Package 'mlumr'

Description

Generate quasi-Monte Carlo integration points using Sobol sequences and a Gaussian copula to account for correlations between covariates in the AgD.

Usage

add_integration(
  data,
  n_int = 64,
  cor = NULL,
  cor_adjust = NULL,
  verbose = TRUE,
  ...
)

Arguments

Value

An mlumr_data object with integration points added

Examples

## Not run: 
dat <- add_integration(
  dat,
  n_int = 64,
  x1 = distr(qnorm, mean = x1_mean, sd = x1_sd),
  x2 = distr(qbern, prob = x2_mean)
)

## End(Not run)

Description

Computes the Deviance Information Criterion using the variance-based effective-parameters formula from Gelman et al. (2004): pD = 0.5 * Var(D). This is more stable than the plug-in alternative for multimodal posteriors.

Usage

calculate_dic(object)

Arguments

Details

DIC is retained for backward compatibility and rough comparison. For principled Bayesian model comparison, prefer calculate_loo() or calculate_waic() (Vehtari, Gelman, Gabry 2017).

Value

A list of class mlumr_dic with components DIC, pD, D_bar

Examples

## Not run: 
dic_spfa <- calculate_dic(fit_spfa)
dic_relaxed <- calculate_dic(fit_relaxed)

## End(Not run)

Description

Computes approximate leave-one-out cross-validation (PSIS-LOO, Vehtari, Gelman, Gabry 2017) using the pointwise log-likelihoods stored by the Stan models. Returns a loo object from the loo package.

Usage

calculate_loo(object, ...)

Arguments

Details

Pareto-k diagnostics: values > 0.7 indicate observations for which the PSIS approximation is unreliable; the printed output flags these. Typical remedies are running more iterations, using moment_match = TRUE, or (for highly influential AgD rows) refitting without the offending observation to check sensitivity.

Value

An object of class psis_loo (see loo::loo()).

Note

AgD rows are treated as independent observations. Each AgD row contributes one column to the pointwise log_lik matrix. If two or more AgD rows come from the same study (e.g. subgroup summaries within a single trial) the PSIS-LOO approximation does not account for the within-study clustering; effective sample sizes are inflated and Pareto-k warnings are understated. For clustered AgD, corroborate with prior_sensitivity() or refit omitting suspect rows to check the influence on the posterior.

Examples

## Not run: 
loo_spfa <- calculate_loo(fit_spfa)
print(loo_spfa)

## End(Not run)

Description

Watanabe-Akaike Information Criterion (Watanabe 2010) based on the pointwise log-likelihoods. WAIC is asymptotically equivalent to LOO-CV; prefer calculate_loo() when Pareto-k is well-behaved.

Usage

calculate_waic(object, ...)

Arguments

Value

An object of class waic (see loo::waic()).

Note

As with calculate_loo(), each AgD row is treated as an independent observation. WAIC will be optimistic for AgD rows that share a study (see the note on calculate_loo()).

Examples

## Not run: 
waic_spfa <- calculate_waic(fit_spfa)

## End(Not run)

Description

Compare integration results at the current n_int against a doubled resolution to assess numerical accuracy. Large discrepancies indicate that n_int should be increased.

Usage

check_integration(
  data,
  ...,
  cor = NULL,
  cor_adjust = NULL,
  check_joint = TRUE,
  verbose = TRUE
)

Arguments

Value

A list with components marginals (the original data frame returned by previous versions) and, if check_joint = TRUE, correlations – a data frame of pairwise covariate correlations at the current and doubled n_int for each AgD row. Printed with a pass/warn verdict.

Description

Combine IPD and AgD for unanchored comparison

Usage

combine_data(ipd, agd)

Arguments

Value

An object of class mlumr_data

Examples

## Not run: 
dat <- combine_data(ipd, agd)

## End(Not run)

Description

Compare two or more mlumr_fit objects by DIC (default), LOO, or WAIC. For LOO/WAIC, loo::loo_compare() is used under the hood; the output is the standard loo_compare table. For DIC the return is a data frame ordered by DIC.

