Model-Robust Standardization for Stepped-Wedge Trials (MRStdLCRT) — Tutorial
Xi Fang
1 Overview
MRStdLCRT implements model-robust standardization for longitudinal cluster randomized trials (LCRTs), with emphasis on stepped-wedge cluster-randomized trials (SW-CRTs) in this tutorial. The package computes four treatment-effect estimands using either unadjusted (nonparametric) or augmented (model-robust standardized) estimators.
A key feature of the implementation is that the working model is fit on the full dataset, while the **aggregation step uses only period j=2,…,J-1. Periods with all clusters untreated or all clusters treated are excluded from aggregation, but remain in the working-model fit.
1.1 Estimands
The API returns all four estimands:
- h-iATE: horizontal individual average treatment effect
- h-cATE: horizontal cluster average treatment effect
- v-iATE: vertical individual average treatment effect
- v-cATE: vertical cluster average treatment effect
1.2 Estimators and variance
- Unadjusted: nonparametric estimators based on cluster-period means.
- Adjusted: augmented estimators based on
model-robust standardization with covariate adjustment. The working
model can be:
- Linear mixed effects model (
lmer) for continuous outcomes - Generalized linear mixed effects model
(
glmer) for binary outcomes - Generalized estimating equations (
gee) for continuous or binary outcomes
- Linear mixed effects model (
- Variance: delete-1 cluster jackknife standard errors and covariance matrix.
1.3 Design diagnostics in
summary()
Each summary() call prints key SW-CRT diagnostics,
including:
- which periods are kept by the mixture rule,
- a period mixture table (min/max of treatment by period),
- and whether the design matches the stepped-wedge edge pattern (first period all control; last period all treated).
By default, summary() also prints a global
informative-size (ICS) F-test comparing all four estimands. You
may customize or disable this test via the ics and
ics_method arguments.
2 Installation
Install the development version directly from GitHub:
# install.packages("remotes")
remotes::install_github("fancy575/MRStdLCRT")Load the package:
suppressPackageStartupMessages({
library(MRStdLCRT)
library(dplyr)
library(ggplot2)
})3 Example data: stepped-wedge CRTs
Two example datasets are included for this tutorial:
sw_c: continuous outcome dataset (outcome column:y)sw_b: binary outcome dataset (outcome column:y)
Both contain:
- cluster ID:
cluster - period:
period - treatment indicator:
trt(0/1) - covariates:
x1,x2(and possibly additional covariates depending on the simulated dataset)
data("sw_c", package = "MRStdLCRT")
data("sw_b", package = "MRStdLCRT")3.1 Design overview
The heatmap below shows the treatment assignment for each
cluster-period cell.
Cells in blue indicate treatment (trt=1);
cells in gray indicate control
(trt=0).
4 Outcome overview
4.1 Continuous outcome
(sw_c)
4.2 Binary outcome
(sw_b)
5 API at a glance
Fit
mrstdlcrt_fit(data, formula, cluster_id, period, trt, method, family, corstr, scale)Summarize
summary(object, level = 0.95, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))Plot
plot(object, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
5.1 Notes on formulas
- For GEE, it is recommended to omit random
effects terms like
(1|cluster); the package strips them internally if present. - The package supports complex fixed effects,
including interactions such as
factor(period) * trt, etc.
6 Continuous outcome (stepped-wedge) — working models
We keep the same covariates and vary only the working model specification.
