Calculate Kannisto-Thatcher extension parameters

Calculate optimal parameters \(\alpha\) and \(\beta\) in the Kannisto-Thatcher model for use in extending a single life table.

Usage

calculate_kt_params(lt, age_start_range, fn)

Arguments

lt

data.table() Life table with columns age_start, mx, and qx.

age_start_range

numeric(2) vector of lower and upper inclusive age group start bounds to calculate parameters from.

fn

Optimization function passed to optim().

Value

numeric(2) a named vector of optimal parameters a and b.

Details

Parameter selection

Initial parameters are derived from the model:

$$\text{logit}(m_x) \sim \ln(\alpha) + \beta * \text{age}$$

Optimization is then done using optim() to minimize the function fn. fn must have the method signature fn(params, data), where:

• params is a named vector of the parameters \(\alpha\) (a) and \(\beta\) (b)

• data is a life table similar to lt