apc.forecast.ap {apc}  R Documentation 
Computes forecasts for a model with AP structure.
The data can have any form allowed in, see apc.data.list
. These are all special cases of
generalised trapezoids. If the "lower triangle" with the
largest (age,coh) values are not observed, they can be forecast using this function.
The function extrapolates the AP model to the lower triangle where
per.zero+per.max < per <= age.max+coh.max1
.
The estimates of the age parameters can be used for the lower triangle.
The estimates of the period parameters need to be extrapolated for the lower triangle.
Thus, the function extrapolates
per.forecast.J=age.max+coh.max1per.zeroper.max
period values.
The extrapolation method has to chosen so as not to introduce an identification problem, see
Kuang, Nielsen and Nielsen (2008b,2011).
Two such extrapolation methods are implemented in this function: "I0" and "I1".
The default is to report the linear predictor.
If the model.family="binominal.dose.response"
, that is a logistic model,
then forecasts of dose, response and survival probability are given for lower triangle.
apc.forecast.ap(apc.fit,extrapolation.type="I0",suppress.warning=TRUE)
apc.fit 
List. Output from 
extrapolation.type 
Character. Choices for extrapolating the differenced period parameter ("Delta.beta_per"). Default is "I0".
Both methods are invariant to ad hoc identification of the implied period time effect, by
following the ideas put forward in
Kuang, Nielsen and Nielsen (2008b).
Internally, the extrapolation is done as follows.
The estimated differenced period parameters are found from
"apc.fit$coefficients.canonical" using

suppress.warning 
Logical. If true, suppresses warnings from 
When model.family=binomial.dose.response
forecasts are made by the component method, see Cox (1976).
It is intended to be used for a population analysis situation where the response equals cohortdecrease of dose.
For cell in forecast array with index (age,cohort)
then:
Survival probability is survival=1/(1+exp(predictor_(a,c)))
.
Dose is dose_(a,c)=max(0,dose_(a1,c)response_(a1,c))
.
Response is response_(a,c)=dose_(a,c)*(1survival_(a,c))
.
trap.predictors.forecast 
Matrix. Includes estimates and point forecasts of linear predictor. That is design*coefficient.
Same as the 
index.trap.J 
Matrix. agecoh coordinates for forecast area. Similar structure to

D.xi.per.extrapolated 
Matrix. Extrapolated parameters. Dimension 
trap.dose.forecast 
Matrix. Includes data and point forecasts. Forecasts in lower right triangle.
Dose in cell age,coh equal to dose in cell age1,coh minus response in cell age1,coh.
Only implemented for 
trap.response.forecast 
Matrix. Includes data and point forecasts. Forecasts in lower right triangle.
Response in cell age,coh equal to dose in cell age,coh times 1 minus probability of surviving in that cell.
Only implemented for 
trap.survival.forecast 
Matrix. Point forecasts. Forecasts in lower right triangle
Probability of surviving computed from 
Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> 2 May 2016 (2 Mar 2016)
Cox, P.R. (1976) Demography. 5th Edition. Cambridge: Cambridge University Press. (page 324).
Kuang, D., Nielsen, B. and Nielsen, J.P. (2008b) Forecasting with the ageperiodcohort model and the extended chainladder model. Biometrika 95, 987991. Download: Article; Earlier version Nuffield DP.
Kuang, D., Nielsen B. and Nielsen J.P. (2011) Forecasting in an extended chainladdertype model. Journal of Risk and Insurance 78, 345359. Download: Article; Earlier version: Nuffield DP.