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Test time-homogeneity of the PTE

Source: R/main.R
time_homo_test.Rd

Tests the null hypothesis that the LPTE is constant over time. The test is based on the difference between the conditional and marginal treatment-effect trajectories implied by a fitted "fitted_onlinesurr" object, standardized by an estimated covariance, and uses a max-type statistic to control the family wise error across time points.

Usage

time_homo_test(model, signif.level = 0.05, N.boots = 50000)

Arguments

model

A fitted object of class "fitted_onlinesurr", typically returned by fit.surr. Must contain $T, $n.fixed, and the elements $Marginal and $Conditional with point and smp components.

signif.level

Numeric in (0,1) giving the test significance level used to form the critical value from the bootstrap distribution. Default is 0.05.

N.boots

Integer number of Monte Carlo draws used to approximate the null distribution of the max standardized deviation statistic and to compute the p-value. Default is 50000.

Value

A named list with:

  • T: the observed test statistic (maximum absolute standardized deviation).

  • T.crit: the 1-signif.level critical value.

  • p.value: the Monte Carlo p-value mean(T_null > T_obs).

Details

See dos Santos Jr. and Parast (2026) for the theoretical details about this test.

Notes:

  • The function assumes the first T time-specific treatment-effect parameters are stored contiguously at the beginning of model$Marginal$point and model$Conditional$point (and similarly for smp). It uses the index 1:(n.fixed) as implemented in the code: 1:(T + n.fixed - T).

  • N.boots here is a Monte Carlo size for the null simulation (distinct from the bootstrap size used when fitting model).

References

Silvaneo V. dos Santos Jr., Layla Parast (2026). “A Causal Framework for Evaluating Jointly Longitudinal Outcomes and Surrogate Markers: A State-Space Approach.” 2604.12882, https://arxiv.org/abs/2604.12882.

Examples

fit <- fit.surr(y ~ 1,
  id = id,
  surrogate = ~s,
  treat = trt,
  data = sim_onlinesurr, # This dataset is included in the OnlineSurr package
  time = time,
  verbose = 0,
  N.boots = 500 # Generally, this value would be too small.
  # Remember to increase it for your dataset.
)

time_homo_test(fit, signif.level = 0.05, N.boots = 500)
#> $T
#> [1] 1.058295
#> 
#> $T.crit
#>      95% 
#> 2.341364 
#> 
#> $p.value
#> [1] 0.654
#>