Seropositivity Waning Fit
Fit annual seropositivity retention from two cohort proportions under a waning-only model; new exposure and assay changes are not modeled.
Description
Estimate annual retention of observed seropositivity from two positive/tested proportions under a constant waning-only model.
Seropositivity means that an antibody assay result meets its positivity criterion. It is a binary classification, distinct from an antibody concentration or a direct measure of protection. As antibody responses and assay detectability change, people can move below the positivity threshold; this is called seroreversion.1
A constant annual-retention model expresses follow-up seropositivity as the initial proportion multiplied by the same retention factor for each elapsed year. Comparing proportions accounts for different numbers tested at the two time points. It does not establish that observed changes are entirely due to biological waning.
Seropositivity Waning Fit returns an annual retention fraction and its complementary annual loss percentage. It uses two aggregate counts and elapsed time, without tracking individual transitions.
When to summarize a decline in observed seropositivity
Use this tool for a descriptive two-time-point calculation when the populations, assay, and sampling frame are comparable. A waning-only interpretation also requires considering new exposure, vaccination, and changes in who was tested.
- Annualize a nonincreasing pair of observed positive proportions.
- Check how elapsed time changes the implied retention factor.
- Distinguish annual loss from the total decline over the observation interval.
How to enter the counts and annualize retention
- Enter Initial positive and Initial tested as positive integers, with positives no greater than tested.
- Enter Followup positive as a nonnegative integer and Followup tested as a positive integer using the same positivity definition.
- Enter a positive Elapsed years value, using fractional years when appropriate.
- Run the tool and interpret Annual retention fraction and Annual loss percent under the stated model.
p0 = initialPositive/initialTested; p1 = followupPositive/followupTested; r = (p1/p0)^(1/elapsedYears); annualLossPercent = 100 × (1−r) The implementation rejects p1/p0 greater than one, then raises the ratio to the reciprocal of elapsed years.
{
"input": {
"initialPositive": 80,
"initialTested": 100,
"followupPositive": 40,
"followupTested": 100,
"elapsedYears": 2
},
"output": {
"annualRetentionFraction": 0.7071067811865476,
"annualLossPercent": 29.28932188134524
}
}| Observed proportions | Behavior |
|---|---|
| Unchanged | Retention 1; annual loss 0%. |
| Follow-up proportion zero | Retention 0; annual loss 100% under this formula. |
| Follow-up proportion above initial | Input error: outside the waning-only model. |
| Initial positives zero or elapsed years nonpositive | Input error. |
Limitations of a two-point waning-only fit
- No new exposure, vaccination effect, assay drift, population turnover, or paired-person transition information is modeled.
- Observed seropositivity loss does not establish loss of immunity or a clinical protection threshold.
- The tool fits aggregate proportions without assay sensitivity/specificity correction or confidence intervals.
- A zero follow-up count is treated as zero prevalence in the formula; finite sampling and detection limits are not used to bound retention.
Alternative or Complementary serology interpretation
Preserve assay targets, positivity criteria, and cohort composition with the estimate. For imperfect tests, predictive-value analysis and prevalence correction answer separate questions. A more detailed longitudinal model is needed to distinguish individual antibody trajectories from population changes.
References
-
Durable antibody response one year after hospitalization for COVID-19: A longitudinal cohort study — Journal of Autoimmunity (2021)
Similar or alternative tools
- Prevalence Predictive Values
Evaluate predictive values under specified sensitivity, specificity, and prevalence.
- Serology Adjusted IFR
Apply assay correction to observed seropositivity before a population-level fatality calculation with aligned deaths.