fml_c_lmer_full <- y ~ 0 + factor(period) + trt +
x1 + x2 +
(1 | cluster) + (1 | cluster:period)
fml_c_lmer_cluster <- y ~ 0 + factor(period) + trt +
x1 + x2 +
(1 | cluster)
fml_c_gee <- y ~ 0 + factor(period) + trt + x1 + x26.1 lmer: random intercepts (1|cluster) + (1|cluster:period)
fit_c_lmer_full <- mrstdlcrt_fit(
data = sw_c,
formula = fml_c_lmer_full,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "lmer",
family = "gaussian"
)
summary(fit_c_lmer_full, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: lmer Family: gaussian Scale: RD
#> Clusters: 30 Periods kept: 4 (of 6 total)
#> Kept periods: 2, 3, 4, 5
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 6 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 6 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 0 1 TRUE
#> 5 5 0 1 TRUE
#> 6 6 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 1767 30 30
#> 2 3 1555 30 30
#> 3 4 1808 30 30
#> 4 5 1826 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 164 4
#> 2 2 265 4
#> 3 3 120 4
#> 4 4 277 4
#> 5 5 225 4
#> 6 6 223 4
#> 7 7 319 4
#> 8 8 290 4
#> 9 9 250 4
#> 10 10 285 4
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 13.14064 1.3e-05
#> 2 adjusted 3 29 13.42155 1.1e-05
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.202067 1.248330 5.648944 10.75519
#> adjusted 8.270074 1.249275 5.715020 10.82513
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 7.361880 1.345551 4.609919 10.11384
#> adjusted 7.419341 1.332643 4.693780 10.14490
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.131903 1.238139 5.599625 10.66418
#> adjusted 8.200893 1.239615 5.665596 10.73619
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 5.499351 1.126920 3.194540 7.804162
#> adjusted 5.584481 1.108943 3.316439 7.852523
plot(fit_c_lmer_full, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
6.2 lmer: random intercept (1|cluster)
fit_c_lmer_cluster <- mrstdlcrt_fit(
data = sw_c,
formula = fml_c_lmer_cluster,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "lmer",
family = "gaussian"
)
summary(fit_c_lmer_cluster, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: lmer Family: gaussian Scale: RD
#> Clusters: 30 Periods kept: 4 (of 6 total)
#> Kept periods: 2, 3, 4, 5
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 6 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 6 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 0 1 TRUE
#> 5 5 0 1 TRUE
#> 6 6 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 1767 30 30
#> 2 3 1555 30 30
#> 3 4 1808 30 30
#> 4 5 1826 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 164 4
#> 2 2 265 4
#> 3 3 120 4
#> 4 4 277 4
#> 5 5 225 4
#> 6 6 223 4
#> 7 7 319 4
#> 8 8 290 4
#> 9 9 250 4
#> 10 10 285 4
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 13.14064 1.3e-05
#> 2 adjusted 3 29 13.42642 1.1e-05
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.202067 1.248330 5.648944 10.75519
#> adjusted 8.269740 1.248793 5.715671 10.82381
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 7.361880 1.345551 4.609919 10.11384
#> adjusted 7.419017 1.332088 4.694592 10.14344
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.131903 1.238139 5.599625 10.66418
#> adjusted 8.200562 1.239139 5.666238 10.73489
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 5.499351 1.126920 3.194540 7.804162
#> adjusted 5.584460 1.108341 3.317648 7.8512716.3 GEE: independence
fit_c_gee_ind <- mrstdlcrt_fit(
data = sw_c,
formula = fml_c_gee,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "gee",
family = "gaussian",
corstr = "independence"
)
summary(fit_c_gee_ind, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: gee Family: gaussian Scale: RD
#> GEE corstr: independence
#> Clusters: 30 Periods kept: 4 (of 6 total)
#> Kept periods: 2, 3, 4, 5
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 6 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 6 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 0 1 TRUE
#> 5 5 0 1 TRUE
#> 6 6 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 1767 30 30
#> 2 3 1555 30 30
#> 3 4 1808 30 30
#> 4 5 1826 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 164 4
#> 2 2 265 4
#> 3 3 120 4
#> 4 4 277 4
#> 5 5 225 4
#> 6 6 223 4
#> 7 7 319 4
#> 8 8 290 4