Usage

compare_models(..., criterion = c("dic", "loo", "waic"))

Arguments

Details

DIC is the default for backward compatibility and because it has no additional package dependencies. For principled Bayesian model comparison, LOO (Vehtari, Gelman, Gabry 2017) is preferred and requires the optional loo package.

Value

For "loo" / "waic": a compare.loo table from loo::loo_compare(). For "dic": a data frame (invisibly) with columns Model, DIC, pD, Delta_DIC.

Description

Compute conditional (individual-level) treatment effects at specific covariate values from a fitted ML-UMR model. Unlike marginal_effects(), which averages over a population's covariate distribution, conditional effects evaluate the treatment effect at a particular covariate profile.

Usage

conditional_effects(
  object,
  newdata = NULL,
  effect = "all",
  summary = TRUE,
  probs = c(0.025, 0.5, 0.975)
)

Arguments

Details

For SPFA models, the conditional link-scale treatment effect is constant across all covariate values because the shared beta cancels in the treatment contrast on the fitted link scale. However, risk difference (RD) and risk ratio (RR) still vary with covariates because they depend on absolute probability levels. For relaxed models, all conditional effects vary with covariate values because the index and comparator treatments have different regression coefficients.

The conditional link-scale effect is computed directly as eta_index - eta_comparator. This avoids numerical distortion from transforming extreme response-scale probabilities back through the link function.

Conditional vs marginal on non-identity links. Conditional effects are evaluated at a single covariate profile, so there is no averaging over a population and no Jensen's-inequality gap between the conditional and marginal response. Compare with marginal_effects() and predict.mlumr_fit(), which average over either the IPD individuals (index population) or the AgD integration points (comparator population) and therefore return E[g^{-1}(eta)], not g^{-1}(E[eta]).

Value

A data frame. If summary = TRUE, contains columns profile, effect, mean, sd, and quantile columns. If summary = FALSE, returns a single combined data frame of full posterior draws with a profile column indicating which covariate profile each draw belongs to.

See Also

marginal_effects() for population-averaged treatment effects; conditional_predict() for absolute predictions at specific profiles; predict.mlumr_fit() for population-level predictions.

Examples

## Not run: 
# Conditional effects at IPD covariate means (default)
conditional_effects(fit)

# At specific covariate values
conditional_effects(fit, newdata = data.frame(age = 60, sex = 1))

# Multiple profiles
profiles <- data.frame(age = c(50, 60, 70), sex = c(0, 0, 1))
conditional_effects(fit, newdata = profiles)

## End(Not run)

Description

Generate absolute predictions at specific covariate values for both treatments.

Usage

conditional_predict(
  object,
  newdata = NULL,
  type = c("response", "link"),
  summary = TRUE,
  probs = c(0.025, 0.5, 0.975)
)

Arguments

Value

A data frame with predictions for each treatment at each profile

See Also

conditional_effects() for covariate-conditional treatment effects; predict.mlumr_fit() for population-level predictions.

Examples

## Not run: 
conditional_predict(fit)
conditional_predict(fit, newdata = data.frame(age = 60, sex = 1))

## End(Not run)

Description

Bernoulli PMF

Usage

dbern(x, prob, log = FALSE)

Arguments

Value

Numeric vector

Default priors used by mlumr()

Description

These accessors return the current default priors used by mlumr(), tagged with ⁠$default = TRUE⁠ and the package version. prior_summary() prints the version so cross-release reproducibility is diagnosable: if a later release changes a default, fits produced with an older version will still carry the correct ⁠$version⁠ tag.

Usage

default_prior_intercept()

default_prior_beta()

default_prior_sigma()

Value

A prior list (see prior_normal()).

