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Appendix — Relating risk factors to health outcomes WARNING: this chapter has recently been converted to MS Word, so some algebraic errors may have been introduced. Estimating exposure-specific incidence and attributable risk from a casecontrol when the crude incidence is known This procedure makes use of the fact that the crude incidence can be expressed as a weighted average of exposure-specific incidences: where: I = P1I1 + P0I0 I = crude incidence I1 = incidence in exposed population I0 = incidence in unexposed population P1 = proportion of the population that is exposed P0 = proportion of the population that is unexposed Since the RR (relative risk, CIR, IDR) = I1/I0, it is possible to substitute RR x I0 for I1 in the above expression: I = P1 × RR × I0 + P0I0 Similarly, since P1 + P0 = 1, we can substitute for 1 - P1 for P0: I = P1 × RR × I0 + (1 – P1) × I0 Solving for I0 yields: I0 I I = ———————— = —————— P1 x RR + (1 – P1) 1 + P1 (RR – 1) Since for a rare disease we can estimate RR by using OR, the final formula is: _____________________________________________________________________________________________ www.epidemiolog.net, © Victor J. Schoenbach 2000 7. Relating risk factors to health - 202 rev. 10/9/2000, 5/8/2001, 2/19/2002, 4/26/2002
I0 I = ——————— 1 + P1 (OR – 1) This formula can be used for a case-control study where: 1. The control group has been selected in such a way that the proportion exposed estimates P1 in the population; 2. There is information available to estimate the crude incidence of the disease; 3. The disease is sufficiently rare (e.g., incidence less than 10% by the end of follow-up) so that the OR estimates the RR fairly well. Once we have estimated I0, we estimate I1 by multiplying by the OR. From I1 and I0 we can estimate attributable risk. Demonstration that OR estimates CIR when CI's are small For this demonstration and the following one, a different notation will simplify the presentation. We will use D and E for disease and exposure, so that we can upper case for presence and lower case for absence. Thus, subscript E will refer to the presence of exposure, subscript e will refer to the absence of exposure. Similarly, subscript D refers to cases, subscript d to noncases. P stands for probability, which can also be interpreted as prevalence (when applied to exposure) or risk (when applied to disease). The vertical bar means “given” or “conditional on”. Thus: PE = Probability of being exposed (i.e., prevalence of exposure) Pe = Probability of being unexposed (1 - PE) PD = Probability of disease (risk) Pd = Probability of nondisease (1 - PD) PE|D = Probability of exposure conditional on disease (i.e., prevalence of exposure in cases) Pe|D = Probability of nonexposure conditional on disease (i.e., 1 - PE|D) PE|d = Probability of exposure conditional on non-disease (i.e., prevalence of exposure in noncases) Pe|d = Probability of nonexposure conditional on non-disease (i.e., 1 - PE|d ) PD|E = Probability of disease (risk) conditional on exposure (i.e., risk of disease in the exposed) Pd|E = Probability of nondisease conditional on exposure (i.e., 1 - PD|E) PD|e = Probability of disease conditional on non-exposure (i.e., risk of disease in the unexposed) Pd|e = Probability of nondisease conditional on non-exposure (i.e., 1 - PD|e) _____________________________________________________________________________________________ www.epidemiolog.net, © Victor J. Schoenbach 2000 7. Relating risk factors to health - 203 rev. 10/9/2000, 5/8/2001, 2/19/2002, 4/26/2002
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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
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3. For the following hypothetical d
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c. ________________ 6 fatalities /
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Measuring disease and exposure - As
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5. a. Flow Diagram Population of si
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New cases Q ID = ------------------
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Overview 6. Standardization of rate
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differences between the groups in f
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∑ (stratum-specific rates × stan
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especially important when comparing
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copy this cell to the other columns
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where the RR k are the stratum-spec
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and the observed number of deaths i
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Directly standardized rate for A =