#> 9 9 250 4
#> 10 10 285 4
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 13.14064 1.3e-05
#> 2 adjusted 3 29 13.42656 1.1e-05
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.202067 1.248330 5.648944 10.75519
#> adjusted 8.269544 1.249144 5.714757 10.82433
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 7.361880 1.345551 4.609919 10.11384
#> adjusted 7.418796 1.332380 4.693772 10.14382
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.131903 1.238139 5.599625 10.66418
#> adjusted 8.200374 1.239530 5.665251 10.73550
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 5.499351 1.126920 3.194540 7.804162
#> adjusted 5.584761 1.108609 3.317401 7.8521226.4 GEE: exchangeable
fit_c_gee_exch <- mrstdlcrt_fit(
data = sw_c,
formula = fml_c_gee,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "gee",
family = "gaussian",
corstr = "exchangeable"
)
summary(fit_c_gee_exch, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: gee Family: gaussian Scale: RD
#> GEE corstr: exchangeable
#> Clusters: 30 Periods kept: 4 (of 6 total)
#> Kept periods: 2, 3, 4, 5
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 6 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 6 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 0 1 TRUE
#> 5 5 0 1 TRUE
#> 6 6 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 1767 30 30
#> 2 3 1555 30 30
#> 3 4 1808 30 30
#> 4 5 1826 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 164 4
#> 2 2 265 4
#> 3 3 120 4
#> 4 4 277 4
#> 5 5 225 4
#> 6 6 223 4
#> 7 7 319 4
#> 8 8 290 4
#> 9 9 250 4
#> 10 10 285 4
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 13.14064 1.3e-05
#> 2 adjusted 3 29 13.42644 1.1e-05
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.202067 1.248330 5.648944 10.75519
#> adjusted 8.269738 1.248794 5.715669 10.82381
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 7.361880 1.345551 4.609919 10.11384
#> adjusted 7.419015 1.332088 4.694589 10.14344
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.131903 1.238139 5.599625 10.66418
#> adjusted 8.200560 1.239140 5.666235 10.73489
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 5.499351 1.126920 3.194540 7.804162
#> adjusted 5.584459 1.108341 3.317646 7.8512726.5 Interaction example (continuous outcome)
This example illustrates period-specific treatment effects and covariate interactions that are common in stepped-wedge analyses.
fml_c_lmer_int <- y ~ 0 + factor(period) * trt +
factor(period) * x1 + x2 +
(1 | cluster) + (1 | cluster:period)fit_c_lmer_int <- mrstdlcrt_fit(
data = sw_c,
formula = fml_c_lmer_int,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "lmer",
family = "gaussian"
)
summary(fit_c_lmer_int, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: lmer Family: gaussian Scale: RD
#> Clusters: 30 Periods kept: 4 (of 6 total)
#> Kept periods: 2, 3, 4, 5
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 6 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 6 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 0 1 TRUE
#> 5 5 0 1 TRUE
#> 6 6 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 1767 30 30
#> 2 3 1555 30 30
#> 3 4 1808 30 30
#> 4 5 1826 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 164 4
#> 2 2 265 4
#> 3 3 120 4
#> 4 4 277 4
#> 5 5 225 4
#> 6 6 223 4
#> 7 7 319 4
#> 8 8 290 4
#> 9 9 250 4
#> 10 10 285 4
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 13.14064 1.3e-05
#> 2 adjusted 3 29 13.55606 1.0e-05
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.202067 1.248330 5.648944 10.75519
#> adjusted 8.276692 1.236036 5.748714 10.80467
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 7.361880 1.345551 4.609919 10.11384
#> adjusted 7.419988 1.334398 4.690837 10.14914
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 8.131903 1.238139 5.599625 10.66418
#> adjusted 8.206131 1.226589 5.697474 10.71479
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 5.499351 1.126920 3.19454 7.804162
#> adjusted 5.584906 1.115516 3.30342 7.8663937 Binary outcome (stepped-wedge) — working models (scale = OR)
For binary outcomes, we recommend specifying the reporting scale via
scale = "OR", which reports the log odds
ratio and also prints exponentiated OR in the
summary output.
