The familial aggregation of respiratory disease is a well-established clinical phenomenon. However, whether this aggregation is due to genetic or environmental factors or both is somewhat controversial. An investigator wishes to study a particular environmental factor, namely the relationship of cigarette-smoking habits in the parents to the presence or absence of asthma in their oldest child age 5 to 9 years living in the household (referred to below as their offspring). Suppose the investigator finds that (1) if both the mother and father are current smokers, then the
Suppose, alternatively, that if the father is a current smoker, then the probability that the mother is a current smoker is .6; whereas if the father is not a current smoker, then the probability that the mother is a current smoker is .2. Also assume that statements 1, 2, 3, and 4 above hold.
What is the posterior probability that the mother is a current smoker if the child has asthma?
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Chapter 3 Solutions
WebAssign for Rosner's Fundamentals of Biostatistics, 8th Edition [Instant Access], Single-Term
- Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forwardIn August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed; of those that survived, many required extensive cleaning. It was thought that cleaning flood-damaged homes might present a health hazard due to the large amounts of mold present in many of the homes. The article “Health Effects of Exposure to Water-Damaged New Orleans Homes Six Months After Hurricanes Katrina and Rita” (K. Cummings, J. Cox-Ganser, et al., American Journal of Public Health, 2008:869–875) reports that in a sample of 365 residents of Orleans Parish who had participated in the cleaning of one or more homes, 77 had experienced symptoms of wheezing, and in a sample of 179 residents who had not participated in cleaning, 23 reported wheezing symptoms (numbers read from a graph). Can you conclude that the frequency of wheezing symptoms is greater among those residents who participated in the cleaning of flood-damaged…arrow_forwardA healthcare provider notices an outbreak of foodborne illness among individuals who attended a holiday cookout. Which study type would be most beneficial in identifying the source of the outbreak?arrow_forward
- Study 2: Two hundred people were randomly selected from a list of all people living in Minneapolis who receive Social Security. Each person in the sample was asked whether or not they took calcium supplements. These people were followed for 5 years, and whether or not they had a heart attack during the 5-year period was noted. The researchers found that the proportion of heart attack victims in the group taking calcium supplements was significantly higher than the proportion of heart attack victims in the group not taking calcium supplements. A) observational study or an experiment B) Did the study use random selection from some population? (Yes or No) C) Did the study use random assignment to the experimental groups? (Yes or No) D) Based on the description of the study, is it reasonable to conclude that taking calcium supplements if the cause of the increased risk of a heart attack? (Yes or No)arrow_forwardBased on a graph below which of the following statement describes the best types of associations between Factors A, C, and D and the Disease: (choose one best answer) Factor Factor C Disease Factor A O Factor A is sufficient but not necessary, while Factors C and D and neither sufficient not necessary. O Factors A, C and D are neither sufficient nor necessary. O Factor A is necessary but not sufficient, while Factors C and D are necessary but not sufficient. O Factor A is sufficient but not necessary, while Factors C and D are neither sufficient not necessary.arrow_forwardFor a variety of reasons, self-reported disease outcomes are frequently used without verification in epidemiologic research. In a study by Parikh-Patel et al. (A-12), researchers looked at the relationship between self-reported cancer cases and actual cases. They used the self-reported cancer data from a California Teachers Study and validated the cancer cases by using the California Cancer Registry data. The following table reports their findings for breast cancer: Cancer Reported (A) Yes No Total Cancer in Registry (B) 2991 112 3103 Cancer Not in Registry 2244 115849 118093 Total 5235 115961 121196 10. 11. Source: Arti Parikh-Patel, Mark Allen, William E. Wright, and the California Teachers Study Steering Committee, “Validation of Self-reported Cancers in the California Teachers Study,” American Journal of Epidemiology, 157 (2003), 539–545. (a) Let A be the event of reporting breast cancer in the California Teachers Study. Find the probability of A in this study. (b)…arrow_forward
- For a variety of reasons, self-reported disease outcomes are frequently used without verification in epidemiologic research. In a study by Parikh-Patel et al. (A-12), researchers looked at the relationship between self-reported cancer cases and actual cases. They used the self-reported cancer data from a California Teachers Study and validated the cancer cases by using the California Cancer Registry data. The following table reports their findings for breast cancer: Cancer Reported (A) Yes No Total Cancer in Registry (B) 2991 112 3103 Cancer Not in Registry 2244 115849 118093 Total 5235 115961 121196 10. 11. Source: Arti Parikh-Patel, Mark Allen, William E. Wright, and the California Teachers Study Steering Committee, “Validation of Self-reported Cancers in the California Teachers Study,” American Journal of Epidemiology, 157 (2003), 539–545. (g) Find the specificity of using self-reported breast cancer as a predictor of actual breast cancer in the California registry.arrow_forwardFor a variety of reasons, self-reported disease outcomes are frequently used without verification in epidemiologic research. In a study by Parikh-Patel et al. (A-12), researchers looked at the relationship between self-reported cancer cases and actual cases. They used the self-reported cancer data from a California Teachers Study and validated the cancer cases by using the California Cancer Registry data. The following table reports their findings for breast cancer: Cancer Reported (A) Yes No Total Cancer in Registry (B) 2991 112 3103 Cancer Not in Registry 2244 115849 118093 Total 5235 115961 121196 10. 11. Source: Arti Parikh-Patel, Mark Allen, William E. Wright, and the California Teachers Study Steering Committee, “Validation of Self-reported Cancers in the California Teachers Study,” American Journal of Epidemiology, 157 (2003), 539–545. (d) FindðAjBÞ (e) Find PðB j AÞ (f) Find the sensitivity of using self-reported breast cancer as a predictor of actual…arrow_forwardImmunization of Schoolchildren. In the article, “Reasons for Non-uptake of Measles, Mumps, and Rubella Catch Up Immunisation in a Measles Epidemic and Side Effects of the Vaccine” (British Medical Journal, Vol. 310, pp. 1629–1632), R. Roberts et al. discussed a follow-up survey to examine why almost 10,000 children, ages 11–15, whose records showed no previous immunization were not immunized. In the survey, 10 of the 46 schools participating in the immunization campaign were randomly chosen and then the parents of all the nonimmunized children at the 10 selected schools were sent a questionnaire. What type of sampling design was used by these authors in their survey? Explain your answer.arrow_forward
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