Welcome! Webinar Biostatistics: sample size & power. Thursday, April 26, 12:30 1:30 pm (NDT)
|
|
- Matthew Holmes
- 5 years ago
- Views:
Transcription
1 . Welcome! Webinar Biostatistics: sample size & power Thursday, April 26, 12:30 1:30 pm (NDT) Get started now: Please check if your speakers are working and mute your audio. Please use the chat box to ask questions.
2 How to participate in this webinar Any issues? Technical Support Locally: or go to 2
3 Introduction Speaker Hensley H Mariathas Ph.D., Biostatistic Lead NL SUPPORT 3
4 Webinar # Biostatistics: sample size & power
5 Sample Size Calculation and Power Analysis Lead Biostatistician NL SUPPORT Faculty of Medicine Memorial University of Newfoundland Canada April 26, 2018
6 Why and What Why sample size calculation? Part of study design to determine the number of participants needed to detect clinically relevant treatment effect Number of patients in a study restricted because of ethical, cost and time consideration What we need? Requires prior estimation of study results May use data from other prior studies Will use investigator judgment and choice
7 Key Things to Decide Things You Have to Decide First Type of question: estimation, comparison etc. Study design: trial, cluster, case-control etc. Type of outcome measure: data level Likely analytic method Hypothesis test verses confidence interval approach Things You May Have to Decide Next Desired maximal type I & II error rates or Desired % ile and width of CI Likely outcome in controls Effect size you wish to detect (e.g. minimal difference in group outcome) Measure of variation expected (e.g. group SD for outcome)
8 Research Questions Example 1: Estimating a population proportion We want to estimate the true immunization coverage in a community of school children to be within 4% of the true value. Example 2: Trial to reduce blood pressure Suppose researcher wants to compare two treatments designed to reduce blood pressure. Researcher decide that a clinically important difference would be 10 mm Hg.
9 Two approaches to sample size calculations Precision-based With what precision do you want to estimate the quantum of one or more characteristics of the population, called parameter(s),(for example, mean hemoglobin level or prevalence of asthma ect.,)? To estimate the value of the parameter under study for a prefixed precision and level of confidence. Power-based How small a difference is it important to detect and with what degree of certain? To achieve a desired power for detecting a clinically or scientifically meaningful difference at a prefixed level of significance.
10 Precision-based sample size calculation Suppose you want be able to estimate your unknown parameter with a certain degree of precision. A 100(1 α)% confidence interval with certain width. The narrower the interval is, the more precise the inference is Consider the maximum half width of the 100(1 α)% confidence interval of the unknown parameter and usually referred to as the maximum error or margin of error In general a 100(1 α)% confidence interval of the unknown parameter is given by Estimate ± z α/2 SE, SE = σ n where z α/2 is the upper (α/2) th quartile of the standard normal distribution and σ is the population SD which is unknown The sample size required can be chosen as n = z2 α/2 σ2 E 2, E = maximum error
11 Precision-based sample size calculation-one sample Sample size for estimating a population mean ( zα/2 σ ) 2 n = (1) E
12 Precision-based sample size calculation-one sample Sample size for estimating a population mean ( zα/2 σ ) 2 n = (1) E Sample size for estimating a population proportion n = p(1 p) ( zα/2 ) 2 ( zα/2 ) 2 = pq (2) E E
13 Precision-based sample size calculation-one sample Sample size for estimating a population mean ( zα/2 σ ) 2 n = (1) E Sample size for estimating a population proportion n = p(1 p) The values of σ and p ( zα/2 E ) 2 ( zα/2 ) 2 = pq (2) E The values of σ and p can be taken from a similar published studies or based on a pilot studies.
14 Precision-based sample size calculation-two sample Sample size for estimating mean difference ( 2 unrelated group) n 1 = n 2 = n(per group) = z2 α/2 ( σ 2 E σ2 2 ) (3)
15 Precision-based sample size calculation-two sample Sample size for estimating mean difference ( 2 unrelated group) n 1 = n 2 = n(per group) = z2 α/2 ( σ 2 E σ2 2 ) (3) Sample size for estimating of difference in proportions n 1 = n 2 = n(per group) = z2 α/2 E 2 (p 1(1 p 1 ) + p 2 (1 p 2 )) (4)
16 Precision-based sample size calculation-two sample Sample size for estimating mean difference ( 2 unrelated group) n 1 = n 2 = n(per group) = z2 α/2 ( σ 2 E σ2 2 ) (3) Sample size for estimating of difference in proportions n 1 = n 2 = n(per group) = z2 α/2 E 2 (p 1(1 p 1 ) + p 2 (1 p 2 )) (4) About σ i and p i for i = 1, 2 are: Where, σ i is the standard deviation expected in group i, p i is the expected proportion with events in group i and E is the half the desired width of the CI.
17 Practical Problem Example 1 Suppose you wish to carry out a trial of a new treatment for hypertension (high blood pressure) among men aged between 50 and 60. You would like your 95% confidence interval to have width 10 mmhg (i.e. you want to be 95% sure that the true difference in means is within ±5 mmhg of your estimated difference in means). How many subjects will you need to include in your study?
