# Glossary

## Incidence / Mortality

Incidence

The number of new cancer cases diagnosed during a specified period of time in a given population.

Mortality

Number of deaths from cancer during a specific period of time in a given population.

Number of cases / deaths per year (N/year)

Number of (incident cases / deaths) during a given period of time divided by the number of years in this period.

Relative frequency (FR or %)

NNumber of (incident cases / deaths) of a type of cancer during the study period divided by the total cancers / total deaths from cancer in the same period of time in the study population. It is expressed as a percentage.

Crude rate (TB)

It is calculated by dividing the total number of (new cancers / deaths) occurring in a certain specific population during a specific time period the total number of person-years of observation and multiplying the result, usually, 100.000. This type of rate is affected by the age structure of populations and is not appropriate for comparison, although it does reflect the true value of the rate of cancer.

$$\text{TB} = \Bigg(\frac{\text{Number of} \enspace {(\frac{\text{incident cases}}{\text{deaths}}) \enspace \text{in the period}}}{\text{number of people} - \text {year at risk}} \Bigg) * 100000$$
Age-specific rate (TEE)

It is the rate of (incidence / mortality) for a specific age group. It is calculated by dividing the number of (cases / deaths) that occur in an age group by the corresponding person- years of observation and multiplying, generally, by 10.000.

Age-adjusted rates are used to compare rates of (incidence / mortality) between different populations that differ from each other in their demographic structure or from the same population in different periods of time (temporal evolution) due to the close relationship between the appearance of the cancer and age and different levels of aging of different populations. To avoid this influence of age, the rates adjusted by the direct method are calculated, normally taking the world standard population or the European standard population as a reference.
The adjusted rate is a summary measure of the rate that a given population would have if it had the same age structure as the population considered standard. It is generally expressed as the number of (cancers / deaths) per 100,000 people per year.

$$\text{AT} = \frac{\textstyle\sum_{i=1}^{18}{wi}*{\text{TEE}}_i}{\textstyle\sum_{i=1}^{18}{wi}_i}*\frac{N}{N-SE}$$ Where:
• w are the weights of each age group in the standard population (world or European).
• N is the number of (incident cases / deaths) in the period.
• SE is the number of (incident cases / deaths) with no known age in the period
Depending on the populations that we want to compare, we can use the following types of standard populations:
• World standard population: When we want to compare ourselves with countries around the world.
• European standard population: We use it when we compare ourselves with European countries, since our age structure is more similar. In Europe, that of Waterhouse et al., From 1976, continues in force. Eurostat has been proposing a new population for the calculation of standardization since 2013 to more accurately reproduce demographic change in Europe
• Others: When you want to compare between populations of territorial areas is smaller, sometimes other pyramids are used. For example, if data only from Spanish cancer registries are used, a pyramid of the entire Spanish population can be used. The disadvantage of using these pyramids is that the results cannot be compared with results from registries in other countries.
Standard populations
Age World P. 1960 European 1976 European 2013 European 2013 * Age
<1 2400 1600 1000 1000 <1
1-4 9600 6400 4000 4000 1-4
5-9 10000 7000 5500 5500 5-9
10-14 9000 7000 5500 5500 10-14
15-19 9000 7000 5500 5500 15-19
20-24 8000 7000 6000 6000 20-24
25-29 8000 7000 6000 6000 25-29
30-34 6000 7000 6500 6500 30-34
35-39 6000 7000 7000 7000 35-39
40-44 6000 7000 7000 7000 40-44
45-49 6000 7000 7000 7000 45-49
50-54 5000 7000 7000 7000 50-54
55-59 4000 6000 6500 6500 55-59
60-64 4000 5000 6000 6000 60-64
65-69 3000 4000 5500 5500 65-69
70-74 2000 3000 5000 5000 70-74
75-79 1000 2000 4000 4000 75-79
80-84 500 1000 2500 2500 80-84
>=85 500 1000 2500 1500 85-89
800 90-94
200 >=95
Truncated rate (TTr)

It is a type of adjusted rate that only takes into account the age groups between 35 and 64 years. Its interest lies in the fact that it is considered that the cases of the higher age groups are more difficult to register completely and that in the lower age groups, the probability of the appearance of cancer is very low and take them into account in the calculation of global rates distorts the results to some extent. It is generally expressed as the number of cancers per 100,000 person-years.

Accumulated rate (TAC)

It is the sum of the age-specific rates, up to a limit, usually 75 years.

