Fit Relative Survival Model
Description
flexrsurv
is used to fit relative survival regression model.
Time dependent variables, nonproportionnal (time dependent) effects,
nonlinear effects are implemented using Splines (Bspline and truncated power basis).
Simultaneously non linear and non proportional effects are implemented
using approaches developed by Remontet et al.(2007) and Mahboubi et al. (2011).
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49  flexrsurv(formula=formula(data),
data=parent.frame(),
knots.Bh,
degree.Bh=3,
Spline=c("bspline", "tpspline", "tpispline"),
log.Bh=FALSE,
bhlink=c("log", "identity"),
Min_T=0,
Max_T=NULL,
model=c("additive","multiplicative"),
rate=NULL,
weights=NULL,
na.action=NULL,
int_meth=c("BANDS", "CAV_SIM", "SIM_3_8", "BOOLE"),
bands=NULL,
stept=NULL,
init=NULL,
initbyglm=TRUE,
initbands=bands,
optim.control=list(trace=100, REPORT=1, fnscale=1, maxit=25),
optim_meth=c("BFGS", "CG", "NelderMead", "LBFGSB", "SANN", "Brent"),
control.glm=list(epsilon=1e8, maxit=100, trace=FALSE, epsilon.glm=1e1, maxit.glm=25),
vartype = c("oim", "opg", "none"),
debug=FALSE
)
flexrsurv.ll(formula=formula(data),
data=parent.frame(),
knots.Bh=NULL,
degree.Bh=3,
Spline=c("bspline", "tpspline", "tpispline"),
log.Bh=FALSE,
bhlink=c("log", "identity"),
Min_T=0,
Max_T=NULL,
model=c("additive","multiplicative"),
rate=NULL,
weights=NULL,
na.action=NULL,
int_meth=c("CAV_SIM", "SIM_3_8", "BOOLE", "GLM", "BANDS"),
stept=NULL,
bands=NULL,
init=NULL,
optim.control=list(trace=100, REPORT=1, fnscale=1, maxit=25),
optim_meth=c("BFGS", "CG", "NelderMead", "LBFGSB", "SANN", "Brent"),
vartype = c("oim", "opg", "none"),
debug=FALSE
)

Arguments
formula 
a formula object, with the response on the left of a ~ operator, and the terms on the
right. The response must be a survival object as returned by the 
data 
a data.frame in which to interpret the variables named in the formula. 
knots.Bh 
the internal breakpoints that define the spline used to estimate the baseline hazard. Typical values are the mean or median for one knot, quantiles for more knots. 
degree.Bh 
degree of the piecewise polynomial of the baseline hazard. Default is 3 for cubic splines. 
Spline 
a character string specifying the type of spline basis. "bspline" for Bspline basis, "tpspline" for truncated power basis and "tpispline" for monotone (increasing) truncated power basis. 
log.Bh 
logical value: if TRUE, an additional basis equal to log(time) is added to the spline bases of time. 
bhlink 
logical value: if TRUE, log of baseline hazard is modelled, if FALSE, the baseline hazard is out of the log. 
Min_T 
minimum of time period which is analysed. Default is 
Max_T 
maximum of time period which is analysed. Default is 
model 
character string specifying the type of model for both nonproportionnal and non linear effects.
The model 
rate 
an optional vector of the background rate for a relevant comparative population to be used in the fitting process. Should be a numeric vector (for relative survival model).

weights 
an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. If not null, the total likelihood is the weighted sum of individual likelihood. 
na.action 
a missingdata filter function, applied to the model.frame, after any subset argument has been used. Default is options()$na.action. 
int_meth 
character string specifying the the numerical integration method. Possible values are "CAV_SIM" for CavalieriSimpson's rule, "SIM_3_8" for the Simpson's 3/8 rule, "BOOLE" for the Boole's rule, or "BANDS" for the midpoint rule with specified bands. 
bands 
bands used to split data in the numerical integration when 
stept 
scalar value of the timestep in numerical integration. It is required only when 
init 
starting values of the parameters. 
initbyglm 
a logical value indicating indicating how are found or refined init values. If TRUE, the fitting method described in Remontet et al.(2007) is ued to find or refine starting values. This may speedup the fit. If FALSE, the maximisation of the likelihood starts at values given in 
initbands 
bands used to split data when 
optim.control 
a list of control parameters passed to the 
optim_meth 
method to be used to optimize the likelihood.
See 
control.glm 
a list of control parameters passed to the 
vartype 
character string specifying the type of variance matrix computed by 
debug 
control the volum of intermediate output 
... 
unused arguments 
Details
A full description of the additive and the multiplicative both nonlinear and nonproportional models is given respectively in Remontet (2007) and Mahboubi (2011).
flexrsurv.ll
is the workhorse function: it is not normally called
directly.
Value
flexrsurv
returns an object of class "flexrsurv"
.
An object of class "flexrsurv"
is a list containing at least the following components:
coefficients 
a named vector of coefficients 
loglik 
the loglikelihood 
var 
estimated covariance matrix for the estimated coefficients 
informationMatrix 
estimated information matrix 
init 
vector of the starting values supplied 
converged 
logical, Was the optimlizer algorithm judged to have converged? 
linear.predictors 
the linear fit on link scale 
fitted.values 
the estimated value of the hazard rate at each event time, obtained by transforming the linear predictors by the inverse of the link function 
cumulative.hazard 
the estimated value of the cumulative hazard in the time interval 
call 
the matched call 
formula 
the formula supplied 
terms 
the 
data 
the 
rate 
the rate vector used 
time 
the time vector used 
workingformula 
the formula used by the fitter 
optim.control 
the value of the 
control.glm 
the value of the 
method 
the name of the fitter function used 
References
Mahboubi, A., M. Abrahamowicz, et al. (2011). "Flexible modeling of the effects of continuous prognostic factors in relative survival." Stat Med 30(12): 13511365. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("DOI:10.1002/sim.4208")}
Remontet, L., N. Bossard, et al. (2007). "An overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies." Stat Med 26(10): 22142228. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.1002/sim.2656")}
See Also
print.flexrsurv
,
summary.flexrsurv
,
NPH
,
NLL
, and
NPHNLL
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  # data from package relsurv
data(rdata, package="relsurv")
# rate table from package relsurv
data(slopop, package="relsurv")
# get the death rate from slopop for rdata
rdata$iage < findInterval(rdata$age*365.24, attr(slopop, "cutpoints")[[1]])
rdata$iyear < findInterval(rdata$year, attr(slopop, "cutpoints")[[2]])
therate < rep(1, dim(rdata)[1])
for( i in 1:dim(rdata)[1]){
therate[i] < slopop[rdata$iage[i], rdata$iyear[i], rdata$sex[i]]
}
rdata$slorate < therate
# change sex coding
rdata$sex01 < rdata$sex 1
# centering age
rdata$agec < rdata$age 60
# fit a relative survival model with a non linear effect of age
fit < flexrsurv(Surv(time,cens)~sex01+NLL(age, Knots=60, Degree=3),
rate=slorate, data=rdata,
knots.Bh=1850, # one interior knot at 5 years
degree.Bh=3,
Spline = "bspline",
initbyglm=TRUE,
int_meth= "BOOLE",
step=50
)
summary(fit, correlation=TRUE)

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