Title:	Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data
Version:	1.0.0
Description:	For the problem of indirect treatment comparison with limited subject-level data, this package provides tools for model-based standardisation with several different computation approaches. See Remiro‐Azócar A, Heath A, Baio G (2022) "Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data", Res. Synth. Methods, 1–31. ISSN 1759-2879, <doi:10.1002/jrsm.1565>.
License:	GPL (≥ 3)
Encoding:	UTF-8
Language:	en-GB
RoxygenNote:	7.3.3
Depends:	R (≥ 4.1.0)
Imports:	boot, cli, copula, crayon, dplyr, ggplot2, glue, pillar, purrr, rlang, rstanarm, stats, stringr, tibble, tidyr, tidyselect, Rdpack (≥ 0.7)
Suggests:	causaldata, doSNOW, gridExtra, here, knitr, maicplus, marginaleffects, MASS, parallel, reshape2, rmarkdown, stdReg2, testthat (≥ 3.0.0)
Config/testthat/edition:	3
RdMacros:	Rdpack
URL:	https://StatisticsHealthEconomics.github.io/outstandR/
BugReports:	https://github.com/StatisticsHealthEconomics/outstandR/issues/
LazyData:	false
NeedsCompilation:	no
Packaged:	2026-01-16 12:24:42 UTC; n8than
Author:	Nathan Green [aut, cre, cph], Chengyang Gao [aut], Antonio Remiro-Azocar [aut]
Maintainer:	Nathan Green <n.green@ucl.ac.uk>
Repository:	CRAN
Date/Publication:	2026-01-21 20:00:02 UTC

outstandR: Model-Based Standardisation for Indirect Treatment Comparison with Limited Subject-Level Data

Description

For the problem of indirect treatment comparison with limited subject-level data, this package provides tools for model-based standardisation with several different computation approaches. See Remiro‐Azócar A, Heath A, Baio G (2022) "Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data", Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565.

Author(s)

Maintainer: Nathan Green n.green@ucl.ac.uk (ORCID) (ROR) [copyright holder]

Authors:

• Chengyang Gao chengyang.gao.15@ucl.ac.uk

• Antonio Remiro-Azocar antonio.remiro-azocar@bayer.com (ORCID)

See Also

Useful links:

• https://StatisticsHealthEconomics.github.io/outstandR/

• Report bugs at https://github.com/StatisticsHealthEconomics/outstandR/issues/

Individual-level patient data for binary outcome, continuous covariates

Description

This data set contains simulated patient covariate and outcome values.

Usage

data(AC_IPD_binY_contX)

Format

y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)

id

Numeric unique identifier

PF_cont_1

Numeric prognostic factor continuous covariate

PF_cont_2

Numeric prognostic factor continuous covariate

EM_cont_1

Numeric effect modifier continuous covariate

EM_cont_2

Numeric effect modifier continuous covariate

trt

Factor treatment identifier. Levels A, C

y

Integer binary outcome

true_eta

Numeric linear predictor

Source

Simulated data

References

Remiro‐Azocar A, Heath A, Baio G (2022)

Individual-level patient data for continuous outcome, mixed covariates

Description

This data set contains simulated patient covariate and outcome values. Corresponds to ALD data set.

Usage

data(AC_IPD_contY_mixedX)

Format

y ~ X1 + X3 + X4 + trt + trt:(X2 + X3 + X4)

id

Numeric unique identifier

X1

Numeric prognostic factor continuous covariate

X2

Numeric prognostic factor and effect modifier binary covariate

X3

Numeric prognostic factor and effect modifier continuous covariate

X4

Numeric effect modifier binary covariate

trt

Factor treatment identifier. Levels A, C

y

Integer binary outcome

true_eta

Numeric linear predictor

Source

Simulated data

References

Remiro‐Azocar A, Heath A, Baio G (2022)

Individual-level patient data for count outcome, continuous covariates

Description

This data set contains simulated patient covariate and outcome values. Corresponds to ALD data set.

Usage

data(AC_IPD_countY_contX)

Format

y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)

id

Numeric unique identifier

PF_cont_1

Numeric prognostic factor continuous covariate

PF_cont_2

Numeric prognostic factor continuous covariate

EM_cont_1

Numeric effect modifier continuous covariate

EM_cont_2

Numeric effect modifier continuous covariate

trt

Factor treatment identifier. Levels A, C

y

Integer non-negative count outcome

true_eta

Numeric linear predictor

Source

Simulated data

References

Remiro‐Azocar A, Heath A, Baio G (2022)

Aggregate level patient data for binary outcome, continuous covariates

Description

This data set contains summaries of simulated patient covariate and outcome values.

