Hemagglutination Dilution Endpoint

Find an observed HA reciprocal-dilution endpoint with monotonicity and censoring checks.

Description

Find the highest tested reciprocal dilution with observed hemagglutination and report whether it is beyond the tested range.

Hemagglutination is the clumping of red blood cells observed in an assay with agglutinating virus. A dilution endpoint records the highest tested dilution still scored positive. A reciprocal value of 8 represents a 1:8 dilution, with larger reciprocals representing greater dilution.^[1]

The endpoint is an observed dilution, not an interpolated concentration. If the final tested dilution remains positive, the endpoint may lie above the tested range and should be recorded as right-censored. No positive observations instead gives a below-range result.

Hemagglutination Dilution Endpoint reads an already scored binary series and returns the reciprocal endpoint, a detection flag, and a right-censoring flag. It measures agglutination, which is distinct from antibody-mediated hemagglutination inhibition.

When to summarize a scored agglutination series

Use the tool after the wells have been scored and dilution order established. Preserve the assay volume and observation criteria separately, since the calculator does not evaluate raw images or convert to an infectious titer.

Read the final positive result in a dilution series.
Retain the distinction between no detected endpoint and an above-range endpoint.

How to enter a binary dilution series and read its endpoint

Enter nonempty positive Reciprocal dilutions in strictly increasing order.
Enter aligned Agglutination flags using 1 for positive and 0 for negative. Positives must precede negatives, with no later return to positive.
Run the tool and interpret Endpoint reciprocal together with Endpoint detected and Right censored.

The implementation validates binary nonincreasing flags and scans for the last 1. It returns that dilution reciprocal. Dilutions need not follow a regular fold step.

Flags	Outputs
At least one 1 followed by a 0	Last positive reciprocal; detected true; rightCensored false.
All 1	Final reciprocal; detected true; rightCensored true.
All 0	Reciprocal 0 sentinel; detected false; rightCensored false.

json

{
  "input": {
    "reciprocalDilutions": [
      2,
      4,
      8,
      16
    ],
    "agglutinationFlags": [
      1,
      1,
      0,
      0
    ]
  },
  "output": {
    "endpointReciprocal": 4,
    "endpointDetected": true,
    "rightCensored": false
  }
}

Empty or misaligned lists, repeated/unordered dilutions, nonpositive reciprocals, nonbinary flags, and a negative-to-positive reversal produce errors. A single positive observation is accepted and right-censored.

Limitations and interpretation

A detected endpoint means a positive observation exists; it does not locate the true endpoint when the final dilution is positive.
The zero reciprocal is a no-positive sentinel, not a measured zero titer.
No interpolation, assay-image scoring, replicate combination, infectivity conversion, or confidence interval is supplied.
HA and HAI have different interpretations; antibody inhibition results must not be substituted for agglutination-positive flags.

Alternative or Complementary methods

Use an independently measured stock HA-unit concentration when calculating an antigen dilution. Paired HAI ratios summarize antibody inhibition titers and address a different measurement.

References

Manual for the laboratory diagnosis and virological surveillance of influenza — World Health Organization (2011)

Similar or alternative tools

HAI Antigen Unit Standardization
Calculate dilution volumes from supplied stock HA units and a desired unit amount.
Paired HAI Titer Rise
Compare supplied acute and convalescent reciprocal HAI titers against a fold-rise criterion.