fml_b_glmer_full <- y ~ 0 + factor(period) + trt +
x1 + x2 +
(1 | cluster) + (1 | cluster:period)
fml_b_glmer_cluster <- y ~ 0 + factor(period) + trt +
x1 + x2 +
(1 | cluster)
fml_b_gee <- y ~ 0 + factor(period) + trt + x1 + x27.1 glmer: (1|cluster) + (1|cluster:period), scale = OR (log OR)
fit_b_glmer_full_or <- mrstdlcrt_fit(
data = sw_b,
formula = fml_b_glmer_full,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "glmer",
family = "binomial",
scale = "OR"
)
summary(fit_b_glmer_full_or, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: glmer Family: binomial Scale: OR
#> Clusters: 30 Periods kept: 2 (of 4 total)
#> Kept periods: 2, 3
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 4 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 2 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 894 30 30
#> 2 3 823 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 35 2
#> 2 2 44 2
#> 3 3 85 2
#> 4 4 28 2
#> 5 5 86 2
#> 6 6 68 2
#> 7 7 57 2
#> 8 8 94 2
#> 9 9 62 2
#> 10 10 33 2
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 7.466581 0.000753
#> 2 adjusted 3 29 7.213823 0.000926
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.296039 0.266029 1.751949 2.840129
#> adjusted 2.283548 0.260173 1.751434 2.815662
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.934751 5.765828 17.11797
#> adjusted 9.811431 5.762861 16.70423
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 2.003200 0.327325 1.333745 2.672655
#> adjusted 1.997093 0.323183 1.336110 2.658076
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 7.412739 3.795228 14.47836
#> adjusted 7.367609 3.804217 14.26882
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.286101 0.264796 1.744532 2.827671
#> adjusted 2.273927 0.258807 1.744607 2.803248
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.836514 5.723224 16.90603
#> adjusted 9.717490 5.723650 16.49815
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 1.762751 0.287326 1.175104 2.350398
#> adjusted 1.760738 0.282326 1.183315 2.338160
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 5.828450 3.238481 10.48974
#> adjusted 5.816726 3.265181 10.36215
plot(fit_b_glmer_full_or, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
7.2 glmer: (1|cluster), scale = OR (log OR)
fit_b_glmer_cluster_or <- mrstdlcrt_fit(
data = sw_b,
formula = fml_b_glmer_cluster,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "glmer",
family = "binomial",
scale = "OR"
)
summary(fit_b_glmer_cluster_or, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: glmer Family: binomial Scale: OR
#> Clusters: 30 Periods kept: 2 (of 4 total)
#> Kept periods: 2, 3
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 4 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 2 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 894 30 30
#> 2 3 823 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 35 2
#> 2 2 44 2
#> 3 3 85 2
#> 4 4 28 2
#> 5 5 86 2
#> 6 6 68 2
#> 7 7 57 2
#> 8 8 94 2
#> 9 9 62 2
#> 10 10 33 2
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 7.466581 0.000753
#> 2 adjusted 3 29 7.221413 0.000920
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.296039 0.266029 1.751949 2.840129
#> adjusted 2.284734 0.260309 1.752343 2.817126
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.934751 5.765828 17.11797
#> adjusted 9.823075 5.768099 16.72870
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 2.003200 0.327325 1.333745 2.672655
#> adjusted 1.998302 0.322935 1.337825 2.658779
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 7.412739 3.795228 14.47836
#> adjusted 7.376520 3.810746 14.27884
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.286101 0.264796 1.744532 2.827671
#> adjusted 2.275069 0.258939 1.745480 2.804659
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.836514 5.723224 16.90603