Examples

default_prior_intercept()
default_prior_beta()
default_prior_sigma()

Description

Used to specify marginal distributions for covariates when adding integration points. Wraps an inverse CDF (quantile) function with its parameters.

Usage

distr(qfun, ...)

Arguments

Value

A list with class "mlumr_distr" containing the distribution specification

Examples

# Normal distribution
distr(qnorm, mean = 0, sd = 1)

# Bernoulli distribution with probability 0.3
distr(qbern, prob = 0.3)

Description

Extract marginal treatment effects from a fitted ML-UMR model. For binomial: log odds ratio, risk difference, risk ratio. For normal: mean difference. For poisson: rate ratio.

Usage

marginal_effects(
  object,
  population = c("both", "index", "comparator"),
  effect = "all",
  summary = TRUE,
  probs = c(0.025, 0.5, 0.975)
)

Arguments

Value

A data frame

See Also

predict.mlumr_fit() for absolute predictions; conditional_effects() for covariate-conditional effects at specific profiles; prior_sensitivity() to check how strongly the marginal effect depends on prior_beta.

Examples

## Not run: 
# All effect measures for both populations
marginal_effects(fit)

# Only the log odds ratio in the index population
marginal_effects(fit, population = "index", effect = "lor")

# Full posterior draws rather than summary statistics
marginal_effects(fit, summary = FALSE)

## End(Not run)

Description

Fit a Bayesian multilevel unanchored meta-regression model using individual patient data (IPD) and aggregate data (AgD). Supports binary, continuous, and count outcomes.

Usage

mlumr(
  data,
  model = c("spfa", "relaxed"),
  link = NULL,
  prior_intercept = default_prior_intercept(),
  prior_beta = default_prior_beta(),
  prior_sigma = default_prior_sigma(),
  chains = 4,
  iter = 2000,
  warmup = 1000,
  seed = NULL,
  adapt_delta = 0.95,
  max_treedepth = 15,
  refresh = 200,
  engine = NULL,
  verbose = TRUE,
  ...
)

Arguments

Details

The model assumes that all AgD rows come from the same comparator treatment and that, conditional on covariates, there is no between-study heterogeneity. If AgD rows come from multiple studies with different designs or unmeasured confounders, this assumption may not hold. No random effects for study-level heterogeneity are included.

AgD scale assumptions (family = "normal"). The AgD likelihood is y_agd ~ normal(E[exp(eta)], se_agd) under link = "log" and y_agd ~ normal(E[eta], se_agd) under link = "identity". In both cases set_agd() expects outcome_mean and outcome_se on the arithmetic (original, untransformed) scale, not log-scale or geometric. Passing log-scale summaries silently misspecifies the likelihood. See set_agd() for details.

Comparator-population weighting is family-dependent. Integrated marginal predictions in the comparator population (⁠*_comparator⁠ generated quantities) are weighted by:

• binomial: n_agd[k] (AgD sample size), so larger AgD rows contribute more to the marginal mean.

• normal: equal weights across AgD rows (⁠/ n_agd_rows⁠), reflecting the normal likelihood's treatment of each row as a single summary statistic.

• poisson: E_agd[k] (AgD exposure), matching the rate-based likelihood.

Each weighting is natural for the corresponding likelihood; users comparing marginal effects across families should be aware they are not identically weighted.

Weakly-identified coefficients in the relaxed model — beta_comparator is identified only through AgD, so the relaxed model needs informative priors (or many AgD rows) to estimate effect modification reliably. prior_sensitivity() is the recommended diagnostic.

Value

An object of class mlumr_fit

See Also

prior_sensitivity() for sensitivity of the posterior to prior_beta; set_agd() for AgD scale requirements; prior_summary() for introspection of the priors actually used.

