Question

A 9 monthold boy is insulin dependent diabetes mellitus (DDM) was seen in a pediatric diabetic clinic in London. He was well and had no gastrointestical symptoms. He was screened for antibodies. The screening test has a sensitivity of .93 and specificity of .90. The prevalence is 4.5 It was estimated that the patient.s CD willo be 4.5%. What will his post test probability be?

Answer 1

Sensitivity is the probability that the patient with the disease has a positive test. (0.93)

Specificity is the probability that the patient without the disease has a negative test. (0.90)

Prevalence is the probability of having the disease, also called the prior probability of having the disease or the pretest probability. (4.5%)

Given the numbers of specificity, sensitivity and prevalence, we get the following numbers-

The calculations are as below-

Likelihood Ratio-

LR+ = Sensitivity/(1 - Specificity) = 0.93/(1-.90)= 9.3
LR - = (1 - Sensitivity)/Specificity= (1-0.93)/0.90= 0.07777778

Post test probability can be found in different ways-

1) Likelihood Ratio

Pre-Test Probability(Prevalence)= .045 ; Likelihood Ratio = 9.3

Pre-Test Odds = P/(1 - P) = 0.047

Post-Test Odds = Pre-Test Odds * LR(r) = 0.438

Post-Test Probability = Post-Test Odds/(1 + Post-Test Odds) = 0.305

2)Bayes Theorem

PV+=Prevalence×Sensitivity/

(Prevalence×Sensitivity) {(1−Prevalence)×(1−Specificity)}

= (0.045*.93)/

(1-.045)*(1-.90) =0.3046

PV−=(1−Prevalence)×Specificity/

{(1−Prevalence)×Specificity)}+{Prevalence×(1−Sensitivity)}

=(1-0.045)*.90/

(1-0.045)*.90 + (0.045*(1-.93))

=0.9963