In a-chernofsky/project2: Thesis project 2: causal mediation analysis with an interval censored outcome

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Project 2

The goal of project2 is to to estimate the indirect and direct effects of a treatment A on a time-to-event outcome T with a mediator M, when T is interval censored. The primary purpose of the package is to provide functions for estimating the indirect and direct effects from data. A secondary goal is to provide functions to conduct a simulation study to evaluate the proposed estimators. We deomonstrate the simulation functionality of the package below.

Installation

You can install the released version of project2 from the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("a-chernofsky/project2")

Prerequisites

library(survival)
library(interval)
library(project2)

Overview

1. Simulate time-to-event outcomes conditional on covariates using sim_cph with the following arguments: a. N simulated sample size b. formula or X defining the covariates c. beta covariate effects
   d. tfun time function based on the assumed hazard function
2. Create interval censored outcome based on when the simulated time-to-event occurs with sim_interval and the following arguments: a. t true event times b. pmiss probability of missing c. visits a vector of study visit times
3. Define a study visit schedule mimicking one way in which interval censored outcomes arise.
4. Recognizing that subjects miss study visits, set a probability of a subject missing a specific visit.

Simulating Cox Proportional Hazards model data

Bender 2005 discussed a method to simulate time-to-event data from a Cox Proportional Hazards model with hazard function based on the probability integral transformation theorem. The method involves inverting the cumulative hazard function. While the method is generalized to any hazard function, choosing from popular survival distributions such as exponential, weibull, and gompertz provides a closed form inverse function that is simple to define. The sim_cph currently has functions to simulate survival times from these common distributions.

The sim_cph function takes the following arguments:

1. N simulated sample size
2. formula or X defining the covariates
3. beta covariate effects
4. tfun time function based on the assumed hazard.

Assume the following CPH model with a constant baseline hazard function $\lambda$:

$h(t) = \lambda \exp(\beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3).$

The variables $x_1, x_2, x_3$ are simulated from the following distributions:

#simulate covariates
x1 <- rbinom(100, 1, 0.5)
x2 <- rnorm(100)
x3 <- factor(sample(c(1,2,3), size = 100, replace = T, prob = c(0.33, 0.33, 0.33)))

We now set the values for the $N$, $\beta$'s and $\lambda$,

#N
n <- 100
#betas
b <- c(-0.5, -0.02, 0.01, 0.01)
#lambda
lam <- 0.1

There are two ways to input the covariates into sim_cph: 1. X as a model matrix (use model.matrix function) 2. formula as a formula e.g. ~x1 + x2 + x3.

Make sure that any categorical variables are converted as factors otherwise they will be treated as numeric.

t_data <- sim_cph(N = n, formula = ~ x1 + x2 + x3, 
                  beta = b, 
                  tfun = texp(lam))

We can use functions from the survival package to inspect the simulated data:

t_data$event <- 1

sfit <- survfit(Surv(t, event) ~ x1, data = t_data)
summary(sfit)
plot(sfit, col = c("red", "blue"))

We can fit a CPH model to check the results:

coxph(Surv(t, event) ~ x1 + x2 + x3, data = t_data)

Simulating interval censored data

int_data <- sim_interval(t_data$t, pmiss = 0.10, visits = c(0, 1, 5, 10, 15, 20))

icfit <- icfit(Surv(l, r, type = "interval2") ~ x1, data = int_data)

plot(icfit, XLEG = 15, YLEG = 0.8, shade = F)

Calculating RMST with right censored data

i1 <- summary(sfit)$strata == "x1=1"
i0 <- summary(sfit)$strata == "x1=0"
t1 <- summary(sfit)$time[i1]
s1 <- summary(sfit)$surv[i1]
t0 <- summary(sfit)$time[i0]
s0 <- summary(sfit)$surv[i0]

Calculating RMST with interval censored data

rmst_ic(left = int_data$l[t_data$x1 == 1], 
        right = int_data$r[t_data$x1 == 1], 
        tau = 20)
rmst_ic(left = int_data$l[t_data$x1 == 0], 
        right = int_data$r[t_data$x1 == 0], 
        tau = 20)

Pseudo-observations

a-chernofsky/project2 documentation built on Oct. 21, 2021, 10:23 p.m.