Practical Assignment on Biostatistics (Math Problem Sample)

Practical assignment 6
1 An epidemiologic investigation started on January 1, 2001 identified a population of 100 individuals for a yearlong study, as described in the figure below. For this problem, assume that once individuals develop disease they can never be cured. Note that individuals 12 to 100 do not develop disease or die during the study period. (1point)
* What is the prevalence of disease in January of 2001 and in July of 2001? (0.2 points)
Solution
Prevalence in January 2001= Number of people having the disease as ofJanuary 2001The population as of january 2001
Prevalence in January 2001= 4100*100=4%
Prevalence in July 2001= Number of people having the disease as ofJuly 2001The population as of july 2001
Prevalence in January 2001= 696*100=6.25%
* What is the population at risk of disease at the beginning of the study? (0.2 points)
Solution
The population at risk at the beginning of the study is the number of individuals that were not sick at that time.
Population at risk=Total population-Sick individuals
Population at risk=100-4=96
* What is the cumulative incidence of disease during 2001? (0.2 points)
Solution
Cumulative incidence in January 2001=Number of new cases as of January 2001The population as of january 2001
Cumulative incidence in January 2001=0100*100=0 new cases per 100 people
* What is the population at risk of death at the beginning of the study? (0.2 points)
Solution
The population at risk of death is the population that is already ill. In this case, the population at risk of death is 4.
* What is the cumulative incidence of death during 2001? (0.2 points)
Cumulative incidence in 2001=Number of new cases as of 2001The population as of january 2001
Cumulative incidence in 2001=7100*100=7 new cases per 100 people
2 This prospective cohort study was used to investigate the effects of hormone replacement therapy (HRT) on coronary artery disease in post-menopausal women. The investigators calculated the incidence rate of coronary artery disease in post-menopausal women who had been taking HRT and compared it to the incidence rate in post-menopausal women who had not taken HRT. The findings are summarized in this table:
Calculate the rate ratio and interpret your result? (1 point)
Post-menopausal
Hormone Use

# with Coronary Artery
Disease

Person-Years of
Disease-free Follow-up

Yes

30

54,308.7

No

60

51,477.5

Solution
Rate ratio is the ratio of the incidence rate of an exposed group divided by the incidence rate of an unexposed group. Given the above table, we will first compute the incidence rate per 100,000 person years for the group that took HRT and the one that did not, then calculate rate ratio afterwards.
incidence rate for HRT users=3054,308.7*100,000=55.24
incidence rate for non-HRT users=6051447.5*100,000=116.56
Therefore,
Rate ratio=Incidence rate of the exposed groupincidence rate of the unexposed group=55.24116.56=0.47
3 The following data are from a retrospective cohort study on cocaine use during pregnancy and perinatal outcomes among singleton births (Handler et al. Cocaine use during pregnancy: perinatal outcomes. Am J Epidemiol 1991;133:818-25). (1 point)
Table 1. Low birth weight and cocaine use.
Cocaine use

Low birth weight

Normal birth weight

Total

Users

110

289

399

Nonusers

1073

15896

16969

Total

1183

16185

17368

* What incidence measure can you calculate from this data? (0.2 points)
Incidence risk
* What is the incidence of low birth weight among cocaine users? (0.2 points)
Solution
incidence of low birth weight among cocain users=110399*100=27.57%
* What is the incidence of low birth weight among non-users? (0.2 points)
Solution
incidence of low birth weight among cocain non-users=107316969*100=6.32%
* What is the relative risk of low birth weight for cocaine users vs. non-users? (0.2 points)
Solution
Relative risk(rate ratio)=Incidence rate of the exposed groupincidence rate of the unexposed group=27.576.32=4.36
* Give an interpretation of this relative