2 Inferential statistics Uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.Two basic approaches:Hypothesis testingEstimation
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 associationOR, RR are measures of association on a continuous scaleinfinite number of possible valuesThe best estimate = point estimateRange of “most plausible” values, given the sample dataConfidence 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 measure 95% of the time .”
7 Indicates the amount of random error in the estimate Confidence interval (CI)α/2Lower limit upper limitof 95% CI of 95% CIa = 5%s1 - α95% CI = x – 1.96 SE up to x SEIndicates the amount of random error in the estimateCan be calculated for any „test statistic“, e.g.: means, proportions, ORs, RRs
9 Width of confidence interval depends on … amount of variability in the datasize of the samplelevel of confidence (usually 90%, 95%, 99%)A common way to use CI regarding OR/RR is :If 1.0 is included in CI non significantIf 1.0 is not included in CI significant
10 Looking at the CIRR = 1ABLarge RRStudy A, large sample, precise results, narrow CI – SIGNIFICANTStudy B, small size, large CI - NON SIGNIFICANTStudy A, effect close to NO EFFECTStudy B, no information about absence of large effect
11 More studies are better or worse? 1RR20 studies with different results...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:( )The probability that the CI from 8.9 to 51.8includes 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) CasesControlsC use4No C use3861 250OR = (4 x 1250) / (4 x 386) = 3.2p = ; 95% CI =From Rothman K
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 Test of association, depends on sample sizep value Probability that equal (or more extreme) results can be observed by chance aloneOR, RR Direction & 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 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.
22 2 and Relative Risk E 9 51 60 p = 0.13 NE 5 55 60 RR = 1.8 Cases Non-cases Total 2 = 1.3E p = 0.13NE RR = 1.8Total % CI [ ]Cases Non-cases Total 2 = 12E p =NE RR = 1.8Total % CI [ ]
23 Common source outbreak suspected Exposure Cases Non-cases AR%Yes %No %Total2 = 9.1p = 0.002RR = 2.195%CI =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-TestQuestion: Is the proportion of facilitators wearing glasses equal to the proportion of fellows wearing glasses?Estimation of quantities: ProportionWhat is the proportion of fellows/facilitators wearing glasses?
26 RecommendationsAlways 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 readingKJ Rothman, S Greenland, TL Lash, Modern Epidemiology, Lippincott Williams & Wilkins, Philadelphia, PA, 2008SN Goodman, R Royall, Evidence and Scientific Research, AJPH 78, 1568, 1988SN Goodman, Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy, Ann Intern Med. 130, 995, 1999C 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 AavitslandDoris RadunManuel DehnertÁgnes Hajdu