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

In mstate: Data Preparation, Estimation and Prediction in Multi-State Models

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

Description

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

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.

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

Author(s)

Andrew Titman [e-mail], transported to mstate by Hein Putter [e-mail]

References

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

Examples

## Not run: 
# 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)))

## End(Not run)

mstate documentation built on Sept. 11, 2024, 7:32 p.m.