Answers: Risk

Answers to odd number problems

1. Sensitivity = goes with true positive. If test is 100% sensitive then all positives are true positives

3. false positive

5.
A. Odds only
B. Odds and RRR
C. Odds and RRR

7. Find region of maternal risk that is equivalent to amniocentesis risk (1/200) = 0.005. Multiple 0.005 times 10K to get 50 Down Syndrome (DS) per 10K, which falls between 35-39 and 40+ categories. So if risk of amniocentesis is as great as stated, then risk of problems from amniocentesis are greater than risk of DS for women at age 35-39, but less than at age 40.

Note: risk reported by Mayo Clinic of 1/200 seems high — challenging to study (see Salomon et al 2019 who argue the risk is much lower).

RRR = (415-35)/415 → 0.916 → 92%

ARR =(415-35)/389624 = 0.00098

NNT = 1/ARR = 1025 (interpret like NNH). For every 1 person harmed (by drinking lots of coffee), 1024 are not harmed.

11.

specificity is 0.98, the test correctly identifies 98% who do not have the condition.

FP = 1 – specificity = 0.02 or 2%

13.

About 9,994

15.

RRR = (4-3)/4 = 1/4 = 0.25

ARR = 1/1000 = 0.001

NNT = 1/ARR = 1/0.001 = 1000

or 999 receive no benefit for every 1 who does

17.

	Disease progressed	Disease did not progress
Plasma	a = 77	b = 180
Placebo	c = 81	d = 173

a = 77
b = 180
c = 81
d = 173

OR = (a x d)/(b x c) = 0.9136488 –> 0.92

RR = (a/(a+b))/(c/(c+d)) = 0.9395206 –> 0.94

Control event rate (CER) = c/(c+d) = 0.3188976

Experimental event rate (EER) = a/(a+b) = 0.2996109

RRR = 1 – 0.94 = 0.06
= CER-EER/CER = 0.06047942

ARR = 1 – 0.92 = 0.2
= CER – EER = 0.01928674

NNT = 1/ARR = 51.84909 –> 52. Fifty one receive no benefit for every 1 who does. Not a slam-dunk treatment, but not worthless either. A proper assessment requires consideration of side effects. Plasma therapy is not without risk, but the treatment seems promising. See Joyner, M. J., Carter, R. E., Senefeld, J. W., Klassen, S. A., Mills, J. R., Johnson, P. W., … & Casadevall, A. (2021). Convalescent plasma antibody levels and the risk of death from Covid-19. New England Journal of Medicine, 384(11), 1015-1027.