R/gr_cumhaz_flexrsurv_fromto_GA0B0AB_bh.R

In flexrsurv: Flexible Relative Survival Analysis

gr_cumhaz_flexrsurv_fromto_GA0B0AB_bh<-function(allparam, var,
		Y, X0, X, Z, 
		step, Nstep, 
		intTD=intTD_NC, intweightsfunc=intweights_CAV_SIM,
		intTD_base=intTD_base_NC,
		nT0basis,
		Spline_t0=BSplineBasis(knots=NULL, degree=3,   keep.duplicates=TRUE), Intercept_t0=TRUE,
		ialpha0, nX0,
		ibeta0, nX,
		ialpha, ibeta,                             
		nTbasis,
		Spline_t =BSplineBasis(knots=NULL,  degree=3,   keep.duplicates=TRUE),
		Intercept_t_NPH=rep(TRUE, nX),
		debug=FALSE,  ...){
	# compute gradient of the cumulative hazard of the relatice survival model
	# rate = ( f(t)%*%gamma) * exp(X0%*%alpha0 + X%*%beta0(t) + sum( alphai(zi)betai(t) ))
	#################################################################################################################
	#################################################################################################################
	#  the coef of the first t-basis is constraint to 1 for nat-spline, and n-sum(other beta) if BS using expand() method
	#################################################################################################################
	#################################################################################################################
	#################################################################################################################
	# allparam ; vector of all coefs
	# gamma0 = allparam[1:nY0basis]
	# alpha0= allparam[ialpha0]
	# beta0= matrix(allparam[ibeta0], ncol=nX, nrow=nTbasis)
	# alpha= diag(allparam[ialpha])
	# beta= expand(matrix(allparam[ibeta], ncol=nZ, nrow=nTbasis-1))
	# beta does not contains coef for the first t-basis
	#################################################################################################################
	# Y : object of class Surv with beginning and end of interval
	# X0 : non-time dependante variable (may contain spline bases expended for non-loglinear terms)
	# X : log lineair but time dependante variable 
	# Z : objesct of class DeSignMatrixLPHNLL of time dependent variables (spline basis expended)
	# step : lag of subinterval for numerical integration fr each observation
	# Nstep : number of lag for each observation
	# intTD : function to perform numerical integration 
	# intweightfunc : function to compute weightsfor numerical integration
	# Knots_t0=NULL,Intercept_t0=FALSE, degree_t0=3, Boundary.knots_t0 time spline parameters for baseline hazard
	# Knots_t=NULL,Intercept_t=FALSE, degree_t0=, Boundary.knots_t  time spline parameters for time-dependant effects (same basis for each TD variable)
	# nT0basis : number of spline basis for NPHLIN effects
	# nX0   : nb of PH variables dim(X0)=c(nobs, nX0)
	# nX    : nb of NPHLIN variables dim(X)=c(nobs, nX)
	# nTbasis : number of time spline basis
	#  ... not used args
	# the function do not check the concorcance between length of parameter vectors and the number of knots and the Z@signature
	# returned value : the log liikelihood of the model
	
	if (debug) cat("# computing gradient of the cumulative hazard: gr_cumhaz_flexrsurv_fromto_GA0B0AB_bh\n")
	
	if(is.null(Z)){
		nZ <- 0
	} else {
		nZ <- Z@nZ
	}
	
	if(is.null(Spline_t0)){
		YT0 <- NULL
		YT0Gamma0 <- 0.0
		Spt0g <- NULL
		igamma0 <- NULL
		tmpgamma0 <- NULL
	}
	else {
		igamma0 <- 1:nT0basis
		if(Intercept_t0){
			tmpgamma0 <- allparam[igamma0]
		}
		else {
			tmpgamma0 <- c(0, allparam[igamma0])
		}
		# baseline hazard at the end of the interval
		
		Spt0g <- Spline_t0*tmpgamma0
		YT0Gamma0 <- predictSpline(Spt0g, Y[,2])
		YT0 <- fevaluate(Spline_t0, Y[,2], intercept=Intercept_t0)
	}
	
	# contribution of non time dependant variables
	if( nX0){
		PHterm <-exp(X0 %*% allparam[ialpha0])
	} else {
		PHterm <- 1
	}
	# contribution of time d?pendant effect
	# parenthesis are important for efficiency
	if(nZ) {
		# add a row for the first basis
		tBeta <- t(ExpandAllCoefBasis(allparam[ibeta], ncol=nZ,  value=1))
		# Zalpha est la matrice des alpha(Z)
		# parenthesis important for speed ?
		Zalpha <- Z@DM %*%( diag(allparam[ialpha]) %*% Z@signature )
		Zalphabeta <- Zalpha  %*% tBeta 
		if(nX) {
			# add a row of 0 for the first T-basis when !Intercept_T_NPH
			Zalphabeta <- Zalphabeta + X %*% t(ExpandCoefBasis(allparam[ibeta0],
							ncol=nX,
							splinebasis=Spline_t,
							expand=!Intercept_t_NPH,
							value=0))
		}
	} else {
		if(nX) {
			Zalphabeta <- X %*% t(ExpandCoefBasis(allparam[ibeta0],
							ncol=nX,
							splinebasis=Spline_t,
							expand=!Intercept_t_NPH,
							value=0))
		}
		else {
			Zalphabeta <- NULL
		}
	}
	
