Confidence intervals Kristin Tolksdorf (based on previous EPIET material) 18th EPIET/EUPHEM Introductory course 01.10.2012 1.

Slides:



Advertisements
Similar presentations
You have been given a mission and a code. Use the code to complete the mission and you will save the world from obliteration…
Advertisements

Introductory Mathematics & Statistics for Business
Chapter 1 The Study of Body Function Image PowerPoint
STATISTICS HYPOTHESES TEST (I)
STATISTICS INTERVAL ESTIMATION Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University.
Statistical vs Clinical or Practical Significance
Significance testing Ioannis Karagiannis (based on previous EPIET material) 18 th EPIET/EUPHEM Introductory course
Significance testing and confidence intervals Ágnes Hajdu EPIET Introductory course
Sample size calculation
Critical review of significance testing F.DAncona from a Alain Morens lecture 2006.
1 Matching EPIET introductory course Mahón, 2011.
Statistical inference Ian Jolliffe University of Aberdeen CLIPS module 3.4b.
Statistical Significance and Population Controls Presented to the New Jersey SDC Annual Network Meeting June 6, 2007 Tony Tersine, U.S. Census Bureau.
Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13
Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13
Copyright © 2010 Pearson Education, Inc. Slide
Lecture 2 ANALYSIS OF VARIANCE: AN INTRODUCTION
STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS
1 From the analytical uncertainty to uncertainty in data interpretation D. Concordet, J.P. Braun
Chapter 7 Sampling and Sampling Distributions
The basics for simulations
You will need Your text Your calculator
Elementary Statistics
The t-distribution William Gosset lived from 1876 to 1937 Gosset invented the t -test to handle small samples for quality control in brewing. He wrote.
6. Statistical Inference: Example: Anorexia study Weight measured before and after period of treatment y i = weight at end – weight at beginning For n=17.
PP Test Review Sections 6-1 to 6-6
Contingency Tables Prepared by Yu-Fen Li.
Biostatistics Unit 10 Categorical Data Analysis 1.
1 Slides revised The overwhelming majority of samples of n from a population of N can stand-in for the population.
VOORBLAD.
II. Potential Errors In Epidemiologic Studies Random Error Dr. Sherine Shawky.
Confidence Intervals Objectives: Students should know how to calculate a standard error, given a sample mean, standard deviation, and sample size Students.
Hypothesis Tests: Two Independent Samples
Chapter 4 Inference About Process Quality
Comparing Two Groups’ Means or Proportions: Independent Samples t-tests.
Copyright © 2012, Elsevier Inc. All rights Reserved. 1 Chapter 7 Modeling Structure with Blocks.
Hours Listening To Music In A Week! David Burgueño, Nestor Garcia, Rodrigo Martinez.
© 2012 National Heart Foundation of Australia. Slide 2.
Statistical Analysis SC504/HS927 Spring Term 2008
Understanding Generalist Practice, 5e, Kirst-Ashman/Hull
Module 17: Two-Sample t-tests, with equal variances for the two populations This module describes one of the most utilized statistical tests, the.
Before Between After.
25 seconds left…...
Slippery Slope
Putting Statistics to Work
Statistical Inferences Based on Two Samples
Evaluation of precision and accuracy of a measurement
We will resume in: 25 Minutes.
©Brooks/Cole, 2001 Chapter 12 Derived Types-- Enumerated, Structure and Union.
Essential Cell Biology
Chapter Thirteen The One-Way Analysis of Variance.
Ch 14 實習(2).
Chapter 8 Estimation Understandable Statistics Ninth Edition
PSSA Preparation.
CHAPTER 14: Confidence Intervals: The Basics
Multiple Regression and Model Building
January Structure of the book Section 1 (Ch 1 – 10) Basic concepts and techniques Section 2 (Ch 11 – 15): Inference for quantitative outcomes Section.
Unit 4 – Inference from Data: Principles
What is the experimental unit in premix bioequivalence ? June 2010 Didier Concordet
Chapter 8 Estimating with Confidence
Thomas Songer, PhD with acknowledgment to several slides provided by M Rahbar and Moataza Mahmoud Abdel Wahab Introduction to Research Methods In the Internet.
Evidence-Based Medicine 3 More Knowledge and Skills for Critical Reading Karen E. Schetzina, MD, MPH.
Instructor Resource Chapter 5 Copyright © Scott B. Patten, Permission granted for classroom use with Epidemiology for Canadian Students: Principles,
Significance testing and confidence intervals Col Naila Azam.
Issues concerning the interpretation of statistical significance tests.
Measures of association Tunisia, 29th October 2014
Significance testing and confidence intervals
Significance testing Introduction to Intervention Epidemiology
Presentation transcript:

Confidence intervals Kristin Tolksdorf (based on previous EPIET material) 18th EPIET/EUPHEM Introductory course 01.10.2012 1

Inferential statistics Uses patterns in the sample data to draw inferences about the population represented, accounting for randomness. Two basic approaches: Hypothesis testing Estimation

Criticism on significance testing “Epidemiological application need more than a decision as to whether chance alone could have produced association.” (Rothman et al. 2008) → Estimation of an effect measure (e.g. RR, OR) rather than significance testing. → Estimation of a mean → Estimation of a proportion

Why estimation? Norovirus outbreak on a Greek island: “The risk of illness was higher among people who ate raw seafood (RR=21.5).” How confident can we be in the result? What is the precision of our point estimate?