Usage

data(BC_ALD_binY_contX)

Format

y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)

variable

String covariate or outcome name. From EM_cont_1, EM_cont_2, PF_cont_1, PF_cont_2, y.

statistic

String summary statistic name. From mean, sd, sum, N

value

Numeric value

trt

Treatment (arm) name. From B, C

Source

Simulated data

References

Remiro‐Azocar A, Heath A, Baio G (2022)

Aggregate level patient data for continuous outcome, mixed covariates

Description

This data set contains summaries of simulated patient covariate and outcome values. Corresponds to IPD data set.

Usage

data(BC_ALD_contY_mixedX)

Format

y ~ X1 + X3 + X4 + trt + trt:(X2 + X3 + X4)

variable

String covariate or outcome name. From X1, X2, X3, X4, y.

statistic

String summary statistic name. From mean, sd, prob, sum, N

value

Numeric value

trt

Treatment (arm) name. From B, C

Source

Simulated data

References

Remiro‐Azocar A, Heath A, Baio G (2022)

Aggregate level patient data for count outcome, continuous covariates

Description

This data set contains summaries of simulated patient covariate and outcome values. Corresponds to IPD data set.

Usage

data(BC_ALD_countY_contX)

Format

y ~ PF_cont_1 + PF_cont_2 + trt + trt:(EM_cont_1 + EM_cont_2)

variable

String covariate or outcome name. From EM_cont_1, EM_cont_2, PF_cont_1, PF_cont_2, y.

statistic

String summary statistic name. From mean, sd, sum, N

value

Numeric value

trt

Treatment (arm) name. From B, C

Source

Simulated data

References

Remiro‐Azocar A, Heath A, Baio G (2022)

Factory function for creating calc_IPD_stats methods

Description

Creates a method for computing IPD mean and variance statistics based on the supplied function.

Usage

IPD_stat_factory(ipd_fun)

Arguments

Value

A function that computes mean and variance statistics for a given strategy.

Objective function to minimize for standard method of moments MAIC

Description

Objective function to minimize for standard method of moments MAIC

Usage

Q(beta, X)

Arguments

Value

Numeric value

Aggregate-level data mean and variance statistics

Description

Computes the mean and variance of marginal treatment effects for aggregate-level trial data.

Usage

calc_ALD_stats(strategy, analysis_params)

Arguments

Value

A list containing:

mean

The marginal treatment effect mean.

var

The marginal treatment effect variance.

See Also

marginal_treatment_effect(), marginal_variance()

Examples

strategy <- list(family = list(family = "binomial"))  # basic version

ald <- data.frame(trt = c("B","C","B","C"),
                  variable = c(NA, NA, "y", "y"),
                  statistic = c("N", "N", "sum", "sum"),
                  value = c(100, 100, 50, 60))

calc_ALD_stats(strategy = strategy,
               list(ald = ald,
                    ref_trt = "C",
                    ald_comp = "B",
                    scale = "log_odds"))

Calculate individual-level patient data statistics

Description

Computes mean and variance statistics for individual-level patient data using various approaches, including Matching-Adjusted Indirect Comparison (MAIC), Simulated Treatment Comparison (STC), and G-computation via Maximum Likelihood Estimation (MLE) or Bayesian inference.

Usage

calc_IPD_stats(strategy, analysis_params, ...)

## Default S3 method:
calc_IPD_stats(...)

## S3 method for class 'stc'
calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)

## S3 method for class 'maic'
calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)

## S3 method for class 'gcomp_ml'
calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)

## S3 method for class 'gcomp_bayes'
calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)

## S3 method for class 'mim'
calc_IPD_stats(strategy, analysis_params, var_method = NULL, ...)

Arguments

Value

A list containing:

• contrasts: A list with elements mean and var.

• absolute: A list with elements mean and var.

Simulated treatment comparison statistics

IPD for reference "C" and comparator "A" trial arms are used to fit a regression model describing the observed outcomes y in terms of the relevant baseline characteristics x and the treatment variable z.

Matching-adjusted indirect comparison statistics

Marginal IPD comparator treatment "A" vs reference treatment "C" treatment effect estimates using bootstrapping sampling.

G-computation maximum likelihood statistics

Compute a non-parametric bootstrap with default R=1000 resamples.

G-computation Bayesian statistics

Using Stan, compute marginal relative effects for IPD comparator "A" vs reference "C" treatment arms for each MCMC sample by transforming from probability to linear predictor scale.

Multiple imputation marginalisation

Using Stan, compute marginal relative treatment effect for IPD comparator "A" vs reference "C" arms for each MCMC sample by transforming from probability to linear predictor scale. Approximate by using imputation and combining estimates using Rubin's rules.

