R/ll_flexrsurv_fromto_1WCEaddBr0Control.R

In flexrsurv: Flexible Relative Survival Analysis

ll_flexrsurv_fromto_1WCEaddBr0Control<-function(allparam,
		Y, X0, X, Z, W,
		BX0,
		Id, FirstId, LastId,
		expected_rate,
		expected_logit_end,
		expected_logit_enter,
		weights=NULL,
		Ycontrol, BX0control, 
		weightscontrol=NULL,
		Idcontrol, FirstIdcontrol, LastIdcontrol,
		expected_ratecontrol,
		expected_logit_endcontrol,
		expected_logit_entercontrol,
		step, Nstep,
		intTD=intTD_NC, intweightsfunc=intweights_CAV_SIM,
		intTD_base=intTD_base,
		intTD_WCEbase=intTD_WCEbase,
		ialpha0, nX0,
		ibeta0, nX,
		ialpha,
		ibeta,
		nTbasis,
		ieta0, iWbeg, iWend, nW, 
		Spline_t =BSplineBasis(knots=NULL,  degree=3,   keep.duplicates=TRUE),
		Intercept_t_NPH=rep(TRUE, nX), 
		ISpline_W =MSplineBasis(knots=NULL,  degree=3,   keep.duplicates=TRUE),
		Intercept_W=TRUE,
		nBbasis,
		Spline_B, Intercept_B=TRUE,
		ibrass0, nbrass0, 
		ibalpha0, nBX0,
		debug=FALSE,  ...){
	# compute log likelihood of the relative survival model
	# excess rate =  WCE(W , eta0)(t)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
	# eta0 = allparam[ieta0]
	# alpha0= allparam[ialpha0]
	# beta0= matrix(allparam[ibeta0], ncol=nX, nrow=nTbasis)
	# alpha= diag(allparam[ialpha])
	# beta= expand(matrix(allparam[ibeta], ncol=Z@nZ, nrow=nTbasis-1))
	# beta does not contains coef for the first t-basis
	# brass0 = allparam[ibrass0]
	# balpha0 = allparam[ibalpha0]
	
	
	# corection of lifetable according to generalized brass method
	# Cohort-independent generalized Brass model in an age-cohort table
	# stratified brass model according to fixed effects BX0 (one brass function per combination)
	# for control group
	# rate = brass0(expected-ratecontrol, expected_logitcontrol)*exp(BX0control balpha0) 
	# but for other
	# rate = brass0(expected-rate, expected_logit)*exp(BX0 balpha0) + exp(gamma0(t) + time-independent effect(LL + NLL)(X0) + NPH(X) + NPHNLL(Z) + WCE(W))
	# brass0 : BRASS model wiht parameter Spline_B
	# logit(F) = evaluate(Spline_B, logit(F_pop), brass0) * exp(Balpha %*% BX0)
	# HCum(t_1, t_2) = log(1 + exp(evaluate(Spline_B, logit(F_pop(t_2)), brass0)) -  log(1 + exp(evaluate(Spline_B, logit(F_pop(t_1)), brass0))
	# rate(t_1) = rate_ref * (1 + exp(-logit(F_pop(t)))/(1 + exp(evaluate(Spline_B, logit(F_pop(t)), brass0)))*
	#                        evaluate(deriv(Spline_B), logit(F_pop(t)), brass0)
	# expected_logit_end =  logit(F_pop(t_2))
	# expected_logit_enter =  logit(F_pop(t_1))
	# brass0 = allparam[ibrass0]
	# Spline_B : object of class "AnySplineBasis" (suitable for Brass model) with method deriv() and evaluate()
	#            IMPORTANT : the coef of the first basis is constraints to one and evaluate(deriv(spline_B), left_boundary_knots) == 1 for Brass transform 
	#
	# parameters for exposed group
	#################################################################################################################
	# Y : object of class Surv but the matrix has 4 columns :
	# Y[,1] beginning(1) , fromT
	# Y[,2] end(2), toT,
	# Y[,3] status(3) fail
	# Y[,4] end of followup(4) 
	#     end of followup is assumed constant by Id
	# 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)
	# W : vector or nX1 matrix with ONE Exposure variable used in Weighted Cumulative Exposure Models
	# BX0 : non-time dependante variable for the correction of life table (may contain spline bases expended for non-loglinear terms)
	# Id : varibale indicating individuals Id, lines with the same Id are considered to be from the same individual
	# FirstId : all lines in FirstId[iT]:iT in the data comes from the same individual 
	# LastId  : all lines in FirstId[iT]:LastId[iT] in the data comes from the same individual Id[iT] 
	# expected_rate : expected rate at event time T
	# expected_logit_end : logit of the expected survival at the end of the followup
	# expected_logit_enter : logit of the expected survival at the beginning of the followup 
	# weights : vector of weights  : LL = sum_i w_i ll_i
	# parameters for exposd population
	#################################################################################################################
	# parameters for exposed group
	#################################################################################################################
	# Ycontrol : object of class Surv but the matrix has 4 columns :
	# Ycontrol[,1] beginning(1) , fromT
	# Ycontrol[,2] end(2), toT,
	# Ycontrol[,3] status(3) fail
	# Ycontrol[,4] end of followup(4) 
	#     end of followup is assumed constant by Id
	# BX0control : non-time dependante variable for the correction of life table (may contain spline bases expended for non-loglinear terms)
	# Idcontrol : varibale indicating individuals Id, lines with the same Id are considered to be from the same individual
	# FirstIdcontrol : all lines in FirstIdcontrol[iT]:iT in the data comes from the same individual 
	# LastIdcontrol  : all lines in FirstId[controliT]:LastIdcontrol[iT] in the data comes from the same individual Id[iT] 
	# expected_ratecontrol : expected rate at event time T
	# expected_logit_endcontrol : logit of the expected survival at the end of the followup
	# expected_logit_entercontrol : logit of the expected survival at the beginning of the followup 
	# weightscontrol : vector of weights  : LL = sum_i w_i ll_i
	#################################################################################################################
	# model parameters
	# step : object of class "NCLagParam" or "GLMLagParam"
	# Nstep : number of lag for each observation
	# intTD : function to perform numerical integration 
	# intweightfunc : function to compute weightsfor numerical integration
	# nW    : nb of WCE variables dim(W)=c(nobs, nW)
	############# nW must be 1 in this function
	# iWbeg, iWend : coef of the ith WCE variable is eta0[iWbeg[i]:iWend[i]]
	############# iWbeg = 1 in this finction and ieta0=1:iWend
	#  ISpline_W, list of nW spline object for WCE effects,  with evaluate() method
	#             ISpline is already integreted 
	# nTbasis : number of time spline basis for NPH or NLL effects
	# nX0   : nb of PH variables dim(X0)=c(nobs, nX0)
	# nX    : nb of NPHLIN variables dim(X)=c(nobs, nX)
	#  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
	
