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Diagnostic specificity is the probability that a test is negative in someone without the target condition. For an antibody test, relevant negative controls can include samples with antibodies to related pathogens to assess cross-reactivity. With true positive fraction $p$, observed positivity is $Sep+(1-Sp)(1-p)$.

Palpation is examination by touch with the hands or fingers. It uses physical contact to assess features such as an organ's apparent size, position, consistency and tenderness. The observed feature and the resulting clinical diagnosis are separate: feeling a moving or resistant region does not by itself identify the complete underlying anatomy or disease.^[ref]

The force applied during palpation is part of the measurement. In an original simplified indentation example, suppose a probe produces $2\mathrm{mm}$ of displacement under a $1\mathrm{N}$ load. The secant stiffness for that observation isA second specimen requiring $2\mathrm{N}$ at the same displacement has twice this apparent stiffness. That ratio is not automatically a ratio of intrinsic elastic modulus values: contact geometry, specimen thickness, support and deformation rate can alter the force-displacement curve. Touch supplies a mechanical observation whose interpretation requires an appropriate model.

A clinical measurement study makes the distinction concrete. S. D. Eilen and colleagues compared precordial palpation with two-dimensional echocardiography in 41 patients. They compared the location and palpable diameter of the apical impulse with left ventricle end-diastolic volume. A lateral impulse location was sensitive but not specific for enlargement. Within the reported subgroup without ventricular hypertrophy, an impulse diameter above $3\mathrm{cm}$ in the left-lateral position had reported diagnostic sensitivity $92\%$ and diagnostic specificity $91\%$. Those are results for that study's condition and subgroup, rather than universal performance figures for touch.^[ref]

A small probability example explains why both attributes matter. In a stipulated set with 20 enlarged and 80 non-enlarged hearts, a rule detecting 18 enlarged hearts but also flagging 24 non-enlarged hearts has diagnostic sensitivity $18/20=90\%$ and diagnostic specificity $56/80=70\%$. Only $18/42\simeq 43\%$ of its positive results identify enlargement. These invented counts are not a reconstruction of the 41-patient study. They show why a palpable feature must be tested against an independent reference and interpreted with the population being examined.

Repeating a specified observation can assess reproducibility, while comparison with echocardiography assesses a different question: correspondence with the chosen anatomical reference. Holding body position and observation method consistent helps distinguish those sources of variation. A reliable description of what was felt is necessary evidence, but reproducibility alone does not establish the causal explanation.

Assume a constant annual force of infection $\lambda >0$ across ages and calendar years. For independent sampled people with ages $a_i>0$ and binary results $y_i$, fitApplying the complementary log-log link givesTherefore fit a binomial regression with the complementary log-log link, an intercept, and $\ln a_i$ as an offset with coefficient fixed at one. Age is measured in years. An ordinary freely fitted coefficient of age, or even a freely fitted coefficient of $\ln a_i$, would describe a different exposure model. The annual force of infection estimate isAn infection-naive person's one-year infection probability is $1-e^{-\hat{\lambda }}$, which is approximately $\hat{\lambda }$ only when that rate is small.

The log-likelihood being maximized is, apart from constants,A confidence interval for ${\beta }_0$ can be exponentiated to give a positive interval for $\lambda$. For groups of $n_j$ people at a common age $a_j$, use $Y_j\sim \mathrm{Binomial}(n_j,1-e^{-\lambda a_j})$ with the same offset. If an age band is broad, use individual ages or average $1-e^{-\lambda a}$ over the band's age distribution instead of treating its midpoint as exact. No numerical estimate is possible without the survey observations.

The biological interpretation assumes that immunoglobulin G positivity records previous infection, persists over the relevant ages, and is not substantially produced by maternal antibodies or vaccination. These are conditions to check, rather than conclusions from the fitted curve. Use known-positive and known-negative serum controls to assess the assay threshold, and validate specificity against relevant other infections. Cross-reactive antibodies to other flaviviruses can produce positive dengue virus serology, so a positive result need not be a marker specific to dengue virus exposure.^[ref]

If independently established assay diagnostic sensitivity and diagnostic specificity are $Se$ and $Sp$, the observed positive probability isUse that observation model in the binomial likelihood; it is generally no longer the simple intercept-plus-offset complementary log-log link fit. With only the stated survey, one cannot freely estimate $Se$, $Sp$, antibody loss and an arbitrary infection history simultaneously. A single binary result also does not identify how many subsequent infections a person has experienced.

Seroprevalence is the proportion of a specified population with a positive result for a specified antibody assay. Its biological interpretation depends on assay diagnostic sensitivity, diagnostic specificity and the persistence and origin of the measured antibodies. It is not itself the incidence rate of new infection.