R/ll_flexrsurv_fromto_alpha0alpha.R

In flexrsurv: Flexible Relative Survival Analysis

ll_flexrsurv_fromto_alpha0alpha<-function(alpha0alpha, beta0, beta, gamma0,
		Y, X0, X, Z, 
		expected_rate,
		weights=NULL,
		step, Nstep, 
		intTD=intTD_NC, intweightsfunc=intweights_CAV_SIM,
		nT0basis,
		Spline_t0=BSplineBasis(knots=NULL,  degree=3,   keep.duplicates=TRUE), Intercept_t0=TRUE,
		ialpha0, nX0,
		nX, 
		ialpha,
		nTbasis,
		Spline_t =BSplineBasis(knots=NULL,  degree=3,   keep.duplicates=TRUE),
		Intercept_t_NPH=rep(TRUE, nX), 
		debug=FALSE,  ...){
	# compute log likelihood of the relative survival model
	# rate = exp( f(t)%*%gamma + X0%*%alpha0 + X%*%beta0(t) + sum( alphai(zi)betai(t) ))
	# case where nX0 > 0 ie, there are PH effects 
	# gamma : vector of coef for baseline hazard
	# alpha0alpa ; vector of all coefs for non time dependant variables (may contain non-loglinear terms 
	#              such as spline) AND alpah(Z) for NLG and NPH
	# alpha0= alpha0alpha[ialpha0]
	# alpha= alpha0alpah[ialpha]
	# beta0 ; matrix of all coefs for log-linear but  time dependant variables  X%*%beta0(t)
	# beta  : matrix of coefs for beta(t) nTbasis * nTDvars for NLG and NPH
	# 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 : object of class "DesignMatrixNPHNLL" time dependent variables (spline basis expended)
	# expected_rate : expected rate at event time T
	# weights : vector of weights  : LL = sum_i w_i ll_i
	# 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
	#  Spline_t0, spline object for baseline hazard, with evaluate() method
	#  Intercept_t0=FALSE, option for evaluate, = TRUE all the basis, =FALSE all but first basis 
	# 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
	#  Spline_t, spline object for time dependant effects,  with evaluate() method
	# Intercept_t_NPH vector of intercept option for NPH spline (=FALSE when X is NLL too, ie in case of remontet additif NLLNPH)
	#  ... 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(is.null(Z)){
		nZ <- 0
	} else
	{
		nZ <- Z@nZ
	}
	
	
	
	if(Intercept_t0){
		tmpgamma0 <- gamma0
	}
	else {
		tmpgamma0 <- c(0, gamma0)
	}
	
	# baseline hazard at the end of the interval
	
	YT0Gamma0 <- predictSpline(Spline_t0*tmpgamma0, Y[,1], intercept=Intercept_t0)
	
	
	
	# contribution of non time dependant variables
	if( nX0){
		PHterm <-exp(X0 %*% alpha0alpha[ialpha0])
	}
	else PHterm <- 1
	# contribution of time d?pendant effect
	# parenthesis are important for efficiency
	if(nZ) {
		Zalphabeta <- Z@DM %*%( diag(alpha0alpha[ialpha]) %*% Z@signature  %*% t(ExpandAllCoefBasis(beta, ncol=nZ,  value=1)) )
		if(nX) {
			Zalphabeta <- Zalphabeta +  X %*% t(ExpandCoefBasis(beta0,
							ncol=nX,
							splinebasis=Spline_t,
							expand=!Intercept_t_NPH,
							value=0))
		}
	}
	else {
		if(nX) {
			Zalphabeta <-  X %*% t(ExpandCoefBasis(beta0,
							ncol=nX,
							splinebasis=Spline_t,
							expand=!Intercept_t_NPH,
							value=0))
		}
		else {
			Zalphabeta <- NULL
		}
	}
	
	if(nX + nZ) {
		NPHterm <- intTD(rateTD_gamma0alphabeta,  intFrom=Y[,1], intTo=Y[,2], intToStatus=Y[,3],
				step, Nstep,
				intweightsfunc=intweightsfunc, 
				fromT=Y[,1], toT=Y[,2],
				gamma0=gamma0, Zalphabeta=Zalphabeta, 
				Spline_t0=Spline_t0*tmpgamma0, Intercept_t0=Intercept_t0,
				Spline_t = Spline_t, Intercept_t=TRUE)
	}
	else {
		NPHterm <- intTD(rateTD_gamma0,   intFrom=Y[,1], intTo=Y[,2], intToStatus=Y[,3],
				step=step, Nstep=Nstep,
				intweightsfunc=intweightsfunc, 
				fromT=Y[,1], toT=Y[,2], 
				gamma0=gamma0,
				Spline_t0=Spline_t0*tmpgamma0, Intercept_t0=Intercept_t0)
	}
	# spline bases for baseline hazard at the end of intervals
	YT0 <- evaluate(Spline_t0, Y[,2], intercept=Intercept_t0)
	# spline bases for each TD effect
	if(nX + nZ){
		# spline bases for each TD effect at the end of intervals
		YT <- evaluate(Spline_t, Y[,2], intercept=TRUE)
		eventterm <- ifelse(Y[,3] ,
				log( PHterm * exp(YT0Gamma0 + apply(YT * Zalphabeta, 1, sum)) + expected_rate ), 
				0)
	} 
	else {
		eventterm <- ifelse(Y[,3] , 
				log( PHterm * exp(YT0Gamma0) + expected_rate ), 
				0)
	}
	
	
	if (!is.null(weights)) {
		ret <- crossprod(eventterm - PHterm * NPHterm , weights)
	}
	else {
		ret <- sum( eventterm - PHterm * NPHterm )
	}
	
	ret
}