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Some of the relationships just presented can be readily demonstrated using simple algebra. Let ai, bi, ci, di, n1i, and n0i in each stratum take on the values implied by the table below, and let their respective totals across all strata by a, b, c, d, n1, and n0 (i.e., a = all exposed cases, b = all unexposed cases, c = all exposed noncases, d = all unexposed noncases, n1 = all exposed persons, n0 = all unexposed persons). Exposure Disease Yes No Total Yes ai bi m1 (ai + bi) No ci di m2 (ci + di) Total n1i n0i ni (ai + ci) (bi + di) The incidence in exposed persons is ai/n1i within each stratum and a/n1 when the strata are ignored (i.e., the total, or crude table). The (weighted) average incidence in the exposed across the strata is: Σ ( n1i ai ai a ––– × ––– = ––– = ––– n n n n1i ) Σ ( where the summation goes over all strata. a/n is simply the crude incidence in the exposed. Similarly, the weighted average of the stratum-specific risk ratios can be expressed as the sum across all strata of: wi ai /n1i wi ai n0i ––– × ––– = ––– × ––––– W bi /n0i W bi n1i where wi are the weights for each stratum and W is the sum of the wi. If we let wi = bin1i /n0i, then we have the sum across strata of: Meanwhile, W is the sum across all strata of: bi n1i /n0i ai n0i ai wi ––––––––– × ––––– = ––––– W bi n1i W _____________________________________________________________________________________________ www.epidemiolog.net, © Victor J. Schoenbach 2000 11. Multicausality: Confounding - 374 rev. 10/28/2000, 11/2/2000, 5/11/2001 )
i n1i wi = ––––– If exposure is unrelated to the stratification variables, so that the distribution of exposed n1i /(a + c) is the same across strata as the distribution of the unexposed n0i /n0, then the ratio of exposed to unexposed in all strata must be the same as in the overall table, n1 /n0. Therefore bi n1i _____________________________________________________________________________________________ www.epidemiolog.net, © Victor J. Schoenbach 2000 11. Multicausality: Confounding - 375 rev. 10/28/2000, 11/2/2000, 5/11/2001 n0i b n1i wi = ––––– , whose sum is simply W = ––––– n0i ai a Thus, the sum of –––– is ––––––– , which equals wi bn1 / n0 a / n1 ––––– , the overall risk ratio. b n0 So, when there is no confounding, the following three summary measures are all equal: Overall incidence in exposed Overall risk (or rate) ratio = –––––––––––––––––––––––––– Overall incidence in unexposed Weighted average of incidence in exposed, across strata = –––––––––––––––––––––––––––––––––––––––––––––– Weighted average of incidence in unexposed, across strata = Weighted average of stratum-specific risk (or rate) ratios With incidence odds and odds ratios, however, the above does not apply. The overall incidence odds are simply a/c. In contrast, the average of the stratum-specific odds, weighted by the number of exposed, is the sum over all strata of: n0i
Page 1 and 2:
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
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Cases per 100,000 Mean annual incid
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d. dt Indirectly standardized rates
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The second ingredient for an standa
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Group US rate /100,000 County pop.
