model_survival {mpmsim}

Model mortality hazard, survivorship and age-specific survival probability using a mortality model

Description

Generates an actuarial life table based on a defined mortality model.

Usage

model_survival(params, age = NULL, model, truncate = 0.01)

model_mortality(params, age = NULL, model, truncate = 0.01)

Arguments

params

Numeric vector representing the parameters of the mortality model.

age

Numeric vector representing age. The default is NULL, whereby the survival trajectory is modelled from age 0 to the age at which the survivorship of the synthetic cohort declines to a threshold defined by the truncate argument, which has a default of 0.01 (i.e. 1% of the cohort remaining alive).

model

A character string specifying the name of the mortality model to be used. Options are gompertz, gompertzmakeham, exponential, siler, weibull, and weibullmakeham. These names are not case-sensitive.

truncate

a value defining how the life table output should be truncated. The default is 0.01, indicating that the life table is truncated so that survivorship (lx) > 0.01 (i.e. the age at which 1% of the cohort remains alive).

Details

The required parameters varies depending on the mortality model. The parameters are provided as a vector.

*For gompertz and weibull, the parameters are b0, b1. *For gompertzmakeham and weibullmakeham the parameters are b0, b1 and C. *For exponential, the parameter is C. *For siler, the parameters are a0, a1, C, b0 and b1.

Note that the parameters must be provided in the order mentioned here. x represents age.

• Gompertz: h_x = b_0 \mathrm{e}^{b_1 x}

• Gompertz-Makeham: h_x = b_0 \mathrm{e}^{b_1 x} + c

• Exponential: h_x = c

• Siler: h_x = a_0 \mathrm{e}^{-a_1 x} + c + b_0 \mathrm{e}^{b_1 x}

• Weibull: h_x = b_0 b_1 (b_1 x)^(b_0 - 1)

• Weibull-Makeham: h_x = b_0 b_1 (b_1 x)^(b_0 - 1) + c

In the output, the probability of survival (px) (and death (qx)) represent the probability of individuals that enter the age interval [x,x+1] survive until the end of the interval (or die before the end of the interval). It is not possible to estimate a value for this in the final row of the life table (because there is no x+1 value) and therefore the input values of age (x) may need to be extended to capture this final interval.

Value

A dataframe in the form of a lifetable with columns for age (x), hazard (hx), survivorship (lx) and mortality (qx) and survival probability within interval (px).

Author(s)

Owen Jones [e-mail]

References

Cox, D.R. & Oakes, D. (1984) Analysis of Survival Data. Chapman and Hall, London, UK.

Pinder III, J.E., Wiener, J.G. & Smith, M.H. (1978) The Weibull distribution: a method of summarizing survivorship data. Ecology, 59, 175–179.

Pletcher, S. (1999) Model fitting and hypothesis testing for age-specific mortality data. Journal of Evolutionary Biology, 12, 430–439.

Siler, W. (1979) A competing-risk model for animal mortality. Ecology, 60, 750–757.

Vaupel, J., Manton, K. & Stallard, E. (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454.

See Also

model_fertility() to model age-specific fertility using various functions.

Other trajectories: model_fertility()

Examples

model_mortality(params = c(b_0 = 0.1, b_1 = 0.2), model = "Gompertz")

model_mortality(
  params = c(b_0 = 0.1, b_1 = 0.2, C = 0.1),
  model = "GompertzMakeham",
  truncate = 0.1
)

model_mortality(params = c(c = 0.2), model = "Exponential", age = 0:10)

model_mortality(
  params = c(a_0 = 0.1, a_1 = 0.2, C = 0.1, b_0 = 0.1, b_1 = 0.2),
  model = "Siler",
  age = 0:10
)

model_mortality(
  params = c(b_0 = 1.4, b_1 = 0.18),
  model = "Weibull"
)

model_mortality(
  params = c(b_0 = 1.1, b_1 = 0.05, c = 0.2),
  model = "WeibullMakeham"
)

model_mortality(params = c(b_0 = 0.1, b_1 = 0.2), model = "Gompertz")