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5,022 Indirectly standardized = —
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the situation among older age group
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Appendix on Standardized Mortality
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across age strata, then the damage
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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 r
Page 173 and 174: CHD and oral contraceptives in Brea
Page 175 and 176: Some basic measures Before diving i
Page 177 and 178: esophageal cancer? First, if we did
Page 179 and 180: ought in here as well. When we cont
Page 181 and 182: Exposure Disease Yes No Total Yes a
Page 183 and 184: Relation of the odds ratio to the r
Page 185 and 186: the case-control study estimates th
Page 187 and 188: If the data had come from a cross-s
Page 189 and 190: Excess risk = CIR - 1 = 1.0 (i.e.,
Page 191 and 192: strength of the relationship (e.g.,
Page 193 and 194: drawn on ordinary graph paper. Howe
Page 195 and 196: Measures of Impact Concept Relative
Page 197 and 198: Attributable risk proportion The AR
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Page 201 and 202: Incidence Diagrammatic representati
Page 203 and 204: 1. high frequency of disease 2. pow
Page 205 and 206: With this diagram and notation we c
Page 207 and 208: vaguer) “attributed to”. Incide
Page 209 and 210: Summary There are three categories
Page 211: CIR can be directly estimated if th
Page 215 and 216: PD|e PE (RR - 1) PD|e PE (RR - 1) P
Page 217 and 218: Walter, Stephen D. Choice of effect
Page 219 and 220: a. Quit rates were measured as the
Page 221 and 222: 1. Definitions: Relating risk facto
Page 223 and 224: There is an extremely strong associ
Page 225 and 226: 8. Analytic study designs The archi
Page 227 and 228: Progression of types of studies In
Page 229 and 230: Cross-sectional A cross-sectional s
Page 231 and 232: Follow-up studies Along with case-c
Page 233 and 234: of interest community-level influen
Page 235 and 236: ecological approach may be the appr
Page 237 and 238: What measures can be estimated from
Page 239 and 240: Ability to estimate risk Ascertainm
Page 241 and 242: individuals, this relationship does
Page 243 and 244: Odds Ratio (OR) Exposure odds in ca
Page 245 and 246: Simple randomization - assignment o
Page 247 and 248: The relationship of an attribute to
Page 249 and 250: (a / m1) / (b / m1) ad ORe (Exposur
Page 251 and 252: Validity The validity of a case-con
Page 253 and 254: Since the strategic advantage of th
Page 255 and 256: c = f0N1 = number of exposed noncas
Page 257 and 258: experienced the event under study.
Page 259 and 260: approach, the odds ratio computatio
Page 261 and 262: Exposure Yes No Total Cases A B M1
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Miettinen, Olli S. The clinical tri
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Mantel, N. and Haenszel, W.: Statis
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Peto, R., Pike, M.C., Armitage, P.,
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4. The authors state that "There we
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5. In contrast to many earlier inve
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In this study the use of hospitaliz
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Follow-up must be longer for any gi
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While acknowledging the very import
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world. Even as late as the 1950's,
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Causal Inference Direct observation
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data on the effects of radiation on
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But excluding an explanation based
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Strength of the association Pronou
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Experimental evidence Certain types
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To issue an indictment, the grand j
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10. Sources of error A systematic f
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the data in the table. (Note that t
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associations. So the same terms may
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"Negative bias" - The observed meas
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Classifying sources of bias Inspite
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The study population is a subset of
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This estimate of the prevalence of
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unmatched control groups will presu
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The odds ratio for this table is 3.