18 Solution for the practical problem We know that the 95% confidence interval for a difference in means is given by σ1 2 ( x 1 x 2 ) ± 2 + σ2 2 (5) n 1 n 2 Hence, we want 2 σ 2 1 n 1 + σ2 2 n 2 to be equal to 5, that is for n 1 = n 2 = n and equal variance σ σ = 2 σ n 1 n 2 n = 5 σ n = 2.5 since we are aiming for groups of the same size
19 Solution for the practical problem cont... Need to know what σ is likely to be This is known from (a) previous experience (i.e. knowledge of the distribution of systolic blood pressure among men with hypertension in this age group), (b) using other published papers on blood pressure studies in a similar group of people or (c) carrying out a pilot study From option (b) assume σ = 20 mmhg. This gives 2 20 n = 2.5 n ( ) = n =
20 Power-based sample size calculation Relates to hypothesis testing Four possible outcomes of a test of hypothesis True State of Nature Clinical Decision H 0 True H a True Do not reject H 0 Correct Decision Type II error (β) Reject H 0 Type I error(α) Correct Decision Type I error (False positive): Rejecting H 0 when H 0 is true α: Type I error rate. Maximum p-value considered statistically significant Type II error (False negative): Failing to reject H 0 when H 0 is false β: Type II error rate. Power: The statistical power of a test is defined to be 1 β.
21 Power-based sample size calculation Power analysis Type I error is usually considered to be a more important and/or serious error which one would like to avoid Control α at an acceptable level and try to minimize β by choosing an appropriate sample size
22 Power-based sample size calculation Power analysis Type I error is usually considered to be a more important and/or serious error which one would like to avoid Control α at an acceptable level and try to minimize β by choosing an appropriate sample size Key steps of power analysis Select a significance level (type I error), which is willing to tolerate (i.e. typically α = 0.05) A choice of power is either 90% or 80% Specify a clinically meaningful difference( ). The knowledge regarding the standard deviation (i.e.,σ) of the primary endpoint considered in the study is also required for sample size determination
23 Comparing Means One-Sample Design The sample size need to achieve power 1 β can be obtained by solving the following equation, where, n = (z α/2 + z β ) 2 σ 2 2 (6) z p is the upper p th quartile of the standard normal distribution. = µ µ 0 is the difference between true mean (µ) and a reference value (µ 0 ). σ 2 is the population variance need to be replace by prior knowledge.
24 Comparing Means Two-Sample Design: Two independent groups The formula for estimating the sample size in each of the study group n 1 = n 2 = n is given by where, n = 2(z α/2 + z β ) 2 σ 2 2 or n = 2(z α/2 + z β ) 2 δ 2 (7) n is the minimum sample size required in each group (equal sample size and hence total size is 2n) = µ 1 µ 2 is the chosen difference in means to be detected with. σ 2 anticipated endpoint group variance ( You may assume σ 2 1 = σ 2 2 = σ2 ). δ = σ is the effect size, minimum difference we wish to detect relative to the endpoint group variance.
25 Comparing Means Two-Sample Design: Two dependent groups (Paired) These observations cannot be assumed to be independent of each other; the statistical test and the sample size estimation will have to take into account this dependency. Because of this we can use the sample size formula as given in (6) for one sample: n = (z α/2 + z β ) 2 σ 2 d 2 d (8) where, σ d is the unknown population SD of the differences between pairs of observations But σ d = σ 2(1 r), with σ is the SD of the observations at one time point and r is the correlation between observations within subjects over measurements
26 If two groups of unequal size Applies even if not using t-test Assuming n per group needed if groups equal n 1 as the size of the first unequal group (say, standard treatment group) kn 1 as the size of the second group ( say, new treatment group) (k + 1)n Then n 1 = 2k From (7), n = 2(z α/2 + z β ) 2 σ 2 2.
27 Comparison of Proportions between Two Groups Two independent groups, Binary The number of participants per group required to detect a difference p 1 p 2 in the proportions with significance level α and power 1 β is given by n = (z α/2 + z β ) 2 (p 1 (1 p 1 ) + p 2 (1 p 2 )) (p 1 p 2 ) 2 (9) where, p 1 is the expected proportion in Group 1 and p 2 is the expected proportion in Group 2.
28 Comparison of Proportions between Two Groups Two independent groups, Odds If the difference is specified as an odds ratio OR = p 1/(1 p 1 ) p 2 /(1 p 2 ) = p 1(1 p 2 ) p 2 (1 p 1 ) then an approximate formula is given by n = 2(z α/2 + z β ) 2 [ln(or)] 2 p(1 p) (10) where, p = p 1 + p 2 2 and OR is the odds ratio to be detected.
29 Comparison of Proportions between Two Groups Case Control Study, Odds In case-control study, data are usually summarized in odds ratio, rather than difference between two proportions when the outcome variables of interest were categorical If p 1 and p 2 are proportions of cases and controls respectively, exposed to a risk factor OR = p 1/(1 p 1 ) p 2 /(1 p 2 ) = p 1(1 p 2 ) p 2 (1 p 1 ) If we know the prevalence of exposure in the general population p, the total sample size N for estimating an OR is N = (1 + k)2 k (z α/2 + z β ) 2 [ln(or)] 2 p(1 p), k = n 1 (11) n 2
30 Comparison of Proportions between Two Groups Ordered categorical data n = 6(z α/2 + z β ) 2 [ln(or)] 2 (1 k i=1 p 3 i ) (12) where OR is the odds ratio of a patient being in category i or less for one treatment compared to the other k is the number of categories and p i is the mean proportion expected in category i, that is, p i = (p 1i + p 2i )/2 where p 1i and p 2i are the proportions expected in category i for the two groups 1 and 2 respectively.
