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Perturbation family: reference-based multiple imputation

Source: R/reference.R
stress_reference.Rd

Imputes the missing responses from a multivariate-normal imputation model (an MMRM on the observed data with treatment by visit, the subject-level covariates and an unstructured covariance) under the standard reference-based assumptions (Carpenter, Roger and Kenward, 2013), refits the pre-specified model on each completed data set and pools with Rubin's rules:

Usage

stress_reference(
  spec,
  methods = c("MAR", "J2R", "CR", "CIR"),
  m = 25,
  seed = 1,
  delta = 0,
  arm = NULL,
  impute_covariates = NULL,
  same_cov = TRUE,
  max_tries = 3L,
  cores = 1L
)

Arguments

spec

A stress_spec().

methods

Assumptions to run, from "MAR", "J2R", "CR", "CIR".

m

Number of imputations.

seed

Random seed (the same seed is used for every delta). The m imputations are drawn in turn from one stream started at seed, so different seeds give unrelated imputations.

delta

Shift added to the active arm's imputed values (response units); 0 for none.

arm

Treatment level receiving the shift; defaults to the active arm.

impute_covariates

Subject-level covariates used as predictors in the imputation model (with treatment and the visit columns); NULL uses every spec covariate that is constant within subject. Covariates that vary within subject cannot be used.

same_cov

If TRUE one covariance matrix is shared by both arms in the imputation model; if FALSE each arm has its own, and the reference arm's is used for the reference-based draws.

max_tries

Bootstrap refits attempted per imputation before giving up.

cores

Number of worker processes; 1 fits sequentially.

Value

A stress_rows data frame, one counted row per method (role = "sensitivity"), with the number of imputations and the Monte Carlo standard error in note.

Details

  • MAR: every subject's missing values follow their own arm.

  • J2R (jump to reference): an active-arm subject's visits after the last observed one take the reference arm's means.

  • CR (copy reference): an active-arm subject with any missing value follows the reference arm's means at every visit.

  • CIR (copy increments in reference): after the last observed visit the subject keeps their own-arm mean at that visit and then changes as the reference arm does.

Visits missing before the last observed one are treated as missing at random under every assumption. Parameter uncertainty is carried by approximate Bayesian draws: for each imputation the imputation model is refitted on a bootstrap sample of subjects (stratified by arm) and its fixed effects and covariance are used to draw the missing values from the conditional normal distribution given the subject's observed values. An optional delta is added to every imputed value of the active arm.

Imputation i uses seed seed + i on whichever worker draws it, so the result is the same for any number of cores. Two seeds less than m apart therefore share imputations (seeds 1 and 2 share 24 of 25 when m = 25); to estimate Monte Carlo error by repeating the analysis, use seeds at least m apart, such as 1000, 2000, 3000. Within an imputation the methods share the bootstrap refit and the standard-normal draws (common random numbers), so they differ only through the means they impute from: a method gives the same rows whether it is requested alone or with others, and delta is exactly a shift of the imputed values.

References

Carpenter JR, Roger JH, Kenward MG (2013). Analysis of longitudinal trials with protocol deviation: a framework for relevant, accessible assumptions, and inference via multiple imputation. Journal of Biopharmaceutical Statistics 23, 1352-1371.

Examples

small <- mmrm::fev_data[mmrm::fev_data$USUBJID %in% paste0("PT", 1:100), ]
spec <- stress_spec(small, "FEV1", "USUBJID", "AVISIT", "ARMCD", "PBO", covariates = ~ FEV1_BL,
                    covariance = "cs", method = "Satterthwaite", vcov = "Asymptotic")
stress_reference(spec, methods = c("MAR", "J2R"), m = 3)
#>                                family label        kind        role is_base
#> 1 reference-based multiple imputation   MAR alternative sensitivity   FALSE
#> 2 reference-based multiple imputation   J2R alternative sensitivity   FALSE
#>   converged
#> 1      TRUE
#> 2      TRUE
#>                                                                                                      note
#> 1 reference PBO, shift 0 on TRT, common covariance, seed 1; m = 3 of 3 converged; MC SE of estimate 0.669
#> 2 reference PBO, shift 0 on TRT, common covariance, seed 1; m = 3 of 3 converged; MC SE of estimate 0.355
#>   estimate   stderr        df       lcl      ucl          p n_subj n_obs aicc
#> 1 4.793579 1.907971  8.257192 0.4175297 9.169627 0.03537227    100   400   NA
#> 2 3.756516 1.543304 44.872676 0.6478990 6.865133 0.01897400    100   400   NA
#>   param covariance        method       vcov covariates alpha
#> 1    NA         cs Satterthwaite Asymptotic    FEV1_BL  0.05
#> 2    NA         cs Satterthwaite Asymptotic    FEV1_BL  0.05