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
ϕ $phi $, screening sensitivity
a $a$, specificity
b $b$, false-positive rate
f
=
1
−
b $f=1-b$, and positive likelihood ratio
κ
=
a
∕
f $kappa =aunicode{x02215}f$, we derive closed-form expressions for posterior probability after
n $n$ 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 (
Δ
Cost
∕
Δ
Effect ${rm{Delta }}text{Cost}unicode{x02215}{rm{Delta }}text{Effect}$) 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
κ $kappa $ with
κ
n ${kappa }^{n}$:
ρ
n
(
ϕ
)
=
κ
n
ϕ
1
+
(
κ
n
−
1
)
ϕ
. ${rho }_{n}(phi )=frac{{kappa }^{n}phi }{1+({kappa }^{n}-1)phi }.$
False positives fall geometrically through
f
n ${f}^{n}$, while true positives fall through
a
n ${a}^{n}$. Expected screening workload follows a thinning process:
E
n
=
ϕ
1
−
a
n
1
−
a
+
(
1
−
ϕ
)
1
−
f
n
1
−
f
. ${E}_{n}=phi frac{1-{a}^{n}}{1-a}+(1-phi )frac{1-{f}^{n}}{1-f}.$
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.