 Sampling limits in anatomical variant frequencies

Sampling limits in anatomical variant frequencies distinguish how often a structure was observed in a specimen set from how common it is in a defined population. The denominator must identify the independent anatomical unit: people, hearts, limbs or images are different units. Preserved material and the detection procedure also determine what can be observed.

A primary example dissected 37 formalin-fixed adult human hearts, finding the small cardiac vein in 54% of specimens and an approximately 1 mm venous connection in 19%.^[ref] Those percentages describe that study's material; they do not establish a universal frequency across populations or measurement methods.

Under an original independent, representative-sampling model with perfect detection, a binomial distribution gives $X\sim \mathrm{Bin}(n,p)$. If no examples of a specified variant are seen, $\mathrm{Pr}(X=0)=(1-p{)}^n$. Inverting the one-sided test at level $\alpha$ givesFor a hypothetical zero observations among 37 specimens and $\alpha =0.05$, the upper limit is approximately 0.0778, not zero. The familiar approximation $-\log (\alpha )/n$ is about 0.0810 here. These are illustrations, not unreported results from the anatomical paper.

Detection-limited anatomical prevalence bounds add another assumption explicitly. If a real variant is detected with probability $q$ and false detections are absent, the observed-event probability is $qp$. Zero observed cases therefore gives $p_{\mathrm{upper}}=\min \{1,(1-{\alpha }^{1/n})/q\}$ when $q$ is known. At stipulated $q=0.5$, the example limit becomes approximately 0.156. Unknown detection probability cannot be repaired by reporting a more precise count.

Repeated photographs of the same heart do not create independent new hearts. Counting every image as an independent specimen would artificially narrow a confidence interval. Selection of unusually accessible, preserved or clinically referred specimens can also produce bias that a binomial distribution does not quantify. A useful anatomical report states selection, preservation, observation criteria and the denominator alongside its frequency; uncertainty calculations then make their sampling and detection assumptions visible.