 Detection-limited anatomical prevalence bounds

Detection-limited anatomical prevalence bounds account for the fact that a structure can exist without being recognized by the observation method. Zero observed variants constrain the probability of observing a variant; translating that into a population frequency requires a detection model. In anatomical research, specimen preservation, resolution and the definition of a positive observation belong to that model.

A primary coronary-venous study dissected 37 formalin-fixed hearts and reported frequencies of visible venous structures.^[ref] Its specimen count is a concrete setting for explaining sampling, but the detection probabilities below are hypothetical, not estimates from that paper.

Let $p$ be population prevalence and $q$ the probability of detecting a present variant, with no false detections. For independent specimens, the observed count has a binomial distribution with event probability $r=qp$. Zero detections among $n$ gives the one-sided upper boundAt $n=37$, $\alpha =0.05$ and known $q=0.5$, this gives $p_U\approx 0.156$. The confidence statement depends on $q$ being known, not merely on a convenient assumed value.

Joint coverage in detection-calibrated prevalence bounds matters when $q$ is estimated. Suppose a calibration gives a lower bound $q_L>0$ with coverage at least $1-\beta$, while $r_U$ has coverage at least $1-\alpha$. Whenever both bounds cover, $p\le r_U/q_L$; the union bound guarantees combined coverage at least $1-\alpha -\beta$, without requiring independence of the two bounds. Allocating $\alpha =\beta =0.025$ and stipulating a calibrated lower bound $q_L=0.5$ gives $p_U\approx 0.190$ for the same zero count.

False detections change the relation to $r=f+(q-f)p$, where $f$ is the false-detection probability for absent structures. If $q=f$, the observed frequency carries no information about prevalence. Simply dividing by $q$ is then invalid. Detection controls should therefore distinguish missed structures from false recognitions.

These bounds do not repair unrepresentative specimen selection or treating repeated images as independent bodies. Report the anatomical unit, detection validation and target population alongside a confidence interval; more decimal places cannot substitute for those assumptions.