31 Comparison of Proportions between Two Groups Example 3 Randomized trial of two treatments for HIV patients Primary outcome = proportion of patients with viral load (VL) less than the limit of detection at 48 weeks Expect that 60% of patients in the standard of care arm will have suppressed VL Interested in difference of 20% p 1 = 0.6, p 2 = 0.8, α = 0.05 and β = 0.2, The sample size per group is 81
32 Problems Problem 1 An investigator wish to estimate the sample size necessary to detect a 10 mg/dl difference in cholesterol level in a diet intervention group compared to the control group. The SD from the other data is estimated to be 50 mg/dl. For two sided 5% significance level, z α/2 = 1.96 and for 90% power z β = Thus the required sample size in each group is n = 2 ( ) = 526
33 Problems Problem 2 The Canadian Contraceptive Study 2002 is used as the best evidence for rates of oral contraceptive pills (OCP) use in the Canadian Population. It reported that 80% of women report ever use of OCP and 20% report use more than 10years. The average time duration of OCP use was 6.4 years. Meta-analysis reviewing the extent of relative risk reduction of endometrial cancer with OCP use report 0.44 at 4 years of use, 0.33 at 8years of use and 0.28 at 12 years of use. ( decreased rates of 56%, 67% and 72% respectively). Calculating that the probability of exposure to OCP for greater than 5 years at 60% and that women without the exposure have a risk of endometrial cancer that is 3 times higher. What sample size needed at α = 5% with power of 80%?
34 Problems Problem 2: Solution For two sided 5% significance level, z α/2 = 1.96 and for 80% power z β = 0.84 OR = 3 For k = 1 from (11), the total sample size N is N = (1 + 1)2 1 ( ) 2 [ln(3)] = 108 Since k = 1, then n 1 = n 2 = 54
35 Problems SAS output using proc power for problem 2
36 Problems From Example 3 Instead of 81, if we had only 60 samples in each group If we had 110 samples in each group
37 Questions?
38 Thank You!
39 Funding opportunity
40 Save the date: Upcoming sessions Webinar: Knowledge Translation beyond Publications. Thursday May 24, Time: 12:30 PM 1:30 PM (NDT) Webinar: Let's Talk Policy. Thursday June 21, Time: 12:30 PM 1:30 PM (NDT) Workshop: Writing in Plain Language. Thursday May 17, Time: 12:00 PM 2:00 PM (NDT) Go to to register Check out our past events, slides and recordings on our website.
41 Keep in touch Eva Vat, Training and Capacity lead / Patient Engagement lead eva.vat@med.mun.ca Sign up for our Newsletter
Answer keys for Assignment 10: Measurement of study variables (The correct answer is underlined in bold text)
Answer keys for Assignment 10: Measurement of study variables (The correct answer is underlined in bold text) 1. A quick and easy indicator of dispersion is a. Arithmetic mean b. Variance c. Standard deviation
More informationa Sample By:Dr.Hoseyn Falahzadeh 1
In the name of God Determining ee the esize eof a Sample By:Dr.Hoseyn Falahzadeh 1 Sample Accuracy Sample accuracy: refers to how close a random sample s statistic is to the true population s value it
More informationSample Size. Vorasith Sornsrivichai, MD., FETP Epidemiology Unit, Faculty of Medicine Prince of Songkla University
Sample Size Vorasith Sornsrivichai, MD., FETP Epidemiology Unit, Faculty of Medicine Prince of Songkla University All nature is but art, unknown to thee; All chance, direction, which thou canst not see;
More informationPubH 7470: STATISTICS FOR TRANSLATIONAL & CLINICAL RESEARCH
PubH 7470: STATISTICS FOR TRANSLATIONAL & CLINICAL RESEARCH The First Step: SAMPLE SIZE DETERMINATION THE ULTIMATE GOAL The most important, ultimate step of any of clinical research is to do draw inferences;
More informationTwo sample hypothesis testing
Statistics February 26, 2014 Debdeep Pati Two sample hypothesis testing 1. Suppose we want to study the relationship between use of oral contraceptives (OC) and level of blood pressure (BP) in women. 2.
