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Confidence intervals

Confidence intervals. Kristin Tolksdorf (based on previous EPIET material) 18 th EPIET /EUPHEM Introductory course 01 . 10 .201 2. Inferential statistics. Uses patterns in the sample data to draw inferences about the population represented, accounting for randomness .

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Confidence intervals

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

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

  3. 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

  4. 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?

  5. 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

  6. 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 measure95% of the time.”

  7. Confidenceinterval (CI) a = 5% 1 - α α/2 α/2 s Lower limit upper limit of 95% CI of 95% CI 95% CI = x – 1.96 SEuptox + 1.96 SE Indicates the amount of random error in the estimate Can becalculatedforany „teststatistic“, e.g.: means, proportions,ORs, RRs

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

  9. 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

  10. A B Large RR RR = 1 Looking at the CI 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

  11. 1 RR  20 studies with different results... More studies are better or worse? clinical or biological significance ?

  12. 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 8.9to 51.8 includes the true relative risk is 95%.

  13. 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).”

  14. Example: Chlordiazopoxide use and congenital heart disease (n=1 644) OR = (4 x 1250) / (4 x 386) = 3.2 p = 0.080 ; 95% CI=0.6 - 17.5 From Rothman K

  15. 3.2 p=0.080 0.6 – 17.5

  16. Example: Chlordiazopoxide use and congenital heart disease – large study (n=17 151) OR = (240 x 8800) / (211 x 7900) = 1.3 p = 0.013 ; 95% CI=1.1 -1.5

  17. Precision and strength of association Strength Precision

  18. 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 !

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

  20. 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”.

  21. 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 pvalues. • 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.

  22. 2 and Relative Risk 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 ]

  23. 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.

  24. 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?

  25. 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

  26. 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.

  27. 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

  28. Previous lecturers • Alain Moren • Paolo D’Ancona • Lisa King • Preben Aavitsland • Doris Radun • Manuel Dehnert • ÁgnesHajdu

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