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Epidemiology Kept Simple. Chapter 7 Rate Adjustment. Goal. To reduce distortions and incomparability of rates when making comparison over time and among populations To encourage “like-to-like” comparisons. Illustrative Example Table 7.2 (p. 144).

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## Epidemiology Kept Simple

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**Epidemiology Kept Simple**Chapter 7 Rate Adjustment**Goal**To reduce distortions and incomparability of rates when making comparison over time and among populations To encourage “like-to-like” comparisons**Illustrative ExampleTable 7.2 (p. 144)**Rate in Population B is 9× that of Population A**Illustrative Example (cont.) Table 7.2 (p. 144)**Within young, rates are identical**Illustrative Example (cont.)Table 7.2 (p. 144)**Within old, rates are identical**Why the apparent paradox?**Pop. A mostly old, Pop. B mostly young**Confounding**• Explanatory factor (population) associated with age • Extraneous factor (age) associated with disease rate • Age confounds relation between explanatory factor and disease rate • Biased comparison confounder Age Population Rate explanatory factor disease**Strata-specific comparisons**You’re OK as long as you compare like-to-like**We can also adjust overall rate to compensate for**confounding • Rate adjustment methods • Direct adjustment • Indirect adjustment • Other statistical method of adjustment • Mantel-Haenszel methods • Regression model**Terminology**• “Rate” – any incidence or prevalence (economy of language) • Crude rate – rate for entire population • Strata-specific rate - rate within subgroup • Adjusted rate – overall rate compensated for extraneous factor • Two methods of adjustment • Direct • Indirect**§7.2 Direct Age-Adjustment**• Study population – the population rate you want to adjust • Reference population - external population used as age norm, • Reference population may be • arbitrary • age distribution of some place at some time (“standard million”)**General Idea, Direct Adjustment**• Apply strata-specific rates from study to a standard age age distribution • Adjusted rate is a weighted average of strata-specific rates (with weights from reference population)**Method**where Ni = population size, reference population, strata i ri = rate, study population, strata I Note: caps denote reference pop. values, while lower case denotes study pop. values**Florida & Alaska Mortality Example (pp. 146 – 147)**• Crude rates (per 100,000) • cRFlorida = 1026 • cRAlaska = 387 • See TABLE 7.5 for raw data**Comparing Adjusted Rates**• Direct adjustment of Florida mortality rate using same standard million (Table 7.8, p. 147) derives aRFlorida = 784 • Recall, aRAlaska = 843 • Conclude: slight advantage goes to Florida**The section on indirect adjustment (§7.3) may or may not be**covered**§7.3 Indirect Age-Adjustment**• Same goal as direct adjustment • Based on multiplying crude rate by Standardized Mortality Ratio (SMR) whereA = observed number of cases in study population = the expected number of cases (next slide)**Expected Number of Cases ()**where Ri = rate, reference population, strata i ni = population size, study population, strata i Recall: caps denote reference pop. values and lower case denote study pop. values This is number of cases expected in study population if it had reference population’s rates**Zimbabwe SMR**• Observed 98,808 deaths in Zimbabwe • Expected 36,381 (based on US rate) • SMR = 98,808 / 36,381 = 2.72 • Interpretation: Zimbabwe mortality rate is 2.72× that of US after adjusting for age**Indirectly Adjusted Rate**• Zimbabwe crude rate = 886 (per 100,000) • aRindirect = (886)(2.72) = 2340 • c.f. to US rate of 860**§7.4 Adjustment for Multiple Factors**• Any extraneous factor can be adjusted for • Mortality rates are often adjusted for year, age, and sex • Principles of adjusting for potential confounders apply to more advanced study

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