Relative survival and net survival: meaning and when to use

Relative survival measures the survival of people with a disease against the survival of the general population of the same age, sex and calendar year, taken to be what they would have had without the disease. It is used when the cause of death is unknown or unreliable, as in many population cancer registries. Instead of asking who died of the cancer, it compares the mortality of the patients with the mortality expected for such people, taken from a life table, and treats the excess as due to the disease and its treatment.

The term is used for two different things. The relative survival ratio is the observed survival of the patients divided by the survival expected for them. Net survival is the survival the patients would have if the disease were the only cause of death. They are not the same thing, and which one is meant matters when populations are compared (Pohar Perme et al., 2016).

Observed, expected and relative survival

The observed survival of a group of patients is the Kaplan–Meier estimate with death from any cause as the event. The expected survival is what a group with the same mix of age, sex and calendar year would have, calculated from life tables, which give the mortality rate for each single year of age, by sex and calendar year, and are published for most countries by the national statistics office. The relative survival ratio is the first divided by the second.

Take two hypothetical groups of patients followed for five years. In the group aged 70 to 79, 55% are alive at five years, where 72% would be expected to be, so the relative survival ratio is 0.55/0.72 = 0.76. In the group aged 50 to 59, 84% are alive where 97% would be expected, a ratio of 0.87. The older group has the lower observed survival, but much of that is old age itself, which the expected survival takes out. What is left is the shortfall: observed survival 17 percentage points below expected in the older group and 13 in the younger.

The excess hazard

The usual regression models for relative survival are additive. They split each person's hazard into two parts, $h (t) = h^{*} (t) + λ (t)$ . The expected hazard $h^{*} (t)$ comes from the life table for that person's attained age, sex and calendar year and is treated as known. The excess hazard $λ (t)$ is the part due to the disease, and it is what the model describes, with covariates acting on it (Dickman et al., 2004). Net survival then follows from the excess hazard alone. For a person with given covariates it is $\exp {- \int_{0}^{t} λ (u) d u}$ , the survival of a patient who faces only the excess, and the net survival of a group is the average of these over its members.

Estimating net survival

The traditional estimators (Ederer I, Ederer II and Hakulinen), long in routine use at cancer registries, do not consistently estimate net survival, because the relative survival ratio they target depends on the general population's mortality. They give close results when the data are stratified finely by age and sex. Pohar Perme et al. (2012) proposed an estimator that is consistent for net survival and needs no modelling. It can be imprecise when many patients are old and few remain at risk (Pohar Perme et al., 2016), and comparisons across populations still need age standardisation.

When to use it

The cause of death is missing or unreliable. The recorded cause can be misclassified, and deaths from late effects of treatment may not be attributed to the cancer. Relative survival needs only that people died, not why.
You compare populations. Different countries, regions or periods differ in background mortality and in the age of their patients. Net survival does not depend on the first, but it does depend on the second, so compare it within age groups or age-standardised. Pohar Perme et al. (2016) conclude that for such comparisons net survival is the only measure to use.
You also want the crude risk. The probability that a patient dies of the cancer, allowing for other causes, is a different question, answered by the cumulative incidence of death from the cancer. Without the cause of death it can still be estimated from the excess hazard (Cronin and Feuer, 2000), and Pohar Perme et al. (2016) find that reporting crude probabilities beside net survival gives a complete picture.

Assumptions and cautions

The expected rates must fit the patients. The life table should match the patients' country, sex, age and calendar year, and, where the table allows it, region or deprivation. The method assumes that without the disease the patients would have died at the table's rate, which is not testable. If patients differ from the general population in smoking or other risks, as in lung cancer, some of the excess is not due to the disease.
Death from the disease and from other causes are assumed independent among people with the same age, sex and calendar year. The data cannot test this. The additive model also takes a patient's total hazard to be the sum of the expected and excess hazards.
Net survival is a hypothetical quantity. It describes a world in which the disease is the only cause of death. It is the right basis for comparison but not what any patient will experience, which is one reason a crude probability is often reported beside it.
Time scales matter. Survival is counted from diagnosis, while the expected hazard depends on attained age and calendar year, so each person's rate has to be looked up for the age and year they have reached at each time.
It is not the only route. Where the cause of death is reliable and the question is about deaths from the disease, cause-specific analyses are an alternative (What are competing risks?).

In software

In R, the relsurv package estimates net survival with the Pohar Perme estimator (Pohar Perme and Pavlic, 2018) and also fits additive and multiplicative relative survival regression models. In Stata, among other routes, strs estimates relative survival, net survival and crude probabilities of death from population mortality rates (Dickman and Coviello, 2015). In merlin the expected rate is passed through the bhazard() option of a survival model, which turns it into a model for the excess hazard, as worked through in Relative survival analysis. When no life table suits the population, stexcess models the expected hazard from a reference population in the same data.

Using relative survival in a submission?

In a health technology assessment, relative survival is one way to keep an extrapolation from falling below the general population's mortality. The choices of life table, model and scale are judgements a reviewer will test. We can help you make and justify them: see our HTA survival modelling service, or talk to us about your data.

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