landmix.estimator {landmix}

Dynamic landmark prediction estimator for mixture data with covariates

Description

Estimates the distribution function for mixture data where the population identifiers are unknown, but the probability of belonging to a population is known. The distribution functions are evaluated at time points tval and adjust for dynamic landmark prediction and one discrete covariate (zz) and one continuous covariate (ww).

Usage

landmix.estimator(n, m, p, qvs, q, x, delta, ww, zz, run.NPNA,
  run.NPNA_avg, tval, tval0, z.use, w.use)

Arguments

n

sample size, must be at least 1.

m

number of different mixture proportions, must be at least 2.

p

number of populations, must be at least 2.

qvs

a numeric matrix of size p by m containing all possible mixture proportions (i.e., the probability of belonging to each population k, k=1,...,p.).

q

a numeric matrix of size p by n containing the mixture proportions for each person in the sample.

x

a numeric vector of length n containing the observed event times for each person in the sample.

delta

a numeric vector of length n that denotes censoring (1 denotes event is observed, 0 denotes event is censored).

ww

a numeric vector of length n containing the values of the continuous covariate for each person in the sample.

zz

a numeric vector of length n containing the values of the discrete covariate for each person in the sample.

run.NPNA

a logical indicator. If TRUE, then the output includes the estimated distribution function for mixture data that accounts for covariates and dynamic landmarking. This estimator is called "NPNA" in the referenced paper.

run.NPNA_avg

a logical indicator. If TRUE, then the output includes the estimated distribution function for mixture data that averages out over the observed covariates. This is referred to as NPNA_marg in the referenced paper.

tval

numeric vector of time points at which the distribution function is evaluated, all values must be non-negative.

tval0

numeric vector of time points representing the landmark times. All values must be non-negative and smaller than the maximum of tval.

z.use

numeric vector at which to evaluate the discrete covariate Z at in the estimated distribution function. The values of z.use must be in the range of the observed zz.

w.use

numeric vector at which to evaluate the continuous covariate W at in the estimated distribution function. The values of w.use must be in the range of the observed ww.

Value

landmix.estimator returns a list containing

• Ft.estimate: a numeric array containing the estimated distribution functions for all methods for all p populations. The distribution function is evaluated at each tval, tval0, z.use, w.use, and for all p populations. The dimension of the array is the number of methods by length(tval) by lenth(tval0) by length(z.use) by length(w.use) by p. The distribution function is only valid for t\geq t_0, so Ft.estimate shows NA for any combination for which t<t_0.

• St.estimate: a numeric array containing the estimated distribution functions for all methods for all m mixture proportion subgroups. The distribution function is evaluated at each tval, tval0, z.use, w.use, and for all m mixture proportion subgroups. The dimension of the array is the number of methods by length(tval) by lenth(tval0) by length(z.use) by length(w.use) by m. The distribution function is only valid for t\geq t_0, so St.estimate shows NA for any combination for which t<t_0.

Details

We estimate the distribution function for mixture data where the population identifiers are unknown, but the probability of belonging to a population is known. The distribution functions are evaluated at time points tval and adjust for dynamic landmark prediction and one discrete covariate (zz) and one continuous covariate (ww). Dynamic landmark prediction means that the distribution function is computed knowing that the survival time, T, satisfies T >t_0 where t_0 are the time points in tval0.

Examples

# Setup parameters to generate the data
set.seed(1)
censoring.rate <- 40
p <- 2
n <- 2000
m <- 4
tval <- seq(0,80,by=5)  
tval0 <- c(0,20,30,40,50)
z.use <- c(0,1)
w.use <- seq(35,55,by=1)
simu.setting <- "2A"
covariate.dependent <- TRUE
run.NPMLEs <- TRUE
run.NPNA <- TRUE
run.OLS <- FALSE
run.WLS <- FALSE
run.EFF <- FALSE
run.NPNA_avg <- FALSE


## compute the finite set of mixture proportions
qvs <- qvs.values(p,m)

## generate the data

data.gen <- GenerateData(n,p,m,qvs,censoring.rate,simu.setting,covariate.dependent)

x <- data.gen$x
delta <- data.gen$delta
q <- data.gen$q
ww <- data.gen$ww
zz <- data.gen$zz


## true group membership (needed to compute the AUC/BS for simulated data
true.groups <- data.gen$true.groups

## Perform the estimation			
estimators.out <- landmix.estimator(n,m,p,qvs,q,
				x,delta,ww,zz,
				run.NPNA,
				run.NPNA_avg,
				tval,tval0,
				z.use,w.use)