Examples

## Not run: 
# Binary SPFA model
fit_spfa <- mlumr(dat, model = "spfa")

# Relaxed SPFA (allows effect modification)
fit_relaxed <- mlumr(dat, model = "relaxed")

## End(Not run)

Description

Control which Stan backend mlumr uses for model fitting. The default engine is "rstan" (compiled C++ models via rstantools). Users who prefer cmdstanr can switch engines after installation.

Usage

mlumr_engine(engine = NULL)

Arguments

Details

When switching to "cmdstanr", this function checks whether the cmdstanr package and CmdStan toolchain are installed. If either is missing, it offers to install them interactively.

Engine names must be matched exactly. Partial strings such as "c" are not accepted.

The engine preference is stored as options(mlumr.stan_engine = ...) and persists for the current R session. To set a permanent default, add to your .Rprofile:

options(mlumr.stan_engine = "cmdstanr")

Value

The current engine (character), returned invisibly when setting.

Examples

# Check current engine
mlumr_engine()

# Switch to cmdstanr (interactive)
## Not run: 
mlumr_engine("cmdstanr")

## End(Not run)

Description

Compute an unadjusted (naive) indirect treatment comparison by comparing crude outcomes from the IPD and AgD without any covariate adjustment. Returns treatment effect on the link scale plus absolute predictions (event probabilities, risk difference, risk ratio) for both populations.

Usage

naive(data, link = NULL, conf_level = 0.95)

Arguments

Details

For binomial outcomes, event-probability intervals use Wald standard errors and are bounded to ⁠[0, 1]⁠. For Poisson outcomes, the log-rate contrast uses a 0.5 continuity correction when an observed event count is zero.

Value

An object of class mlumr_naive

Examples

## Not run: 
result <- naive(dat)
print(result)

## End(Not run)

Description

Bernoulli CDF

Usage

pbern(q, prob, lower.tail = TRUE, log.p = FALSE)

Arguments

Value

Numeric vector

Description

Generate population-average absolute-outcome predictions in the index and comparator populations.

Usage

## S3 method for class 'mlumr_fit'
predict(
  object,
  population = c("both", "index", "comparator"),
  type = c("response", "link"),
  summary = TRUE,
  probs = c(0.025, 0.5, 0.975),
  ...
)

Arguments

Details

Marginalization on non-identity links. For type = "response" the reported values are E[g^{-1}(eta)] — the posterior expectation of the inverse-link-transformed linear predictor — not g^{-1}(E[eta]). The two differ whenever g is non-linear (logit, probit, cloglog, log) by Jensen's inequality. In the index population the expectation is taken over IPD individuals; in the comparator population it is taken over the integration points constructed by add_integration() from the AgD moments. This is the correct population-average prediction for an individual randomly drawn from that population, and it matches what the Stan ⁠generated quantities⁠ block computes. For the link scale (type = "link") the reported value is E[eta], a linear functional, and the two interpretations coincide.

Value

A data frame with predictions. When type = "link", values are mean linear predictors computed directly from parameter draws (avoiding Jensen's inequality bias).

See Also

marginal_effects() for treatment-effect summaries; conditional_predict() and conditional_effects() for predictions at specific covariate profiles.

Description

Cauchy is Student-t with df = 1; this constructor is a convenience wrapper around prior_student_t(). It has very heavy tails and should be used with care — modern recommendations generally prefer ⁠prior_student_t(df in 3:7, ...)⁠ over Cauchy for regression coefficients to keep sampling well-behaved (see Piironen & Vehtari on the horseshoe; Ghosh et al. 2015).

Usage

prior_cauchy(mean = 0, sd = 2.5, autoscale = FALSE)

Arguments

Value

A list with components distribution = "student_t", df = 1, mean, sd, autoscale.

Examples

prior_cauchy(mean = 0, sd = 2.5)

Description

Exponential prior on a positive scalar. Currently supported for prior_sigma (normal-family residual SD) only; rejected for unconstrained intercepts and regression coefficients. prior_exponential(rate = 1) has mean 1 and is a reasonable weakly-informative choice when the outcome is standardized.

