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For one, "5 years" will remain accurate indefinitely, whereas "twice" (or "100% more") are accurate only this year. For another, human growth and aging, at least from a societal point of view and perhaps from a biological point of view as well, are processes which are marked by absolute increases, not relative ones. For example, we generally think of school entrance and graduation, puberty, eligibility for a drivers' license, presbyopia, and retirement in terms of specific age ranges, not proportional increases. We say "in 15 years you will probably need bifocals", rather than "when your age is 50% greater". In contrast, when adjusting a recipe for a larger or smaller number of guests, we multiply or divide the amounts of each ingredient by a common factor, rather than subtract a common amount from each one. For scaling a recipe, we are interested in proportionate (relative) increases. Similarly, when we quantify the comparison of two incidences (or two prevalences), we can take the absolute difference (incidence difference) or the relative difference (excess risk). Which one, absolute or relative, is of greater interest to us in quantifying the comparison of two measures of occurrence or extent? This question has inspired no small amount of debate in the early days of modern epidemiology (ca. 1955) and, as so often happens, a case can be made for both approaches. The choice depends on our objective, our concept of the phenomena, and the availability of data. One problem with using the absolute difference (variously called "risk difference", "rate difference", "cumulative incidence difference", "incidence density difference", "attributable risk" - according to fashion, the group of epidemiologists with which the epidemiologist wishes to identify him/herself, the decade in which she/he learned epidemiology, or whether the comparison involves incidence rates, incidence proportions, prevalences, or mortality rates) as a measure of strength of association is that if the incidences themselves are small, as will always be the case for a rare disease, then the difference must also be small. For example, if the annual mortality rate for a rare disease such as esophageal cancer is 60/100,000 in persons with low vitamin C intake and 20/100,000 in persons with high vitamin C intake, the difference is only 40/100,000. In contrast, the difference for an association involving a more common disease, such as vitamin E and CHD, might be 1,200/100,000 for low vitamin E intake and 800/100,000 for high vitamin E intake = 400/100,000, an order of magnitude greater. The much greater size of the second difference indicates that if these two vitamins are causal factors many more lives could be saved from increasing vitamin E intake than from increasing vitamin C intake. Vitamin E appears to have a greater public health impact. But is it logical to conclude from the greater difference for vitamin E that its association with CHD is stronger than vitamin C's with esophageal cancer? First, if we did draw that conclusion it would imply that nearly any association involving a common disease must be stronger than all associations involving very rare diseases. Second, since the actual incidence of most conditions varies by all sorts of factors (age, gender, economic resources, smoking, alcohol intake, physical activity, diet, genetics, cofactors), the absolute difference is very likely to vary, possibly greatly, across populations (however, the relative difference may also vary). In contrast, expressing the incidence differences relative to the size of the actual incidences produces measures of association that appear to be comparable. Thus we can compute a relative difference in incidence of esophageal cancer mortality in relation to vitamin C as (I1 - I0)/I0 = (0.00060- 0.00020)/0.00020 = 2.0 and a relative difference for CHD mortality in relation to vitamin E as _____________________________________________________________________________________________ www.epidemiolog.net, © Victor J. Schoenbach 2000 7. Relating risk factors to health - 166 rev. 7/25/1999, 9/4/1999, 12/22/1999, 10/2/2000, 10/9/2000, 5/8/2001
(I1 - I0)/I0 = (0.01200-0.00800 / 0.00800) = 0.50. On this basis, the association involving vitamin C is substantially greater than that involving vitamin E. This relative difference measure is often called the excess risk (or "excess rate", since the data are rates, not proportions). If we add 1.0 to the excess risk or rate, we obtain an even simpler relative measure, I1/I0, which is variously termed relative risk, risk ratio, rate ratio, cumulative incidence ratio, incidence density ratio, or, for prevalences, prevalence ratio. Here are two real-life examples that contrast relative and absolute measures of association. The first is based on data from a follow-up study by Mann et al. (presented in a seminar at UNC by Bruce Stadel): Relative versus Absolute Measures of Association Incidence of myocardial infarction (MI) in oral contraceptive (OC) users per 100,000 women-years Age (years) Cigarettes/day Oral contraceptive users Non-users RR** AR*** 30-39 0-14 6 2 3 4 15 + 30 11 3 19 40-44 0-14 47 12 4 35 Notes: 15 + 246 61 4 185 * RR=relative risk (rate ratio) ** AR=attributable risk (rate difference, absolute difference) In this table, the incidence of MI is clearly greater for OC users, since in each age-smoking stratum the OC users have a higher incidence (ID) than do the nonusers. Moreover, the ratio of the two incidences (the RR) is nearly constant across strata, a desirable property for a summary measure, whereas the rate difference (AR) varies widely. According to Breslow and Day, the rate ratio tends to be more stable across strata, supporting its desirability as a measure of association. Not all quantitative epidemiologists agree with them. The second example comes from a follow-up study of lung cancer and coronary artery disease in relation to cigarette smoking: _____________________________________________________________________________________________ www.epidemiolog.net, © Victor J. Schoenbach 2000 7. Relating risk factors to health - 167 rev. 7/25/1999, 9/4/1999, 12/22/1999, 10/2/2000, 10/9/2000, 5/8/2001
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Understanding the Fundamentals of E
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Preface Introductory epidemiology c
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Table of Contents Chapter (in Acrob
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1. Introduction Definition, charact
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problems (Schwartz and Carpenter, 1
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HIV - a new or newly-recognized vir
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d = principal investigator's degree
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Analytic studies typically involve
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Observational sciences especially a
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McGavran EG. What is public health?