More informationBINF 702 SPRING Chapter 8 Hypothesis Testing: Two-Sample Inference. BINF702 SPRING 2014 Chapter 8 Hypothesis Testing: Two- Sample Inference 1
BINF 702 SPRING 2014 Chapter 8 Hypothesis Testing: Two-Sample Inference Two- Sample Inference 1 A Poster Child for two-sample hypothesis testing Ex 8.1 Obstetrics In the birthweight data in Example 7.2,
More informationPower and sample size calculations
Patrick Breheny October 20 Patrick Breheny University of Iowa Biostatistical Methods I (BIOS 5710) 1 / 26 Planning a study Introduction What is power? Why is it important? Setup One of the most important
More informationHYPOTHESIS TESTING II TESTS ON MEANS. Sorana D. Bolboacă
HYPOTHESIS TESTING II TESTS ON MEANS Sorana D. Bolboacă OBJECTIVES Significance value vs p value Parametric vs non parametric tests Tests on means: 1 Dec 14 2 SIGNIFICANCE LEVEL VS. p VALUE Materials and
More informationBIO5312 Biostatistics Lecture 6: Statistical hypothesis testings
BIO5312 Biostatistics Lecture 6: Statistical hypothesis testings Yujin Chung October 4th, 2016 Fall 2016 Yujin Chung Lec6: Statistical hypothesis testings Fall 2016 1/30 Previous Two types of statistical
More informationEpidemiology Wonders of Biostatistics Chapter 11 (continued) - probability in a single population. John Koval
Epidemiology 9509 Wonders of Biostatistics Chapter 11 (continued) - probability in a single population John Koval Department of Epidemiology and Biostatistics University of Western Ontario What is being
More informationProbability and Probability Distributions. Dr. Mohammed Alahmed
Probability and Probability Distributions 1 Probability and Probability Distributions Usually we want to do more with data than just describing them! We might want to test certain specific inferences about
More informationLecture 25. Ingo Ruczinski. November 24, Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Johns Hopkins University
Lecture 25 Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Johns Hopkins University November 24, 2015 1 2 3 4 5 6 7 8 9 10 11 1 Hypothesis s of homgeneity 2 Estimating risk
More informationBIOS 312: Precision of Statistical Inference
and Power/Sample Size and Standard Errors BIOS 312: of Statistical Inference Chris Slaughter Department of Biostatistics, Vanderbilt University School of Medicine January 3, 2013 Outline Overview and Power/Sample
More informationMAT 2379, Introduction to Biostatistics, Sample Calculator Questions 1. MAT 2379, Introduction to Biostatistics
MAT 2379, Introduction to Biostatistics, Sample Calculator Questions 1 MAT 2379, Introduction to Biostatistics Sample Calculator Problems for the Final Exam Note: The exam will also contain some problems
More informationSampling and Sample Size. Shawn Cole Harvard Business School
Sampling and Sample Size Shawn Cole Harvard Business School Calculating Sample Size Effect Size Power Significance Level Variance ICC EffectSize 2 ( ) 1 σ = t( 1 κ ) + tα * * 1+ ρ( m 1) P N ( 1 P) Proportion
More informationClass 24. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700
Class 4 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 013 by D.B. Rowe 1 Agenda: Recap Chapter 9. and 9.3 Lecture Chapter 10.1-10.3 Review Exam 6 Problem Solving
More informationConditional Probabilities
Lecture Outline BIOST 514/517 Biostatistics I / pplied Biostatistics I Kathleen Kerr, Ph.D. ssociate Professor of Biostatistics University of Washington Probability Diagnostic Testing Random variables:
More informationE509A: Principle of Biostatistics. GY Zou
E509A: Principle of Biostatistics (Week 4: Inference for a single mean ) GY Zou gzou@srobarts.ca Example 5.4. (p. 183). A random sample of n =16, Mean I.Q is 106 with standard deviation S =12.4. What
More informationAnnouncements. Unit 3: Foundations for inference Lecture 3: Decision errors, significance levels, sample size, and power.
Announcements Announcements Unit 3: Foundations for inference Lecture 3:, significance levels, sample size, and power Statistics 101 Mine Çetinkaya-Rundel October 1, 2013 Project proposal due 5pm on Friday,
More informationFundamentals to Biostatistics. Prof. Chandan Chakraborty Associate Professor School of Medical Science & Technology IIT Kharagpur
Fundamentals to Biostatistics Prof. Chandan Chakraborty Associate Professor School of Medical Science & Technology IIT Kharagpur Statistics collection, analysis, interpretation of data development of new
More informationStatistics in medicine
Statistics in medicine Lecture 3: Bivariate association : Categorical variables Proportion in one group One group is measured one time: z test Use the z distribution as an approximation to the binomial
More informationSample Size Calculations for Group Randomized Trials with Unequal Sample Sizes through Monte Carlo Simulations
Sample Size Calculations for Group Randomized Trials with Unequal Sample Sizes through Monte Carlo Simulations Ben Brewer Duke University March 10, 2017 Introduction Group randomized trials (GRTs) are
More informationOnline supplement. Absolute Value of Lung Function (FEV 1 or FVC) Explains the Sex Difference in. Breathlessness in the General Population
Online supplement Absolute Value of Lung Function (FEV 1 or FVC) Explains the Sex Difference in Breathlessness in the General Population Table S1. Comparison between patients who were excluded or included
More informationHYPOTHESIS TESTING. Hypothesis Testing
MBA 605 Business Analytics Don Conant, PhD. HYPOTHESIS TESTING Hypothesis testing involves making inferences about the nature of the population on the basis of observations of a sample drawn from the population.
