markovMSM (version 0.1.3)

AUC.test: Global test and local test for checking the Markov condition on Multi-state Models based on the Area Under the two curves (AUC) given by the non-Markov estimators of the transition probabilities to the Markov Aalen-Johansen estimators.

Description

This function is used to obtain the local and global tests for checking the Markov condition.

Usage

AUC.test(
  data,
  from = 1,
  to = 3,
  type = "global",
  times = NULL,
  quantiles = c(0.05, 0.1, 0.2, 0.3, 0.4),
  tmat = NULL,
  replicas = 10,
  limit = 0.9,
  positions = list(c(2, 3), c(3), c()),
  namesStates = c("Alive", "Rec", "Death"),
  timesNames = c(NA, "time1", "Stime"),
  status = c(NA, "event1", "event")
)

Value

In case of the AUC global test, an object with a list with the following outcomes:

globalTest

p-value of AUC global tests for each transition. These values are obtained through the minimum of the means of each two contiguous quantiles times of the AUC global tests.

localTest

AUC local tests of the transition probability for each times and transitions.

quantiles

Quantiles times used for the AUC global tests.

times

Times used for the AUC global tests.

DIF

Differences between the AJ and the LMAJ estimates for each transition probabilites from the starting state until the receiving state given by only one replica where 's' represent each of the quantile times.

from

The starting state considered for the AUC global tests.

to

The last receiving state considered for the the AUC Local tests.

ET.qiAll

The lower limit of the diferences between the AJ and the LMAJ estimates given by the Monte Carlo simulation in each transition for each "s" quantile times. ET.qi2All means the same but missing values were replaced by the previous diferences of estimators.

ET.qsAll

The upper limit of the diferences between the AJ and the LMAJ estimates given by the Monte Carlo simulation in each transition for each "s" quantile times. ET.qs2All means the same but missing values were replaced by the previous diferences of estimators.

replicas

Number of replicas for the Monte Carlo simulation.

limit

Percentil of the times used in the AUC global tests.

In case of the AUC local test, an object with a list with the following outcomes:

localTest

p-value of AUC local tests for each times and transitions.

trans

The transition matrix describing the states and transitions of the multi-state model.

times

Times selected for the AUC Local tests.

DIF

Differences between the AJ and the LMAJ estimates for each transition probabilites from the starting state until the receiving state given by only one replica where 's' represent each of the quantile times.

from

The starting state considered for the AUC Local tests.

to

The last receiving state considered for the the AUC Local tests.

ET.qiAll

The lower limit of the diferences between the AJ and the LMAJ estimates given by the Monte Carlo simulation in each transition for each "s" quantile times. ET.qi2All means the same but missing values were replaced by the previous diferences of estimators.

ET.qsAll

The upper limit of the diferences between the AJ and the LMAJ estimates given by the Monte Carlo simulation in each transition for each "s" quantile times. ET.qs2All means the same but missing values were replaced by the previous diferences of estimators.

replicas

Number of replicas for the Monte Carlo simulation.

limit

Percentil of the times used in the AUC local tests.

Arguments

data

A data frame in long format containing the subject id; from corresponding to the starting state;the receiving state, to; the transition number, trans; the starting time of the transition given by Tstart; the stopping time of the transition, Tstop, and status for the status variable, with 1 indicating an event (transition), 0 a censoring.

from

The starting state of the transition probabilities.

to

The last receiving state considered for the estimation of the transition probabilities. All the probabilities among the first and the last states are also computed.

type

Type of test for checking the Markov condition: "local" or "global". By default type='global'.

times

For the local test, times represents the starting times of the transition probabilities. In case of a global test, the argument is given by times between the minimum time and the third quartile times used in the formula of this test. Default to NULL.

quantiles

Quantiles used in the formula of the Global test for the AUC methods. By default takes the percentiles 0.05, 0.10, 0.20, 0.30, 0.40.

tmat

The transition matrix for multi-state model.

replicas

Number of replicas for the Monte Carlo simulation to standardization of the T-statistic given by the difference of the areas of AJ and LM transition probabilities estimates.

limit

Percentile of the event time used as the upper bound for the computation of the AUC-based test.

positions

List of possible transitions; x[[i]] consists of a vector of state numbers reachable from state i.