Usage

prior_exponential(rate = 1)

Arguments

Value

A list with components distribution = "exponential", rate, and placeholders (mean = 0, sd = 1 / rate) so the same Stan-field translation works.

Examples

prior_exponential(rate = 1)

Description

Construct a normal prior for passing to mlumr() via prior_intercept, prior_beta, or prior_sigma. The resulting list is consumed by the Stan models.

Usage

prior_normal(mean = 0, sd = 10, autoscale = FALSE)

Arguments

Value

A list with components distribution, mean, sd, df, autoscale.

Choosing a scale

The Stan community's prior-choice wiki (Vehtari et al., 2025) describes five broad categories, from least to most informative:

1. Flat prior — not recommended.

2. Super-vague proper prior, e.g., normal(0, 1e6) — not recommended.

3. Weakly informative, very weak, e.g., normal(0, 10).

4. Generic weakly informative, e.g., normal(0, 1).

5. Specific informative, e.g., normal(0.4, 0.2).

Those scales assume parameters are on roughly unit scale. In ML-UMR models the natural scales are:

Treatment intercepts

On the linear-predictor (link) scale. For a binary outcome with logit link, the intercept is a baseline log odds; normal(0, 10) spans ±20 log-odds at 95 percent and is "very weak". It is the default because the data usually constrain the intercept strongly. Tightening to normal(0, 5) is reasonable when the expected event rate is far from the extremes.

Regression coefficients (beta)

On the link scale, per unit of covariate. For logistic regression with predictors on unit scale, Gelman et al. (2008) and the Stan wiki recommend student_t(df, 0, 2.5) with df in 3:7, or — as a practical approximation — normal(0, 2.5). That is the default used by mlumr(). Use normal(0, 1) if you expect small effects (e.g., standardized predictors in a normal-outcome model). If predictors are on very different scales, set autoscale = TRUE so the scale is divided by each covariate's SD.

Residual SD (sigma, normal family only)

prior_sigma is interpreted as a half-normal via the Stan ⁠<lower=0>⁠ constraint. The default normal(0, 2.5) (i.e., half-normal(0, 2.5)) is weakly informative for residual SDs on the scale of the outcome. Scale to the outcome if it is far from unit scale, or use prior_exponential().

Prior sensitivity is especially important for the relaxed model, where beta_comparator is identified only by the AgD likelihood. Run prior_sensitivity() to quantify how much conclusions move under alternative scales; see vignette("mlumr-models").

References

Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y.-S. (2008). A weakly informative default prior distribution for logistic and other regression models. Annals of Applied Statistics, 2(4), 1360–1383.

Vehtari, A. et al. Prior Choice Recommendations (Stan wiki): https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations.

Examples

# Default weakly-very-weak intercept prior
prior_normal(mean = 0, sd = 10)

# Gelman 2008 default for logistic-regression coefficients
prior_normal(mean = 0, sd = 2.5)

# Autoscaled coefficient prior (dividing 2.5 by each covariate's SD)
prior_normal(mean = 0, sd = 2.5, autoscale = TRUE)

Description

Refit an mlumr() model across a grid of prior_beta scales (keeping the family, mean, and df fixed) and summarize how the posterior for the marginal treatment effects (delta_index, delta_comparator) moves. This is the workflow recommended by Vehtari et al.'s prior-choice wiki for judging how much of the posterior is driven by the data versus the prior.

Usage

prior_sensitivity(
  fit,
  prior_beta_scales = c(0.5, 1, 2.5, 5, 10),
  probs = c(0.025, 0.5, 0.975),
  verbose = TRUE,
  ...
)

Arguments

Details

Only the scale of the prior_beta family is varied; its distribution (normal / student_t) and mean are preserved so comparisons are apples to apples. prior_intercept and prior_sigma are carried through unchanged from the original fit. Each value in prior_beta_scales is used as the absolute scale for every coefficient at that refit — if the original fit used per-coefficient priors, all coefficients are set to the same scale (the sweep is deliberately homogeneous so the grid reflects a single level of prior informativeness per refit, not a rescaling of existing relative differences). If the original prior_beta used an exponential family, it is swapped for a prior_normal(0, scale) at each grid point since exponential has no scale parameter to vary.