More informationInference for Distributions Inference for the Mean of a Population
Inference for Distributions Inference for the Mean of a Population PBS Chapter 7.1 009 W.H Freeman and Company Objectives (PBS Chapter 7.1) Inference for the mean of a population The t distributions The
More informationOne-sample categorical data: approximate inference
One-sample categorical data: approximate inference Patrick Breheny October 6 Patrick Breheny Biostatistical Methods I (BIOS 5710) 1/25 Introduction It is relatively easy to think about the distribution
More informationLab #11. Variable B. Variable A Y a b a+b N c d c+d a+c b+d N = a+b+c+d
BIOS 4120: Introduction to Biostatistics Breheny Lab #11 We will explore observational studies in today s lab and review how to make inferences on contingency tables. We will only use 2x2 tables for today
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression Sasivimol Rattanasiri, Ph.D Section for Clinical Epidemiology and Biostatistics Ramathibodi Hospital, Mahidol University E-mail: sasivimol.rat@mahidol.ac.th 1 Outline
More informationPower of a test. Hypothesis testing
Hypothesis testing February 11, 2014 Debdeep Pati Power of a test 1. Assuming standard deviation is known. Calculate power based on one-sample z test. A new drug is proposed for people with high intraocular
More informationModule 17: Two-Sample t-tests, with equal variances for the two populations
Module 17: Two-Sample t-tests, with equal variances for the two populations This module describes one of the most utilized statistical tests, the two-sample t-test conducted under the assumption that the
More informationSample Size and Power I: Binary Outcomes. James Ware, PhD Harvard School of Public Health Boston, MA
Sample Size and Power I: Binary Outcomes James Ware, PhD Harvard School of Public Health Boston, MA Sample Size and Power Principles: Sample size calculations are an essential part of study design Consider
More informationMarginal versus conditional effects: does it make a difference? Mireille Schnitzer, PhD Université de Montréal
Marginal versus conditional effects: does it make a difference? Mireille Schnitzer, PhD Université de Montréal Overview In observational and experimental studies, the goal may be to estimate the effect
More informationBIOS 2041: Introduction to Statistical Methods
BIOS 2041: Introduction to Statistical Methods Abdus S Wahed* *Some of the materials in this chapter has been adapted from Dr. John Wilson s lecture notes for the same course. Chapter 0 2 Chapter 1 Introduction
More informationComparing p s Dr. Don Edwards notes (slightly edited and augmented) The Odds for Success
Comparing p s Dr. Don Edwards notes (slightly edited and augmented) The Odds for Success When the experiment consists of a series of n independent trials, and each trial may end in either success or failure,
More informationChapter Six: Two Independent Samples Methods 1/51
Chapter Six: Two Independent Samples Methods 1/51 6.3 Methods Related To Differences Between Proportions 2/51 Test For A Difference Between Proportions:Introduction Suppose a sampling distribution were
More informationTraining and Technical Assistance Webinar Series Statistical Analysis for Criminal Justice Research
Training and Technical Assistance Webinar Series Statistical Analysis for Criminal Justice Research Justice Research and Statistics Association 720 7 th Street, NW, Third Floor Washington, DC 20001 II.
More informationSample Size Determination
Sample Size Determination 018 The number of subjects in a clinical study should always be large enough to provide a reliable answer to the question(s addressed. The sample size is usually determined by
More informationPower and Sample Size Bios 662
Power and Sample Size Bios 662 Michael G. Hudgens, Ph.D. mhudgens@bios.unc.edu http://www.bios.unc.edu/ mhudgens 2008-10-31 14:06 BIOS 662 1 Power and Sample Size Outline Introduction One sample: continuous
More informationChapter 7. Inference for Distributions. Introduction to the Practice of STATISTICS SEVENTH. Moore / McCabe / Craig. Lecture Presentation Slides
Chapter 7 Inference for Distributions Introduction to the Practice of STATISTICS SEVENTH EDITION Moore / McCabe / Craig Lecture Presentation Slides Chapter 7 Inference for Distributions 7.1 Inference for
More informationThe Design of a Survival Study
The Design of a Survival Study The design of survival studies are usually based on the logrank test, and sometimes assumes the exponential distribution. As in standard designs, the power depends on The
More informationBasic Statistics and Probability Chapter 9: Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses
Basic Statistics and Probability Chapter 9: Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses Identifying the Target Parameter Comparing Two Population Means: Independent Sampling
More informationDescriptive Statistics-I. Dr Mahmoud Alhussami
Descriptive Statistics-I Dr Mahmoud Alhussami Biostatistics What is the biostatistics? A branch of applied math. that deals with collecting, organizing and interpreting data using well-defined procedures.
