Introduction to biases in epidemiological delays

Nowcasting and forecasting of infectious disease dynamics

Biases in epidemiological delays

Why might our estimates of epidemiological delays be biased?

data reliability and representativeness

intrinsic issues with data collection and recording

Issue #1: Double censoring

reporting of events usually as a date (not date + precise time)
for short delays this can make quite a difference
accounting for it incorrectly can introduce more bias than doing nothing

Double censoring: example

We are trying to estimate an incubation period. For person A we know exposure happened on day 1 and symptom onset on day 3.

Double censoring: example

We are trying to estimate an incubation period. For person A we know exposure happened on day 1 and symptom onset on day 3.

Double censoring: example

We are trying to estimate an incubation period. For person A we know exposure happened on day 1 and symptom onset on day 3.

Double censoring: example

We are trying to estimate an incubation period. For person A we know exposure happened on day 1 and symptom onset on day 3.

The true incubation period of A could be anywhere between 1 and 3 days (but not all equally likely).

Issue #2: right truncation

reporting of events can be triggered by the secondary event
in that case, longer delays might be missing because whilst the primary events have occurred the secondary events have not occurred yet

Example: right truncation

We are trying to estimate an incubation period. Each arrow represents one person with an associated pair of events (infection and symptom onset).

Example: right truncation

We are trying to estimate an incubation period. Each arrow represents one person with an associated pair of events (infection and symptom onset).

Example: right truncation

We are trying to estimate an incubation period. Each arrow represents one person with an associated pair of events (infection and symptom onset).

Example: right truncation

We are trying to estimate an incubation period. Each arrow represents one person with an associated pair of events (infection and symptom onset)

On the day of analysis we have not observed some onsets yet. The delay from infection to onset for these delays tended to be longer. This is made worse during periods of exponential growth.

Example: right truncation

We are trying to estimate an incubation period. Each arrow represents one person with an associated pair of events (infection and symptom onset)

We need to account for infections with longer delays that we haven’t yet observed. We can best do this by using a lognormal distribution for the delays that we do have data on.

Censoring and right truncation

When analysing data from an outbreak in real time, we are likely to have double censoring and right truncation, making things worse
In the practical we will only look at the two separately to keep things simple

Your Turn

Simulate epidemiological delays with biases
Estimate parameters of a delay distribution, correcting for biases

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