# Methods

### Model

Mortality baseline is modelled using a glm poisson corrected for over dispersion. The model is fitted on valid historical period as defined by the user, with a maximum of 5 years, excluding

- The period to correct for delay (defined by user)
- The data after week 2009-34 (this to exclude data before the possible influence of H1N1 pandemic. That condition may be modified in the future according to the epidemiological context after consensus with the EuroMOMO hub and partners).

### Requirements of the algorithm

Requirements were defined based on consensus of the EuroMOMO partners.

The algorithm must be able to:

- Compute all causes weekly observed, expected and excess mortality
- Total, by age group
- Be applicable for countries with various mortality pattern
- Be robust for short historical period, low counts
- Correct for delay in data transmission
- Compute standardised indicators for comparison between population subgroups

Additionally, the algorithm should be able to:

- Compute all cause weekly observed, expected and excess mortality by sex, sub-national level (NUTS 2)
- Compute cumulative excess over chosen time period
- Be run retrospectively in order to test the performances of delay correction and detection on past events

### Correction for delay

The method for delay correction works with the assumption that the proportion of deaths registered over a defined period is proportional to the number of days when administration is open.

Modelling of delay is computed only according to the historical period containing a valid date of registration. For each week requiring correction for delay the proportions of deaths already registered at the date of aggregation are computed and modelled according to the number of “days off” (administrations are closed) during the registration period (period between the death and the date of aggregation) and a trend, using a glm (binomial family). The total number of death is then modelled using this proportion and the number of death already registered using a glm of the Poisson family. The corrected number of death is forecasted for the period to correct, as defined by the user.

It is important to notice that the day of the week the aggregation is done is accounted for in the modelling of the corrected number of death: if we aggregate on a Wednesday, all historical data are analysed as if aggregations were done every Wednesday.

**VALIDITY:** the correction for delay will perform well if the transmission of data is smooth and regular, even if the reporting delay is very large. If there is batch reporting and irregular data transmission, the system will perform less well and is likely to predict a mean mortality rather than expected variations. CONTROL graphs help to evaluate the regularity of information flow and determine the length of the period requiring correction for delay.

### Modelling of the baseline

The hypothesis made to generate the model are very simple and do not aim at describing what really happens but aims at providing simple principle for modelling.

### Hypothesis

- The main mortality pattern in European countries is a Poisson distributed time series following a trend and in some cases a sine cycle of a period of one year.
- During winter and summer, that process is modified by additional factors mainly related to winter infections such as influenza and summer heat waves leading to yearly excess of deaths of variable amplitude.
- Parts of Spring and Autumn are less likely to be influenced by additional processes leading to excess deaths and the main pattern of mortality can therefore be modelled using only those periods, resulting in a baseline being the number of deaths expected when no particular process increases mortality.
- A stable time series process can be modelled using only samples of the time series.

### Type of models

Four slightly different models can be chosen by the user, to better fit the local pattern and specific population subgroups. The trend is modelled by either by a straight line or by a linear spline with 2 knots, meaning that non linear trends can be modelled using 3 different linear segments joining at the knots, equally spaced along the data set. Seasonality is modelled by a sine curve of period one year, but model without seasonality can also be designed.

For the age groups defined for EuroMOMO, the models by default will be

- 0 to 4 and 5 to 14: trend = linear trend, no seasonality
- 15 to 64, >= 65 and Total: linear trend, seasonality 25

### Sample of the series used to fit the model

To fit the baseline, only the period of the year when it is assumed that additional processes leading to excess deaths are not likely to happen were chosen. In order to be adapted to most of the participating countries, the variability of influenza and heat waves occurrences, these periods are relatively short compared to the whole of the series and were defined as “Spring”, from week 15 to week 26 and “Autumn”, from week 36 to week 45.