Survival probability from conditional hazards

Read the equation

Each hazard is the conditional probability of an event in that period given survival up to that period. Multiplying successive complements yields the probability of remaining event-free through the selected period. Hazards in [0,1] give a nonincreasing survival curve in [0,1]; the application uses this for remaining open rather than a biological survival outcome.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

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Original context

		if atRisk[m] > 0 {
			hazard[m] = events[m] / atRisk[m]
		}
	}
	return hazard
}

// Survival returns the cumulative survival curve from a per period hazard vector: S[t] = product over i in 0..t
// of (1 - hazard[i]). S has the same length as hazards; S[t] is the probability of still being open (not yet
// filled) at the end of period t+1. A hazard clamped outside [0,1] is treated as its nearest bound so the
// survival stays a valid probability.
func Survival(hazards []float64) []float64 {
	s := make([]float64, len(hazards))
	running := 1.0
	for t, h := range hazards {
		if h < 0 {
			h = 0
		}

Survival returns the cumulative survival curve from a per period hazard vector: S[t] = product over i in 0..t
of (1 - hazard[i]). S has the same length as hazards; S[t] is the probability of still being open (not yet

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