Relative survival

Relative survival of a disease, in survival analysis, is calculated by dividing the overall survival after diagnosis by the survival as observed in a similar population not diagnosed with that disease. A similar population is composed of individuals with at least age and gender similar to those diagnosed with the disease.

When describing the survival experience of a group of people or patients typically the method of overall survival is used, and it presents estimates of the proportion of people or patients alive at a certain point in time. The problem with measuring overall survival by using the Kaplan-Meier or actuarial survival methods is that the estimates include two causes of death: deaths from the disease of interest and deaths from all other causes, which includes old age, other cancers, trauma and any other possible cause of death. In general, survival analysis is interested in the deaths by a disease rather than all causes. Thus, a "cause-specific survival analysis" is employed to measure disease-specific survival. Thus, there are two ways in performing a cause-specific survival analysis "competing risks survival analysis" and "relative survival."

This form of analysis is known by its use of death certificates. In traditional overall survival analysis, the cause of death is irrelevant to the analysis. In a competing risks survival analyses, each death certificate is reviewed. If the disease of interest is cancer, and the patient dies of a car accident, the patient is labelled as censored at death instead of being labelled as having died. Issues with this method arise, as each hospital and or registry may code for causes of death differently.

For example, there is variability in the way a patient who has cancer and commits suicide is coded/labelled. In addition, if a patient has an eye removed from an ocular cancer and dies getting hit while crossing the road because he did not see the car, he would often be considered to be censored rather than having died from the cancer or its subsequent effects.

The relative survival form of analysis is more complex than "competing risks" but is considered the gold-standard for performing a cause-specific survival analysis. It is based on two rates: the overall hazard rate observed in a diseased population and the background or expected hazard rate in the general or background population.

Deaths from the disease in a single time period are the total number of deaths (overall number of deaths) minus the expected number of deaths in the general population. If a population of cancer sufferers suffer 10 deaths per hundred population but only 1 death occurs per hundred general population, the disease specific number of deaths (excess hazard rate) is 9 deaths per hundred population. The classic equation for the excess hazard rate is as follows:

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