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The probability associated with being "Z" standard deviations away from the mean of a normal distribution can be computed and is readily available in statistical tables (see table excerpt below). The value of a normally-distributed random variable is usually (i.e., probability 95%) less than two standard deviations from its mean, so if Z exceeds 1.96 we say "p
C = area between -z and +z D = area beyond |z| (i.e., to the left of -z and the right of +z) E = area to the left of z (Source: National Bureau of Standards – Applied Mathematics Series–23, U.S. Government Printing Office, Washington, D.C., 1953, as abstracted in Table A-4 in Richard D. Remington and M. Anthony Schork, Statistics with applications to the biological and health sciences. Englewood Cliffs, NY, 1970.] One-sided versus two-sided p-values Recall that the p-value is the probability of obtaining an association as strong as (or stronger than) the association that was observed. It turns out, though, that the phrase "as strong as (or stronger than)" is ambiguous, because it doesn't specify whether or not it is intended to include inverse associations, i.e., associations in the opposite direction from the putative association that motivated the study. For example, if we observe a 2.5 relative risk, does "as strong" mean only relative risks of 2.5 or larger, or does it also mean relative risks of 0.4 or smaller? If the former (only 2.5 and larger), then the corresponding p-value is "one-sided" (or "one-tailed"). In contrast, if HA is "either greater than or equal to 2.5 or [inclusive] less than or equal to 0.4", then a two-sided p-value is indicated. [Only one-sided p-values can be interpreted as the "probability of observing an association as strong or stronger under the chance model" (Rothman and Greenland,185).] The issue of one-sided versus two-sided p-values can arouse strong emotions. For a given calculated value of Z, the one-sided p-value is exactly half of the two-sided p-value. Proponents of two-sided p-values argue that a one-sided p-value provides an inflated measure of the statistical significance (low probability of obtaining results by chance) of an association. Appropriate situations for using one-sided p-values are sometimes characterized as ones where the investigator has no interest in finding an association in the opposite direction and would ignore it even it occurred. However, a posting on the EPIDEMIOL-L listserv asking for situations of this sort produced very few persuasive examples. Here is a dramatical presentation of some of the issues in choosing between 1-sided and 2-sided p-values: The wife of a good friend of yours has tragically died from lung cancer. Although she was a life-long nonsmoker, your friend used to smoke quite heavily. Before her death she had become an anti-smoking activist, and her last wishes were that your friend bring suit against R.J. Morris, Inc., the manufacturer of the cigarette brand your friend used to smoke. Knowing that he cannot afford expert consultation, your friend turns to you and prevails upon you to assist him with the lawsuit. In preparation for the trial, the judge reviews with both sides the standard of evidence for this civil proceeding. She explains that for the court to find for the plaintiff (your side) it must _____________________________________________________________________________________________ www.sph.unc.edu/courses/EPID 168, © Victor J. Schoenbach 14. Data analysis and interpretation – 469 rev. 11/8/1998, 10/26/1999, 12/26/1999
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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
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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
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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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Page 433 and 434: 13. Multicausality - analysis appro
Page 435 and 436: very far on instruments but needs t
Page 437 and 438: Summarizing the relationships Often
Page 439 and 440: We saw in the chapter on effect mod
Page 441 and 442: So the multiplicative model for joi
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Page 445 and 446: w1 CID1 + w2 CID2 Summary CID = —
Page 447 and 448: c d bcn0 + adn1 Var(ln(CIR)) ≈
Page 449 and 450: Kleinbaum, Kupper, and Morgenstern;
Page 451 and 452: 1 + 1 + 1 3 ORMH = —————
Page 453 and 454: Risk = R00 + Obesity effect Obesity
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Page 457 and 458: OR = exp(β3) β3 is the difference
Page 459 and 460: Other regression models [Optional f
Page 461 and 462: Know the epidemiologic meaning of t
Page 463 and 464: 14. Data analysis and interpretatio
Page 465 and 466: and questionable data. Monitoring p
Page 467 and 468: presence of particular proteins (e.
Page 469 and 470: 4. Count - the number of entities,
Page 471 and 472: Algorithms - A procedure that uses
Page 473 and 474: Imputation causes the least distort
Page 475 and 476: Prenatal exposure to diethylstilbes
Page 477 and 478: Possible outcomes (Colors of pairs
Page 479: In a strict decision-making mode, t
Page 483 and 484: two-tailed 5% significance level).
Page 485 and 486: If the p-value is not small (i.e.,
Page 487 and 488: OR we observed was greater than 1.0
Page 489 and 490: Large trials (e.g., 250 deaths) Tru
Page 491 and 492: The concept behind the confidence i
Page 493 and 494: Formulas for confidence intervals f
Page 495 and 496: Woolf SH, Battista RN, Anderson GM,
Page 497 and 498: Stallones, Reuel A. The use and abu
Page 499 and 500: C - Clustered observations, which d
Page 501 and 502: For example, suppose that n, the sa
Page 503 and 504: * See previous table Margin of erro
Page 505 and 506: Even in randomized trials problems
Page 507 and 508: Pr(H|T) is therefore a function of
Page 509 and 510: That information gives you pause. C
Page 511 and 512: Part II 1. In table 2 from the Rose
Page 513 and 514: If the OR for Current OC use were t
Page 515 and 516: 6. There are no interaction (produc
Page 517 and 518: 24. Submit manuscript from previous
Page 519 and 520: Cooperative agreement A cooperative
Page 521 and 522: Assurances by the applicant and her
Page 523 and 524: The new element is the grant award.
Page 525 and 526: 1. What needs to be done? 2. How lo
Page 527 and 528: Postaward Final report What to do
Page 529 and 530: 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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