model_survival {mpmsim} | R Documentation |
Model mortality hazard, survivorship and age-specific survival probability using a mortality model
Description
Model mortality hazard, survivorship and age-specific survival probability using a 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 |
model |
Mortality model: |
truncate |
a value defining how the life table output should be
truncated. The default is |
Details
The required parameters varies depending on the mortality model. The
parameters are provided as a vector. For Gompertz
, the parameters are
b0
, b1.
For GompertzMakeham
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}
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 data frame with columns for age (x
), hazard (hx
),
survivorship (lx
) and mortality (qx
) and survival probability within
interval (px
).
Author(s)
Owen Jones jones@biology.sdu.dk
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_survival(params = c(b_0 = 0.1, b_1 = 0.2), model = "Gompertz")
model_survival(
params = c(b_0 = 0.1, b_1 = 0.2, C = 0.1),
model = "GompertzMakeham",
truncate = 0.1
)
model_survival(params = c(c = 0.2), model = "Exponential", age = 0:10)
model_survival(
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 = 0.1, b_1 = 0.2), model = "Gompertz")