fit.nonpar {causalCmprsk}R Documentation

Nonparametric estimation of ATE corresponding to the target population

Description

Implements nonparametric estimation (based on the weighted Aalen-Johansen estimator) of ATE meaning that it does not assume any model for potential outcomes. It provides three measures of treatment effects on time-to-event outcomes: (1) cause-specific hazard ratios which are time-dependent measures under a nonparametric model, (2) risk-based measures such as cause-specific risk differences and cause-specific risk ratios, and (3) restricted-mean-time differences which quantify how much time on average was lost (or gained) due to treatment by some specified time point. Please see our package vignette for more details.

Usage

fit.nonpar(
  df,
  X,
  E,
  trt.formula,
  A,
  C = NULL,
  wtype = "unadj",
  cens = 0,
  conf.level = 0.95,
  bs = FALSE,
  nbs.rep = 400,
  seed = 17,
  parallel = FALSE,
  verbose = FALSE
)

Arguments

df

a data frame that includes time-to-event X, type of event E, a treatment indicator A and covariates C.

X

a character string specifying the name of the time-to-event variable in df.

E

a character string specifying the name of the "event type" variable in df.

trt.formula

a formula expression, of the form response ~ predictors. The response is a binary treatment/exposure variable, for which a logistic regression model (a Propensity Scores model) will be fit using glm. See the documentation of glm and formula for details. As an alternative to specifying formula, arguments A and C, defined below, can be specified. Either formula or a pair of A and C must be specified.

A

a character specifying the name of the treatment/exposure variable. It is assumed that A is a numeric binary indicator with 0/1 values, where A=1 is assumed a treatment group, and A=0 a control group.

C

a vector of character strings with variable names (potential confounders) in the logistic regression model for Propensity Scores, i.e. P(A=1|C=c). The default value of C is NULL corresponding to wtype="unadj" that will estimate treatment effects in the raw (observed) data.

wtype

a character string variable indicating the type of weights that will define the target population for which the ATE will be estimated. The default is "unadj" - this will not adjust for possible treatment selection bias and will not use propensity scores weighting. It can be used, for example, in data from a randomized controlled trial (RCT) where there is no need for emulation of baseline randomization. Other possible values are "stab.ATE", "ATE", "ATT", "ATC" and "overlap". See Table 1 from Li, Morgan, and Zaslavsky (2018). "stab.ATE" is defined as P(A=a)/P(A=a|C=c) - see Hernán et al. (2000).

cens

an integer value in E that corresponds to censoring times recorded in X. By default fit.nonpar assumes cens=0

conf.level

the confidence level that will be used in the bootstrap confidence intervals. The default is 0.95

bs

a logical flag indicating whether to perform bootstrap in order to obtain confidence intervals. There are no analytical confidence intervals in fit.nonpar

nbs.rep

number of bootstrap replications

seed

the random seed for the bootstrap, in order to make the results reproducible

parallel

a logical flag indicating whether to perform bootstrap sequentially or in parallel, using several cores simultaneously. The default value is FALSE. In parallel execution, the number of available cores is detected, and the parallel jobs are assigned to the number of detected available cores minus one.

verbose

a logical flag indicating whether to show a progress of bootstrap. The progress bar is shown only for sequential bootstrap computation. The default value is FALSE.

Value

A list of class cmprsk with the following fields:

time
a vector of time points for which all the parameters are estimated
trt.0
a list of estimates of the absolute counterfactual parameters corresponding to A=0 and the type of event E. trt.0 has the number of fields as the number of different types of events in the data set. For each type of event there is a list of estimates:
trt.1
a list of estimates of the absolute counterfactual parameters corresponding to A=1 and the type of event E. trt.1 has the number of fields as the number of different types of events in the data set. For each type of event there is a list of estimates:
trt.eff
a list of estimates of the treatment effect measures corresponding to the type of event E. trt.eff has the number of fields as the number of different types of events in the data set. For each type of event there is a list of estimates:

References

F. Li, K.L. Morgan, and A.M. Zaslavsky. 2018. Balancing Covariates via Propensity Score Weighting. Journal of the American Statistical Association 113 (521): 390–400.

M.A. Hernán, B. Brumback, and J.M. Robins. 2000. Marginal structural models and to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology, 11 (5): 561-570.

See Also

fit.cox, get.pointEst, causalCmprsk

Examples

# create a data set
n <- 1000
set.seed(7)
c1 <-  runif(n)
c2 <- as.numeric(runif(n)< 0.2)
set.seed(77)
cf.m.T1 <- rweibull(n, shape=1, scale=exp(-(-1 + 2*c1)))
cf.m.T2 <-  rweibull(n, shape=1, scale=exp(-(1 + 1*c2)))
cf.m.T <- pmin( cf.m.T1, cf.m.T2)
cf.m.E <- rep(0, n)
cf.m.E[cf.m.T1<=cf.m.T2] <- 1
cf.m.E[cf.m.T2<cf.m.T1] <- 2
set.seed(77)
cf.s.T1 <- rweibull(n, shape=1, scale=exp(-1*c1 ))
cf.s.T2 <-  rweibull(n, shape=1, scale=exp(-2*c2))
cf.s.T <- pmin( cf.s.T1, cf.s.T2)
cf.s.E <- rep(0, n)
cf.s.E[cf.s.T1<=cf.s.T2] <- 1
cf.s.E[cf.s.T2<cf.s.T1] <- 2
exp.z <- exp(0.5 + 1*c1 - 1*c2)
pr <- exp.z/(1+exp.z)
TRT <- ifelse(runif(n)< pr, 1, 0)
X <- ifelse(TRT==1, cf.m.T, cf.s.T)
E <- ifelse(TRT==1, cf.m.E, cf.s.E)
covs.names <- c("c1", "c2")
data <- data.frame(X=X, E=E, TRT=TRT, c1=c1, c2=c2)
form.txt <- paste0("TRT", " ~ ", paste0(covs.names, collapse = "+"))
trt.formula <- as.formula(form.txt)
wei <- get.weights(formula=trt.formula, data=data, wtype = "overlap")
hist(wei$ps[data$TRT==1], col="red", breaks = seq(0,1,0.05))
hist(wei$ps[data$TRT==0], col="blue", breaks = seq(0,1,0.05))
# Nonparametric estimation:
res.ATE <- fit.nonpar(df=data, X="X", E="E", trt.formula=trt.formula, wtype="stab.ATE")
nonpar.pe <- get.pointEst(res.ATE, 0.5)
nonpar.pe$trt.eff[[1]]$RD

# please see our package vignette for practical examples
[Package causalCmprsk version 2.0.0 Index]