The epidemiologist needs measurements rather than probabilities 2 is a test of association OR, RR are measures of association on a continuous scale infinite number of possible values The best estimate = point estimate Range of “most plausible” values, given the sample data Confidence interval  precision of the point estimate

Confidence interval (CI) Range of values, on the basis of the sample data, in which the population value (or true value) may lie. Frequently used formulation: „If the data collection and analysis could be replicated many times, the CI should include the true value of the measure 95% of the time .”

Indicates the amount of random error in the estimate Confidence interval (CI) α/2 Lower limit upper limit of 95% CI of 95% CI a = 5% s 1 - α 95% CI = x – 1.96 SE up to x + 1.96 SE Indicates the amount of random error in the estimate Can be calculated for any „test statistic“, e.g.: means, proportions, ORs, RRs

CI terminology RR = 1.45 (0.99 – 2.13) Point estimate Confidence interval RR = 1.45 (0.99 – 2.13) Lower confidence limit Upper confidence limit

Width of confidence interval depends on … amount of variability in the data size of the sample level of confidence (usually 90%, 95%, 99%) A common way to use CI regarding OR/RR is : If 1.0 is included in CI  non significant If 1.0 is not included in CI  significant

Looking at the CI RR = 1 A B Large RR Study A, large sample, precise results, narrow CI – SIGNIFICANT Study B, small size, large CI - NON SIGNIFICANT Study A, effect close to NO EFFECT Study B, no information about absence of large effect

More studies are better or worse? 1 RR  20 studies with different results... clinical or biological significance ?

Norovirus on a Greek island How confident can we be in the result? Relative risk = 21.5 (point estimate) 95% CI for the relative risk: (8.9 - 51.8) The probability that the CI from 8.9 to 51.8 includes the true relative risk is 95%.

Norovirus on a Greek island “The risk of illness was higher among people who ate raw seafood (RR=21.5, 95% CI 8.9 to 51.8).”

Example: Chlordiazopoxide use and congenital heart disease (n=1 644) Cases Controls C use 4 No C use 386 1 250 OR = (4 x 1250) / (4 x 386) = 3.2 p = 0.080 ; 95% CI = 0.6 - 17.5 From Rothman K

3.2 p=0.080 0.6 – 17.5

Example: Chlordiazopoxide use and congenital heart disease – large study (n=17 151) Cases Controls C use 240 211 No C use 7 900 8 800 OR = (240 x 8800) / (211 x 7900) = 1.3 p = 0.013 ; 95% CI = 1.1 - 1.5

Precision and strength of association

Confidence interval provides more information than p value Magnitude of the effect (strength of association) Direction of the effect (RR > or < 1) Precision of the point estimate of the effect (variability) p value can not provide them !

What we have to evaluate the study 2 Test of association, depends on sample size p value Probability that equal (or more extreme) results can be observed by chance alone OR, RR Direction & strength of association if > 1 risk factor if < 1 protective factor (independently from sample size) CI Magnitude and precision of effect

Comments on p-values and CIs Presence of significance does not prove clinical or biological relevance of an effect. A lack of significance is not necessarily a lack of an effect: “Absence of evidence is not evidence of absence”.

Comments on p-values and CIs A huge effect in a small sample or a small effect in a large sample can result in identical p values. A statistical test will always give a significant result if the sample is big enough. p values and CIs do not provide any information on the possibility that the observed association is due to bias or confounding.

2 and Relative Risk E 9 51 60 p = 0.13 NE 5 55 60 RR = 1.8 Cases Non-cases Total 2 = 1.3 E 9 51 60 p = 0.13 NE 5 55 60 RR = 1.8 Total 14 106 120 95% CI [ 0.6 - 4.9 ] Cases Non-cases Total 2 = 12 E 90 510 600 p = 0.0002 NE 50 550 600 RR = 1.8 Total 140 1060 1200 95% CI [ 1.3-2.5 ]

Common source outbreak suspected Exposure Cases Non-cases AR% Yes 15 20 42.8% No 50 200 20.0% Total 65 220 2 = 9.1 p = 0.002 RR = 2.1 95%CI = 1.4 - 3.4 23% REMEMBER: These values do not provide any information on the possibility that the observed association is due to a bias or confounding.

The ultimative (eye) test Hypothesis testing: X²-Test Question: Is the proportion of facilitators wearing glasses equal to the proportion of fellows wearing glasses? Estimation of quantities: Proportion What is the proportion of fellows/facilitators wearing glasses?

The ultimative (eye) test Glasses among fellows : Yes 11 No 27 Total 38 Glasses among facilitators : Yes 6 No 8 Total 14 Proportion = 11/38 = 0.29 SE = 0.074 95%CI = 0.14 - 0.44 Proportion = 6/14 = 0.43 SE = 0.132 95%CI = 0.17 - 0.69

Recommendations Always look at the raw data (2x2-table). How many cases can be explained by the exposure? Interpret with caution associations that achieve statistical significance. Double caution if this statistical significance is not expected. Use confidence intervals to describe your results.

Suggested reading KJ Rothman, S Greenland, TL Lash, Modern Epidemiology, Lippincott Williams & Wilkins, Philadelphia, PA, 2008 SN Goodman, R Royall, Evidence and Scientific Research, AJPH 78, 1568, 1988 SN Goodman, Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy, Ann Intern Med. 130, 995, 1999 C Poole, Low P-Values or Narrow Confidence Intervals: Which are more Durable? Epidemiology 12, 291, 2001

Previous lecturers Alain Moren Paolo D’Ancona Lisa King Preben Aavitsland Doris Radun Manuel Dehnert Ágnes Hajdu