More informationLecturer: Dr. Adote Anum, Dept. of Psychology Contact Information:
Lecturer: Dr. Adote Anum, Dept. of Psychology Contact Information: aanum@ug.edu.gh College of Education School of Continuing and Distance Education 2014/2015 2016/2017 Session Overview In this Session
More informationCOMPARING GROUPS PART 1CONTINUOUS DATA
COMPARING GROUPS PART 1CONTINUOUS DATA Min Chen, Ph.D. Assistant Professor Quantitative Biomedical Research Center Department of Clinical Sciences Bioinformatics Shared Resource Simmons Comprehensive Cancer
More informationThe Difference in Proportions Test
Overview The Difference in Proportions Test Dr Tom Ilvento Department of Food and Resource Economics A Difference of Proportions test is based on large sample only Same strategy as for the mean We calculate
More informationTests for Two Correlated Proportions in a Matched Case- Control Design
Chapter 155 Tests for Two Correlated Proportions in a Matched Case- Control Design Introduction A 2-by-M case-control study investigates a risk factor relevant to the development of a disease. A population
More informationCategorical Data Analysis 1
Categorical Data Analysis 1 STA 312: Fall 2012 1 See last slide for copyright information. 1 / 1 Variables and Cases There are n cases (people, rats, factories, wolf packs) in a data set. A variable is
More informationHypothesis testing. Data to decisions
Hypothesis testing Data to decisions The idea Null hypothesis: H 0 : the DGP/population has property P Under the null, a sample statistic has a known distribution If, under that that distribution, the
More informationHarvard University. Rigorous Research in Engineering Education
Statistical Inference Kari Lock Harvard University Department of Statistics Rigorous Research in Engineering Education 12/3/09 Statistical Inference You have a sample and want to use the data collected
More informationStudy Design: Sample Size Calculation & Power Analysis
Study Design: Sample Size Calculation & Power Analysis RCMAR/CHIME/EXPORT April 21, 2008 Honghu Liu, Ph.D. Contents Background Common Designs Examples Computer Software Summary & Discussion Background
More informationNI - INTEGRATED PUBLIC PROVISION OF HEALTH CARE SERVICES (P164452)
LATIN AMERICA AND CARIBBEAN Nicaragua Health, Nutrition & Population Global Practice IBRD/IDA Investment Project Financing FY 2018 Seq No: 2 ARCHIVED on 26-Dec-2018 ISR35016 Implementing Agencies: Ministry
More informationIntroduction to Statistical Data Analysis III
Introduction to Statistical Data Analysis III JULY 2011 Afsaneh Yazdani Preface Major branches of Statistics: - Descriptive Statistics - Inferential Statistics Preface What is Inferential Statistics? The
More informationSample Size/Power Calculation by Software/Online Calculators
Sample Size/Power Calculation by Software/Online Calculators May 24, 2018 Li Zhang, Ph.D. li.zhang@ucsf.edu Associate Professor Department of Epidemiology and Biostatistics Division of Hematology and Oncology
More informationClinical Trials. Olli Saarela. September 18, Dalla Lana School of Public Health University of Toronto.
Introduction to Dalla Lana School of Public Health University of Toronto olli.saarela@utoronto.ca September 18, 2014 38-1 : a review 38-2 Evidence Ideal: to advance the knowledge-base of clinical medicine,
More informationLecture 1 Introduction to Multi-level Models
Lecture 1 Introduction to Multi-level Models Course Website: http://www.biostat.jhsph.edu/~ejohnson/multilevel.htm All lecture materials extracted and further developed from the Multilevel Model course
More informationEstimating Optimal Dynamic Treatment Regimes from Clustered Data
Estimating Optimal Dynamic Treatment Regimes from Clustered Data Bibhas Chakraborty Department of Biostatistics, Columbia University bc2425@columbia.edu Society for Clinical Trials Annual Meetings Boston,
More informationSample Size Estimation for Studies of High-Dimensional Data
Sample Size Estimation for Studies of High-Dimensional Data James J. Chen, Ph.D. National Center for Toxicological Research Food and Drug Administration June 3, 2009 China Medical University Taichung,
More information6 Sample Size Calculations
6 Sample Size Calculations A major responsibility of a statistician: sample size calculation. Hypothesis Testing: compare treatment 1 (new treatment) to treatment 2 (standard treatment); Assume continuous
More informationRejection regions for the bivariate case
Rejection regions for the bivariate case The rejection region for the T 2 test (and similarly for Z 2 when Σ is known) is the region outside of an ellipse, for which there is a (1-α)% chance that the test
More informationAnalysing data: regression and correlation S6 and S7
Basic medical statistics for clinical and experimental research Analysing data: regression and correlation S6 and S7 K. Jozwiak k.jozwiak@nki.nl 2 / 49 Correlation So far we have looked at the association
More informationStatistical methods for comparing multiple groups. Lecture 7: ANOVA. ANOVA: Definition. ANOVA: Concepts
Statistical methods for comparing multiple groups Lecture 7: ANOVA Sandy Eckel seckel@jhsph.edu 30 April 2008 Continuous data: comparing multiple means Analysis of variance Binary data: comparing multiple
More informationLecture 3: Measures of effect: Risk Difference Attributable Fraction Risk Ratio and Odds Ratio
Lecture 3: Measures of effect: Risk Difference Attributable Fraction Risk Ratio and Odds Ratio Dankmar Böhning Southampton Statistical Sciences Research Institute University of Southampton, UK March 3-5,
