haplomatch.cif: Competings Risks Regression for effect of haplo-match for BMT...

In HaploSurvival: Modelling of haplo-effects for survival data, including competing risks. Effect of haplomatch for BMT studies.

Description

Fits a semiparametric model for the cause-specific quantities :

P(T ≤q t, cause=1 | x,h_d,h_p) = P_1(t,x,h_d,h_p) = 1 - \exp(- g(t,x(h_d,h_p)) )

for the probability of dying from cause 1 in a situation with competing causes of death where x(h,h_d,h_p) is a design vector that depends on the unobserved haplotype for donor and patient. We only observe the related genotype that is the same for the unrelated donor and patient. The haplotype pairs for donor and patient are using integer codes that can be read off the geno.setup function.

The model is considered in two situations :

g(t,x,z,h_d,h_p) = x(h_d,h_p)^T A(t) + (diag(t^p) z(h_d,h_p))^T β

the additive situation (with additive subdistribution hazard) and the proportional setting that includes the Fine & Gray (FG) model and some extensions

g(t,x,z,h_d,h_p) = \exp(x(h_d,h_p)^T A(t) + (diag(t^p) z(h_d,h_p))^T β)

The FG model is obtained when x=1. Where p is 1 for the additive model and 0 for the proportional model. In general p may be powers of the same length as z.

The marginal model, given genotype g and covariates x,z are then given as

P(T ≤q t, cause=1 | x,z,g) = ∑_{h_d,h_p} P_1(t,x,z,h_d,h_p) P_θ(H_d=h_d|G=g) P_θ(H_p=h_p|G=g)

and this is the model that is fitted to the data.

The call of the function must contain information about the MLE for the underlying haplotype frequencies under HWE equilibrium

P(H=(h_k,h_j)) = π_k pi_j

with K different haplotypes, where we parametrize the frequencies as

π_k= \frac{ \exp(θ_k) }{1+θ_1+...+θ_{K-1}+0}

We allow a regression design on the haplotype parameters to reduce the dimensionality

θ = G α

Resampling is used for computing p-values for tests of time-varying effects.

Usage

haplomatch.cif(formula,data=sys.parent(),
cause,times,designfuncX,designfuncZ,Nit=50,
clusters=NULL,gamma=0,n.sim=500,weighted=0,model="additive",
causeS=1,cens.code=0,detail=0,interval=0.01,resample.iid=1,
cens.model="KM",time.pow=0,fix.haplofreq=0,haplo.freq=NULL,
alpha.iid=NULL,geno.setup=NULL,fit.haplofreq=NULL,design.test=0,
covnamesX=NULL,covnamesZ=NULL)

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 ‘Surv’ function. The status indicator is not important here. Time-invariant regressors are specified by the wrapper const(), and cluster variables (for computing robust variances) by the wrapper cluster().
data	a data.frame with the variables.
cause	specifies the causes related to the death times, the value 0 is the censoring value.
times	specifies the times at which the estimator is considered. This is typically all cause "1" jump times.
designfuncX	R-function(x,h_d,h_p) that gives the X design given x and donor and patient haplotype pairs h_d and h_p.
designfuncZ	R-function(x,h_d,h_p) that gives the Z design given x and donor and patient haplotype pairs h_d and h_p.
Nit	number of iterations for Newton-Raphson algorithm.
clusters	specifies cluster structure, for backwards compability.
gamma	starting value for constant effects.
n.sim	number of simulations in resampling.
weighted	Not implemented. To compute a variance weighted version of the test-processes used for testing time-varying effects.
model	"additive" or "prop"ortional.
causeS	specificies which cause we consider.
cens.code	specificies the code for the censoring.
detail	if 0 no details are printed during iterations, if 1 details are given.
interval	specifies that we only consider timepoints where the Kaplan-Meier of the censoring distribution is larger than this value.
resample.iid	to return the iid decomposition, that can be used to construct confidence bands for predictions
cens.model	specified which model to use for the ICPW, KM is Kaplan-Meier alternatively it may be "cox"
time.pow	specifies that the power at which the time-arguments is transformed, for each of the arguments of the const() terms, default is 1 for the additive model and 0 for the proportional model.
fix.haplofreq	is 1 when haplofrequencies are considered as known. Default is 0
haplo.freq	the known haplofrequencies, or estimated MLE.
alpha.iid	iid decomposition of haplofrequency paramters for uncertainty related to haplotypefrequencies.
geno.setup	analysis of genotype by geno.setup() function
fit.haplofreq	MLE fit of haplofrequency model using HWE.
design.test	prints out the design matrices so one can check that the design is correctly specified in the functions, designfuncX and designfuncX.
covnamesX	names for output related to additive part of model.
covnamesZ	names for output related to proportional part of model.