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2. An evolving historical perspecti
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Time line for the history of public
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as a one-room bacteriology laborato
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− Health surveys − Research fun
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his scientific peers of the correct
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Kuhn, Thomas S. The structure of sc
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3. Studying populations - basic dem
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The demographic balancing equation
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ates. Similarly, bulges in the repr
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When the baby boom cohort retires 1
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The pervasiveness, strength, viciou
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Total fertility rate (TFR) Standard
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Life expectancy The technique, of u
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Excerpt from the U.S. 1993 abridged
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At the other end of the life table,
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to change, hopefully to decline. If
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Thought question: Professors typica
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Descriptive studies and surveillanc
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4. The Phenomenon of Disease Concep
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Classification is the foundation As
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As we gain more sophisticated under
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To recapitulate the above discussio
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Classifying cause of death Since mo
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Laboratory and other objectively me
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distribution but are not diabetic (
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program in the general population,
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Infectious disease Incubation "time
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the direct effects of carcinogenic
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patient outcomes. The design and ev
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detected by screening will appear b
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Morrison, Alan S. Screening in chro
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e relevant. Compromises might be fo
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educational attainment by the numbe
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Distributions - the fuller picture
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Per capita income: Should health ca
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Deaths of children < 1 year of age
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No. of persons with senile dementia
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Incidence Immigration Relationship
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Examples: arthritis, cholelithiasis
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Cohort - entrance into the populati
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Sample calculation: 200 people free
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• The units of time must be state
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Calculation of person-time in a coh
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Original Calculation of person-time
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average risk for a member of the co
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However: Nurses: 601 cases/89,538 w
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treated. If the rate at which patie
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Incidence and prevalence in a popul
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small prevalence. So if the seropre
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Appendix on weighted averages Becau
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Appendix on exponents and logarithm
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and epidemiology. The notation ln(x
Page 125 and 126: 3. For the following hypothetical d
Page 127 and 128: c. ________________ 6 fatalities /
Page 129 and 130: Measuring disease and exposure - As
Page 131 and 132: 5. a. Flow Diagram Population of si
Page 133 and 134: New cases Q ID = ------------------
Page 135 and 136: Overview 6. Standardization of rate
Page 137 and 138: differences between the groups in f
Page 139 and 140: ∑ (stratum-specific rates �× s
Page 141 and 142: especially important when comparing
Page 143 and 144: copy this cell to the other columns
Page 145 and 146: where the RR k are the stratum-spec
Page 147 and 148: and the observed number of deaths i
Page 149 and 150: Directly standardized rate for A =
Page 151 and 152: 5,022 Indirectly standardized = —
Page 153 and 154: the situation among older age group
Page 155 and 156: Appendix on Standardized Mortality
Page 157 and 158: across age strata, then the damage
Page 159 and 160: d. How would you feel about the con
Page 161 and 162: Cases per 100,000 Mean annual incid
Page 163 and 164: d. dt Indirectly standardized rates
Page 165 and 166: The second ingredient for an standa
Page 167 and 168: Group US rate /100,000 County pop.
