The hazard function in survival analysis is a key tool for assessing the instantaneous risk of an event at a given time, provided the event has not yet occurred. It is defined mathematically and involves components such as the baseline hazard function, covariates, and the survival function. The cumulative hazard function offers a broader risk perspective over time. These functions are crucial in healthcare, engineering, and finance for predicting event timing and guiding decisions.
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The hazard function measures the immediate risk of an event occurring at a specific time
Limit definition
The hazard function is defined as the limit of the probability of an event occurring in a small interval divided by the length of the interval
Ratio of probability density function and survival function
The hazard function is the ratio of the probability density function to the survival function, providing a conditional measure of risk
The baseline hazard function, covariates, and survival function are key components of the hazard function
The hazard function is used in healthcare, engineering, and finance
In healthcare, it helps analyze patient survival rates and treatment efficacy, while in engineering, it aids in predicting failure rates of machinery
The hazard function assists in forecasting events and guiding strategic decisions in various sectors
The hazard function is calculated by dividing the probability density function by the survival function
Computing the hazard function is crucial for extracting meaningful insights from survival analysis data
The hazard function differs from the cumulative hazard function, which provides a broader perspective on risk over time
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In ______ analysis, the ______ function represents the immediate risk of an event at a specific time, assuming it hasn't happened yet.
survival
hazard
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Hazard function limit definition
h(t) = lim(Δt→0) [P(t ≤ T < t + Δt | T ≥ t) / Δt] - Measures instantaneous event risk.
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Relationship between PDF and hazard function
h(t) = f(t) / S(t) - Hazard function is the ratio of PDF to the survival function.
