excess_lifetime: Excess lifetime

In n8thangreen/QALY: Calculate Quality Adjusted Life Years (QALYs) Gains with Discounting and Inflated Costs

Description

The difference between two future time points (the first of these can be, trivially, the present). Allows discounting of future times so that they are valued less than sooner times.

Usage

excess_lifetime(start, end, discount = 0.035)

Arguments

start	time
end	time
discount	default: 0.035

Details

These are usually two years of death such that this (discounted) time is years of life lost due to illness. This is a component of the DALY calculation by including as a product with the probability of early death (p) and population size (N), i.e. DALY = YLD + YDD, such that YLD = N x p x t

The later time to death is all-cause expected lifetime at a given age which can be obtained from life-tables e.g. from the ONS.

The expanded sum is

\frac{1}{d^{m+1}} + \cdots + \frac{1}{d^{n}}, n > m

Using a finite series identity this is

\frac{1 - (1/d)^{n+1}}{1 - 1/d} - \frac{1 - (1/d)^{m+1}}{1 - 1/d}

= \frac{(1/d)^{m+1} - (1/d)^{n+1}}{1 - 1/d}

n8thangreen/QALY documentation built on Oct. 25, 2020, 10:07 p.m.