#cat("************ll_flexrsurv_fromto_1WCEaddBr0Control ")
#print(allparam)
	
	
	################################################################################
#  excess rate
	if(is.null(Z)){
		nZ <- 0
		Zalphabeta <- NULL
	} else {
		nZ <- Z@nZ
	}
	
	# 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 of one for the first T-basis 
		Beta <- t(ExpandAllCoefBasis(allparam[ibeta], ncol=nZ,  value=1))
		# parenthesis important for speed ?
		Zalphabeta <- Z@DM %*%( diag(allparam[ialpha]) %*% Z@signature  %*% Beta )
		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,
							# no log basis for NPH and NPHNLL effects
							expand=!Intercept_t_NPH,
							value=0))
		}
		else {
			Zalphabeta <- NULL
		}
	}
	
	IS_W<- ISpline_W
	eta0 <- allparam[ieta0]
	if(Intercept_W){
		IS_W <- ISpline_W * eta0
	}
	else {
		IS_W <- ISpline_W * c(0, eta0)
	}
	
	if(nX + nZ) {
		# with time dependent terms in the exp()
		# NPHTERM is the cumulative rate effect between Tfrom and Tto
		# numerical integration
		NPHterm <- intTD(rateTD_alphabeta_1addwce, intFrom=Y[,1], intTo=Y[,2], intToStatus=Y[,3],
				step=step, Nstep=Nstep,
				intweightsfunc=intweightsfunc, 
				fromT=Y[,1], toT=Y[,2], FirstId=FirstId, LastId=LastId,
				Zalphabeta=Zalphabeta,
				W = W, 
				Spline_t = Spline_t, Intercept_t=TRUE,
				ISpline_W = IS_W, Intercept_W=Intercept_W)
	} else {
		# no time dependent terms in the exp()
		# NPHTERM is the cumulative WCE effect between Tfrom and Tto
		# algebric formula
		
		wce2 <- predictwce(object=integrate(IS_W), t=Y[,2], Increment=W, fromT=Y[,1], tId=(1:dim(Y)[1]),
				FirstId=FirstId, LastId=LastId, intercept=Intercept_W, outer.ok=TRUE)
		wce1 <-  predictwce(object=integrate(IS_W), t=Y[,1], Increment=W, fromT=Y[,1], tId=(1:dim(Y)[1]),
				FirstId=FirstId, LastId=LastId, intercept=Intercept_W, outer.ok=TRUE)
		NPHterm <- wce2 - wce1
		
