Package 'outstandR'

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)

---

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

strategy	A list containing the strategy details, including the family distribution.
analysis_params	A list containing: ald Aggregate-level trial data ref_trt Treatment labels reference (common; e.g. placebo) ald_comp Treatment labels comparator scale A scaling parameter for the calculation. From "log_odds", "risk_difference", "log_relative_risk".

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"))

---

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

strategy	A list specifying the model strategy, including: formula: A linear regression formula object. family: A family object specifying the distribution and link function (e.g., binomial). iter: Number of iterations for the MCMC sampling. warmup: Number of warmup iterations for the MCMC sampling. chains: Number of MCMC chains.
analysis_params	List of analysis parameters. Must contain ipd and ald.
...	Additional arguments passed to rstanarm::stan_glm().

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

strategy	A list specifying the model strategy, including: R: Number of bootstrap replications. formula: A linear regression formula object. family: A family object specifying the distribution and link function (e.g., binomial). N: Synthetic sample size for g-computation.
analysis_params	List of analysis parameters.

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 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

strategy	A list corresponding to different modelling approaches
analysis_params	A list containing: ipd: Individual-level patient data (data frame) ald: Aggregate-level trial data (data frame) ref_trt: Treatment label for the reference arm (common; e.g., "C") ipd_comp: Treatment label for the comparator arm in the IPD (e.g., "A") scale: Scaling parameter ("log_odds", "risk_difference", "log_relative_risk")
...	Additional arguments
var_method	A string specifying the variance estimation method, either "sample" (default) or "sandwich".

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"))

---

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

mean_comp, mean_ref	Mean of the outcome for the comparator and reference / common
effect	A character string specifying the effect scale. Options are: "log_odds" Log-odds difference. "risk_difference" Risk difference. "delta_z" Probit scale difference (z-scores). "log_relative_risk_rare_events" Log relative risk for rare events. "log_relative_risk" Log relative risk.

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

ald	Aggregate level data. Data frame in long format.
tid	Treatment ID
effect	Effect name. String.
family	Family distribution

Value

Numeric mean value.

---

Calculate Trial Mean Binary Data

Description

Calculate Trial Mean Binary Data

Usage

calculate_trial_mean_binary(ald, tid, effect)

Arguments

ald	Aggregate level data. Data frame in long format.
tid	Treatment ID
effect	Effect name. String.

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

ald	Aggregate level data. Data frame in long format.
tid	Treatment ID
effect	Effect name. String.
verbatim	Print messages, logical

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

ald	Aggregate level data. Data frame in long format.
tid	Treatment ID
effect	Effect name. String.
verbatim	Print messages, logical

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

ald	Aggregate-level data. Data frame.
tid	Treatment identifier used to extract relevant columns from ald.
effect	A character string specifying the effect scale (e.g., "log_odds", "risk_difference").
family	A character string specifying the model family (e.g., "binomial", "gaussian").

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

ald	Aggregate level data
tid	Treatment ID
effect	Effect

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

ald	Aggregate level data. Data frame in long format.
tid	Treatment ID
effect	Effect name. String.
verbatim	Print messages, logical

Value

Numeric value of total variance.

---

Calculate trial variance count

Description

Calculate trial variance count

Usage

calculate_trial_variance_count(ald, tid, effect)

Arguments

ald	Aggregate level data. Data frame in long format.
tid	Treatment ID.
effect	Effect name. String.

Value

Numeric value of total variance.

---

Estimate Variance Sandwich Estimator

Description

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

Usage

estimate_var_sandwich(strategy, analysis_params, ...)

Arguments

strategy	An object of class strategy created by functions such as strategy_maic(), strategy_stc(), or strategy_mim(). Contains modelling details like the formula and family.
analysis_params	List of analysis parameters (ipd, ald, etc.)
...	Additional arguments

Value

Numeric variance estimate for the treatment contrast

---

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

link	A character string specifying the link function. Options are: "logit" Log-odds scale. "identity" Risk difference. "probit" Probit scale. "cloglog" Log relative risk for rare events. "log" Log relative risk.

Value

A character string representing the treatment effect scale.

Examples

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

---

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

ald	Aggregate-level data
ref_trt	Treatment labels reference (common; e.g. placebo)
comp_trt	Treatment labels comparator
scale	A scaling parameter for the calculation.
family	A character string specifying the family distribution (e.g., "binomial").

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

ald	Aggregate-level data
ref_trt	Treatment labels reference (common; e.g. placebo)
comp_trt	Treatment labels comparator
scale	A scaling parameter for the calculation.
family	A character string specifying the family distribution (e.g., "binomial").

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")

---

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

ipd_trial	Individual-level patient data. For example, suppose between studies A and C. In a long format and must contain a treatment column and outcome column consistent with the formula object. The labels in the treatment are used internally so there must be a common treatment with the aggregate-level data trial.
ald_trial	Aggregate-level data. For example, suppose between studies B and C. The column names are variable: Covariate name. In the case of treatment arm sample size this is NA, statistic: Summary statistic name from "mean", standard deviation "sd", probability "prop", or "sum", value: Numerical value of summary statistic, trt: Treatment label. Because we assume a common covariate distribution between treatment arms this is NA.
strategy	Computation strategy function. These can be strategy_maic(), strategy_stc(), strategy_gcomp_ml() and strategy_gcomp_bayes().
ref_trt	Reference / common / anchoring treatment name.
CI	Confidence interval level; between 0,1 with default 0.95.
scale	Relative treatment effect scale. If NULL, the scale is automatically determined from the model. Choose from "log-odds", "log_relative_risk", "risk_difference", "delta_z", "mean_difference", "rate_difference" depending on the data type.
var_method	Variance estimation method.
seed	Random seed.
...	Additional arguments. Currently, can pass named arguments to rstanarm::stan_glm() via strategy_gcomp_bayes().

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

x	An object of class 'outstandR' or a list of 'outstandR' objects.
...	Additional 'outstandR' objects for comparison.
type	Character, one of "both" (default), "contrasts", or "absolute".
labels	Optional character vector of names for the models.

Value

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

---

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

x	Objects of the class "outstandR"
...	Additional arguments passed to other methods

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

df	A dataframe of ALD

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

df	A Dataframe of ALD

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))

---

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

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
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

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()

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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.

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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

object	outstandR() output object.
CI	Confidence interval level.
...	Additional arguments.
x	An object used to select a method.
digits	Minimal number of significant digits, see print.default.

Value

List of class summary.outstandR

Original argument, but mainly called for side effects

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