#> adjusted 9.728593 5.728648 16.52144
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 1.762751 0.287326 1.175104 2.350398
#> adjusted 1.761877 0.282002 1.185119 2.338635
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 5.828450 3.238481 10.48974
#> adjusted 5.823358 3.271075 10.367087.3 GEE: independence, scale = OR (log OR)
fit_b_gee_ind_or <- mrstdlcrt_fit(
data = sw_b,
formula = fml_b_gee,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "gee",
family = "binomial",
corstr = "independence",
scale = "OR"
)
summary(fit_b_gee_ind_or, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: gee Family: binomial Scale: OR
#> GEE corstr: independence
#> Clusters: 30 Periods kept: 2 (of 4 total)
#> Kept periods: 2, 3
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 4 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 2 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 894 30 30
#> 2 3 823 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 35 2
#> 2 2 44 2
#> 3 3 85 2
#> 4 4 28 2
#> 5 5 86 2
#> 6 6 68 2
#> 7 7 57 2
#> 8 8 94 2
#> 9 9 62 2
#> 10 10 33 2
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 7.466581 0.000753
#> 2 adjusted 3 29 7.216555 0.000924
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.296039 0.266029 1.751949 2.840129
#> adjusted 2.284458 0.259908 1.752886 2.816031
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.934751 5.765828 17.11797
#> adjusted 9.820366 5.771234 16.71039
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 2.003200 0.327325 1.333745 2.672655
#> adjusted 1.997916 0.322800 1.337715 2.658116
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 7.412739 3.795228 14.47836
#> adjusted 7.373670 3.810328 14.26938
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.286101 0.264796 1.744532 2.827671
#> adjusted 2.274790 0.258577 1.745941 2.803640
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.836514 5.723224 16.90603
#> adjusted 9.725880 5.731293 16.50461
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 1.762751 0.287326 1.175104 2.350398
#> adjusted 1.761609 0.281899 1.185061 2.338157
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 5.828450 3.238481 10.48974
#> adjusted 5.821796 3.270887 10.362127.4 GEE: exchangeable, scale = OR (log OR)
fit_b_gee_exch_or <- mrstdlcrt_fit(
data = sw_b,
formula = fml_b_gee,
cluster_id = "cluster",
period = "period",
trt = "trt",
method = "gee",
family = "binomial",
corstr = "exchangeable",
scale = "OR"
)
summary(fit_b_gee_exch_or, estimand = c("h-iATE","h-cATE","v-iATE","v-cATE"))
#>
#> MRS-LCRT Summary
#> ========================================================================
#> Method: gee Family: binomial Scale: OR
#> GEE corstr: exchangeable
#> Clusters: 30 Periods kept: 2 (of 4 total)
#> Kept periods: 2, 3
#> CIs: 95.0% (t, df = 29)
#> Stepped-wedge edge pattern: YES (first period 1 all control; last period 4 all treatment)
#>
#> Period mixture table (min/max of Z_ij by period)
#> ------------------------------------------------------------------------
#> # A tibble: 4 × 4
#> period minZ maxZ is_mixed
#> <int> <int> <int> <lgl>
#> 1 1 0 0 FALSE
#> 2 2 0 1 TRUE
#> 3 3 0 1 TRUE
#> 4 4 1 1 FALSE
#>
#> Counts used in aggregation (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 2 × 4
#> period n_obs n_clusters n_cp_cells
#> <int> <int> <int> <int>
#> 1 2 894 30 30
#> 2 3 823 30 30
#>
#> Per-cluster counts (kept periods only)
#> ------------------------------------------------------------------------
#> # A tibble: 30 × 3
#> cluster n_obs n_periods
#> <int> <int> <int>
#> 1 1 35 2
#> 2 2 44 2
#> 3 3 85 2
#> 4 4 28 2
#> 5 5 86 2
#> 6 6 68 2
#> 7 7 57 2
#> 8 8 94 2
#> 9 9 62 2
#> 10 10 33 2
#> # ℹ 20 more rows
#>
#> ICS hypothesis test (linear-contrast F test)