Value

A data frame (tibble-style) with one row per (scale, population, quantile) combination and columns scale, parameter, mean, sd, and the requested quantiles. Side effect: prints a summary table at the end.

See Also

prior_summary() for a one-shot description of the priors on a fit; marginal_effects() for the posterior summary quantities this sweep tracks.

Examples

## Not run: 
sens <- prior_sensitivity(fit_spfa, prior_beta_scales = c(1, 2.5, 5))

## End(Not run)

Description

Heavier-tailed alternative to prior_normal(). For logistic-regression coefficients with unit-scale predictors, the Stan community prior-choice recommendations suggest Student-t with df between 3 and 7 as a robust weakly informative prior (Gelman et al., 2008).

Usage

prior_student_t(df = 5, mean = 0, sd = 2.5, autoscale = FALSE)

Arguments

Value

A list with components distribution = "student_t", df, mean, sd, autoscale.

Examples

# Gelman et al. 2008 recommendation for logistic-regression coefficients
prior_student_t(df = 5, mean = 0, sd = 2.5)

Description

Print a human-readable summary of every prior that was used to fit an mlumr() model, including the effective per-coefficient scales after autoscaling. Mirrors the spirit of rstanarm::prior_summary().

Usage

prior_summary(object, ...)

## Default S3 method:
prior_summary(object, ...)

## S3 method for class 'mlumr_fit'
prior_summary(object, digits = 3, ...)

Arguments

Value

Invisibly returns a list describing the priors; the side effect is printing a formatted summary.

See Also

prior_sensitivity() to quantify how much the posterior moves under alternative prior_beta scales; prior_normal(), prior_student_t(), prior_cauchy(), prior_exponential() for the prior constructors themselves.

Examples

## Not run: 
fit <- mlumr(dat)
prior_summary(fit)

## End(Not run)

Description

Bernoulli quantile function

Usage

qbern(p, prob, lower.tail = TRUE, log.p = FALSE)

Arguments

Value

Integer vector of 0s and 1s

Description

Prepare AgD from the comparator treatment for an unanchored indirect comparison.

Usage

set_agd(
  data,
  treatment,
  family = c("binomial", "normal", "poisson"),
  outcome_n = NULL,
  outcome_r = NULL,
  outcome_mean = NULL,
  outcome_se = NULL,
  outcome_E = NULL,
  cov_means,
  cov_sds = NULL,
  cov_types = NULL,
  study = NULL
)

Arguments

Details

Scale assumptions for family = "normal". The AgD likelihood is y_agd ~ normal(E[exp(eta)], se_agd) under link = "log" and y_agd ~ normal(E[eta], se_agd) under link = "identity". In both cases outcome_mean and outcome_se must be on the arithmetic (original, untransformed) scale. If a publication reports only a log-scale mean / SD or a geometric mean, back-transform before calling set_agd() and propagate uncertainty via the delta method; passing log-scale or geometric summaries silently misspecifies the likelihood and biases the posterior.

Scale assumptions for family = "poisson". outcome_r is the total count in each AgD row and outcome_E is the total person-time (or other exposure). The Stan likelihood uses log(E_agd) as an offset, so rates are modeled on the log scale regardless of how outcome_r is tabulated.

Scale assumptions for family = "binomial". outcome_r / outcome_n are counts of events and trials. The log-odds (or probit / cloglog under alternative links) are formed from outcome_r / outcome_n, so no scale conversion is required.