Page 169 and 170: Crude rates are comparable because
Page 171 and 172: The "Big Picture" 7. Relating risk
Page 173 and 174: Consider first the table on the lef
Page 175: The epidemiologist first arranges t
Page 179 and 180: Descriptive adjectives for magnitud
Page 181 and 182: Odds ratio The odds ratio (OR) is a
Page 183 and 184: Duncan C. Thomas, "On the need for
Page 185 and 186: 6. Odds of exposure in controls Pro
Page 187 and 188: CID = CI1 - CI0 = .20 - .10 = .10 (
Page 189 and 190: When both disease and exposure have
Page 191 and 192: variables is linear. An r of zero m
Page 193 and 194: 2. In HIV-discordant couples in whi
Page 195 and 196: Incidence Diagrammatic representati
Page 197 and 198: PAR = AR × P1 = (I1 - I0)P1 = I -
Page 199 and 200: expresses the prevented cases as a
Page 201 and 202: Incidence Diagrammatic representati
Page 203 and 204: The result, (NHIH)/(NLIL+NHIH), is
Page 205 and 206: Proportion with = 0.5 ( 22 --- ) +
Page 207 and 208: CI may be preferred: � if the hea
Page 209 and 210: Appendix — Relating risk factors
Page 211 and 212: By definition, oddsr = risk / (1 -
Page 213 and 214: Bibliography Measures of effect: Te
Page 215 and 216: Relating risk factors to health - A
Page 217 and 218: 4. In a study of adverse effects of
Page 219 and 220: number of "permanent" quits (define
Page 221 and 222: = I1n1- I0n1 + I0n0 - I0n0 ——
Page 223 and 224: 2. Imprecision in determining the t
Page 225 and 226: Sometimes the appearance of a new s
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Case-control (case-referent, etc.)
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ealistic setting and results may th
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"ecologic fallacy", the erroneous i
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can vary substantially among indivi
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e estimated from that study since t
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Risk ratio Consider the example of
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Dietary Salt Intake and hypertensio
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Intervention trials can include tes
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Treatment allocation can be 1) fixe
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Example Cases Case-control studies
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Cases Controls ____________________
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population and that the controls we
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Estrogen users (N1) Nonusers (N0) N
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In the 3 × 10 6 unexposed women-ye
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similar to that in the case group t
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A modern perspective In general, de
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of exposed to unexposed persons sam
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Case-control studies: Armenian, Har
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Wingo, Phyllis A.; Howard W. Ory, P
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Part I Analytic study designs - Ass
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1. Doll and Hill state (page 1451,
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Part I Analytic study designs - Ass
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� Possible motivation to change b
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9. Causal inference * The desire to
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1955:35). Quarantine of sick person
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The mother who replaced the burned-
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As presented in Kleinbaum, Kupper,
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Popper maintains that it is fundame
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1. Is the association real or artef
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Temporality First exposure, then di
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confer upon us a freedom to ignore
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Lave, Lester B.; E.P. Seskin. Epide
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Precision The presence of random va
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the point estimate is based and thu
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methodological literature. Validity
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disease detection may be mistakenly
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In cohort studies, the primary sour
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present, then the D&C would detect
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Controls in an experiment In a true
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Southern endometrial cancer and est
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Cases ` The ` "detection bias" hypo
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from ETS, then a cohort study of ha
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employing lead exposure measures fr
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which the both measures increase in
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coefficient (slope) is to 1.0 and t
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_ _ Se = Pr(D'|D) Sp = PR(D'|D) _ _
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Differential misclassification, how
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subject plus or minus a random nois
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Appendix 2 More on the concern to a
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Bibliography Henneckens and Buring.
