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# Class Note for PUBHLTH 540 at UMass(1)

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Date Created: 02/06/15

Puleth 540 Introductory Biostatistics Page 1 of 3 Unit 2 Introduction to Probability Week 4 Practice Problems SOLUTIONS corrected 0142008 1 In introductory epidemiology one of the study designs that are introduced is the prospective cohort study In this type of study involving two groups the investigator enrolls preset and known numbers of participants into each of the two groups that are generically described as exposed and not exposed and follows them forward to a designated end of the observation period at which point some outcome is measured Consider the following prospective cohort study A total of 1500 never smoker consenting heart attack survivors aged 6065 are enrolled as nonexposed An equal number 1500 current smoker heart attack survivors aged 6065 are enrolled as exposed All are followed for a full 10 years and the occurrence of death recorded Following are the data Vital Status at 10 Years Dead Alive Exposure Current Smoker 40 1460 1500 Status Never Smoker 10 1490 1500 50 2950 3000 a Is it possible to estimate the probability of 10 year survival on the basis of these data Answer Yes but the question is a poor one as it does not specify time zero nor among whom 2950300009833 b Is it possible to estimate the relative risk of 10 year mortality that is associated with current cigarette use Answer Yes but this question too is poor Without a meaningful time zero the interpretation of the answer is non existent 4015001015004 c Is it possible to estimate the probability that a randomly selected person with Vital status of Alive at 10 years is a current smoker Answer Yes Even though the study design called for xed numbers of enrollments of current smokers and never smokers it is possible to estimate the conditional probability of current smoker for a randomly selected person from among the vital status at 10 years of Alive d Using these data estimate the relative risk of 10 year mortality that is associated with current cigarette use Answer 4015001015004 e Using these data estimate the relative odds of 10 year mortality that is associated with current cigarette use Note 7 This question is asking you to compute an odds ratio Answer The event of interest is 10 year mortality For this event OR Odds among current smokersOdds among never smokers 4014601014904082 docu wk4gsolutionsdoc Puleth 540 Introductory Biostatistics Page 2 of 3 f Using these data estimate the relative odds of a current smoker notation for non survivors relative to survivors Answer Here the event of interest is current smoker For this event OR Odds among n0n surviv0rsOdds among survivors 4010146014904082 g What do you notice about your answers to e and f Answer They are the same This con rms what is noted in the lecture notes that the OR for the event of disease in a cohort study comparison of exposure groups is equal to the OR for the event of history of exposure in a case control comparison of diseasenon disease groups h How do your answers to e and f compare to your answer to d Answer The OR is bigger than the RR for rare diseases the discrepancy becomes negligible 2 Another study design that is introduced in introductory epidemiology is the retrospective case control study This is by definition a study that compares two groups Here the investigator enrolls preset and known numbers of participants into each of the two groups de ned by disease status cases are the enrollees with disease controls do not have the disease under investigation Retrospective review of the histories of all study participants is performed to identify the subsets in each of the case and control groups who have a history of the exposure of interest Consider the following retrospective casecontrol study of the association between coffee consumption and tumors of the lower urinary tract The investigator enrolls 30 consenting cases that are patients with one or more tumors of the lower urinary tract For comparison purposes heshe also enrolls 100 consenting controls who have no such tumors Following are the data Tumors of Lower Urinary Tract Yes No History of 5 cups day 20 44 64 Coffee consumption ltl cupday 10 56 66 30 100 130 a Is it possible to estimate the probability of one or more tumors of the lower urinary tract on the basis of these data Answer No because the case control study design calls for xed numbers of enrollment into the tumorsyes and tumorsn0 groups b Is it possible to estimate the relative risk of one or more tumors of the lower urinary tract that is associated with consumption of 5 or more cups of coffeeday Answer No for a reason that relates to the answer to a It is not possible to estimate the component probabilities docu wk4gsolutionsdoc Puleth 540 Introductory Biostatistics Page 3 of 3 c Using these data estimate the relative odds of high coffee consumption 5 cupsday among cases relative to controls Answer For the event high coffee consumption OR Odds among tumoryes Odds among tumorsno 201044562545 d Using these data estimate the relative odds of tumors of the lower urinary tract among high coffee consumers 5 cups day relative to noncoffee drinkers Answer For the event tumorsyes OR Odds among high coffee Odds among non coffee 204410562545 e What do you notice about your answers to c and d Answer They are the same 3 Now consider a fully cross sectional study design this time with generic counts a b c and d In this design the investigator does not do any formal enrollment Counts are accumulated by observation CDC surveillance programs are examples Disease Yes No History of Yes a b Exposure N0 c d a Using the letters a b c and d what is the formula for estimating relative odds of the event of exposure for persons with disease compared to that for persons without disease Answer ac bd adbc b Using the letters a b c and d what is the formula for estimating relative odds of the event of disease for exposed persons compared to that for nonexposed persons Answer ab cd adbc c Using the letters a b c and d what is the formula for estimating relative risk of the event of disease for exposed persons compared to that for nonexposed persons Answer aab ccd d What happens to your formula in your answer to 3c when the counts of disease a and c are very very small Comment Answer As a gets smaller and smaller ab 9 b As c gets smaller and smaller cld 9 d As a result RR aab ccd 9 ab cd adbc OR So it is sometimes possible to estimate RR from a case control study because OR eventdisease OR eventexposure When the disease is rare OR even jisease RR eventwisease When the disease is rare OR eveonpmum RR eventdisease docu Wk4gsolutionsdoc

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