	if(nX + nZ) {
		NPHterm <- intTD(rateTD_bh_alphabeta,  intFrom=Y[,1], intTo=Y[,2], intToStatus=Y[,3],
				step=step, Nstep=Nstep,
				intweightsfunc=intweightsfunc, 
				gamma0=tmpgamma0, Zalphabeta=Zalphabeta, 
				Spline_t0=Spt0g, Intercept_t0=Intercept_t0,
				Spline_t = Spline_t, Intercept_t=TRUE)
		if(is.null(Spline_t0)){
			Intb0 <- rep(0.0, dim(Y)[1])
		}
		else {
			Intb0 <-  intTD_base(func=ratioTD_bh_alphabeta, intFrom=Y[,1], intTo=Y[,2], intToStatus=Y[,3],
					Spline=Spline_t0,
					step=step, Nstep=Nstep,
					intweightsfunc=intweightsfunc, 
					gamma0=tmpgamma0, Zalphabeta=Zalphabeta, 
					Spline_t0=Spt0g, Intercept_t0=Intercept_t0,
					Spline_t = Spline_t, Intercept_t=TRUE,
					debug=debug)
		}
		Intb <-  intTD_base(func=rateTD_bh_alphabeta, intFrom=Y[,1], intTo=Y[,2], intToStatus=Y[,3],
				Spline=Spline_t,
				step=step, Nstep=Nstep,
				intweightsfunc=intweightsfunc,
				gamma0=tmpgamma0, Zalphabeta=Zalphabeta, 
				Spline_t0=Spt0g, Intercept_t0=Intercept_t0,
				Spline_t = Spline_t, Intercept_t=TRUE)
		if(!Intercept_t0 & !is.null(Spline_t0)){
			Intb0<- Intb0[,-1]
		}
		indx_without_intercept <- 2:getNBases(Spline_t)
		
	}
	else {
#    NPHterm <- intTD(rateTD_gamma0_bh,  intFrom=Y[,1], intTo=Y[,2],
#                     intToStatus=Y[,3],
#                     step=step, Nstep=Nstep, intweightsfunc=intweightsfunc, 
#                     gamma0=allparam[1:nT0basis],
#                     Spline_t0=Spline_t0, Intercept_t0=Intercept_t0)
#   NPHterm <- integrate(Spline_t0, Y[,1], intercep=Intercept_t0) %*% allparam[1:nT0basis]
		#  only gamma0(t) Intb0[,i] = int_0^T bi(t) det
		if(is.null(Spline_t0)){
			NPHterm <- rep(0.0, dim(Y)[1])
			Intb0 <- NPHterm
		}
		else {    
			NPHterm <- predict(integrate(Spt0g), Y[,2], intercep=Intercept_t0) -
					predict(integrate(Spt0g), Y[,1], intercep=Intercept_t0)
			Intb0 <-  integrate(Spline_t0, Y[,2], intercep=Intercept_t0) - 
					integrate(Spline_t0, Y[,1], intercep=Intercept_t0) 
		}
		Intb <- NULL
	}
	
	if(nX + nZ) {
		if(nX0>0) {
			Intb <- Intb * c(PHterm)
		}
	}
	Intb0 <- Intb0 * c(PHterm)
	
	
	#####################################################################"
# now computes the mean score
	
# d<dgamma0
	if(is.null(Spline_t0)){
		dLdgamma0 <- NULL
	}
	else {
		dLdgamma0 <- Intb0 
	}
	
	if (nX0) {
		dLdalpha0 <- X0 * c(PHterm * NPHterm) 
	}
	else {
		dLdalpha0 <- NULL
	}
	
	if (nX){
#  traiter les Intercept_t_NPH
		dLdbeta0 <- NULL
		for(i in 1:nX){
			if ( Intercept_t_NPH[i] ){
				dLdbeta0 <- cbind(dLdbeta0,  X[,i] * Intb)
			}
			else {
				dLdbeta0 <- cbind(dLdbeta0, X[,i] * Intb[,indx_without_intercept])
			}
		}
	}
	else {
		dLdbeta0 <- NULL
	}
	
	if (nZ) { 
		baseIntb <- Intb  %*% t(tBeta)
		indZ <- getIndex(Z)
		
		dLdalpha <- NULL
		dLdbeta <- NULL
		for(iZ in 1:nZ){
			dLdalpha <- cbind(dLdalpha, Z@DM[,indZ[iZ,1]:indZ[iZ,2]] * baseIntb[,iZ])
			dLdbeta <- cbind(dLdbeta, Intb[,-1, drop=FALSE] * Zalpha[,iZ])
		}
	}
	else {
		dLdalpha <- NULL
		dLdbeta <- NULL
	}
	
	rep <- cbind(dLdgamma0,          
			dLdalpha0,          
			dLdbeta0,          
			dLdalpha,          
			dLdbeta )
	
	if(debug){
		attr(rep, "intb0") <- Intb0
		attr(rep, "intb") <- Intb
	}
	
	rep
	
}