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

ABSTRACT Objective 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. Methods For disease prevalence , screening sensitivity , specificity , false‐positive rate , and positive likelihood ratio , we derive closed‐form expressions for posterior probability after 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 () that prices missed cases explicitly and identifies the value of a detected case at which the ranking reverses. Results Persistent positivity compounds evidence by replacing with : False positives fall geometrically through , while true positives fall through . Expected screening workload follows a thinning process: 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. Conclusions 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.