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Crude rates are comparable because
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The “Big Picture” 7. Relating r
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CHD and oral contraceptives in Brea
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Some basic measures Before diving i
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esophageal cancer? First, if we did
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ought in here as well. When we cont
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Exposure Disease Yes No Total Yes a
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Relation of the odds ratio to the r
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the case-control study estimates th
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If the data had come from a cross-s
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Excess risk = CIR - 1 = 1.0 (i.e.,
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strength of the relationship (e.g.,
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drawn on ordinary graph paper. Howe
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Measures of Impact Concept Relative
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Attributable risk proportion The AR
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show that a large proportion (i.e.,
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Incidence Diagrammatic representati
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1. high frequency of disease 2. pow
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With this diagram and notation we c
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vaguer) “attributed to”. Incide
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Summary There are three categories
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CIR can be directly estimated if th
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I0 I = ——————— 1 + P1
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PD|e PE (RR - 1) PD|e PE (RR - 1) P
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Walter, Stephen D. Choice of effect
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a. Quit rates were measured as the
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1. Definitions: Relating risk facto
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There is an extremely strong associ
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8. Analytic study designs The archi
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Progression of types of studies In
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Cross-sectional A cross-sectional s
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Follow-up studies Along with case-c
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of interest community-level influen
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ecological approach may be the appr
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What measures can be estimated from
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Ability to estimate risk Ascertainm
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individuals, this relationship does
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Odds Ratio (OR) Exposure odds in ca
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Simple randomization - assignment o
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The relationship of an attribute to
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(a / m1) / (b / m1) ad ORe (Exposur
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Validity The validity of a case-con
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Since the strategic advantage of th
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c = f0N1 = number of exposed noncas
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experienced the event under study.
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approach, the odds ratio computatio
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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
Page 329 and 330: Gregorio, David L.; James R. Marsha
Page 331 and 332: Sources of error - Assignment 1. Th
Page 333 and 334: Alpha (α) is the probability by wh
Page 335 and 336: Sources of error - Assignment solut
Page 337 and 338: 3. ii) Selective survival--if OC us
Page 339 and 340: a. Flow diagram: 1960-1962 1967-196
Page 341 and 342: Introduction 11. Multicausality: Co
Page 343 and 344: estimate of what the outcomes would
Page 345 and 346: A hypothetical example (with apolog
Page 347 and 348: Questions to ask: There are many as
Page 349 and 350: Confounding arises from unequal dis
Page 351 and 352: CHD Incidence by Behavior Pattern a
Page 353 and 354: In this way, the 1,129 Type A's wit
Page 355 and 356: exposure. If we assume a baseline r
Page 357 and 358: Further insight can be gained by co
Page 359 and 360: Table 7a Colon cancer and drinking
Page 361 and 362: atio of the observed number of expo
Page 363 and 364: ural-specific exposure prevalences,
Page 365 and 366: eing infected, and the more of them
Page 367 and 368: studies deal with a delimited geogr
Page 369 and 370: University of Massachusetts at Amhe
Page 371 and 372: similarly distributed in cases and
Page 373 and 374: "There have been many important ste
Page 375 and 376: MAIN POINTS Confounding is a disto
Page 377 and 378: Greenland, S. and Neutra R.: Contro
Page 379: Appendix The following discussion i
Page 383 and 384: Multicausality: Confounding - Assig
Page 385 and 386: 4. The following table, published i
Page 387 and 388: 1. Multicausality: Confounding - As
Page 389 and 390: link between HCS and MI to ensure t
Page 391 and 392: Multicausality 12. Multicausality:
Page 393 and 394: Interdependent effects The precedin
Page 395 and 396: epidemiologic data. Put simply, the
Page 397 and 398: BP 0 These two lines are parallel;
Page 399 and 400: ean intake and B representing genet
Page 401 and 402: Fourth, proportion of disease attri
Page 403 and 404: Incidence and incidence ratios of f
Page 405 and 406: % with evidence of impaired red blo
Page 407 and 408: cancer rate among the light smokers
Page 409 and 410: Age standardized lung cancer rates
Page 411 and 412: R11 - R00 = R10 - R00 + R01 - R00 (
Page 413 and 414: and R111 = R100 × R010 × R001 / (
Page 415 and 416: R110 = R100 × R010 / R000 (multipl
Page 417 and 418: Risk ln(risk) 0.19 -1.67 0.13 -2.01
Page 419 and 420: have clinical or public health sign
Page 421 and 422: Baseline Characteristics Associated
Page 423 and 424: Weiss, Noel S. Accounting for the m
Page 425 and 426: A. Synergism apparently exists in t
Page 427 and 428: 5. Walker (International Journal of
Page 429 and 430: (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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