Download Quiz 10

Quiz 10
Suppose that a study was conducted to assess the relationship between breast cancer
and a family history of breast cancer. 100 women with breast cancer provided family
history information. 5 of these women had a family history of breast cancer. 1000 women
without breast cancer also provided family history information. 20 of these women had a
family history of breast cancer.
a) If family history of breast cancer is being considered as a screening tool for breast
cancer, define sensitivity, specificity, predictive value positive and predictive value
negative for the scenario. Be specific.
Sensitivity = the probability that family history is positive given that breast cancer is
present
Specificity = the probability that family history is negative given that breast Ca is not
present
Predictive value positive = the probability that a subject with family history truly has
breast Ca
Predictive value negative = the probability that a subject with no family history truly
does not have breast Ca
T+
T-
D+
5
95
100
D20
980
1000
25
1075
1100
b) Use the data provided above to compute 4 fractions useful for a).
Sensitivity = 5/100 = 0.05
Specificity = 980/1000 = 0.98
Predictive value positive = 5/25 = 0.20
Predictive value negative = 980/1075 = 0.91
What are these fractions called? Estimates of the probabilities
What assumptions are needed to make these fractions useful? For PV to be valid,
the prevalence needs to be accurately reflected in the numbers we are using, ie
100/1100 = 9.1% among our patient group.
c) Define the likelihood ratio for this scenario. Be specific. = the ratio of the
probability that family history is positive given that breast cancer is present divided
by 1 minus the probability that family history is negative given that breast cancer is
not present, ie the ratio of sensitivity of family history given breast cancer divided by
1- the specificity of no family history given no breast cancer.
d) Compute a fraction useful for c) = 0.05/(1-0.98) = 2.5
e) Consider a clinical setting where the pre-test probability of breast cancer is
assumed to be 20%. Compute a possible post-test probability.
Prevalence = Pre-test probability of disease = 20%.
Pre-test odds of disease = p/ (1-p) = 0.20/(1-0.2) = 0.25
Post-test odds of disease = pre-test odds of disease X likelihood ratio =
0.25 X 2.5 = 0.625
We need to convert this to the post test probability of disease
Probability = odds/ (1+ odds) = 0.625/(1+ 0.625) = 0.385
f) What inferential tool would be used with your result in e)? Why? It would be
useful to have the confidence interval for the Likelihood ratio and then we
could calculate the plausible range of values for the post-test probability of
disease.