xz76/sop_test

README

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 sopt_test()

The function sopt_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 or Kolmogorov–Smirnov 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.
• j: the state j in P**r(X(t) = j|X(s) = h).
• B: number of nonparametric cluster bootstrap replications. The default value is 1000.
• method: “linear” or “KS”.

Example

The artificial dataset 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, 2, 2),
                 to = c(2, 3, 3, 1))
tmatrix

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

The following example data has 10 clusters:

##   cid id    Tstart     Tstop from to Z R group
## 1   1  1 0.0000000 0.1315225    1  2 0 1     0
## 2   1  1 0.1315225 0.3154674    2  3 0 1     0
## 3   1  2 0.0000000 0.4189244    1  3 0 1     0
## 4   1  3 0.0000000 0.4867005    1  2 0 1     0
## 5   1  3 0.4867005 0.9478138    2  1 0 1     0
## 6   1  3 0.9478138 0.9860794    1  3 0 1     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

For linear test:

set.seed(1234)
sopt_test(data = tdat, tmat = tmatrix, cid = "cid",
          id = "id", group = "group", j = 2, B = 1000,
          method = "linear")

## p-value at State2 
##         0.1369707

For Kolmogorov–Smirnov test:

set.seed(1234)
sopt_test(data = tdat, tmat = tmatrix, cid = "cid", 
          id = "id", group = "group", j = 2, B = 1000,
          method = "KS")

## p-value at State2 
##             0.251

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