Value

returns an object of type 'comprisk'. With the following arguments:

cum	cumulative timevarying regression coefficient estimates are computed within the estimation interval.
var.cum	pointwise variances estimates.
gamma	estimate of proportional odds parameters of model.
var.gamma	variance for gamma.
score	sum of absolute value of scores.
gamma2	estimate of constant effects based on the non-parametric estimate. Used for testing of constant effects.
obs.testBeq0	observed absolute value of supremum of cumulative components scaled with the variance.
pval.testBeq0	p-value for covariate effects based on supremum test.
obs.testBeqC	observed absolute value of supremum of difference between observed cumulative process and estimate under null of constant effect.
pval.testBeqC	p-value based on resampling.
obs.testBeqC.is	observed integrated squared differences between observed cumulative and estimate under null of constant effect.
pval.testBeqC.is	p-value based on resampling.
conf.band	resampling based constant to construct 95% uniform confidence bands.
B.iid	list of iid decomposition of non-parametric effects.
gamma.iid	matrix of iid decomposition of parametric effects.
test.procBeqC	observed test process for testing of time-varying effects
sim.test.procBeqC	50 resample processes for for testing of time-varying effects

Author(s)

Thomas Scheike

References

Scheike and Zhang and Gerds (2008), Predicting cumulative incidence probability by direct binomial regression, Biometrika, 2008.

Scheike and Zhang (2009), Competing risks with missing covariates: Effect of matching haplotypes on BMT patients, work in progress.

Examples

data(bmt); 
times<-bmt$time[bmt$cause==1]; 

# simulated genotype data 
Gbmt<-matrix(rbinom(4*nrow(bmt),1,0.5),nrow(bmt),4)
setup<-geno.setup(Gbmt)

# fits MLE under HWE 
out<-haplo.freqs(Gbmt,geno.setup=setup) 

designXM<-function(x,hd,hp) {
hd<-round(hd); hp<-round(hp);
match<-(hd[1]==hp[1])*(hd[2]==hp[2])
y<-c(x,match)
return(y)
}

designZM<-function(x,z,hd,hp) {
hd<-round(hd); hp<-round(hp);
match<-(hd[1]==hp[1])*(hd[2]==hp[2])
y<-c(x,match)
return(x)
}

# nonparametric additive model 
add<-haplomatch.cif(Surv(time,cause>0)~platelet+age+tcell,bmt,
bmt$cause,times[-c(1:5)],designXM,designZM,geno.setup=setup,
causeS=1,fit.haplofreq=out)
summary(add)

par(mfrow=c(2,4))
plot(add)

pout<-predict(add,X=rbind(
c(1,0,0,0,1), # with 1 for match
c(1,0,0,0,0)  # without match 
))

par(mfrow=c(1,3))
plot(pout,multiple=0,col=1:2)
plot(pout,multiple=1,uniform=0,col=1:2,lty=1,se=0)

# fits semiparmatric model, first specifies design vectors
designXM<-function(x,z,hd,hp) {
hd<-round(hd); hp<-round(hp);
match<-(hd[1]==hp[1])*(hd[2]==hp[2])
y<-c(x,match)
return(x)
}

designZM<-function(x,z,hd,hp) {
hd<-round(hd); hp<-round(hp);
match<-(hd[1]==hp[1])*(hd[2]==hp[2])
y<-c(z,match)
return(y)
}

sadd<-haplomatch.cif(Surv(time,cause>0)~const(platelet)+const(age)+
const(tcell),bmt,bmt$cause,times[-c(1:5)],designXM,designZM,geno.setup=setup,
causeS=1,fit.haplofreq=out)
summary(sadd)

pout<-predict(sadd,X=rbind(c(1),c(1)),
Z=rbind( c(0,0,0,1), # with 1 haplotype 0
         c(0,0,0,0)  # without haplotype 0
))

plot(pout,multiple=1,uniform=0,col=1:2,lty=1,se=0)

HaploSurvival documentation built on May 2, 2019, 5:49 p.m.