	}
	
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	################################################################################
	#***** 
	
	# WCE at end of interval
	# no eta0 in predictwce() L because IS_W = ISpline_W * eta0
	WCEevent <- predictwce(object=IS_W, t=Y[,2], Increment=W, fromT=Y[,1], tId=(1:dim(Y)[1]),
			FirstId=FirstId, LastId=LastId, intercept=Intercept_W, outer.ok=TRUE)
	
	
	################################################################################
	# control group
# only Brass model
	if(!is.null(Ycontrol)){
		if(is.null(Spline_B)){
			modified_ratecontrol <-  expected_ratecontrol 
			modified_cumratecontrol <- log((1 + exp( expected_logit_endcontrol))/(1 + exp(expected_logit_entercontrol)))
		}
		else {
			# parameter of the first basis is one
			brass0 <- c(1.0, allparam[ibrass0])
			S_B <- Spline_B * brass0
			Y2C <- exp(predictSpline(S_B, expected_logit_endcontrol)) 
			evalderivbrasscontrol <- predictSpline(deriv(S_B), expected_logit_endcontrol) 
			# contribution of non time dependant variables
			modified_ratecontrol <-  expected_ratecontrol * (1 + exp(-expected_logit_endcontrol))/(1+ 1/Y2C) * evalderivbrasscontrol
			modified_cumratecontrol <- log((1 + Y2C)/(1 + exp(predictSpline(S_B, expected_logit_entercontrol))))
		}
		if( nBX0){
			BPHtermcontrol <-exp(BX0control %*% allparam[ibalpha0])
			modified_ratecontrol <-  modified_ratecontrol * BPHtermcontrol
			modified_cumratecontrol <- modified_cumratecontrol * BPHtermcontrol  
		}
		
		if(sum(is.na(modified_ratecontrol)) | sum(is.na(modified_cumratecontrol))){
			warning(paste0(sum(is.na(modified_ratecontrol)), 
							" NA rate control and ", 
							sum(is.na(modified_cumratecontrol)), 
							" NA cumrate control with Brass coef", 
							paste(format(brass0), collapse = " ")))
		}
		if(min(modified_ratecontrol, na.rm=TRUE)<0 | min(modified_cumratecontrol, na.rm=TRUE)<0){
			warning(paste0(sum(modified_ratecontrol<0, na.rm=TRUE), 
							" negative rate control and ", 
							sum(modified_cumratecontrol<0, na.rm=TRUE), 
							" negative cumrate control with Brass coef", 
							paste(format(brass0), collapse = " ")))
		}
		
		eventtermcontrol <- ifelse(Ycontrol[,3], log( modified_ratecontrol ),  0)
		if (!is.null(weightscontrol)) {
			llcontrol <- crossprod(eventtermcontrol  - modified_cumratecontrol, weightscontrol)
		}
		else {
			llcontrol <- sum( eventtermcontrol - modified_cumratecontrol )
		}
		
	}
	else {
		modified_ratecontrol <-  NULL
		modified_cumratecontrol <- NULL
		llcontrol <- 0.0
	}
	################################################################################
	# exposed group
# Brass model
	
	if(is.null(Spline_B)){
		modified_rate <-  expected_rate 
		modified_cumrate <-log((1 + exp( expected_logit_end))/(1 + exp(expected_logit_enter)))  
	}
	else {
		brass0 <- c(1.0, allparam[ibrass0])
		S_B <- Spline_B * brass0
		Y2E <- exp(predictSpline(S_B, expected_logit_end)) 
		evalderivbrass <- predictSpline(deriv(S_B), expected_logit_end) 
		
		# contribution of non time dependant variables
		
		modified_rate <-  expected_rate * (1 + exp(-expected_logit_end))/(1+ 1/Y2E) * evalderivbrass
		modified_cumrate <- log((1 + Y2E)/(1 + exp(predictSpline(S_B, expected_logit_enter))))
		
#    print(summary(predictSpline(S_B, expected_logit_enter)))
#    print(summary(Y2E))
#    print(brass0)
	}
	
	#proportional corrections
	if( nBX0){
		BPHterm <-exp(BX0 %*% allparam[ibalpha0])
		modified_rate <-  modified_rate  * BPHterm
		modified_cumrate <- modified_cumrate * BPHterm 
	}
	
	if(sum(is.na(modified_rate)) | sum(is.na(modified_cumrate))){
		warning(paste0(sum(is.na(modified_rate)), 
						" NA rate and ", 
						sum(is.na(modified_cumrate)), 
						" NA cumrate with Brass coef", 
						paste(format(brass0), collapse = " ")))
	}
	if(min(modified_rate, na.rm=TRUE)<0 | min(modified_cumrate, na.rm=TRUE)<0){
		warning(paste0(sum(modified_rate<0, na.rm=TRUE), 
						" negative rate and ", 
						sum(modified_cumrate<0, na.rm=TRUE), 
						" negative cumrate with Brass coef", 
						paste(format(brass0), collapse = " ")))
	}