More information10: Crosstabs & Independent Proportions
10: Crosstabs & Independent Proportions p. 10.1 P Background < Two independent groups < Binary outcome < Compare binomial proportions P Illustrative example ( oswege.sav ) < Food poisoning following church
More informationReview. December 4 th, Review
December 4 th, 2017 Att. Final exam: Course evaluation Friday, 12/14/2018, 10:30am 12:30pm Gore Hall 115 Overview Week 2 Week 4 Week 7 Week 10 Week 12 Chapter 6: Statistics and Sampling Distributions Chapter
More informationBios 6649: Clinical Trials - Statistical Design and Monitoring
Bios 6649: Clinical Trials - Statistical Design and Monitoring Spring Semester 2015 John M. Kittelson Department of Biostatistics & Informatics Colorado School of Public Health University of Colorado Denver
More informationClass 19. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700
Class 19 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 2017 by D.B. Rowe 1 Agenda: Recap Chapter 8.3-8.4 Lecture Chapter 8.5 Go over Exam. Problem Solving
More informationBiost 518 Applied Biostatistics II. Purpose of Statistics. First Stage of Scientific Investigation. Further Stages of Scientific Investigation
Biost 58 Applied Biostatistics II Scott S. Emerson, M.D., Ph.D. Professor of Biostatistics University of Washington Lecture 5: Review Purpose of Statistics Statistics is about science (Science in the broadest
More informationEcon 325: Introduction to Empirical Economics
Econ 325: Introduction to Empirical Economics Chapter 9 Hypothesis Testing: Single Population Ch. 9-1 9.1 What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population
More informationStatistics: revision
NST 1B Experimental Psychology Statistics practical 5 Statistics: revision Rudolf Cardinal & Mike Aitken 29 / 30 April 2004 Department of Experimental Psychology University of Cambridge Handouts: Answers
More information10.1. Comparing Two Proportions. Section 10.1
/6/04 0. Comparing Two Proportions Sectio0. Comparing Two Proportions After this section, you should be able to DETERMINE whether the conditions for performing inference are met. CONSTRUCT and INTERPRET
More informationComparing Means from Two-Sample
Comparing Means from Two-Sample Kwonsang Lee University of Pennsylvania kwonlee@wharton.upenn.edu April 3, 2015 Kwonsang Lee STAT111 April 3, 2015 1 / 22 Inference from One-Sample We have two options to
More informationTutorial 4: Power and Sample Size for the Two-sample t-test with Unequal Variances
Tutorial 4: Power and Sample Size for the Two-sample t-test with Unequal Variances Preface Power is the probability that a study will reject the null hypothesis. The estimated probability is a function
More informationStatistical Inference
Statistical Inference Classical and Bayesian Methods Class 6 AMS-UCSC Thu 26, 2012 Winter 2012. Session 1 (Class 6) AMS-132/206 Thu 26, 2012 1 / 15 Topics Topics We will talk about... 1 Hypothesis testing
More informationDISCRETE PROBABILITY DISTRIBUTIONS
DISCRETE PROBABILITY DISTRIBUTIONS REVIEW OF KEY CONCEPTS SECTION 41 Random Variable A random variable X is a numerically valued quantity that takes on specific values with different probabilities The
More informationStatistics for IT Managers
Statistics for IT Managers 95-796, Fall 2012 Module 2: Hypothesis Testing and Statistical Inference (5 lectures) Reading: Statistics for Business and Economics, Ch. 5-7 Confidence intervals Given the sample
More informationConfidence Intervals of the Simple Difference between the Proportions of a Primary Infection and a Secondary Infection, Given the Primary Infection
Biometrical Journal 42 (2000) 1, 59±69 Confidence Intervals of the Simple Difference between the Proportions of a Primary Infection and a Secondary Infection, Given the Primary Infection Kung-Jong Lui
More informationSummarizing and Displaying Measurement Data/Understanding and Comparing Distributions
Summarizing and Displaying Measurement Data/Understanding and Comparing Distributions Histograms, Mean, Median, Five-Number Summary and Boxplots, Standard Deviation Thought Questions 1. If you were to
More informationThe t-distribution. Patrick Breheny. October 13. z tests The χ 2 -distribution The t-distribution Summary
Patrick Breheny October 13 Patrick Breheny Biostatistical Methods I (BIOS 5710) 1/25 Introduction Introduction What s wrong with z-tests? So far we ve (thoroughly!) discussed how to carry out hypothesis
More informationMarginal Structural Cox Model for Survival Data with Treatment-Confounder Feedback
University of South Carolina Scholar Commons Theses and Dissertations 2017 Marginal Structural Cox Model for Survival Data with Treatment-Confounder Feedback Yanan Zhang University of South Carolina Follow
More informationReview 6. n 1 = 85 n 2 = 75 x 1 = x 2 = s 1 = 38.7 s 2 = 39.2
Review 6 Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected ) A researcher finds that of,000 people who said that
More information16.400/453J Human Factors Engineering. Design of Experiments II
J Human Factors Engineering Design of Experiments II Review Experiment Design and Descriptive Statistics Research question, independent and dependent variables, histograms, box plots, etc. Inferential
More informationStatistics 262: Intermediate Biostatistics Regression & Survival Analysis
Statistics 262: Intermediate Biostatistics Regression & Survival Analysis Jonathan Taylor & Kristin Cobb Statistics 262: Intermediate Biostatistics p.1/?? Introduction This course is an applied course,
More informationDetermining a Statistically Valid Sample Size: What Does FDA Expect to See?
