GaussianNPP class

This class represents a Gaussian model using the NPP (Noninformative Power Prior) approach. It inherits from the Model class.

Super class

Model -> GaussianNPP

Public fields

power_parameter_mean

The mean of the prior on the power parameter.

power_parameter_std

The standard deviation of the prior on the power parameter.

target_treatment_effect_estimate

Estimate of the treatment effect in the target study

target_treatment_effect_standard_error

Standard error on the estimate of the treatment effect in the target study

p

Parameter of the initial Beta prior on the power parameter

q

Parameter of the initial Beta prior on the power parameter

prior_normconst

Normalization constant of the prior

posterior_normconst

Normalization constant of the posterior

max_posterior_pdf

Maximum value of the posterior p.d.f., used for rejection sampling of the posterior p.d.f.

method

Name of the method

summary_measure_likelihood

Summary measure likelihood

Methods

Public methods

• GaussianNPP$summary_rows()

• GaussianNPP$new()

• GaussianNPP$unnormalized_posterior_power_parameter_pdf()

• GaussianNPP$power_parameter_posterior_pdf()

• GaussianNPP$normalizing_constant_power_parameter()

• GaussianNPP$vectorised_replicate_inference()

• GaussianNPP$inference()

• GaussianNPP$credible_interval()

• GaussianNPP$posterior_median()

• GaussianNPP$sample_posterior()

• GaussianNPP$sample_prior()

• GaussianNPP$posterior_cdf()

• GaussianNPP$posterior_pdf()

• GaussianNPP$prior_pdf()

• GaussianNPP$plot_power_parameter_posterior_pdf()

• GaussianNPP$plot_power_parameter_vs_drift()

• GaussianNPP$clone()

Inherited methods

• Model$calibrate_for_design()
• Model$check_data()
• Model$create()
• Model$empirical_bayes_update()
• Model$estimate_bayesian_operating_characteristics()
• Model$estimate_frequentist_operating_characteristics()
• Model$hypothesis_space_transformation()
• Model$inference_cache_scope()
• Model$plot_pdfs()
• Model$plot_posterior_pdf()
• Model$plot_prior_pdf()
• Model$posterior_beta_mixture()
• Model$posterior_ess()
• Model$posterior_mean()
• Model$posterior_moments()
• Model$posterior_quantile()
• Model$posterior_to_RBesT()
• Model$print_model_summary()
• Model$prior_cdf()
• Model$prior_elir_ess()
• Model$prior_to_RBesT()
• Model$simulation_for_given_treatment_effect()
• Model$test_decision()

---

GaussianNPP$summary_rows()

Rows of the model summary, with the prior on the power parameter

Usage

GaussianNPP$summary_rows()

Returns

A data frame with columns Attribute and Value.

---

GaussianNPP$new()

Initialize a new GaussianNPP object.

Usage

GaussianNPP$new(prior)

Arguments

prior

Prior object containing method parameters.

Returns

A new GaussianNPP object.

---

GaussianNPP$unnormalized_posterior_power_parameter_pdf()

Calculate the unnormalized posterior power parameter PDF.

Usage

GaussianNPP$unnormalized_posterior_power_parameter_pdf(
  power_parameter,
  target_data
)

Arguments

power_parameter

Power parameter value.

target_data

Target study data.

Returns

Unnormalized posterior power parameter PDF value.

---

GaussianNPP$power_parameter_posterior_pdf()

Return the posterior distribution of the power parameter

Usage

GaussianNPP$power_parameter_posterior_pdf(power_parameter, target_data)

Arguments

power_parameter

Power parameter value.

target_data

Target study data.

Returns

Posterior power parameter PDF value.

---

GaussianNPP$normalizing_constant_power_parameter()

Calculate the normalizing constant for the power parameter.

Usage

GaussianNPP$normalizing_constant_power_parameter(target_data)

Arguments

target_data

Target study data.