Value

An object of class mlumr_agd

Examples

## Not run: 
# Binary outcome
agd <- set_agd(
  data = trial_b,
  treatment = "trt",
  outcome_n = "n_total",
  outcome_r = "n_events",
  cov_means = c("age_mean", "sex_prop"),
  cov_sds = c("age_sd", NA),
  cov_types = c("continuous", "binary")
)

# Continuous outcome
agd <- set_agd(
  data = trial_b,
  treatment = "trt",
  family = "normal",
  outcome_mean = "mean_score",
  outcome_se = "se_score",
  outcome_n = "n_total",
  cov_means = c("age_mean", "sex_prop")
)

# Count outcome
agd <- set_agd(
  data = trial_b,
  treatment = "trt",
  family = "poisson",
  outcome_r = "n_events",
  outcome_E = "person_years",
  cov_means = c("age_mean", "sex_prop")
)

## End(Not run)

Description

Prepare IPD from the index treatment for an unanchored indirect comparison.

Usage

set_ipd(
  data,
  treatment,
  outcome,
  covariates,
  family = c("binomial", "normal", "poisson"),
  exposure = NULL,
  study = NULL
)

Arguments

Value

An object of class mlumr_ipd

Examples

## Not run: 
# Binary outcome
ipd <- set_ipd(
  data = trial_a,
  treatment = "trt",
  outcome = "response",
  covariates = c("age", "sex")
)

# Continuous outcome
ipd <- set_ipd(
  data = trial_a,
  treatment = "trt",
  outcome = "score",
  covariates = c("age", "sex"),
  family = "normal"
)

# Count outcome with exposure
ipd <- set_ipd(
  data = trial_a,
  treatment = "trt",
  outcome = "events",
  covariates = c("age", "sex"),
  family = "poisson",
  exposure = "person_years"
)

## End(Not run)

Description

Perform an unanchored simulated treatment comparison (STC) using parametric G-computation. Fits a regression on IPD, predicts counterfactual outcomes in both the index and comparator populations, and computes marginal treatment effects with delta-method standard errors.

Usage

stc(data, link = NULL, conf_level = 0.95)

Arguments

Details

For binomial outcomes, returns the treatment effect on the link scale plus event probabilities, risk difference, and log risk ratio with SEs and CIs for both populations. Event-probability intervals use Wald standard errors and are bounded to ⁠[0, 1]⁠. For Poisson outcomes, the comparator log rate uses a 0.5 continuity correction when the observed event count is zero.

The STC procedure is:

1. Fit a GLM on IPD (binomial/gaussian/poisson as appropriate).

2. Predict on comparator-population covariates (from integration points or AgD covariate means).

3. Marginalize predictions over the comparator population.

4. Predict on index-population covariates (IPD).

5. Compute treatment effects and SEs via the delta method.

STC is a parametric G-computation benchmark. It relies on the IPD outcome model being correctly specified and transportable to the comparator population. It does not model posterior uncertainty in population covariate distributions or relax treatment-specific covariate effects. When clinically meaningful effect modification is plausible, prefer mlumr(..., model = "relaxed") as the primary analysis and use STC as a sensitivity or benchmarking analysis.

For binomial outcomes, the comparator-population treatment contrast is transported to the index population assuming the treatment contrast is constant on the fitted link scale (i.e., no effect modification on that scale). Under this assumption, the index-population comparator probability is computed as inv_link(link(p_A_index) - (link(p_A_comp) - link(p_B))), and its uncertainty is propagated through the delta method. If effect modification is expected, fit a Bayesian relaxed model with mlumr(..., model = "relaxed") and use predict(..., population = "index") instead, which does not require this assumption.

Value

An object of class mlumr_stc

Examples

## Not run: 
result <- stc(dat)
print(result)

## End(Not run)

Description

Expand integration points into a long-format data frame

Usage

unnest_integration(data)

Arguments

Value

A data frame with columns for each covariate plus .int_id and .agd_row