namesStates

A character vector containing the names of either the competing risks or the states in the multi-state model specified by the competing risks or illness-death model. names should have the same length as the list x (for transMat), or either K or K+1 (for trans.comprisk), or 3 (for trans.illdeath).

timesNames

Either 1) a matrix or data frame of dimension n x S (n being the number of individuals and S the number of states in the multi-state model), containing the times at which the states are visited or last follow-up time, or 2) a character vector of length S containing the column names indicating these times. In the latter cases, some elements of time may be NA, see Details

status

Either 1) a matrix or data frame of dimension n x S, containing, for each of the states, event indicators taking the value 1 if the state is visited or 0 if it is not (censored), or 2) a character vector of length S containing the column names indicating these status variables. In the latter cases, some elements of status may be NA, see Details.

Author

Gustavo Soutinho and Luis Meira-Machado.

References

Soutinho G, Meira-Machado L (2021). Methods for checking the Markov condition in multi-state survival data. Computational Statistics. de Una-alvarez J, Meira-Machado L (2015). Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study. Biometrics, 71(2), 364-375. Putter H, Spitoni C (2018). Non-parametric estimation of transition probabilities in non-Markov multi-state models: The landmark Aalen-Johansen estimator. Statistical Methods in Medical Research, 27, 2081-2092. Meira-Machado L, Sestelo M (2019). Estimation in the progressive illness-death model: A nonexhaustive review. Biometrical Journal, 61(2), 245-263.

Examples

# \donttest{
set.seed(1234)
library(markovMSM)
data("colonMSM")
db_wide<-colonMSM
positions<-list(c(2, 3), c(3), c())
namesStates =  c("Alive", "Rec",  "Death")
tmat <-transMatMSM(positions, namesStates)
timesNames = c(NA, "time1","Stime")
status=c(NA, "event1","event")
trans = tmat
db_long<- prepMSM(data=db_wide, trans, timesNames, status)
res<-AUC.test(data=db_long, times=180, from=1, to=3, type='local',
               replicas = 20, tmat = tmat)
res$localTest
res2<-AUC.test(data=db_long, times=180, from=2, to=3, type='local',
               replicas = 20, tmat = tmat)
res2$localTest

res3<-AUC.test(data=db_long, from=1, to=3, replicas = 20, tmat=tmat)
round(res3$globalTest,3)

res4<-AUC.test(data=db_long, from=2, to=3, type='global', replicas = 20,
             tmat=tmat)
round(res4$globalTest,3)

round(res4$localTest,3)
round(res4$localTest,3)

#AUC global for the individuals with the treatment "Obs" of covariate `"rx"
#for colonMSM data set

set.seed(12345)

db_wide.obs<-db_wide[db_wide$rx=='Obs',]

db_long.obs <- prepMSM(data = db_wide.obs, trans, timesNames, status)

res3a<-AUC.test(data=db_long.obs, times=365, from=1, to=3, 
type='local', replicas= 20, tmat = tmat)

res3a$localTest

set.seed(12345)

res4a<-AUC.test(data=db_long.obs, times=365, from=2, to=3, 
type='local', replicas= 20, tmat = tmat)

res4a$localTest

#' data("ebmt4")
db_wide <- ebmt4
positions <- list(c(2, 3, 5, 6), c(4, 5, 6), c(4, 5, 6),
                 c(5, 6), c(), c())
state.names <- c("Tx", "Rec", "AE", "Rec+AE", "Rel", "Death")
tmat <-transMatMSM(positions, state.names)
timesNames <- c(NA, "rec", "ae","recae", "rel", "srv")
status <- c(NA, "rec.s", "ae.s", "recae.s","rel.s", "srv.s")
trans <- tmat

db_long <- prepMSM(data=db_wide, trans, timesNames, status)
db_long[1:10,]

res5<-AUC.test(data=db_long, from=1, to=5, type='global',
               quantiles=c(.05, .10, .20, .30, 0.40),
               tmat = tmat, replicas = 5,
               positions=positions, namesStates=state.names,
               timesNames=timesNames, status=status)
               
round(res5$globalTest, 4)
round(res5$localTests,4)

res6<-AUC.test(data = prothr, from=2, to=3,
               type='global', replicas= 5, limit=0.90,
               quantiles=c(.05, .10, .20, .30, 0.40))
round(res6$globalTest,4)

round(res6$localTests,4)

# }