Alternating recurrent event data arise frequently in biomedical and social sciences where two types of events such as hospital admissions and discharges occur alternatively over time. BivRec implements a collection of nonparametric and semiparametric methods to analyze such data.
The main functions are:
- bivrecReg: Use for the estimation of covariate effects on the two alternating event gap times (Xij and Yij) using semiparametric methods. The method options are “Lee.et.al” and “Chang”.
- bivrecNP: Use for the estimation of the joint cumulative distribution function (cdf) for the two alternating events gap times (Xij and Yij) as well as the marginal survival function for type I gap times (Xij) and the conditional cdf of the type II gap times (Yij) given an interval of type I gap times (Xij) in a nonparametric fashion.
The package also provides options to simulate and visualize the data and results of analysis.
BivRec depends on the following system requirements:
- Rtools. Download Rtools 35 from https://cran.r-project.org/bin/windows/Rtools/
Once those requirements are met you can install BivRec from github as follows:
#Installation requires devtools package.
#install.packages("devtools")
library(devtools)
#install_github("SandraCastroPearson/BivRec")
This is an example using a simulated data set.
# Simulate bivariate alternating recurrent event data
library(BivRec)
set.seed(28)
sim_data <- simBivRec(nsize=100, beta1=c(0.5,0.5), beta2=c(0,-0.5), tau_c=63, set=1.1)
head(sim_data)
#> id epi xij yij ci d1 d2 a1 a2
#> 1 1 1 5.396514 2.649410 11.76916 1 1 0 0.7455188
#> 2 1 2 3.723235 0.000000 11.76916 0 0 0 0.7455188
#> 3 2 1 5.648637 2.247070 45.31703 1 1 0 0.3344112
#> 4 2 2 2.949107 2.032798 45.31703 1 1 0 0.3344112
#> 5 2 3 4.437588 2.936018 45.31703 1 1 0 0.3344112
#> 6 2 4 3.114917 3.337000 45.31703 1 1 0 0.3344112
# Create a bivrecSurv object
bivrec_object <- with(sim_data, bivrecSurv(id, epi, xij, yij, d1, d2))
# Plot gap times
plot(bivrec_object, main="Example", type = c("Type I", "Type II"), col = c("darkgrey","darkgreen"))
Nonparametric Analysis
# Apply the nonparametric method of Huang and Wang (2005) and visualize joint, marginal and conditional results
library(BivRec)
npresult <- bivrecNP(response = with(sim_data, bivrecSurv(id, epi, xij, yij, d1, d2)),
ai=1, u1 = seq(1, 15, 0.5), u2 = seq(1, 15, 0.5), conditional = TRUE,
given.interval = c(1, 10), level = 0.99)
#> [1] "Estimating joint CDF and marginal survival"
#> [1] "Estimating conditional cdf with 99% confidence interval using 200 bootstrap samples"
head(npresult)
#>
#> Joint CDF:
#> x y Joint Probability SE Lower .99 Upper .99
#> 1 1 1.0 0.05900966 0.01967078 0.008341088 0.1096782
#> 2 1 1.5 0.06086021 0.01995590 0.009457207 0.1122632
#> 3 1 2.0 0.06179946 0.01994861 0.010415238 0.1131837
#> 4 1 2.5 0.06179946 0.01994861 0.010415238 0.1131837
#> 5 1 3.0 0.06179946 0.01994861 0.010415238 0.1131837
#> 6 1 3.5 0.06179946 0.01994861 0.010415238 0.1131837
#>
#> Marginal Survival:
#> Time Marginal Survival SE Lower .99 Upper .99
#> 1 0.3120105 0.9997561 0.0000243843 0.9996933 0.9998189
#> 2 0.3408594 0.9995122 0.0002438430 0.9988841 1.0000000
#> 3 0.3769168 0.9992683 0.0004858536 0.9980168 1.0000000
#> 4 0.3793933 0.9990302 0.0007282511 0.9971543 1.0000000
#> 5 0.3859942 0.9987863 0.0007635383 0.9968196 1.0000000
#> 6 0.3878224 0.9985424 0.0009969369 0.9959745 1.0000000
#>
#> Conditional CDF:
#> Time Conditional Probability Bootstrap SE Bootstrap Lower .99
#> 1 0.0000 0.0000 0.0000 0.00
#> 2 0.0776 0.0000 0.0000 0.00
#> 3 0.1551 0.0000 0.0000 0.00
#> 4 0.2327 0.0018 0.0011 0.00
#> 5 0.3103 0.0095 0.0038 0.00
#> 6 0.3878 0.0224 0.0081 0.01
#> Bootstrap Upper .99
#> 1 0.00
#> 2 0.00
#> 3 0.00
#> 4 0.00
#> 5 0.02
#> 6 0.04
plot(npresult)
# To save individual plots in a pdf file un-comment the following line of code:
# pdf("nonparam_jointcdfplot.pdf")
# plotJoint(npresult)
# dev.off()
# pdf("nonparam_marginalplot.pdf")
# plotMarg(npresult)
# dev.off()
# pdf("nonparam_conditionaplot.pdf")
# plotCond(npresult)
# dev.off()
Semiparametric Regression Analysis
#Explore how the response changes by levels of a categorical covariate using a plot.
#Use attach as follows or specifiy each vector using the $ operator (sim_data$id, sim_data$epi, etc.)
attach(sim_data)
plot(x = bivrecSurv(id, epi, xij, yij, d1, d2), by = data.frame(a1, a2),
type = c("Type I", "Type II"), col = c("darkgrey","darkgreen"))
#> [1] "a2 not used - either continuous or had more than 6 levels."
#> [1] "Subjects for plots: 100."
detach(sim_data)
# Apply Lee, Huang, Xu, Luo (2018) method using multiple covariates.
lee_fit <- bivrecReg(bivrecSurv(id, epi, xij, yij, d1, d2) ~ a1 + a2,
data= sim_data, "Lee.et.al")
#> [1] "Fitting model with covariates: a1, a2"
#> [1] "Estimating standard errors"
summary(lee_fit)
#>
#> Call:
#> bivrecReg(formula = bivrecSurv(id, epi, xij, yij, d1, d2) ~ a1 +
#> a2, data = sim_data, method = "Lee.et.al")
#>
#> Number of Subjects:
#> 100
#>
#> Coefficients:
#> Estimates SE z Pr(>|z|)
#> xij a1 0.686004 0.171881 3.9912 3e-05 ***
#> xij a2 0.293041 0.304425 0.9626 0.16787
#> yij a1 -0.057268 0.294032 -0.1948 0.42279
#> yij a2 -0.911427 0.480674 -1.8961 0.02897 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> exp(coefficients):
#> exp(coeff) Lower .95 Upper .95
#> xij a1 1.98576 1.41782 2.7812
#> xij a2 1.34050 0.73814 2.4344
#> yij a1 0.94434 0.53070 1.6804
#> yij a2 0.40195 0.15668 1.0312
# To apply Chang (2004) method use method="Chang".
# chang_fit <- bivrecReg(bivrecSurv(id, epi, xij, yij, d1, d2) ~ a1 + a2,
# data= sim_data, "Chang")
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