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∑ rai nai ra ∑nai Crude rate for A = ———— = ——— = ra _____________________________________________________________________________________________ www.epidemiolog.net Standardization - Assignment solutions - 159 rev. 12/22/1999, 8/1/2000 nt So the directly standardized rate equals the crude rate (equals the stratum-specific rates). The same can be shown, in a identical manner, for B. Therefore the ratio of directlystandardized rates equals the ratio of crude rates. Moral: if there is no variation in your stratum-specific rates, you don't need to adjust--the crude is fine. c. This question asks about the situation in which there is a constant rate ratio between groups A and B within each age stratum. Since the SMR is calculated using the rates in the standard population (in this case, r bi ) for the denominator (the "expected" deaths), that denominator will be 1/K times the observed deaths, since the rates from the standard population are 1/K times the rates observed in the study population. Using the formulas on pages 4 and 8: SMR = Observed deaths ——————— = ∑ (rainai) ————— = ∑ (rainai) ——————— Expected deaths ∑ (rbinai) ∑ (rainai) = ——————— = K 1 — ∑ (rainai) K nt rai ∑ ( ) nai K This exercise illustrates the underlying rationale for the SMR, i.e., in a situation in which there are too few data to make meaningful judgments about specific rates, we assume that each is a constant multiple of the specific rates in a standard population and then estimate that constant multiple with the SMR. The assumption of a constant multiple may not hold in reality, but it may be reasonably correct with study group we are examining. In any case it is the best we can do given the limited amount of data. d. Intuitively, if two populations are alike in terms of a particular variable, then that variable cannot be responsible for observed differences between them. Directly standardized rates are comparable, regardless of age distributions, because the specific rates in each population are weighted by the same external standard.
Crude rates are comparable because the crude rate for each group may be thought of as a weighted average of the group's specific rates, with weighting by the proportional size of the strata: deaths ∑ (rainai) nai ra = ––––––– = ––––––––– = –––– nat _____________________________________________________________________________________________ www.epidemiolog.net Standardization - Assignment solutions - 160 rev. 12/22/1999, 8/1/2000 nat ∑( rai deaths ∑ (rbnb) nbi rb = ––––––– = ––––––––– = –––– nbt nbt ∑( nat rbi nbt To say that both groups have the same proportional age distribution is to say that for any age stratum (i.e., stratum "i"), nai rb = –––– = –––– = pi na ni nbt So ra=Σ[raipi], rb=Σ[rbipi], and the two sets of specific rates are averaged using the same weights, pi. Indirectly standardized rates: From the formula at the top of page 4, Indirectly standardized rate = rt Rt ) ) rtRt × ————— = ————— ∑ (Rini)/nt nI Rt = rt ———— ∑ (Ripi) ∑(Ri Since R t and R i come from the standard population and pi is the same for groups A and B (though it may vary from stratum to stratum) by the conditions of the problem, the indirectly standardized rates for A and B are each equal to their crude rates times a the same constant. So a comparison of indirectly standardized rates in this case is the same as a comparison of their crude rates, which was shown above to be valid. nt )
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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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Page 119 and 120: Appendix on weighted averages Becau
Page 121 and 122: Appendix on exponents and logarithm
Page 123 and 124: 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 × stan
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: Group US rate /100,000 County pop.
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
Page 199 and 200: show that a large proportion (i.e.,
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 and 212: CIR can be directly estimated if th
Page 213 and 214: I0 I = ——————— 1 + P1
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
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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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(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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