Examples

strategy <- strategy_maic(formula = as.formula(y~trt:X1), family = binomial())
ipd <- data.frame(trt = sample(c("A", "C"), size = 100, replace = TRUE),
                  X1 = rnorm(100, 1, 1),
                  y = sample(c(1,0), size = 100, prob = c(0.7,0.3), replace = TRUE))

ald <- data.frame(trt = c(NA, "B", "C", "B", "C"),
                  variable = c("X1", "y", "y", NA, NA),
                  statistic = c("mean", "sum", "sum", "N", "N"),
                  value = c(0.5, 10, 12, 20, 25))

calc_IPD_stats(strategy,
  analysis_params = list(ipd = ipd, ald = ald, scale = "log_odds"))
  

Bayesian G-computation using Stan

Description

Calculate draws of binary responses from posterior predictive distribution from the Bayesian G-computation method using Hamiltonian Monte Carlo.

Usage

calc_gcomp_bayes(strategy, analysis_params, ...)

Arguments

Value

A list containing:

• means: A list containing:

  • A: Posterior means for comparator treatment group "A".

  • C: Posterior means for reference treatment group "C".

• model: A list containing the fit object (from stan_glm), rho, N, and stan_args.

Examples

strategy <- list(
  formula = y ~ trt:X1,
  family = binomial(),
  rho = NA,
  N = 1000L,
  marginal_distns = NA,
  marginal_params = NA,
  trt_var = "trt",
  iter = 2000,
  warmup = 500,
  chains = 4)

ipd <- data.frame(
   trt = sample(c("A", "C"), size = 100, replace = TRUE),
   X1 = rnorm(100, 1, 1),
   y = sample(c(1,0), size = 100, prob = c(0.7, 0.3), replace = TRUE))

ald <- data.frame(
  trt = c(NA, NA, "B", "C", "B", "C"),
  variable = c("X1", "X1", "y", "y", NA, NA),
  statistic = c("mean", "sd", "sum", "sum", "N", "N"),
  value = c(0.5, 0.1, 10, 12, 20, 25))

calc_gcomp_bayes(
  strategy,
  analysis_params = list(
    ipd = ipd, ald = ald, 
    ref_trt = "C",
    ipd_comp = "A"))

G-computation Maximum Likelihood Bootstrap

Description

Computes the mean difference in treatment effects using bootstrap resampling.

Usage

calc_gcomp_ml(strategy, analysis_params)

Arguments

Value

A list containing:

• means: A list containing:

  • A: Bootstrap estimates for comparator treatment group "A".

  • C: Bootstrap estimates for reference treatment group "C".

• model: A list containing the fit object, rho, and N.

Examples

strategy <- list(
  formula = y ~ trt:X1,
  family = binomial(),
  rho = NA,
  N = 1000L,
  n_boot = 100L,
  marginal_distns = NA,
  marginal_params = NA,
  trt_var = "trt")

ipd <- data.frame(trt = sample(c("A", "C"), size = 100, replace = TRUE),
                  X1 = rnorm(100, 1, 1),
                  y = sample(c(1,0), size = 100, prob = c(0.7,0.3), replace = TRUE))

ald <- data.frame(trt = c(NA, NA, "B", "C", "B", "C"),
                  variable = c("X1", "X1", "y", "y", NA, NA),
                  statistic = c("mean", "sd", "sum", "sum", "N", "N"),
                  value = c(0.5, 0.1, 10, 12, 20, 25))

calc_gcomp_ml(
  strategy,
  analysis_params = 
    list(ipd = ipd, ald = ald, 
         ref_trt = "C", 
         ipd_comp = "A"))
         

Calculate MAIC

Description

Calculate MAIC

Usage

calc_maic(strategy, analysis_params)

Arguments

Value

A list containing:

• means: A list containing:

  • A: Bootstrap estimates for comparator treatment group "A".

  • C: Bootstrap estimates for reference treatment group "C".

• model: A list containing model diagnostics derived from the original data:

  • weights: Vector of calculated weights for the patients in ipd.

  • ESS: The Effective Sample Size.

Multiple imputation marginalization (MIM)

Description

Multiple imputation marginalization (MIM)

Usage

calc_mim(strategy, analysis_params, ...)

Arguments

Value

A list containing:

• means: A list containing vectors of posterior means (one per synthesis n_imp):

  • A: Comparator means.

  • C: Reference means.

• model: A list containing:

  • fit: The first-stage rstanarm::stan_glm() object.

  • hats.v: Vector of variance point estimates for each synthesis.

  • n_imp: Number of posterior prediction draws (syntheses).

  • rho, N, stan_args: Strategy and model parameters.

Calculate simulated treatment comparison statistics

Description

Calculate simulated treatment comparison statistics

Usage

calc_stc(strategy, analysis_params, ...)

Arguments

Value

A list containing:

• means: A list containing:

  • A: Mean for comparator treatment group "A".

  • C: Mean for reference treatment group "C".

