**Age-period-cohort modelling**

Age-period-cohort models were used to calculate these projections. This approach assumes that the probability that someone will get cancer, or die of cancer, will vary by their age, the year that they are born in (period) and which birth cohort (e.g., generation) they are in.

Age effects relate mainly to the biological process of ageing – older people are more likely to get cancer as their cells have had more time to accumulate damage. Period effects refer to changes at a specific time period which affect (albeit to varying degrees) all age groups alive at that time, for example the advent of smoking, or the introduction of tamoxifen. Cohort effects relate to changes which may happen at a specific time but affect each generation alive at that time differently, for example some generations may have started smoking younger than others. Age, period and cohort effects interact with one another, and age-period-cohort models are able to account for all those effects when projecting future cancer incidence and mortality. These models were fitted to observed cancer incidence and mortality rates, with parameters for each of these age, period and cohort effects. The model fitted to the data calculates a trend which is then used to extrapolate the data into the future. The results are projected age-specific incidence rates per 100,000 people, split by sex, five-year age band, cancer site and UK nation. These are weighted to the European standard population to create age-standardised rates that are appropriate for comparison over time and between nations, as they account for differences in population structure.

Models were fit separately for each UK nation and projected cases or deaths were combined to create UK totals. For some cancer sites, a low number of observed cases or deaths in individual nations may have led to unreliable projections. To avoid this, models were fitted to UK-wide data for these sites, and projected cases or deaths for individual nations were calculated as a proportion of national populations. Cancer sites with low numbers of cases even at UK level were grouped together as ‘Other cancers’ and were projected by applying 2014-2018 age- and sex-specific incidence and mortality rates for this group to each UK nation’s projected population; as these sites individually have quite variable observed trends, it was deemed inappropriate to project them using the age-period-cohort approach. The Northern Ireland Cancer Registry recently published projections for cancer incidence in Northern Ireland [1] and kindly provided Cancer Research UK (CRUK) with their data. Therefore, these projections were used where possible and were supplemented with CRUK’s own, using the above method, for cancer sites not included in the provided data. Projections for cancer mortality in Northern Ireland were also provided by the Northern Ireland cancer registry, using the same method as their incidence projections.

The number of cancer cases and deaths were calculated from the projected age-specific rates by applying those rates to projected populations from Office for National Statistics.

**Modifications to the model**

The gradient of the projected trend is reduced over time, as it is unrealistic to assume that the same trends will continue forever – otherwise it would be possible to project that rates could exceed 100%. The gradient was reduced by combining observed (mean average of the last five years of observed data) and projected data in a weighted average with progressively more weight given to the observed data. The first projected datapoint was 95% projected and 5% observed data, with the proportions changing incrementally each year until the last projected datapoint was 60% projected and 40% observed data.

The last data point in the historical cancer incidence and mortality trends can have a large impact on the projected trend. This can lead to unreliable projections if there is some variability in recent incidence and mortality rates. To minimise the impact of this, we fit five models for each cancer site, with each model omitting an additional year of historical data and took the median average of these five projected rates.

**Impact of risk factors**

Risk factors have been modelled implicitly in this analysis. The means that rather than directly adjusting for, say, overweight and obesity rates changing over time, this approach uses the trends seen in the rates of cases and deaths (which are affected by trends in risk factors) to make its projections. The same is true for the effects of new and improved treatments over time on mortality rates, and other variables such as changes to screening and early diagnosis.

The only exceptions to this are smoking rates and HPV vaccination and cervical screening uptake. Smoking rates have been included as an additional parameter for projections of lung cancer incidence and mortality rates due to the close association between smoking and lung cancer. Smoking rates have only been implicitly modelled in projections for other cancer sites for which smoking is a known risk factor. Projected cervical cancer incidence rates are taken from a paper that modelled these rates under the assumption that the nine-valent HPV vaccination would be introduced in 2019, that cervical screening uptake would be 86% and coverage would be at current rates.[2] Projected cervical cancer mortality rates were estimated from projected incidence rates by assuming that the current incidence-to-mortality ratio would continue into the future.

**Statistical significance**

Confidence intervals are not calculated for the projected figures. Projections are by their nature uncertain because unexpected events in future could change the trend. It is not sensible to calculate a boundary of uncertainty around these already uncertain point estimates. Changes are described as ‘increase’ or ‘decrease’ if there is any difference between the point estimates.

### References

- Donnelly DW, Anderson LA, Gavin A; Northern Ireland Cancer Registry Group. Cancer Incidence Projections in Northern Ireland to 2040. Cancer Epidemiol Biomarkers Prev 2020.
- Castanon A, Landy R, Pesola F, Windridge P, Sasieni P. Prediction of Cervical Cancer Incidence in England, UK, up to 2040, Under Four Scenarios: A Modelling Study. Lancet Public Health 2018.

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