xz76/lineartest

README

Description

R code for linear test.

Main Functions

The main functions is patp_test() and get_data(). get_data() is a function to create an example dataset.

Dependencies

patp_test() requires the R packages survival and matrixStats to be installed and loaded.get_data() requires the R packages truncdist and extraDistr to be installed and loaded.

Input data

The input data need to be a data frame in the long format generated by get_data(). The data frame should contain the variables

• id: variable name that identifies the individual observations.
• cid: variable name that identifies the clusters.
• from: the state of the process at Tstart. The possible values are 1,…,k.
• Tstart: starting time of the interval in the record.
• Tstop: ending time of the interval in record.
• trans: an integer that uniquely identifies the transition.
• status: indicator variable. If status=1, the corresponding transition has been observed.
• group: variable name of the binary grouping variable.

Function get_data()

The function get_data() helps to create example data.

• n: number of clusters.
• M0: the minimum number of sample size within one cluster.
• M1: the maximun number of sample size within one cluster.
• tmat: a matrix of indicator transitions between states of the process where different transitions are identified by TRUE or FALSE.

Function patp_test()

The function patp_test() calculates the p-value for the comparison of the population-averaged transition probability P**r(X(t) = j|X(s) = h) between two groups, using a linear test. The function performs has following arguments:

• data: a data.frame in the long format follows get_data() requirements.
• tmat: a matrix of indicator transitions between states of the process where different transitions are identified by TRUE or FALSE.
• id: variable name that identifies the individual observations.
• cid: variable name that identifies the clusters.
• group: variable name of the binary grouping variable.
• h: the state h in P**r(X(t) = j|X(s) = h).
• j: the state j in P**r(X(t) = j|X(s) = h).
• s: the time s in P**r(X(t) = j|X(s) = h). The default value is 0.
• weighted: logical value. If TRUE, the estimators are weighted by the inverse of cluster sizes. This is useful when cluster size is random and expected to be informative. The default value is FALSE.
• LMAJ: logical value. If TRUE, the landmark version of the estimator is used in the test. This is useful when s>0 and the Markov assumption is not plausible. The default value is FALSE.
• B: number of nonparametric cluster bootstrap replications. The default value is 1000.

Example

The artificial dataset generated by get_data() contains clustered observations from an illness-death process without recovery . The matrix tmatrix of possible transition looks as follows.

tmatrix <- trans(state_names = c("health", "illness", "death"),from = c(1, 1, 1, 2, 2),
                 to = c(2, 2, 3, 3, 1))
tmatrix

##         health illness death
## health   FALSE    TRUE  TRUE
## illness   TRUE   FALSE  TRUE
## death    FALSE   FALSE FALSE

Create an example dataset with 10 clusters called tmp. The dataset can be obtained as follows

tmp <- get_data(n = 10, M0 = 10, M1 = 20, tmat = tmatrix)
head(tmp)

##     id cid from to trans    Tstart     Tstop      time status group
## 1.1  1   1    1  2     1 0.0000000 0.6449366 0.6449366      1     0
## 1.2  1   1    2  1     3 0.6449366 0.9683062 0.3233695      0     0
## 1.3  1   1    2  3     4 0.6449366 0.9683062 0.3233695      0     0
## 1.4  1   1    1  2     1 0.0000000 0.6449366 0.6449366      1     0
## 1.5  1   1    2  1     3 0.6449366 0.9683062 0.3233695      0     0
## 1.6  1   1    2  3     4 0.6449366 0.9683062 0.3233695      0     0

Two-sample comparison of the transition probability P(X(t) = 2|X(0) = 1) between the groups defined by the variable group can be performed as follows

set.seed(1234)
patp_test(data = tmp, tmat = tmatrix, cid = "cid", id = "id", group = "group",
          h = 1, j = 2, s = 0, weighted = FALSE, LMAJ = FALSE, B = 1000)

## p-value at State2 
##         0.6167089

It is recommended to use at least 1000 cluster bootstrap replications when performing two-sample hypothesis testing.