• model: The fitted stats::glm() object.

Calculate Average Treatment Effect

Description

Computes the average treatment effect (ATE) based on the specified effect scale.

Usage

calculate_ate(mean_comp, mean_ref, effect)

Arguments

Value

Numeric computed average treatment effect on the specified scale.

Examples

calculate_ate(mean_comp = 0.7, mean_ref = 0.5, effect = "log_odds")
calculate_ate(mean_comp = 0.7, mean_ref = 0.5, effect = "risk_difference")

Calculate Trial Mean Wrapper

Description

Calculate Trial Mean Wrapper

Usage

calculate_trial_mean(ald, tid, effect, family)

Arguments

Value

Numeric mean value.

Calculate Trial Mean Binary Data

Description

Calculate Trial Mean Binary Data

Usage

calculate_trial_mean_binary(ald, tid, effect)

Arguments

Value

Numeric mean value.

Calculate Trial Mean Continuous Data

Description

Calculate Trial Mean Continuous Data

Usage

calculate_trial_mean_continuous(ald, tid, effect, verbatim = FALSE)

Arguments

Value

Numeric mean value.

Calculate Trial Mean Count Data

Description

Calculate Trial Mean Count Data

Usage

calculate_trial_mean_count(ald, tid, effect, verbatim = FALSE)

Arguments

Value

Numeric mean value.

Calculate trial variance

Description

Computes the variance of treatment effects for a trial based on the specified family distribution.

Usage

calculate_trial_variance(ald, tid, effect, family)

Arguments

Value

Numeric computed variance of treatment effects.

Examples

ald <- data.frame(trt = c("B","C","B","C"),
                  variable = c(NA, NA, "y", "y"),
                  statistic = c("N", "N", "sum", "sum"),
                  value = c(100, 100, 50, 60))
                  
calculate_trial_variance(
  ald, tid = "B", effect = "log_odds", family = "binomial")
  

Calculate trial variance binary

Description

Calculate trial variance binary

Usage

calculate_trial_variance_binary(ald, tid, effect)

Arguments

Value

Numeric value of total variance.

Calculate trial variance continuous

Description

Calculate trial variance continuous

Usage

calculate_trial_variance_continuous(ald, tid, effect, verbatim = FALSE)

Arguments

Value

Numeric value of total variance.

Calculate trial variance count

Description

Calculate trial variance count

Usage

calculate_trial_variance_count(ald, tid, effect)

Arguments

Value

Numeric value of total variance.

Check formula

Description

Check formula

Usage

check_formula(formula, trt_var = NULL)

Arguments

Value

No return value, called for side effects

Continuity Correction

Description

Continuity Correction

Usage

continuity_correction(ald, correction = 0.5, verbatim = FALSE)

Arguments

Value

Corrected aggregate level data frame.

Compute covariance matrix

Description

Compute covariance matrix

Usage

cor2cov(cormat, S)

Arguments

Value

Required input for mvrnorm.

Estimate Variance Sandwich Estimator

Description

Computes the robust (sandwich) variance estimator for the treatment effect.

Usage

estimate_var_sandwich(strategy, analysis_params, ...)

Arguments

Value

Numeric variance estimate for the treatment contrast

Bootstrap for G-computation via Maximum Likelihood

Description

This is a statistic function intended for use with a bootstrapping function (e.g., boot::boot()). On each bootstrap sample of the data, it calculates a relative treatment effect (e.g., log odds ratio, log relative risk, or risk difference) using G-computation with maximum likelihood.

Usage

gcomp_ml.boot(
  data,
  indices,
  R,
  formula = NULL,
  family,
  trt_var,
  ref_trt = NA,
  comp_trt = NA,
  rho = NA,
  N = 1000,
  marginal_distns = NA,
  marginal_params = NA,
  ald
)

Arguments

Value

A single numeric value representing the relative treatment effect

See Also

strategy_gcomp_ml()

G-computation maximum likelihood mean outcomes by arm

Description

G-computation maximum likelihood mean outcomes by arm

Usage

gcomp_ml_means(
  formula,
  family,
  ipd,
  ald,
  trt_var,
  rho = NA,
  N = 1000,
  ref_trt,
  comp_trt,
  marginal_distns = NA,
  marginal_params = NA
)

Arguments

Value

A list containing:

• stats: Named vector of marginal mean probabilities

• model: The fitted glm object

See Also

strategy_gcomp_ml(), gcomp_ml.boot()

Retrieve list of allowed variance methods

Description

Retrieve list of allowed variance methods

Usage

get_allowed_var_methods(strategy)

Arguments

Value

Character vector of allowed methods. First element is the default.

