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Terms in Survival Analysis

Survival Rate

It is the percentage of people in a study or treatment group still alive for a given period of time after diagnosis. Survival rates are important for prognosis, but because the rate is based on the population as a whole, an individual prognosis may be different depending on newer treatments since the last statistical analysis as well as the overall general health of the patient.[citation needed][1] There are various types of survival rates (discussed below). They often serve as endpoints of clinical trials and should not be confused with mortality rates, a population metric.

Hazard Rate

The hazard plot displays the instantaneous failure rate for each time t. The famous bathtub curve refers to the hazard rate. It is a nonparametric random variable.Hazard rate refers to the rate of death for an item of a given age (x), and is also known as the failure rate. It is part of a larger equation called the hazard function (denoted by \lambda ), which analyzes the likelihood that something will survive to a certain point in time based on its survival to an earlier time (t). In other words, it is the likelihood that if something survives to one moment, it will also survive to the next. Hazard rate only applies to those items which cannot be repaired.

The hazard rate for any time can be determined using the following equation:
h(t) = f(t) / R(t)
f(t) is the probability density function, or the probability that the value (failure or death) will fall in a specified interval (for example, a specific year).
R(t) is the survival function, or the probability that something will survive past a certain time (t).
The hazard rate cannot be negative, and it is necessary to have a set “lifetime” on which to model the equation.

Cumulative Hazard Rate

Mean Cumulative Function

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