Serial Interval Onset Summary

Summarize transmission-pair onset intervals without discarding negative serial intervals.

Description

Calculate symptom-onset differences for transmission pairs, their median, and the count of negative serial intervals.

A serial interval is the elapsed time from symptom onset in a source case to symptom onset in the person infected by that source. It differs from a generation interval, which measures infection-to-infection time. Symptom timing depends on incubation as well as transmission, so a recipient can develop symptoms before the source and produce a negative serial interval.^[1]

Transmission-pair data require two onset observations on a shared time scale. Subtracting source onset from recipient onset preserves the sign and supports a summary without forcing every interval to be positive. A negative observation may be meaningful, but it can also warrant checking the pair assignment or onset record.

Serial Interval Onset Summary returns the individual signed intervals, their median, and the number below zero. It does not reconstruct infection times or verify who infected whom.

When to summarize paired symptom-onset records

Use this tool after transmission pairs and onset definitions have been established. It is useful for inspecting signed observations before choosing a distribution model or using timing information in an epidemic analysis.

Compute each recipient-minus-source onset difference.
Retain negative intervals when checking the observed data.
Summarize central timing with a median rather than an assumed positive distribution.

How to align onset days and calculate the summary

Enter Source onset days and Recipient onset days as equally long nonempty numeric lists.
Use the same day origin and units, with matching list positions for each source–recipient pair.
Run the tool and read Serial intervals days in the original pair order, Median serial days, and Negative interval count.

serialInterval_i = recipientOnsetDays_i − sourceOnsetDays_i

The calculation accepts finite day values, including fractional or negative coordinates relative to a chosen origin. It does not require either input list to be sorted.

The implementation checks list alignment, computes the differences, sorts a copy for the median, and counts values strictly below zero. For an even number of intervals, the median is the average of the two middle sorted values. Sorting does not change the output interval order.

json

{
  "input": {
    "sourceOnsetDays": [
      2,
      5,
      9
    ],
    "recipientOnsetDays": [
      5,
      7,
      8
    ]
  },
  "output": {
    "serialIntervalsDays": [
      3,
      2,
      -1
    ],
    "medianSerialDays": 2,
    "negativeIntervalCount": 1
  }
}

A zero interval is retained but is not counted as negative. Empty or unequal lists and invalid numeric values produce input errors.

Limitations of an observed onset summary

Pair identity, symptom definitions, reporting errors, and missing onsets are not evaluated. Asymptomatic cases need separate handling outside this two-onset representation.
The summary does not adjust for right truncation, interval censoring, selection of transmission pairs, or changing ascertainment.
No mean, fitted distribution, uncertainty interval, reproduction estimate, or infection-time reconstruction is provided.
Serial intervals should not automatically be substituted for generation intervals, particularly when negative intervals are present.

Alternative or Complementary transmission-timing calculations

If infection-time estimates are available, compare generation and serial intervals explicitly. A renewal reproduction calculation instead needs nonnegative lag weights with a defined daily generation-interval interpretation; a signed onset list does not directly supply that input.

References

Serial interval of novel coronavirus (COVID-19) infections — International Journal of Infectious Diseases; H. Nishiura and colleagues (2020)

Similar or alternative tools

Generation Serial Interval Pairs
Calculate both interval types from aligned infection and onset times, and compare their means.
Renewal Window RT
Calculate rolling renewal ratios from incidence and normalized lag-one-first generation weights.