Get study comparator treatment names

Description

Get study comparator treatment names

Usage

get_comparator(dat, ref_trt, trt_var = "trt")

Arguments

Value

Comparator string names

Get covariate names

Description

Get covariate names

Usage

get_covariate_names(formula)

Arguments

Value

Covariate names character vector

Get effect modifiers

Description

Get effect modifiers

Usage

get_eff_mod_names(formula, trt_var = "trt")

Arguments

Value

Effect modifiers strings names

Get reference treatment

Description

Get reference treatment

Usage

get_ref_trt(ref_trt, trt, ipd_trial, ald_trial)

Arguments

Value

String of reference treatment name.

Compute Robust Covariance Matrix (HC0-style)

Description

Calculates (X'WX)^-1 (X' W^2 r^2 X) (X'WX)^-1

Usage

get_robust_vcov(fit)

Get treatment effect scale corresponding to a link function

Description

Maps a given link function to its corresponding treatment effect scale.

Usage

get_treatment_effect(link)

Arguments

Value

A character string representing the treatment effect scale.

Examples

 get_treatment_effect(link = "logit")
 get_treatment_effect(link = "identity")
 

Get treatment name

Description

Get treatment name

Usage

get_treatment_name(formula, trt_var = NULL)

Arguments

Value

Treatment name string.

Determine and validate variance method for a strategy

Description

Determine and validate variance method for a strategy

Usage

get_var_method(strategy, user_method = NULL)

Arguments

Value

String name of variance method to use

Guess treatment name

Description

Does a variable appear more than once in interactions? If not then pick first LHS interaction term. Finally, if there are no interactions then pick last main effect term.

Usage

guess_treatment_name(formula)

Arguments

Value

Treatment name string.

MAIC bootstrap sample

Description

Matching-adjusted indirect comparison bootstrap sampling.

Usage

maic.boot(
  ipd,
  indices = 1:nrow(ipd),
  formula,
  family,
  ald,
  trt_var,
  hat_w = NULL
)

Arguments

Value

Vector of fitted probabilities for treatments A and C

See Also

calc_IPD_stats.maic()

Estimate MAIC weights

Description

Matching-adjusted indirect comparison weights. Method is taken from (Signorovitch et al. 2010).

Usage

maic_weights(X_EM)

Arguments

Value

Estimated weights for each individual; vector

References

Signorovitch JE, Wu EQ, Yu AP, Gerrits CM, Kantor E, Bao Y, Gupta SR, Mulani PM (2010). “Comparative effectiveness without head-to-head trials: A method for matching-adjusted indirect comparisons applied to psoriasis treatment with adalimumab or etanercept.” Pharmacoeconomics, 28(10), 935–945. ISSN 11707690, doi:10.2165/11538370-000000000-00000, https://pubmed.ncbi.nlm.nih.gov/20831302/.

Marginal treatment effect from reported event counts

Description

Computes the relative treatment effect from aggregate-level data using event counts.

Usage

marginal_treatment_effect(ald, ref_trt = NA, comp_trt = NA, scale, family)

Arguments

Value

Numeric relative treatment effect.

Examples

ald <- data.frame(trt = c("B","C","B","C"),
                  variable = c(NA, NA, "y", "y"),
                  statistic = c("N", "N", "sum", "sum"),
                  value = c(100, 100, 50, 60))
                  
marginal_treatment_effect(ald, ref_trt = "C", comp_trt = "B",
                          scale = "log_odds", family = "binomial")

Marginal effect variance using the delta method

Description

Computes the total variance of marginal treatment effects using the delta method.

Usage

marginal_variance(ald, ref_trt = NA, comp_trt = NA, scale, family)

Arguments

Value

Numeric total variance of marginal treatment effects.

Examples

ald <- data.frame(trt = c("B","C","B","C"),
                  variable = c(NA, NA, "y", "y"),
                  statistic = c("N", "N", "sum", "sum"),
                  value = c(100, 100, 50, 60))
                  
marginal_variance(ald, ref_trt = "C", comp_trt = "B",
                  scale = "log_odds", family = "binomial")

Numerical Gradient

Description

Numerical Gradient

Usage

num_grad(func, x, h = 1e-05)

Calculate the difference between treatments using all evidence

Description

This is the main, top-level wrapper for {outstandR}. Methods taken from (Remiro‐Azócar et al. 2022).

Usage

outstandR(
  ipd_trial,
  ald_trial,
  strategy,
  ref_trt = NA,
  CI = 0.95,
  scale = NULL,
  var_method = NULL,
  seed = NULL,
  ...
)

Arguments

Value

List of length 11 of statistics as a outstandR class object. Containing statistics between each pair of treatments. These are the mean, variances and confidence intervals, for contrasts and absolute values.

References

Remiro‐Azócar A, Heath A, Baio G (2022). “Parametric G‐computation for compatible indirect treatment comparisons with limited individual patient data.” Res. Synth. Methods, 1–31. ISSN 1759-2879, doi:10.1002/jrsm.1565, 2108.12208.

