Diagnostic test selection and Bayesian reasoning in paediatrics — formative SAQs

SAQ 1 — Metrics and residual risk (10 marks)

A colleague says a blood test with high sensitivity “rules out sepsis” in a mottled 12-day-old because the result is negative. ^{[2] [7]}

Questions

1. Define sensitivity and negative predictive value, and state which depends on prevalence. (3 marks) ^[1]
2. Using Bayesian language, explain why a negative result may not make discharge safe in this neonate. (4 marks) ^{[2] [3] [7]}
3. State the residual-risk sentence you would use with the team and family. (3 marks) ^{[4] [9]}

Model answer

Definitions (3). Sensitivity is the proportion of diseased children who test positive (true-positive rate). NPV is the proportion of negative tests that are true negatives. NPV depends on prevalence/pre-test probability; sensitivity does not in the basic formula. ^[1]

Why not safe discharge (4). Pre-test probability in a mottled neonate is high. A negative result multiplies pre-test odds by LR−; if LR− is not extremely small, post-test probability can remain above a safe observation or discharge threshold. Early markers can also be falsely reassuring while disease evolves. Residual must-not-miss risk therefore continues to drive treatment, observation or escalation. ^{[2] [3] [7] [9]}

Residual-risk sentence (3). “Before the test I was highly concerned for serious infection. The negative result lowers concern somewhat but does not make the risk low enough for home. We will treat/observe for residual sepsis risk, reassess trajectory, and explain return triggers.” ^{[4] [9]}