Incidence Conditional Survival Proportion Cumulative Survival Proportion K t k A k N k CI k S k ・ Cumulative survival proportion over the whole time interval is the product of the conditional survival proportions for every subinterval t k-1 to t k . ・ Censored observations have the same probability of the event after censoring as those remaining under observation.
[Measure of Association] Incidence Rate (IR) Incidence Rate Ratio (IRR) IR E − ¿ IR E + ¿ ¿ IRR = ¿ Range: 0 to ∞ No association: 1 ・ (IRR-1)*100% greater rate of outcome among subjects exposed to exposure. ・ A rate of outcome among exposed subjects is IRR times higher than that of rate among unexposed subjects. Incidence Rate Difference (IRD) E − ¿ E + ¿ − IE ¿ IRD = IR ¿ synonym: attributable rate Range: −∞ to ∞ This difference reflects the rate of outcome among exposed subjects that can be attributed to the exposure. Cumulative Incidence (CI) Cumulative Incidence Ratio (CIR) CI E − ¿ = Pr [ Y = 1 ∨ A = 1 ] Pr [ Y = 1 ∨ A = 0 ] CI E + ¿ ¿ CIR = ¿ Range: 0 to ∞ No association: 1 Study participants who were Exposed have AA times the CI of Outcome compared to participants who were unexposed over the study periods. Cumulative Incidence Difference (CID) E − ¿ E + ¿ − CI ¿ CID = CI ¿ Synonym: attributable risk Range: -1 to +1 No association: 0 NNT = 1/CID Odds Ratio Pr [ A = 1 | A = 1 ] / Pr [ Y = 0 ∨ A = 1 ] Pr [ Y = 1 | A = 0 ] / Pr [ Y = 0 ∨ A = 0 ] Range: 0 to ∞ No association: 1 The odds of A = 1 is OR times that of those that do not have A.
[Attributable Fraction] Attributable risk percent (AR%) CI E + ¿ × 100 E + ¿ − CI E − ¿ ¿ CI ¿ AR = ¿ Proportion of disease burden among the exposed caused by exposure Population attributable risk percent CI Total − CI E − ¿ CI Total = AR × Pr [ A = 1 ∨ Y = 1 ] ¿ Proportion of disease burden among total population by exposure
DAG [The association & Causation] The association flows regardless of the direction of the allows The causation flows the direction of the allow (left to right) [Confounder] Definition of a confounder is: ・ Associated with the exposure (A) in the study base that produce the case ・ Associated with the outcome (Y) in the non-exposed ・ Is not a downstream consequence of exposure or outcome [Collider] ・ A common effect ・ Depicted as two arrows intersecting at a variable ・ Blocks the flow of association [Systematic bias] ・ A structural association between exposure and outcome that does not arise from the causal effect ・ Assume the average causal null hypothesis ・ Incorrect estimate of the effect, if a causal effect ・ Biased estimates are not valid [Mediator] ・ No confounding, no backdoor path [Conditioning] ・ A common cause: blocks the flow of association ・ A common effect: opens the flow of association ・ A consequence of a common effect: opens the flow of association ・ A Mediator: Blocks the flow of association [Control for Confounding] ・ Randomization: known & unknown confounders ・ Restriction, matching: known confounders only ・ IP weighting/ standardization: known confounders only ・ Stratification: known confounders only [Selection bias] ・ Can occur in any types of study (observational & randomized study) ・ By conditioning on the common effect of the exposure and the outcome
[Confounding] ・ Definition: − Presence of common causes or lack of exchangeability ・ There is confounding when −
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- Fall '18