See Also

strategy_maic() strategy_stc() strategy_gcomp_ml() strategy_gcomp_bayes()

Examples

data(AC_IPD_binY_contX)  # A vs C individual patient-level data
data(BC_ALD_binY_contX)  # B vs C aggregate-level data

# linear formula
lin_form <- as.formula("y ~ PF_cont_1 + PF_cont_2 + trt*EM_cont_1 + trt*EM_cont_2")
                                
# sampling values of additional arguments picked for speed
# select appropriate to specific analysis

# matching-adjusted indirect comparison
outstandR_maic <- outstandR(
  AC_IPD_binY_contX, BC_ALD_binY_contX,
  strategy = strategy_maic(formula = lin_form, n_boot = 100))

# simulated treatment comparison
outstandR_stc <- outstandR(
  AC_IPD_binY_contX, BC_ALD_binY_contX,
  strategy = strategy_stc(lin_form))


# G-computation with maximum likelihood
outstandR_gcomp_ml <- outstandR(
  AC_IPD_binY_contX, BC_ALD_binY_contX,
  strategy = strategy_gcomp_ml(lin_form, n_boot = 100, N =100))

# G-computation with Bayesian inference
outstandR_gcomp_bayes <- outstandR(
  AC_IPD_binY_contX, BC_ALD_binY_contX,
  strategy = strategy_gcomp_bayes(lin_form),
  chains = 1, iter = 1000, warmup = 20)

# Multiple imputation marginalization
outstandR_mim <- outstandR(
  AC_IPD_binY_contX, BC_ALD_binY_contX,
  strategy = strategy_mim(lin_form,
                          N = 100), # size of pseudo-population
  chains = 1, iter = 1000, warmup = 20)

outstandR class

Description

The outstandR class contains the results from running a model with the function outstandR().

Details

Objects of class outstandR have the following

contrasts

A list containing statistics for relative treatment effects:

• means: Estimated relative effects (e.g., log-odds ratios, risk differences).

• variances: Variance-covariance matrix of the relative effects.

• contrast_ci: Confidence intervals for the relative effects.

absolute

A list containing statistics for absolute treatment outcomes:

• means: Estimated absolute outcomes (e.g., probabilities, mean response).

• variances: Variance-covariance matrix of the absolute outcomes.

• ci: Confidence intervals for the absolute outcomes.

CI

The confidence level used (e.g., 0.95).

ref_trt

The name of the reference treatment.

scale

The scale of the outcome (e.g., "log odds", "probability").

model

A list containing details of the underlying statistical model. Contents vary by strategy:

• family: The error distribution and link function.

• fit: The underlying model object (e.g., for STC, G-Comp ML, or Bayesian G-Comp).

• weights, ESS: (MAIC only) The estimated weights and Effective Sample Size.

• stan_args: (Bayesian G-Comp, MIM) Arguments passed to Stan.

• rho: (G-Comp ML, MIM, Bayesian G-Comp) Correlation coefficient.

• N: (G-Comp ML, MIM, Bayesian G-Comp) Number of iterations.

• nu, hats.v, M: (MIM only) Imputation parameters and matrices.

Default Plot Method for outstandR Objects

Description

Default Plot Method for outstandR Objects

Usage

## S3 method for class 'outstandR'
plot(x, ..., type = c("both", "contrasts", "absolute"), labels = NULL)

Arguments

Value

A ggplot2::ggplot() object representing the forest plot of the results.

Prepare Aggregate Level Data

Description

Prepare Aggregate Level Data

Usage

prep_ald(form, data, trt_var = "trt")

Arguments

Value

A data frame of filtered ALD by variables in formula.

Prepare Individual Patient Data

Description

Prepare Individual Patient Data

Usage

prep_ipd(form, data)

Arguments

Value

Model frame

Prepare Covariate Distributions

Description

Resolves missing distributions and parameters by looking at the ALD. Allows for partial specification (e.g., user specifies one variable, function auto-detects the rest).

Usage

prepare_covariate_distns(
  formula,
  ald,
  trt_var,
  marginal_distns,
  marginal_params,
  verbose = FALSE
)

Print a Summary of a outstandR Object

Description

This is a method for the function print() for objects of the class "outstandR" created by a call to outstandR()

Usage

## S3 method for class 'outstandR'
print(x, ...)

Arguments

Value

No return value, called for side effects

See Also

outstandR()

Convert aggregate data from wide to long format

Description

Convert aggregate data from wide to long format

Usage

reshape_ald_to_long(df)

Arguments

Value

Data frame in long format

Convert aggregate data from long to wide format

Description

Convert aggregate data from long to wide format

Usage

reshape_ald_to_wide(df)

Arguments

Value

Data frame in wide format

Examples

df <- 
  data.frame(
    variable = c("age", "age", "y", "y", "y", "y", "y", "y", "y", "y"),
    statistic = c("mean", "sd", "sum", "bar", "sd", "N", "sum", "bar", "sd", "N"),
    trt = c(NA, NA, "B", "B", "B", "B", "C", "C", "C", "C"),
    value = c(1,1,1,1,1,1,1,1,1,1))

Calculate and arrange result statistics

Description

Combining output from aggregate level data studies BC and adjusted individual level data studies AC into a single object.