Returns

Normalizing constant value.

---

GaussianNPP$vectorised_replicate_inference()

Run every replicate at once

Discretising the Beta prior on the power parameter turns the method into an ordinary normal mixture, so the posterior, its summaries and the effective sample sizes all follow in closed form. This replaces the nested numerical integration the replicate loop performs, in which each evaluation of posterior_cdf() integrates over posterior_pdf(), which itself integrates over the power parameter at every point.

The prior mixture is the same for every replicate, so it is built once.

Usage

GaussianNPP$vectorised_replicate_inference(
  target_data,
  samples,
  to_return,
  critical_value,
  theta_0,
  confidence_level,
  null_space
)

Arguments

target_data

Target study data.

samples

Data frame of generated replicates.

to_return

Character vector of requested outputs.

critical_value

Critical value for hypothesis testing.

theta_0

Null hypothesis value.

confidence_level

Confidence level for the credible interval.

null_space

The null space for hypothesis testing.

Returns

A list of simulation results.

---

GaussianNPP$inference()

Perform inference on the target data.

Usage

GaussianNPP$inference(target_data)

Arguments

target_data

Target study data.

Returns

A string indicating the success status of the inference.

---

GaussianNPP$credible_interval()

Calculate the credible interval.

Usage

GaussianNPP$credible_interval(level = 0.95)

Arguments

level

Credible interval level (default: 0.95).

Returns

A vector containing the lower and upper bounds of the credible interval.

---

GaussianNPP$posterior_median()

Return the median of the posterior distribution.

Usage

GaussianNPP$posterior_median(...)

Arguments

...

Optional arguments

Returns

Median of the posterior distribution.

---

GaussianNPP$sample_posterior()

Sample from the posterior distribution.

Usage

GaussianNPP$sample_posterior(n_samples)

Arguments

n_samples

Number of samples to draw from the posterior distribution.

Returns

A vector of samples from the posterior distribution.

---

GaussianNPP$sample_prior()

Sample from the prior distribution.

Usage

GaussianNPP$sample_prior(n_samples)

Arguments

n_samples

Number of samples to draw from the prior distribution.

Returns

A vector of samples from the prior distribution.

---

GaussianNPP$posterior_cdf()

Calculate the posterior cumulative distribution function (CDF).

Usage

GaussianNPP$posterior_cdf(x)

Arguments

x

Vector of points to evaluate the CDF at.

Returns

Vector of CDF values corresponding to the input points.

---

GaussianNPP$posterior_pdf()

Calculate the posterior probability density function (PDF).

Usage

GaussianNPP$posterior_pdf(x)

Arguments

x

Vector of points to evaluate the PDF at.

Returns

Vector of PDF values corresponding to the input points.

---

GaussianNPP$prior_pdf()

Calculate the prior probability density function (PDF).

Usage

GaussianNPP$prior_pdf(x)

Arguments

x

Vector of points to evaluate the PDF at.

Returns

Vector of PDF values corresponding to the input points.

---

GaussianNPP$plot_power_parameter_posterior_pdf()

Plot posterior probability density function (PDF) of the power parameter

Usage

GaussianNPP$plot_power_parameter_posterior_pdf(target_data)

Arguments

target_data

Target study data

Returns

A plot

---

GaussianNPP$plot_power_parameter_vs_drift()

Plot the power parameter as a function of drift in treatment effect

Usage

GaussianNPP$plot_power_parameter_vs_drift(
  source_treatment_effect_estimate,
  target_data,
  min_drift,
  max_drift,
  resolution
)

Arguments

source_treatment_effect_estimate

Treatment effect estimate in the source study

target_data

Target study data

min_drift

Minimum drift value

max_drift

Maximum drift value

resolution

Number of points on the drift grid.

Returns

The prior PDF.

---

GaussianNPP$clone()

The objects of this class are cloneable with this method.

Usage

GaussianNPP$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.