#> ------------------------------------------------------------------------
#> Contrasts (rows of C):
#> h-iATE h-cATE v-iATE v-cATE
#> [1,] 1 -1 0 0
#> [2,] 0 0 1 -1
#> [3,] 1 0 -1 0
#>
#> method_type df1 df2 F p_value note
#> 1 unadjusted 3 29 7.466581 0.000753
#> 2 adjusted 3 29 7.193214 0.000942
#>
#> h-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.296039 0.266029 1.751949 2.840129
#> adjusted 2.283684 0.259827 1.752278 2.815089
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.934751 5.765828 17.11797
#> adjusted 9.812761 5.767727 16.69467
#>
#> h-cATE
#> Estimate SE LCL UCL
#> unadjusted 2.003200 0.327325 1.333745 2.672655
#> adjusted 1.997582 0.322699 1.337588 2.657576
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 7.412739 3.795228 14.47836
#> adjusted 7.371210 3.809843 14.26168
#>
#> v-iATE
#> Estimate SE LCL UCL
#> unadjusted 2.286101 0.264796 1.744532 2.827671
#> adjusted 2.274056 0.258463 1.745439 2.802673
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 9.836514 5.723224 16.90603
#> adjusted 9.718744 5.728418 16.48867
#>
#> v-cATE
#> Estimate SE LCL UCL
#> unadjusted 1.762751 0.287326 1.175104 2.350398
#> adjusted 1.761323 0.281769 1.185040 2.337607
#>
#> Exponentiated (OR)
#> Ratio Ratio_LCL Ratio_UCL
#> unadjusted 5.828450 3.238481 10.48974
#> adjusted 5.820135 3.270818 10.356428 Interpreting the output
Each summary() call prints:
- Method / family / scale
- Which periods were kept by the mixture rule
- A period mixture table (min/max treatment by period)
- Whether the dataset matches the stepped-wedge edge pattern
- (Optional) the global ICS test comparing all four estimands
For each requested estimand, it reports:
- Unadjusted and Adjusted estimates
- Jackknife SE and t-based CI with
df = clusters − 1
- If
scaleis"RR"or"OR", an exponentiated ratio table is also printed
8.1 Customizing the ICS test (optional)
By default, summary() runs the global
ICS test. You can:
- disable it via
ics = "none", or - request a reduced comparison by passing an estimand set (e.g., compare only horizontal estimands), or
- specify pairwise contrasts.
Examples:
# Disable the ICS test
summary(fit_c_gee_ind, ics = "none")
# Test equality within a subset (e.g., horizontal estimands only)
summary(fit_c_gee_ind, ics = c("h-iATE","h-cATE"))
# Pairwise comparisons via list(pairs = ...)
summary(fit_c_gee_ind, ics = list(pairs = list(c("h-iATE","h-cATE"),
c("v-iATE","v-cATE"))))9 Session info
sessionInfo()
#> R version 4.5.2 (2025-10-31 ucrt)
#> Platform: x86_64-w64-mingw32/x64
#> Running under: Windows 11 x64 (build 26200)
#>
#> Matrix products: default
#> LAPACK version 3.12.1
#>
#> locale:
#> [1] LC_COLLATE=English_United States.utf8
#> [2] LC_CTYPE=English_United States.utf8
#> [3] LC_MONETARY=English_United States.utf8
#> [4] LC_NUMERIC=C
#> [5] LC_TIME=English_United States.utf8
#>
#> time zone: America/New_York
#> tzcode source: internal
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] ggplot2_4.0.1 dplyr_1.1.4 MRStdLCRT_0.1.0
#>
#> loaded via a namespace (and not attached):
#> [1] Matrix_1.7-4 gtable_0.3.6 jsonlite_2.0.0 compiler_4.5.2
#> [5] Rcpp_1.1.0 tidyselect_1.2.1 gee_4.13-29 tidyr_1.3.2
#> [9] jquerylib_0.1.4 splines_4.5.2 scales_1.4.0 boot_1.3-32
#> [13] yaml_2.3.12 fastmap_1.2.0 lattice_0.22-7 R6_2.6.1
#> [17] labeling_0.4.3 generics_0.1.4 knitr_1.50 rbibutils_2.4
#> [21] MASS_7.3-65 tibble_3.3.0 nloptr_2.2.1 minqa_1.2.8
#> [25] bslib_0.9.0 pillar_1.11.1 RColorBrewer_1.1-3 rlang_1.1.6
#> [29] cachem_1.1.0 xfun_0.55 sass_0.4.10 S7_0.2.1
#> [33] cli_3.6.5 withr_3.0.2 magrittr_2.0.4 Rdpack_2.6.4
#> [37] digest_0.6.39 grid_4.5.2 rstudioapi_0.17.1 lme4_1.1-38
#> [41] nlme_3.1-168 lifecycle_1.0.4 reformulas_0.4.3 vctrs_0.6.5
#> [45] evaluate_1.0.5 glue_1.8.0 farver_2.1.2 purrr_1.2.0
#> [49] rmarkdown_2.30 tools_4.5.2 pkgconfig_2.0.3 htmltools_0.5.9