Sequential Screening as Diagnostic Filtering or Substitution: A Bayesian Cost Model of Screening as a Function of...

In low-prevalence settings, standard screening cascades may generate many false-positive referrals for confirmatory testing, increasing cost, delay, and patient burden. We develop a Bayesian cost model comparing the standard cascade with two sequential architectures: substitution, in which repeated screening replaces immediate confirmation, and filtering, in which repeated screening narrows the group referred for confirmation.

For disease prevalence $\varphi$ , screening sensitivity $a$ , specificity $b$ , false-positive rate $f=1-b$ , and positive likelihood ratio $\kappa =a∕f$ , we derive closed-form expressions for posterior probability after $n$ consecutive positive screens, persistent-positive probability, expected screening workload, true-positive yield, residual false positives, referral burden, total cost, and cost per true positive detected. The model assumes conditional independence of repeated screens, a perfectly discriminating confirmatory test, and a restricted cost-per-true-positive criterion. Break-even diagnostic-test costs are derived for substitution and filtering, and linked to the prevalence-threshold framework. Because an average cost-per-true-positive ratio places a missed case in neither its numerator nor its denominator, and so values a false negative at zero, we complement it with an incremental cost-effectiveness analysis ( $\Delta \text{Cost}∕\Delta \text{Effect}$ ) that prices missed cases explicitly and identifies the value of a detected case at which the ranking reverses.

Persistent positivity compounds evidence by replacing $\kappa$ with ${\kappa }^n$ : [Formula: see text] False positives fall geometrically through $f^n$ , while true positives fall through $a^n$ . Expected screening workload follows a thinning process: [Formula: see text] Sequential repetition is most favorable when prevalence is low, screening is inexpensive and repeatable, confirmation is costly or capacity-limited, repeated results are sufficiently independent, and yield loss is acceptable. Geometrically, repetition shifts the prevalence threshold leftward into a more discriminating regime. The validity of ranking strategies by average cost per true positive is itself bounded by the negative prevalence threshold of the screening curve: below it the omission of false negatives is quantitatively benign, while above it the same omission biases the comparison toward the sensitivity-sacrificing architectures.

Sequential screening is a prevalence-dependent design choice, not a universal substitute for diagnosis. Filtering is more clinically conservative because it preserves confirmation while reducing referrals. Substitution is appropriate only when repeated measurements are already embedded in accepted diagnostic standards.