STAT 405 Fall 2014 - Homework 3 (62 points)
Due Monday, September 29th
1. Assessment of Radiological Tests in the Detection of Coronary Artery Disease
Begg et al. (1988) in their paper “Assessment of Radiological Tests: Control of Bias and Other
Design Considerations” looked at the performance of radionuclide ventriculography as a
diagnostic test for detecting coronary artery disease. The following results were obtained when
using the test on 481 individuals known to have coronary artery disease and 452 individuals
who do not have the disease.
Test Result
Positive (T+)
Negative (T-)
Row Total
Coronary Artery
Disease (D+)
302
179
481
Disease
Absent (D-)
80
372
452
Column Total
382
551
n = 933
a) Calculate the sensitivity, specificity, false positive, and false negative probabilities using the
results above. (4 pts.)
b) For a population in which the prevalence of coronary artery disease is .10 (or 10%) calculate
the probability that an individual has coronary artery disease given that they test positive using
radionuclide ventriculography, i.e. calculate the predictive value positive (PV+)? (3 pts.)
c) For the same population, what is the probability that a person that tests negative does not
have coronary artery disease, i.e. calculate the predictive value negative (PV-)? (3 pts.)
2.
Low Birth Weight Risk Factors
(Lowbirth.JMP)
The purpose of this study was to identify potential risk factors for low birth weight. The
following categorical variables were measured and coded as follows:
Prev? = women has previous history of premature labor (History, None)
Hyper = hypertension during pregnancy (HT, Normal)
Smoke = smoked during pregnancy (Cig = smoker, No Cig = non-smoker)
Uterine = uterine irritability during pregnancy (Irritation, None)
Minority = minority status (Nonwhite, White)
Low = low birth weight indicator (Low, Normal)  Response/Outcome
a) For each risk factor calculate P(Low|risk factor present) and P(Low|risk factor absent) for each
of the four potential risk factors. In general, what do these probabilities tell you about each of
the potential risk factors? (5 pts.)
b) Use your answers in part (a) to calculate the relative risk (RR) and the CI for the RR
associated with each potential risk factor and put them in the table below. Interpret the RR
associated with smoking during pregnancy and use the CI to address whether there is a
significant increase in risk associated with smoking. (5 pts.)
c) Calculate the odds ratio (OR) and the CI for the OR associated with each characteristic and
put them in the table on the following page. Interpret the OR associated with uterine irritability
during pregnancy and use the CI to address whether there is a significant increase in risk
associated with uterine irritability during pregnancy. (5 pts.)
d) Use SAS to obtain estimates and CI’s for both the RR and OR for low birth weight associated
with smoking during pregnancy. Copy and paste the results into this document. (5 pts.)
e) Which factor do has the greatest associated risk of having a child with low birth
weight? the least? Explain your answers. (3 pts.)
When completing the table, give the statistic and the associated 95% CI for population value,
e.g. 2.12 (1.31, 3.24)  the CI is of the form (LCL,UCL).
Risk Factor
Previous history of premature
labor
Hypertension during
pregnancy
Smoked during
pregnancy
Uterine irritability during
pregnancy
Minority status
of mother
Relative Risk (RR) & CI
Odds Ratio (OR)
f) Do you think this was a case-control study or a cross-sectional study of births from the
general population? Justify your answer. Which measure of “risk” the RR or the OR is most
appropriate. (3 pts.)
3. Eating Fish and Stroke
The preventative benefits of eating fish have been reported in numerous studies. A
recent cohort study reported that not eating fish increased the risk of stroke. The table
below contains the results of the study:
Stroke Non-stroke
Eating Fish
Cases Cases
Row Totals
Never
82
1549
1631
Almost Daily
23
779
802
Column Totals
105
2328
2433
a) What is the estimate of P(Stroke|Never)? P(Stoke|Almost Daily)? (2 pts.)
b) What is the RR of stroke associated with never eating fish? Interpret. (3 pts.)
c) Find a CI for the RR, does this interval suggest there is a significant increase in
risk of stroke associated with never eating fish? Explain. (4 pts.)
4. Mental Health
The Chinese Mini-Mental Status Test (CMMS) consists of 114 items intended to identify people
with Alzheimer’s disease and senile dementia among people in China. An extensive clinical
evaluation of this instrument was performed, whereby participants were interviewed by
psychiatrists and nurses and a definitive diagnosis of dementia was made. The table below
shows the results obtained for the subgroup of people with at least some formal education.
Suppose a cutoff value of < 20 on the test is used to identify people with dementia.
CMMS Score
0-5
6-10
11-15
16-20
21-25
26-30
Totals
Nondemented
0
0
3
9
16
18
46
Demented
2
1
4
5
3
1
16
a) What is the sensitivity of the test? (2 pts.)
b) What is the specificity of the test? (2 pts.)
c) The cutoff of 20 on the CMMS used to identify people with dementia is arbitrary.
Suppose we consider changing the cutoff. What are the sensitivity and specificity if
cutoffs of 5, 10,15, 20 (done in parts a & b), 25, or 30? Make a table of your results. (4 pts.)
Cutoff
5
10
15
20
25
30
Sensitivity
Specificity
d) Construct an ROC curve based on the table in part (c). (3 pts.)
e) Suppose we want both the sensitivity and specificity to be at least 70%. Use the ROC
curve to identify possible value(s) to use as the cutoff for identifying people with
dementia, based on these criteria. (2 pts.)
f) Calculate the area under the ROC curve. Interpret what this area means in words in the
context of this problem. (4 pts.)