RSSp) + 2p
• Alternative version is AIC = RSS/RMSFull + 2p, equivalent to Cp
• BIC (Bayesian Information Criterion) is
n log(RSSp) + p log n
• Small values = good model
• AIC tends to favour more complex models than BIC
33. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Criteria based on prediction error
• Our final set of criteria use an estimate of prediction
error to evaluate models
• They measure how well a model predicts new data
34. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Mallow’s Cp: estimating prediction error
Suppose we have a model with p regression
coefficients. “Mallows Cp” provides an estimate of
how well the model predicts new data, and is
given by
n
p
RMS
RSS
Cp
FULL
p
−
+
= 2
The subscript FULL refers to the “full model” with k
variables. Small values of Cp with Cp about p are good.
Warning: Ck+1=k+1 always, so don’t take this as
evidence that the full model is good unless all the other
Cp’s are bigger.
35. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Mallow’s Cp : Interpretation
If the p-coefficient model contains all the important
explanatory variables, then RSSp is about the same
as (n-p)s2. Moreover, EMSFULL will also be about the
same as s2. Thus
p
n
p
p
n
n
p
RMS
RSS
Cp
FULL
p
=
−
+
−
≈
−
+
=
2
)
(
2
2
2
σ
σ
36. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Cp plot
• For each model, we plot Cp against p, with the line
Cp= p added.
• Points close to this line having small values of Cp
correspond to good models.
37. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Estimating prediction error: Cross-validation
• Cp is not a very good estimate of prediction error
• If we have plenty of data, we split the data into 2 parts
– The “training set”, used to fit the model and
construct the predictor
– The “test set”, used to estimate the prediction error
• Test set error (=prediction error) estimated by
• Choose model with smallest prediction error
2
1
)
ˆ
( i
test set
i
y
y
n −
∑
− Predicted value
using training set
predictor with new
data
38. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Estimating prediction error: Cross-validation (2)
• If we don’t have plenty of data, we randomly split
the data into 10 parts. One part acts as a test set,
the rest as the training set. We compute the
prediction error from the test set as before.
• Repeat another 9 times, using a different 10th as the
test set each time. Average the estimates to get a
good estimate of prediction error
• Repeat for different “random splits”
• This is “10-fold cross-validation”. Can do 5-fold, or
n-fold, but 10-fold seems to be best.
39. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Example: the fatty acid data
> fatty.lm <- lm(ffa ~ age + skinfold + weight, data = fatty.df)
> library(leaps)
> all.poss.regs(fatty.lm, Cp.plot=T)
rssp sigma2 adjRsq Cp AIC BIC CV age weight skinfold
1 0.910 0.051 0.380 2.406 22.406 24.397 0.114 0 1 0
2 0.794 0.047 0.427 2.062 22.062 25.049 0.107 1 1 0
3 0.791 0.049 0.394 4.000 24.000 27.983 0.117 1 1 1
The R function all.poss.regs does the business: eg
for the fatty acid data NB This function requires the
package “leaps”
40. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
1.0 1.5 2.0 2.5 3.0
2.0
2.5
3.0
3.5
4.0
Cp Plot
Number of variables
Cp
3
1,3
1,2,3
Good model Good model
41. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Example: the evaporation data
• This was discussed in Tutorial 2: the variables are
– evap: the amount of moisture evaporating from the soil in the 24
hour period (response)
– maxst: maximum soil temperature over the 24 hour period
– minst: minimum soil temperature over the 24 hour period
– avst: average soil temperature over the 24 hour period
– maxat: maximum air temperature over the 24 hour period
– minat: minimum air temperature over the 24 hour period
– avat: average air temperature over the 24 hour period
– maxh: maximum humidity over the 24 hour period
– minh: minimum humidity over the 24 hour period
– avh: average humidity over the 24 hour period
– wind: average wind speed over the 24 hour period.
42. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Variable selection
• There are strong relationships between the variables,
so we probably don’t need them all. We can perform an
all possible regressions analysis using the code
evap.df = read.table(evap.txt", header=T)
evap.lm = lm(evap~.,data=evap.df)
library(leaps)
all.poss.regs(evap~.,data=evap.df)
43. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Call:
lm(formula = evap ~ ., data = evap.df)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -54.074877 130.720826 -0.414 0.68164
avst 2.231782 1.003882 2.223 0.03276 *
minst 0.204854 1.104523 0.185 0.85393
maxst -0.742580 0.349609 -2.124 0.04081 *
avat 0.501055 0.568964 0.881 0.38452
minat 0.304126 0.788877 0.386 0.70219
maxvat 0.092187 0.218054 0.423 0.67505
avh 1.109858 1.133126 0.979 0.33407
minh 0.751405 0.487749 1.541 0.13242
maxh -0.556292 0.161602 -3.442 0.00151 **
wind 0.008918 0.009167 0.973 0.33733
Residual standard error: 6.508 on 35 degrees of freedom
Multiple R-Squared: 0.8463, Adjusted R-squared: 0.8023
F-statistic: 19.27 on 10 and 35 DF, p-value: 2.073e-11
45. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
2 4 6 8 10
5
10
15
20
25
30
Cp Plot
Number of variables
Cp
9
6,9
6,9,10
1,3,6,9 1,3,6,8,9
1,3,6,8,9,10
1,3,4,7,8,9,10
1,3,4,6,7,8,9,10
1,3,4,5,6,7,8,9,10
1,2,3,4,5,6,7,8,9,10
6,9,10
1,3,6,9
1,3,6,8,9,10
1,3,6,8,9
46. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
> sub.lm = lm(evap~avat + avh + wind,data=evap.df)
> summary(sub.lm)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 123.901800 24.624411 5.032 9.60e-06 ***
avat 0.222768 0.059113 3.769 0.000506 ***
avh -0.342915 0.042776 -8.016 5.31e-10 ***
wind 0.015998 0.007197 2.223 0.031664 *
Residual standard error: 6.69 on 42 degrees of freedom
Multiple R-Squared: 0.805, Adjusted R-squared: 0.7911
F-statistic: 57.8 on 3 and 42 DF, p-value: 5.834e-15
Full model was
0.8463
47. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Model building strategy
• Step1: Determine your goal:
– For predictive reasons — that is, the model will be used to
predict the response variable from a chosen set of
predictors.
– For theoretical reasons — that is, the researcher wants to
estimate a model based on a known theoretical relationship
between the response and predictors.
– For control purposes — that is, the model will be used to
control a response variable by manipulating the values of the
predictor variables.
– For inferential reasons — that is, the model will be used to
explore the strength of the relationships between the
response and the predictors.
– For data summary reasons — that is, the model will be used
merely as a way to summarize a large set of data by a single
equation.
48. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Model building strategy
• Step 2: Decide which predictor variables and
response variable on which to collect the data.
Collect the data.
• Step 3: Exploration of data
– On a univariate basis, check for outliers, gross data
errors, and missing values.
– Study bivariate relationships to reveal other outliers, to
suggest possible transformations, and to identify possible
multicollinearities.
49. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Model building strategy
• Step 4: Randomly divide the data into a training set
and a test set:
– The training set, with at least 15-20 error degrees of
freedom, is used to estimate the model.
– The test set is used for cross-validation of the fitted
model.
• Step 5: Using the training set, identify several
candidate models:
– Use best subsets regression.
– Use stepwise regression, which of course only
yields one model unless different alpha-to-remove
and alpha-to-enter values are specified.
50. Workshop on Analysis of Clinical Studies – Can Tho University of Medicine and Pharmacy – April 2012
Model building strategy
• Step 6: Select and evaluate a few "good" models:
– Select the models based on the four criteria we learned, as
well as the number and nature of the predictors.
– Evaluate the selected models for violation of the model
conditions.
– If none of the models provide a satisfactory fit, try something
else, such as collecting more data, identifying different
predictors, or formulating a different type of model.
• Step 7 (final): Select the final model
– Compare the competing models by cross-validating them
against the test data.
– The model with a larger cross-validation R2 is abetter
predictive model.
– Consider residual plots, outliers, parsimony, relevance, and
ease of measurement of predictors.