Usage

result_stats(ipd_stats, ald_stats, CI = 0.95)

Arguments

Value

List of ITC output:

• contrasts: A list for relative effects containing:

  • means

  • variances

  • CI

• absolute: A list for absolute effects containing:

  • means

  • variances

  • CI

Simulate Aggregate-Level Data Pseudo-Population

Description

Generates a synthetic cohort using a normal copula based on aggregate-level data.

Usage

simulate_ALD_pseudo_pop(
  formula,
  ipd = NULL,
  ald = NULL,
  trt_var,
  rho = NA,
  N = 1000,
  marginal_distns = NA,
  marginal_params = NA,
  seed = NULL,
  verbose = FALSE
)

Arguments

Value

A data frame representing the synthetic pseudo-population.

Strategy class and subclasses

Description

The strategy class is a virtual class that defines the statistical approach for population adjustment in indirect treatment comparisons These objects are constructors that validate hyperparameters and encapsulate modelling settings before execution by outstandR()

Details

Objects of class strategy have a common structure but carry different subclasses to trigger specific S3 method dispatch

General fields

Shared by all strategies:

• formula: The linear regression formula for the outcome model

• family: A base R family object specifying the distribution and link

• trt_var: The name of the treatment variable.

maic subclass

Additional fields for Matching-Adjusted Indirect Comparison:

• n_boot: Number of bootstrap resamples for variance estimation.

stc subclass

Additional fields for Simulated Treatment Comparison:

• N: Synthetic sample size for the target population.

gcomp_ml subclass

Additional fields for Maximum Likelihood G-computation:

• rho: Named square matrix of covariate correlations.

• marginal_distns: Names of the marginal distributions for covariates.

• marginal_params: Parameters for the marginal distributions.

• N: Synthetic sample size for the pseudo-population.

• n_boot: Number of bootstrap resamples.

gcomp_bayes subclass

Additional fields for Bayesian G-computation:

• rho, marginal_distns, marginal_params, N: Same as gcomp_ml.

• ...: Additional arguments passed to the Stan engine via rstanarm::stan_glm().

mim subclass

Additional fields for Multiple Imputation Marginalization:

• rho: Correlation matrix.

• N: Number of iterations/simulated individuals.

New strategy objects

Description

Create a type of strategy class for each modelling approach.

Usage

strategy_maic(
  formula = NULL,
  family = gaussian(link = "identity"),
  trt_var = NULL,
  n_boot = 1000L
)

strategy_stc(
  formula = NULL,
  family = gaussian(link = "identity"),
  trt_var = NULL
)

strategy_gcomp_ml(
  formula = NULL,
  family = gaussian(link = "identity"),
  trt_var = NULL,
  rho = NA,
  marginal_distns = NA,
  marginal_params = NA,
  n_boot = 1000L,
  N = 1000L
)

strategy_gcomp_bayes(
  formula = NULL,
  family = gaussian(link = "identity"),
  trt_var = NULL,
  rho = NA,
  marginal_distns = NA,
  marginal_params = NA,
  N = 1000L
)

strategy_mim(
  formula = NULL,
  family = gaussian(link = "identity"),
  trt_var = NULL,
  rho = NA,
  N = 1000L
)

new_strategy(strategy, ...)

Arguments

Value

maic class object

stc class object

gcomp_ml class object

gcomp_bayes class object

mim class object

Strategy list object

Matching-adjusted indirect comparison (MAIC)

MAIC is a form of non-parametric likelihood reweighting method which allows the propensity score logistic regression model to be estimated without IPD in the AC population. The mean outcomes \mu_{t(AC)} on treatment t = A,B in the AC target population are estimated by taking a weighted average of the outcomes Y of the N individuals in arm t of the AB population.

Used to compare marginal treatment effects where there are cross-trial differences in effect modifiers and limited patient-level data.

\hat{Y}_{} = \frac{\sum_{i=1}^{N} Y_{it(AB)} w_{it}}{\sum_{i=1}^{N} w_{it}}

where the weight w_{it} assigned to the i-th individual receiving treatment t is equal to the odds of being enrolled in the AC trial vs the AB trial.