	
	# spline bases for each TD effect
	if(nX + nZ){
		# spline bases for each TD effect at the end of the interval
		YT <- evaluate(Spline_t, Y[,2], intercept=TRUE)
		eventterm <- ifelse(Y[,3] ,
				log( modified_rate + PHterm * WCEevent * exp(apply(YT * Zalphabeta, 1, sum))),
				0)
	} else {
#    isneg <- ifelse(Y[,3] , 
#                        (modified_rate + PHterm * WCEevent) <0, 
#                        FALSE)
#    if(sum(isneg)>0){
#      print(cbind(Id, isneg, Y, modified_rate , PHterm, WCEevent)[isneg,])
#    }
		eventterm <- log( ifelse(Y[,3] , 
						modified_rate + PHterm * WCEevent , 
						1.0))
		Eventterm <- ifelse(Y[,3] , 
				modified_rate + PHterm * WCEevent , 
				.0)
	}
	
	if (!is.null(weights)) {
		if( nX0){
			llexposed <- crossprod(eventterm - modified_cumrate - PHterm * NPHterm , weights)
		} else {
			llexposed <- crossprod(eventterm - modified_cumrate - NPHterm , weights)
		}
	}
	else {
		if( nX0){
			llexposed <- sum( eventterm - modified_cumrate - PHterm * NPHterm )
		} else {
			llexposed <- sum( eventterm - modified_cumrate - NPHterm )
		}
	}
	
#print(cbind(PHterm, NPHterm, YT0Gamma0))
#print(c(sum(eventtermcontrol), sum(modified_cumratecontrol), sum(eventterm), sum(modified_cumrate), sum(PHterm * NPHterm), sum(PHterm ), sum(NPHterm)))
#print(c(nX0, nX, nZ, nW))      
	
#print(table(Y[,3]))
#print(summary((modified_rate + PHterm * WCEevent)[Y[,3]==1]))
#print(summary((modified_rate + PHterm * WCEevent)[Y[,3]!=1]))
#  print(sum(eventterm))
#print("**************** fin ll")
#  print(summary(modified_cumrate))
#  print(summary(eventterm))
#  print(summary(WCEevent))
	##  print(sum(modified_cumrate))
	##  print(sum(NPHterm))
#  print(summary(NPHterm))
#  print(summary( eventterm - modified_cumrate - NPHterm ))
#  print(llcontrol)
#  print(llexposed)
#  print(allparam)
#print("fin ll")
	ret <- llcontrol + llexposed
#print(c(ret, allparam))
	
	
#  print(c(ret, llcontrol, llexposed))
	
	if ( debug) {
		attr(ret, "eventterm") <- eventterm
		attr(ret, "PHterm") <- PHterm
		attr(ret, "NPHterm") <- NPHterm
		attr(ret, "modified_rate") <- modified_rate
		attr(ret, "modified_cumrate") <- modified_cumrate
		attr(ret, "llexposed") <- llexposed
		attr(ret, "modified_ratecontrol") <- modified_ratecontrol
		attr(ret, "modified_cumratecontrol") <- modified_cumratecontrol
		attr(ret, "llcontrol") <- llcontrol
		if ( debug > 1000) {
			cat("allparam\n")
			print(allparam)
			cat("eventterm\n")
			print(summary(eventterm[Y[,3]==1]))
			print(summary(Eventterm[Y[,3]==1]))
			cat("modified_cumrate\n")
			print(summary(modified_cumrate[Y[,3]==1]))
			cat("WCEevent\n")
			print(summary(WCEevent[Y[,3]==1]  ))
			cat("rate\n")
			print(summary(modified_cumrate[Y[,3]==1]-WCEevent[Y[,3]==1]  ))
			cat("PHterm\n")
			print(summary(PHterm))
			cat("NPHterm\n")
			print(summary(NPHterm ))
			cat("Y[,3]\n")
			print(summary(Y[,3] ))
			cat("modified_rate\n")
			print(summary( modified_rate ))
		}
		if ( debug > 500) {
			print(allparam)
			cat("fin ll_flexrsurv_fromto_1WCEaddBr0Control **", ret,   "++ \n")
			print(c(ret, llcontrol, llexposed))
		}                          
	}
	
	ret
}