predSNS: Prediction of grouped indicators : population (net) survival...

In survPen: Multidimensional Penalized Splines for (Excess) Hazard Models, Relative Mortality Ratio Models and Marginal Intensity Models

Prediction of grouped indicators : population (net) survival (PNS) and age-standardized (net) survival (SNS)

Description

Allows the prediction of population and age-standardized (net) survival as well as associated confidence intervals

Usage

predSNS(
  model,
  time.points,
  newdata,
  weight.table,
  var.name,
  var.model,
  conf.int = 0.95,
  method = "exact",
  n.legendre = 50
)

Arguments

model	a fitted survPen model
time.points	vector of follow-up values
newdata	dataset containing the original age values used for fitting
weight.table	dataset containing the age classes used for standardization, must be in the same format as the elements of the following list list.wicss
var.name	list containing one element : the column name in newdata that reports age values. This element should be named after the age variable present in the model formula. Typically, if newdata contains an 'age' column while the model uses a centered age 'agec', the list should be: list(agec="age")
var.model	list containing one element : the function that allows retrieving the age variable used in model formula from original age. Typically for age centered on 50, list(agec=function(age) age - 50)
conf.int	numeric value giving the precision of the confidence intervals; default is 0.95
method	should be either 'exact' or 'approx'. The 'exact' method uses all age values in newdata for predictions. The 'approx' method uses either newdata$age (if age values are whole numbers) or floor(newdata$age) + 0.5 (if age values are not whole numbers) and then removes duplicates to reduce computational cost.
n.legendre	number of nodes to approximate the cumulative hazard by Gauss-Legendre quadrature; default is 50

Details

The weight table used should always be in the same format as elements of list.wicss. Only age-standardization is possible for now. All other variables necessary for model predictions should be fixed to a single value. For simplicity, in what follows we will consider that survival only depends on time and age.

Value

List of nine elements

class.table	Number of individuals in each age class
SNS	Vector of predicted age-standardized (net) survival
SNS.inf	Lower bound of confidence intervals associated with predicted age-standardized (net) survival
SNS.sup	Upper bound of confidence intervals associated with predicted age-standardized (net) survival
PNS	Vector of predicted population (net) survival
PNS.inf	Lower bound of confidence intervals associated with predicted population (net) survival
PNS.sup	Upper bound of confidence intervals associated with predicted population (net) survival
PNS_per_class	matrix of predicted population (net) survival in each age class
PNS_per_class.inf	Lower bound of confidence intervals associated with predicted population (net) survival in each age class
PNS_per_class.sup	Upper bound of confidence intervals associated with predicted population (net) survival in each age class

Population Net Survival (PNS)

For a given group of individuals, PNS at time t is defined as

PNS(t)=\sum_i 1/n*S_i(t,a_i)

where a_i is the age of individual i

Standardized Net Survival (SNS)

SNS at time t is defined as

SNS(t)=\sum_i w_i*S_i(t,a_i)

where a_i is the age of individual i and w_i=w_{ref j(i)}/n_{j(i)}. w_{ref j(i)} is the weigth of age class j in the reference population (it corresponds to weight.table$AgeWeights). Where n_{j(i)} is the total number of individuals present in age class j(i): the age class of individual i.

Standardized Net Survival (SNS) with method="approx"

For large datasets, SNS calculation is quite heavy. To reduce computational cost, the idea is to regroup individuals who have similar age values. By using floor(age) + 0.5 instead of age, the gain will be substantial while the prediction error will be minimal (method="approx" will give slightly different predictions compared to method="exact"). Of course, if the provided age values are whole numbers then said provided age values will be used directly for grouping and there will be no prediction error (method="approx" and method="exact" will give the exact same predictions).

SNS(t)=\sum_a \tilde{w}_a*S(t,a)

The sum is here calculated over all possible values of age instead of all individuals. We have \tilde{w}_a=n_a*w_{ref j(a)}/n_{j(a)}. Where j(a) is the age class of age a while n_a is the number of individuals with age a.

Variance and Confidence Intervals

Confidence intervals for SNS are derived assuming normality of log(log(-SNS)) Lower and upper bound are given by

IC_{95\%}(SNS)=[SNS^{1.96*\sqrt(Var(Log(Delta_{SNS})))};SNS^{-1.96*\sqrt(Var(Log(Delta_{SNS})))}]

with

Delta_{SNS}=-log(SNS)

Var(Log(Delta_{SNS})) is derived by Delta method.

Confidence intervals for PNS are derived in the exact same way.

References

Corazziari, I., Quinn, M., & Capocaccia, R. (2004). Standard cancer patient population for age standardising survival ratios. European journal of cancer (Oxford, England : 1990), 40(15), 2307–2316. https://doi.org/10.1016/j.ejca.2004.07.002.

Examples

data(datCancer)
data(list.wicss)

don <- datCancer
don$agec <- don$age - 50 # using centered age for modelling

#-------------------- model with time and age

knots.t<-quantile(don$fu[don$dead==1],probs=seq(0,1,length=6)) # knots for time
knots.agec<-quantile(don$agec[don$dead==1],probs=seq(0,1,length=5))   # knots for age

formula <- as.formula(~tensor(fu,agec,df=c(length(knots.t),length(knots.agec)),
knots=list(fu=knots.t,age=knots.agec)))

mod <- survPen(formula,data=don,t1=fu,event=dead,n.legendre=20, expected=rate)


#-------------------- Age classes and associated weights for age-standardized 
# net survival prediction
		
# weights of type 1					
wicss <- list.wicss[["1"]]					
				
# to estimate population net survival, prediction dataframe
# is needed. It should contain original data for age 

pred.pop <- data.frame(age=don$age)

#-------------------- prediction : age-standardized net survival and population net survival

pred <- predSNS(mod,time.points=seq(0,5,by=0.1),newdata=pred.pop,
weight.table=wicss,var.name=list(agec="age"),
var.model=list(agec=function(age) age - 50),method="approx")

survPen documentation built on April 4, 2025, 3:06 a.m.