Simulated treatment comparison (STC)

Outcome regression-based method which targets a conditional treatment effect. STC is a modification of the covariate adjustment method. An outcome model is fitted using IPD in the AB trial. For example,

g(\mu_{t(AB)}(X)) = \beta_0 + \beta_1^T X + (\beta_B + \beta_2^T X^{EM}) I(t=B)

where \beta_0 is an intercept term, \beta_1 is a vector of coefficients for prognostic variables, \beta_B is the relative effect of treatment B compared to A at X=0, \beta_2 is a vector of coefficients for effect modifiers X^{EM} subvector of the full covariate vector X), and \mu_{t(AB)}(X) is the expected outcome of an individual assigned treatment t with covariate values X which is transformed onto a chosen linear predictor scale with link function g(\cdot).

G-computation maximum likelihood

G-computation marginalizes the conditional estimates by separating the regression modelling from the estimation of the marginal treatment effect for A versus C. For example, a regression model of the observed outcome y on the covariates x and treatment z is fitted to the AC IPD:

g(\mu_n) = \beta_0 + \boldsymbol{x}_n \boldsymbol{\beta_1} + (\beta_z + \boldsymbol{x_n^{EM}} \boldsymbol{\beta_2}) \mbox{I}(z_n=1)

In the context of G-computation, this regression model is called the “Q-model". Having fitted the Q-model, the regression coefficients are treated as nuisance parameters. The parameters are applied to the simulated covariates x* to predict hypothetical outcomes for each subject under both possible treatments. Namely, a pair of predicted outcomes, also called potential outcomes, under A and under C, is generated for each subject.

By plugging treatment C into the regression fit for every simulated observation, we predict the marginal outcome mean in the hypothetical scenario in which all units are under treatment C:

\hat{\mu}_0 = \int_{x^*} g^{-1} (\hat{\beta}_0 + x^* \hat{\beta}_1 ) p(x^*) dx^*

To estimate the marginal or population-average treatment effect for A versus C in the linear predictor scale, one back-transforms to this scale the average predictions, taken over all subjects on the natural outcome scale, and calculates the difference between the average linear predictions:

\hat{\Delta}^{(2)}_{10} = g(\hat{\mu}_1) - g(\hat{\mu}_0)

G-computation Bayesian

The difference between Bayesian G-computation and its maximum-likelihood counterpart is in the estimated distribution of the predicted outcomes. The Bayesian approach also marginalizes, integrates or standardizes over the joint posterior distribution of the conditional nuisance parameters of the outcome regression, as well as the joint covariate distribution.

Draw a vector of size N* of predicted outcomes y*z under each set intervention z* \in \{0, 1\} from its posterior predictive distribution under the specific treatment. This is defined as p(y*_{z*} | \mathcal{D}_{AC}) = \int_{\beta} p(y*_{z*} | \beta) p(\beta | \mathcal{D}_{AC}) d\beta where p(\beta | \mathcal{D}_{AC}) is the posterior distribution of the outcome regression coefficients \beta, which encode the predictor-outcome relationships observed in the AC trial IPD.

This is given by:

p(y*_{z*} \mid \mathcal{D}_{AC}) = \int_{x*} p(y* \mid z*, x*, \mathcal{D}_{AC}) p(x* \mid \mathcal{D}_{AC}) dx*

= \int_{x*} \int_{\beta} p(y* \mid z*, x*, \beta) p(x* \mid \beta) p(\beta \mid \mathcal{D}_{AC}) d\beta dx*

In practice, the integrals above can be approximated numerically, using full Bayesian estimation via Markov chain Monte Carlo (MCMC) sampling.

Multiple imputation marginalization (MIM)

TODO

Note

While current implementations focus on binary, continuous, and count outcomes, support for survival data (using the survival package) is under active development and scheduled for version 1.1.0.

See Also

strategy_gcomp_bayes()

strategy_gcomp_ml(),copula::Mvdc()

Summary method for outstandR

Description

Summary method for outstandR

Usage

## S3 method for class 'outstandR'
summary(object, CI = NA, ...)

## S3 method for class 'summary.outstandR'
print(x, digits = 3, ...)

Arguments

Value

List of class summary.outstandR

Original argument, but mainly called for side effects

Input data validator

Description

Input data validator

Usage

validate_outstandr(ipd_trial, ald_trial, strategy, CI, scale)

Arguments

Value

No return value, called for side effects

Variance estimate by pooling

Description

Use combining rules to estimate.

Usage

var_by_pooling(n_imp, bar.v, b)

Arguments

Value

Numeric value of variance estimate using pooling.

Wald-type interval estimates

Description

Constructed using t-distribution with nu degrees of freedom.

Usage

wald_type_interval(n_imp, bar.v, b)

Arguments

Value

Numeric value of Wald-type interval estimates.