Log-rank based test for the validity of the Markov assumption

MarkovTest(
  data,
  id,
  formula = NULL,
  transition,
  grid,
  B = 1000,
  fn = list(function(x) mean(abs(x), na.rm = TRUE)),
  fn2 = list(function(x) mean(x, na.rm = TRUE)),
  min_time = 0,
  other_weights = NULL,
  dist = c("poisson", "normal")
)

Arguments

data	Multi-state data in `msdata` format. Should also contain (dummy codings of) the relevant covariates; no factors allowed
id	Column name in `data` containing subject id
formula	Right-hand side of the formula. If NULL will fit with no covariates (formula="1" will also work), offset terms can also be specified.
transition	Transition number of the transition to be tested (in the transition matrix as attribute to `data`)
grid	Grid of time points at which to compute the statistic
B	Number of wild bootstrap replications to perform
fn	A list of summary functions to be applied to the individual zbar traces (or a list of lists)
fn2	A list of summary functions to be applied to the overall chi-squared trace
min_time	The minimum time for calculating optimal weights
other_weights	Other (than optimal) weights can be specified here
dist	Distribution of wild bootstrap random weights, either "poisson" for centred Poisson (default), or "normal" for standard normal

Value

MarkovTest returns an object of class "MarkovTest", which is a list with the following items:

orig_stat

Summary statistic for each of the starting states

orig_ch_stat

Overall chi-squared summary statistic

p_stat_wb

P-values corresponding to each of the summary statistics for each starting state

p_ch_stat_wb

P-values for overall chi-squared summary statistic

b_stat_wb

Bootstrap summary statistics for each of the starting states

zbar

Individual traces for each of the starting states

nobs_grid

The number of events after time s for each s in the grid

Nsub

Number of patients who are ever at risk of the transition of interest

est_quant

Pointwise 2.5 and 97.5 quantile limits for each of the traces

obs_chisq_trace

Trace of the chi-squared statistic

nch_wb_trace

Individual values of the chi-squared statistic trace for the wild bootstrap samples

n_wb_trace

Individual values of the log-rank z statistic traces for the wild bootstrap samples

est_cov

Estimated covariance matrix between the log-rank statistics at each grid point

transition

The transition number tested

from

The from state of the transition tested

The to state of the transition tested

The number of wild bootstrap replications

dist

The distribution used in the wild bootstrap

qualset

Set of qualifying states corresponding to the components of the above traces

coxfit

Fitted coxph object

List of functions applied to state-specific trace

fn2

List of functions applied to overall trace

Details

Function MarkovTest performs the log-rank test described in Titman & Putter (2020). Function optimal_weights_matrix implements the optimal weighting for the state-specific trace. Function optimal_weights_multiple implements the optimal weighting for the chi-squared trace.

References

Titman AC, Putter H (2020). General tests of the Markov property in multi-state models. Biostatistics To appear.

Author

Andrew Titman a.titman@lancaster.ac.uk, transported to mstate by Hein Putter H.Putter@lumc.nl

Examples


if (FALSE) {
# Example provided by the prothrombin data
data("prothr")
# Apply Markov test to grid of monthly time points over the first 7.5 years
year <- 365.25
month <- year / 12
grid <- month * (1 : 90)
# Markov test for transition 1 (wild bootstrap based on 25 replications, 1000 recommended)
MT <- MarkovTest(prothr, id = "id", transition = 1,
                 grid = grid, B = 25)

# Plot traces
plot(MT, grid, what="states", idx=1:10, states=rownames(attr(prothr, "trans")),
     xlab="Days since randomisation", ylab="Log-rank test statistic",
     main="Transition Normal -> Low")
plot(MT, grid,what="overall", idx=1:10,
     xlab="Days since randomisation", ylab="Chi-square test statistic",
     main="Transition Normal -> Low")

# Example using optimal weights and adjustment for covariates
oweights_fun <-
  optimal_weights_matrix(prothr, id = "id", grid=grid, transition = 1,
                         other_weights=list(
                           function(x) mean(abs(x),na.rm=TRUE),
                           function(x) max(abs(x),na.rm=TRUE)))

oweights_chi <- optimal_weights_multiple(prothr, id = "id", grid=grid, transition = 1)

# Formula in MarkovTest only works for continuous covariates and dummy coded variables
# No factors allowed
prothr$prednisone <- as.numeric(prothr$treat == "Prednisone")
MT <- MarkovTest(prothr, id = "id", 
                 formula = "prednisone",
                 transition = 1,
                 grid = grid, B = 25,
                 fn = oweights_fun,
                 fn2 = list(
                   function(x) weighted.mean(x, w=oweights_chi, na.rm=TRUE),
                   function(x) mean(x, na.rm=TRUE),
                   function(x) max(x, na.rm=TRUE)))
}