FOI Services Teleconference TC161130 Determining a Statistically Valid Sample Size: What Does FDA Expect to See? Presented by: Steven Walfish When: November 30, 2016 Eastern Standard Time: 1:00pm 2:30pm
More informationSTAC51: Categorical data Analysis
STAC51: Categorical data Analysis Mahinda Samarakoon January 26, 2016 Mahinda Samarakoon STAC51: Categorical data Analysis 1 / 32 Table of contents Contingency Tables 1 Contingency Tables Mahinda Samarakoon
More informationBusiness Statistics. Lecture 10: Course Review
Business Statistics Lecture 10: Course Review 1 Descriptive Statistics for Continuous Data Numerical Summaries Location: mean, median Spread or variability: variance, standard deviation, range, percentiles,
More informationPHP2510: Principles of Biostatistics & Data Analysis. Lecture X: Hypothesis testing. PHP 2510 Lec 10: Hypothesis testing 1
PHP2510: Principles of Biostatistics & Data Analysis Lecture X: Hypothesis testing PHP 2510 Lec 10: Hypothesis testing 1 In previous lectures we have encountered problems of estimating an unknown population
More informationPubH 5450 Biostatistics I Prof. Carlin. Lecture 13
PubH 5450 Biostatistics I Prof. Carlin Lecture 13 Outline Outline Sample Size Counts, Rates and Proportions Part I Sample Size Type I Error and Power Type I error rate: probability of rejecting the null
More informationLogistic regression analysis. Birthe Lykke Thomsen H. Lundbeck A/S
Logistic regression analysis Birthe Lykke Thomsen H. Lundbeck A/S 1 Response with only two categories Example Odds ratio and risk ratio Quantitative explanatory variable More than one variable Logistic
More informationChapter 9. Hypothesis testing. 9.1 Introduction
Chapter 9 Hypothesis testing 9.1 Introduction Confidence intervals are one of the two most common types of statistical inference. Use them when our goal is to estimate a population parameter. The second
More informationPerson-Time Data. Incidence. Cumulative Incidence: Example. Cumulative Incidence. Person-Time Data. Person-Time Data
Person-Time Data CF Jeff Lin, MD., PhD. Incidence 1. Cumulative incidence (incidence proportion) 2. Incidence density (incidence rate) December 14, 2005 c Jeff Lin, MD., PhD. c Jeff Lin, MD., PhD. Person-Time
More informationPower and sample size calculations
Power and sample size calculations Susanne Rosthøj Biostatistisk Afdeling Institut for Folkesundhedsvidenskab Københavns Universitet sr@biostat.ku.dk April 8, 2014 Planning an investigation How many individuals
More informationPower Analysis. Introduction to Power
Power Analysis Dr. J. Kyle Roberts Southern Methodist University Simmons School of Education and Human Development Department of Teaching and Learning When testing a specific null hypothesis (H 0 ), we
More informationReview. More Review. Things to know about Probability: Let Ω be the sample space for a probability measure P.
1 2 Review Data for assessing the sensitivity and specificity of a test are usually of the form disease category test result diseased (+) nondiseased ( ) + A B C D Sensitivity: is the proportion of diseased
More informationStatistics in medicine
Statistics in medicine Lecture 4: and multivariable regression Fatma Shebl, MD, MS, MPH, PhD Assistant Professor Chronic Disease Epidemiology Department Yale School of Public Health Fatma.shebl@yale.edu
More informationChapter 10: STATISTICAL INFERENCE FOR TWO SAMPLES. Part 1: Hypothesis tests on a µ 1 µ 2 for independent groups
Chapter 10: STATISTICAL INFERENCE FOR TWO SAMPLES Part 1: Hypothesis tests on a µ 1 µ 2 for independent groups Sections 10-1 & 10-2 Independent Groups It is common to compare two groups, and do a hypothesis
More informationHypothesis testing I. - In particular, we are talking about statistical hypotheses. [get everyone s finger length!] n =
Hypothesis testing I I. What is hypothesis testing? [Note we re temporarily bouncing around in the book a lot! Things will settle down again in a week or so] - Exactly what it says. We develop a hypothesis,
More informationDescribing distributions with numbers
Describing distributions with numbers A large number or numerical methods are available for describing quantitative data sets. Most of these methods measure one of two data characteristics: The central
More informationLiang Li, PhD. MD Anderson
Liang Li, PhD Biostatistics @ MD Anderson Behavioral Science Workshop, October 13, 2014 The Multiphase Optimization Strategy (MOST) An increasingly popular research strategy to develop behavioral interventions
More informationSample size re-estimation in clinical trials. Dealing with those unknowns. Chris Jennison. University of Kyoto, January 2018
Sample Size Re-estimation in Clinical Trials: Dealing with those unknowns Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj University of Kyoto,
More informationChapter 2: Describing Contingency Tables - I
: Describing Contingency Tables - I Dipankar Bandyopadhyay Department of Biostatistics, Virginia Commonwealth University BIOS 625: Categorical Data & GLM [Acknowledgements to Tim Hanson and Haitao Chu]
More information