Suppose That a Study Was Conducted to Assess the Relationship Between Breast Cancer And

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

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.