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Sackett, D.L.: Bias in analytic res
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e. OPTIONAL: If the reported cumula
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Results from the Evans County Cardi
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2. I1 = incidence in the exposed P1
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makes most sense to view detection
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Sensitivity × cases + (1 - Specifi
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In the factual world, however, we c
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Hypertensive SI participants were t
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3,154 male managers and white colla
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Table 2 Relationship of CHD to Beha
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a group did indeed have higher CHD
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Confounding - comparison of weighte
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Type A smokers) are not very meanin
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Different control groups for hypoth
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Confounding, then, is a function of
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Since the OR is the crossproduct ra
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Case-control study In a case-contro
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First and foremost, a potential con
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is defined in relation to the count
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poor. A scientific basis linking ra
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One way to obtain a better balance
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Stratified analysis is intuitively
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attributed to the exposure of inter
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Bibliography Rothman and Greenland
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Senior P, Bhopal RS. Ethnicity as a
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Some of the relationships just pres
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n1i _______________________________
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2. A 20-year retrospective cohort s
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No. of urinary tract infections Tab
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2. completely attributable to obesi
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5. a. C -- the adjusted relative ri
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of dietary antioxidants. However, c
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epidemiologic research is to identi
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Since the indicator variable (POP)
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Over two decades ago (Causes, Am J
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In this diagram, G and H exhibit ab
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In this situation, the first suffic
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Crude rates as weighted averages Re
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Lung cancer rates by smoking and as
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{B0} Smk Smk Asb. Asb. {B1} {B2} {B
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Notation for joint effects R1 risk
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and R111 = R000 + RD100 + RD010 + R
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RR11 = RR10 × RR01 [End of aside]
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multiplicative model supports the u
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Effect modification as a reflection
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4. Defining subgroups for preventiv
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Bibliography Rothman and Greenland,
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Multicausality: Effect modification
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4. Several studies have shown a syn
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1. Multicausality: Effect modificat
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In these data, or, Expected ROC,SMK
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to drinking in the absence of smoki
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we determine that confounding is pr
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Association between reserpine and b
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R11 R10 × R01 R10 —— = ——
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Hypothetical data on incidence of m
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1. Data conform to an additive mode
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Difference measure - the CID The va
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Distribution of CIR, IDR, OR 0 +1 M
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1 wi = ---------------------------
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5 Y n B 3 n Y C 8 n Y C 4 Y Y D 7 Y
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R11 - R00 = (R10 - R00) + (R01 - R0
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You may well wonder what is the val
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Moreover, the logistic model, we wi
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Key epidemiologic assumptions in th
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a + b1X1 + b2X2 + b3X3 + …) on th
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Wilcosky, Timothy C. and Lloyd E. C
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Data analysis and interpretation Ep
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Range checks Range checks compare e
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� Decisions deferred have to be m
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� Simpler is better � Avoid ext
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educe bias and tend to introduce ad
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data. Perhaps too often generalitie
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When this "analogous experiment" is
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tests are based (e.g., see Sander G
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The probability associated with bei
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conclude that the association is su
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Exposed to diethylstilbesterol? Yes
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For example, suppose that we are co
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The idea behind small studies bias
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Confidence intervals address the qu
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Computing a confidence interval for
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Bibliography General Ahlbom, Anders
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Thompson, W. Douglas. Statistical c
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Appendix Estimating sample size to
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p1 (1 - p1) p2 (1 - p2) σ 2 1 σ 2
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Margin of error (rounded) Point Sam
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Meditations on hypothesis testing a
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Independent replication is the corn
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More meditations on interpreting st
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Part I Data analysis and interpreta
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Part I 1. (a) Restriction Data anal
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9. ORCIG,HYP,OC [multiplicative mod
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15. Practical aspects of epidemiolo
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(CDC, which includes the National I
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cardiovascular area -- notably the
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Disease Control (CDC) decided again
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After submission but before the awa
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Journal of Medicine, Jan 14, 1999,
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Explore the data � Look at data (
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Recently, standardization has come
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Riesenberg, Don; Goerge D. Lundberg
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16. Data management and data analys
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implications, or suspicions or char
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1.4.1.2 Consistency Consistency is
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1.4.5.1.2 Series Runs in series are
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Obviously it will be easier to asse
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2.1.2.1 Statistical There are forma
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2.3.5 Bivariate displays If the sam
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errors. Related to this concern is
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3.3 Expected values Perhaps, the si
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Despite the best efforts, however,
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Complete data cases % distribution
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3.5 Outliers Outliers are now exami
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Bibliography Davidson, Fred. Princi
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attrib ckd length=$1 label='Check d
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17. Epidemiology and public health
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� Geneva - " . . . IFV and allied
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public health, since the best oppor
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Individual-level versus societal le
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14%, so that the burden of the envi
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1. exhausting various non-renewable
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O'Hare WP, Pollard KM, Mann TL, Ken
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� Health for all What contributes
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Challenges in the environment for e
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� What kind of population is requ
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Bibliography American College of Ep
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