EPI 202 Summary.docx - EPI 202 Summary[p-value the probability that a result as extreme or more extreme than the one we observed would occur due to

EPI 202 Summary.docx - EPI 202 Summary[p-value the...

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EPI 202 Summary [p-value] the probability that a result as extreme or more extreme than the one we observed would occur due to random variation, if the null hypothesis were true A small p-value: It is unlikely that the observed data would have been obtained if the null hypothesis were true We may conclude that the data are not very compatible with the state of nature specified by the null Decide to reject the null hypothesis in a testing framework [Null hypothesis and Alternate Hypothesis] H 0 : p 1 is not different from p 0 versus H A : p 1 is different from p 0 [Limitation of hypothesis test] No information on direction or magnitude No information about the range of effects that are consistent with the observed data No information on the power of the study (Reject the null hypothesis if the null hypothesis is false) No information on the consistency of the data with alternative, non-null states of nature [Confidence Intervals] Narrow confidence intervals = Powerful study  Wide confidence intervals = Weak study 100(1-α)% of CI does ot include the null value of X, we can usually reject the null hypothesis The null value for difference measure of association: 0 The null value for ratio measures of association: 1 [Random Variability in Observational Studies] Exposure is not randomly assigned => Additional assumptions are needed Cohort Study: the source population = the unexposed group A full census of exposed individuals from the source population or a random sample of these individuals Case-control study:
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Sample the study base to obtain the controls The cases are either a full census of all cases produced by this study base or a sample of these cases After all known confounders are adjusted, the data can be regarded as a random sample of the conditional relation
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[Person-Time Data] H 0 : There is no association between exposure and outcome. (I 1 =I 0  I 1 -I 0 = 0  I 1 /I 0 = 1  ln(I 1 /I 0 ) = 0) Ha: There is an association between exposure and outcome. (I 1 ≠I 0  I 1 -I 0 ≠0  I 1 /I 0 ≠1  ln(I 1 /I 0 )≠0) The hypothesis test statistic IRD IRR E ´ E Cases a b M1 Person- Time N 1 N 0 T X = ^ IRD = a N 1 b N 0 E ( X | H 0 ) = E ( ^ IRD | H 0 ) = 0, ^ Var ( IRD ) = a N 1 2 + b N 0 2 ^ IRR = a N 1 / b N 0 Let X = ln ( ^ IRR ) ^ Var ( X ) = ^ Var ( ln ( ^ IRR ) ) = 1 a + 1 b Z 2 = [ X E ( X | H 0 ) ] 2 Var ( X | H 0 ) x 1 2 X = a E ( X | H 0 ) = M 1 ×N 1 / T ^ Var ( X | H 0 ) = M 1 N 1 N 0 T 2 Pr [ x 2 > ] < 0.05 95% Confidence Interval: X ± 1.96 ^ Var ( X ) 95% CI for ln(IRR) X ± 1.96 ^ Var ( X ) 95% CI for IRR: e X ± 1.96 ^ Var ( X ) We reject the null hypothesis at the 0.05 level of significance. We conclude that there is statistically significant evidence for an association between exposure and outcome in this data at the level 0.05 of significance, assuming no confounding, no information bias, and These data are consistent with IRD/IRR ranging from A to B with 95% confidence.
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