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

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Inferential statistics Uses patterns in the sample data to draw inferences about the population represented, accounting for randomness. Two basic approaches: – Hypothesis testing – Estimation 2

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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 3

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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? 4

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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 5

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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. 6

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α/2 Lower limit upper limit of 95% CI = 5% s α/2 Confidence interval (CI) Indicates the amount of random error in the estimate Can be calculated for any test statistic, e.g.: means, proportions, ORs, RRs 95% CI = x – 1.96 SE up to x SE 1 - α 7

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CI terminology RR = 1.45 (0.99 – 2.13) Confidence intervalPoint estimate Lower confidence limit Upper confidence limit 8

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amount of variability in the data size of the sample level of confidence (usually 90%, 95%, 99%) Width of confidence interval depends on … 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 9

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Study A, large sample, precise results, narrow CI – SIGNIFICANT Study B, small size, large CI - NON SIGNIFICANT Looking at the CI Study A, effect close to NO EFFECT Study B, no information about absence of large effect RR = 1 A B Large RR 10

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

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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: ( ) The probability that the CI from 8.9 to 51.8 includes the true relative risk is 95%. 12

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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). 13

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Example: Chlordiazopoxide use and congenital heart disease (n=1 644) CasesControls C use44 No C use OR = (4 x 1250) / (4 x 386) = 3.2 p = ; 95% CI = From Rothman K

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3.2 p= –

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Example: Chlordiazopoxide use and congenital heart disease – large study (n=17 151) CasesControls C use No C use OR = (240 x 8800) / (211 x 7900) = 1.3 p = ; 95% CI =

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Precision and strength of association Strength Precision 17

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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 ! 18

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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 > 1risk factor if < 1protective factor (independently from sample size) CI Magnitude and precision of effect What we have to evaluate the study 19

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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. 20

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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. 21

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Cases Non-casesTotal 2 = 1.3 E p = 0.13 NE RR = 1.8 Total % CI [ ] Cases Non-casesTotal 2 = 12 E p = NE RR = 1.8 Total % CI [ ] 2 and Relative Risk 22

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Exposure Cases Non-casesAR% Yes % No % Total65220 Common source outbreak suspected REMEMBER: These values do not provide any information on the possibility that the observed association is due to a bias or confounding. 2 = 9.1 p = RR= %CI = % 23

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The ultimative (eye) test 24 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?

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The ultimative (eye) test 25 Proportion = 11/38 = 0.29 SE = %CI = Glasses among fellows : Yes11 No27 Total38 Glasses among facilitators : Yes6 No8 Total14 Proportion = 6/14 = 0.43 SE = %CI =

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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. 26

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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,

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Previous lecturers Alain Moren Paolo DAncona Lisa King Preben Aavitsland Doris Radun Manuel Dehnert Ágnes Hajdu 28

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