Cumulative risk of (developing / dying from) cancer (Risk)

The risk or cumulative probability of (developing / dying from) cancer is calculated by adding the number of people who (develop / die from) cancer up to a given age group and dividing by the sum of people who were at risk. It indicates the probability that an individual has to develop / die from cancer over a period of his life, in the absence of another cause of death. It is usually calculated for two ranges: from 0 to 64 years and from 0 to 75 years.

$$\text{Risk} = \Bigg(1-exp\bigg(\frac{\text{TAC}}{100}\bigg)\Bigg) * 100$$

## Incidence and mortality trends

Trends over time

The trends show the change in incidence or mortality rates over time expressed as an annual percentage change.

Percentage change

The percentage change of a statistic in a given time interval is:

$$\text{Percentage change} = \Bigg(\frac{\text {Final Value} - {\text{Initial value}}}{\text{Initial value}}\Bigg) * 100$$ A positive percentage change corresponds to an increasing trend, while a negative percentage change corresponds to a decreasing trend.
PAnnual percent change (CAP)

It is the average annual percentage change over several years. The CAP is used to measure trends (change in rates) over time.

Joinpoint

Percentage of change in the number of incidental cases by factor

Percentage of change in the number of incidental cases by factor

In the study of trends over long periods of time, we can decompose the percentage change in the total number of (incidental cases / deaths) between the initial year and the final year of the period into three components (size and structure of the population and risk), using the method described by Bashir and Esteve (Bashir et al, 2000)

## Survival

Survival

Survival analysis consists of estimating the probability that a patient diagnosed with cancer will survive more than a certain time. When applied to a series of patients, the proportion of these who survive more than a given time is estimated. Survival rates are the most direct indicators of the severity of cancer and the impact of treatment. Population survival is measured in cancer registries, which is generally lower than in case series or clinical trials, since these do not include patients who do not have adequate treatment or are not eligible for clinical trials.

Observed Survival

It is the probability that a patient diagnosed with cancer will survive all causes of death during a specific time interval. Observed survival does not consider cause of death, just look at who is alive and who is not. It is sometimes known as general survival.

This survival is calculated from the cohort of cancer cases under study using the actuarial method or the Kaplan- Meier method.

Net Survival

Two types of mortality intervene in the group of cancer patients, a mortality derived from the cancer that we study and another unrelated to this cancer.

Net survival is survival in the absence of causes of death other than cancer. Represents a hypothetical situation where cancer is the only attributable cause of death. We can estimate net survival using cause-specific survival, relative survival, or the Pohar-Perme estimator.

Survival by specific cause

It is an estimate of net survival that is calculated using the cause of death indicated on death certificates to estimate the proportion of deaths from cancer.

Specific survival consists of calculating observed survival excluding deaths from causes other than cancer. The problem of calculating the survival and s that often cannot determine the cause of death for either the cause of death is unknown, or the quality of death certificates is low or cannot know whether the tumour has contributed or not to the death of the patient.

Relative Survival

It is an estimate of net survival that is defined as the ratio between observed survival that ignores the cause of death and expected survival in a group of people with the same initial age and sex distribution, but without the specific disease we are studying. . Depending on the method for calculating the estimate of the expected survival rate in the group of patients, we will have the relative survival by the Ederer I method, the Ederer II method or the Hakulinen method. The relative survival rate is interpreted as the proportion of patients who survive after a certain follow-up time, in the hypothetical situation where the cancer in question is the only possible cause of death and measures the excess mortality to which a diagnosis is associated of cancer.

Estimator Pohar-Perme

The Pohar-Perme estimator is a weighted version of the Ederer II estimator that uses the relative survival framework, but does not estimate relative survival.

The Pohar-Perme estimator , unlike relative survival, presents an unbiased estimator of net survival. For five-year survival, the Pohar-Perme estimates are similar to the estimates by the Ederer I and II and Hakulinen methods, with differences at higher times.

## Prevalence

Prevalence or Complete Prevalence

Number of people who have been diagnosed with cancer before a certain reference date and who are still alive on this date. It is independent of whether or not they are in treatment.

Prevalence rate

It is the proportion of prevalent cases in a given population and is calculated as the number of prevalent cases per 100,000 inhabitants.

Prevalence at "X" years

It is the part of the prevalence that has been diagnosed in the last "x" years. An example of prevalent at "x" years is any person who has been diagnosed with cancer five years before a certain reference date and is still alive on that date.