DTR (version 1.2)

LDT.estimator: Function for calculating LTD estimator

Description

The function computes the survival estimates and estimated standard errors for dynamic treatment regimes (DTRs) at given time points as proposed in Lunceford, Davidian and Tsiatis (2002) Equation (3) and Equation (10). Because different assignments at the first stage are independent to each other, the function only calculates estimates for one of the assignments at the first stage. For example, if there are two first-stage therapies A1 and A2 available, the function only calculates estimates for one of the two arms (e.g. A1).

Usage

LDT.estimator(data, t, L=.Machine$double.xmax)

Arguments

data

a data frame (R, Z, U, delta) representing the data for one of the first-stage assignments from sequentially randomized designs. R: response status, R=1 for responders, and R=0 for non-responders Z: second-stage indicator, Z=0 if assigned to B1, and Z=1

t

a vector with time points of interest. For example, t=c(1, 3, 5) for the survival estimates at 1, 3, and 5 years respectively

L

restricted survival time. Default is .Machine$double.xmax, which is the largest double value of R. Set L to a numeric number smaller than the maximum follow-up time if restricted follow-up time up to L is considered.

Value

• The function returns a matrix for the survival estimates and their standard errors for dynamic treatment regimes A1B1 and A1B2 at given time points. Each row represents one of the time points of interest in order. There are a total of six columns (TIME, SURV1, SURV2, SE1, SE2, COV12).
• TIME
  times of interest
• SURV1
  LDT survival estimates for A1B1
• SURV2
  LDT survival estimates for A1B2
• SE1
  estimated standard error for SURV1
• SE2
  estimated standard error for SURV2
• COV12
  estimated covariance for SURV1 and SURV2

Details

In sequentially randomized designs, there could be more than two therapies available at each stage. For simplicity, and to maintain similarity to the most common sequentially randomized clinical trials, a simple two-stage randomization design allowing two treatment options at each stage is used in the current version of the package. In detail, patients are initially randomized to either A1 or A2 at the first stage. Based on their response status, they are then randomized to either B1 or B2 at the second stage. Therefore, there are a total of four DTRs: A1B1, A1B2, A2B1, and A2B2.

References

Lunceford JK, Davidian M, Tsiatis AA: Estimation of survival distributions of treatment policies in two-stage randomization designs in clinical trials. Biometrics 58:48-57, 2002

See Also

DTR, sim.LDT.data, LDT.mean.estimator, DTR.Wald.test, DTR.surv.plot

Examples

require(DTR)
  
#-------Example function usage-----------
n <- 500
L <- 1.5
max.c <- 2.5
pi.r <- 0.5
pi.z <- 0.5
lambda <- 1.33
alpha <- 6.67
beta1 <- 0.29
beta2 <- -0.67

# Generate A1 data from SRD
set.seed(123)  # Set a seed to reproduce the same data every time running the following command
data <- sim.LDT.data(n,max.c,pi.r,pi.z,lambda,alpha,beta1,beta2,L)

# Calculate LTD estimates
LDT.estimator(data,t=c(0.5,1),L=1.5)