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

Usage

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
to: The to state of the transition tested
B: 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
fn: 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) { # \dontrun{
# 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)))
} # }