Epidemiological Research Methods Formula Sheet

FORMULAS FROM EPIDEMIOLOGY KEPT SIMPLE (3e) Chapter 3: Epidemiologic Measures Basic epidemiologic measures used to quantify: • • • frequency of occurrence the effect of an exposure the potential impact of an intervention. Epidemiologic Measures Measures of disease frequency Incidence Incidence proportion (Cumulative Incidence, Incidence Incidence odds Prevalence Incidence rate (incidence density, hazard rate, person- Measures of association Measures of potential impact (“Measures of Effect”) Absolute measures of effect Relative measures of effect Attributable Fraction in exposed cases Risk difference (Incidence proportion difference) Risk Ratio (Incidence Proportion Ratio) Rate Difference (Incidence density difference) Rate Ratio (Incidence density ratio) Prevalence Difference Odds Ratio Attributable Fraction in the Population 3.1 Measures of Disease Frequency Incidence Proportion = No. of onsets No. at risk at beginning of follow-up • Also called risk, average risk, and cumulative incidence. • Can be measured in cohorts (closed populations) only. • Requires follow-up of individuals. Incidence Rate = No. of onsets ∑ person-time • Also called incidence density and average hazard. • When disease is rare (incidence proportion < 5%), incidence rate ≈ incidence proportion. • In cohorts (closed populations), it is best to sum individual person-time longitudinally. It can also be estimated as Σperson-time ≈ (average population size) × (duration of follow-up). Actuarial adjustments may be needed when the disease outcome is not rare. • In an open populations, Σperson-time ≈ (average population size) × (duration of follow-up). Examples of incidence rates in open populations include: Crude birth rate (per m) = births mid-year population size Crude mortality rate (per m) = Infant mortality rate (per m) = Prevalence Proportion = ×m deaths mid-year population size deaths < 1 year of age live births ×m ×m No. of cases No. of individuals in the study • Also called point prevalence or just prevalence. • The concept of period prevalence should be avoided when possible because it confuses the concepts of incidence and prevalence (Elandt-Johnson & Johnson, 1980). • Prevalence dependence on the “inflow” and “outflow” of disease according to this formula Prevalence ≈ (incidence rate) × (average duration of illness). Additional Notes • Terminology: The term “rate” is often used loosely, to refer to any of the above measures of disease frequency (even though the only true rate is the incidence density rate • Odds: Both prevalence and incidence proportions may be addressed in terms of odds. Let p represent the incidence proportion or prevalence proportion of disease and o represent the odds of disease. Thus, odds o = p / (1 – p). Reporting: To report a risk or rate “per m,” simply multiply it by m. For example, an incidence proportion of 0.0010 = 0.0010 × 10,000 = 10 per 10,000. • • Uni-cohort: To report a risk or rate as a unicohort, take its reciprocal and report it as 1 in “unicohort.” For example, an incidence proportion of 0.0025 = 1 in 1 0.0025 or “1 in 400.” 3.2 Measures of Association (Measures of Effect) Notation and terminology: Concepts apply to incidence proportions, incidence rates, and prevalence proportions, all of which will be loosely called “rates.” Let R1 represent the rate or risk of disease in the exposed group and let R0 represent the rate or risk of disease in the non-exposed group. Absolute Measure of Effect (Rate Difference) RD= R−1 R 0 Relative Measure of Effect (Rate Ratio) R1 R0 RR= The relative effect of an exposure can also captured by the SMR (see section on Rate Adjustment) 2-by-2 Cross-Tabulation D+ A1 A0 M1 E+ (Group 1) E− (Group 0) D− B1 B0 M0 Total N1 N0 N • For person-time data (incidence rates/densities) ignore cells B1 and B0 and let N1 and N0 represent the person-time in group 1 and group 0, respectively. • Rates, Rate Ratio, and Rate Difference: R1 = A1 N1 , R0 = A0 N0 , RR = A1 / N1 A0 / N0 , and RD= A ( 1 /N 1 )− (A 0 /N 0 ) (cohort and cross-sectional data) • • A1 B0 (independent samples only; for matched-pairs and tuples data, see text) A0 B1 Rounding: Basic measures should be reported with 2 or 3 significant digit accuracy. Carry 4 or 5 significant digits to derive a final answer that is accurate to 2 or 3 significant digits, respectively. Odds ratio: OR = 3.3 Measures of Potential Impact • The attributable fraction in exposed cases • The attributable fraction in the population Equivalent,"AFp= AFe× p c AFe = R1 − R0 R1 R − R0 , or equivalently, AFe = RR − 1 RR ."" "" R where pc represents proportion of population cases that are exposed AFp = 3.4 Rate Adjustment (“Standardization”) For uniformity of language, the term rate will be used to refer to any incidence or prevalence measure. Direct Standardization The directly adjusted rate (aRdirect) is a weighted average of strata-specific rates with weights derived from a reference population: aR where wi = direct = ∑w r i i Ni ∑ Ni Ni represents the size of strata i of the reference population ri represents rate in strata i of the study population. Note that capital letters denote values that come from the reference population and lower case letters denote values the come from the study population. Indirect Standardization Indirect standardization is based on the Standardized Mortality Ratio (SMR) SMR= Observed Expected where “Observed” is the observed number of cases and “Expected” is the expected number of cases in the population based on this formula: Expected = Rini where Ri represents the rate in strata i of the reference population ∑ and ni represents the number of people strata i of the study population. The Expected in the population can be understood in terms of the expected number of cases within strata i, which is: Expected i = R ni i . Thus: Expected = Expectedi . ∑ The SMR is a population-based relative risk estimate in which “1” represents a population in which the observed rate equals the expected rate. Optional: Use the SMR to derive the indirectly adjusted rate via this formula: aRindirect = (crude rate)× SMR Chapter 10: Screening for Disease Reproducibility (Agreement) Rater B Rater A pobs = a +d N + − + a b g1 − c d g2 f1 f2 N pexp = f1 g1 +f g2 N2 κ= 2 pobs − pexp 1 − pexp Validity (Sensitivity, Specificity, PVPT, PVNT) Disease + Disease − Test + TP FP Test − FN TN TP + FN FP + TN (those with disease) (those w/out disease) Total SEN = (TP) / (those with disease) = (TP) / (TP + FN) TP + FP (those who test positive) FN + TN (those who test negative) N [note: TP = (SEN)(TP + FN)] SPEC = (TN) / (those without disease) = (TN) / (TN + FP) PVP Total [note: TN = (SPEC)(FP + TN)] = (TP) / (those who test positive) = (TP) / (TP + FP) PVN = (TN) / (those who test negative) = (TN) / (TN + FN) True prevalence = (TP + FN) / N [also known as “prior probability”] Bayesian equivalents for PVP and PVN are presented in the text.