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Selection bias in cohort studies Se
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Information bias Information bias r
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following chapter). The concept of
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P h y s i c i a n A Comparison of d
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item). Alpha values of 0.80 are are
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Hypothetical scenario showing effec
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presumably classified as informatio
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Appendix 1 Formulas to see the effe
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Algebraically, _ Pr(E|D') = — the
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Gregorio, David L.; James R. Marsha
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Sources of error - Assignment 1. Th
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Alpha (α) is the probability by wh
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Sources of error - Assignment solut
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3. ii) Selective survival--if OC us
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a. Flow diagram: 1960-1962 1967-196
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Introduction 11. Multicausality: Co
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estimate of what the outcomes would
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A hypothetical example (with apolog
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Questions to ask: There are many as
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Confounding arises from unequal dis
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CHD Incidence by Behavior Pattern a
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In this way, the 1,129 Type A's wit
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exposure. If we assume a baseline r
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Further insight can be gained by co
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Table 7a Colon cancer and drinking
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atio of the observed number of expo
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ural-specific exposure prevalences,
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eing infected, and the more of them
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studies deal with a delimited geogr
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University of Massachusetts at Amhe
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similarly distributed in cases and
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"There have been many important ste
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MAIN POINTS Confounding is a disto
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Greenland, S. and Neutra R.: Contro
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Appendix The following discussion i
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i n1i wi = ----- If exposure is unr
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Multicausality: Confounding - Assig
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4. The following table, published i
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1. Multicausality: Confounding - As
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link between HCS and MI to ensure t
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Multicausality 12. Multicausality:
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Interdependent effects The precedin
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epidemiologic data. Put simply, the
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BP 0 These two lines are parallel;
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ean intake and B representing genet
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Fourth, proportion of disease attri
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Incidence and incidence ratios of f
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% with evidence of impaired red blo
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cancer rate among the light smokers
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Age standardized lung cancer rates
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R11 - R00 = R10 - R00 + R01 - R00 (
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and R111 = R100 × R010 × R001 / (
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R110 = R100 × R010 / R000 (multipl
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Risk ln(risk) 0.19 -1.67 0.13 -2.01
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have clinical or public health sign
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Baseline Characteristics Associated
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Weiss, Noel S. Accounting for the m
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A. Synergism apparently exists in t
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5. Walker (International Journal of
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(or equivalently, the rate for pers
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impact. Synergism in this sense imp
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13. Multicausality - analysis appro
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very far on instruments but needs t
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Summarizing the relationships Often
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We saw in the chapter on effect mod
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So the multiplicative model for joi
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misleading summary. These circumsta
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w1 CID1 + w2 CID2 Summary CID = —
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c d bcn0 + adn1 Var(ln(CIR)) ≈
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Kleinbaum, Kupper, and Morgenstern;
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1 + 1 + 1 3 ORMH = —————
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Risk = R00 + Obesity effect Obesity
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two (or more) factors that "interac
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OR = exp(β3) β3 is the difference
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Other regression models [Optional f
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Know the epidemiologic meaning of t
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14. Data analysis and interpretatio
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and questionable data. Monitoring p
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presence of particular proteins (e.
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4. Count - the number of entities,
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Algorithms - A procedure that uses
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Imputation causes the least distort
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Prenatal exposure to diethylstilbes
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Possible outcomes (Colors of pairs
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In a strict decision-making mode, t
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C = area between -z and +z D = area
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two-tailed 5% significance level).
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If the p-value is not small (i.e.,
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OR we observed was greater than 1.0
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Large trials (e.g., 250 deaths) Tru
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The concept behind the confidence i
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Formulas for confidence intervals f
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Woolf SH, Battista RN, Anderson GM,
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Stallones, Reuel A. The use and abu
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C - Clustered observations, which d
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For example, suppose that n, the sa
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* See previous table Margin of erro
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Even in randomized trials problems
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Pr(H|T) is therefore a function of
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That information gives you pause. C
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Part II 1. In table 2 from the Rose
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If the OR for Current OC use were t
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6. There are no interaction (produc
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24. Submit manuscript from previous
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Cooperative agreement A cooperative
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Assurances by the applicant and her
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The new element is the grant award.
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1. What needs to be done? 2. How lo
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Postaward Final report What to do
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2. maintain close supervision of th
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Publication Epidemiology Working Gr
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Weed, Douglas L. Between science an
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1.3 Specific Objectives of Data Man
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engender a basic conflict between t
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1.4.2 Integration Integrate the dat
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2. Consistency of the protocol's im
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2. Coding of a sample of data forms
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2.3 The steps in the Editing proces
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Although it is rare to use more tha
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The first stages of data analysis s
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have less power to exclude the stat
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greater nonresponse by heavy drinke
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Imputation is then carried out as f
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(normal) distribution in the popula
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Appendix **************************
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___________________________________
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Public health approach The public h
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health, particularly at the world l
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Causative or preventive agents Scur
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Human behavior is also biology The
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crowded, under-resourced urbanized
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Bibliography Annas, George J.; Leon
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18. Overview and Conclusion A look
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Epidemiology is expanding In recen
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More reliance on "soft money" - res
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__________ This is not a new challe
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