New strategy objects

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,
  moments = 1,
  int = FALSE,
  verbatim = TRUE
)

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,
  marginal_distns = NA,
  marginal_params = NA,
  N = 1000L
)

new_strategy(strategy, ...)

Arguments

formula: Linear regression formula object. Prognostic factors (PF) are main effects and effect modifiers (EM) are interactions with the treatment variable, e.g., y ~ X1 + trt + trt:X2. For covariates as both PF and EM use * syntax.
family: A 'family' object specifying the distribution and link function (e.g., 'binomial'). See stats::family() for more details.
trt_var: Treatment variable name; string
n_boot: The number of resamples used for the non-parametric bootstrap; integer
moments: Integer. The number of moments of the covariates to balance. Setting moments = 2 includes both the original variables and their squared terms, which effectively balances both the means and the variances. Default to 1.
int: Logical. If TRUE, includes two-way interactions between all covariates in the balancing model to effectively balance their covariances. Default FALSE
verbatim: Logical. Output to console during running.
rho: A named square matrix of covariate correlations; default NA
marginal_distns: Marginal distributions names; vector default NA. Available distributions are given in stats::Distributions. See copula::Mvdc() for details
marginal_params: Marginal distributions parameters; list of lists, default NA. See copula::Mvdc() for details
N: Synthetic sample size for g-computation
strategy: Class name from strategy_maic, strategy_stc, strategy_gcomp_ml, strategy_gcomp_bayes, strategy_mim
...: Additional arguments

Value

maic class object

gcomp_ml class object

gcomp_bayes class object

mim class object

Strategy list object

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 a future version.

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.

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)

MIM targets a marginal treatment effect by using parametric G-computation within a multiple imputation framework. This approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. It is particularly useful for ensuring compatibility in indirect comparisons when adjusting for effect modifiers.