Title: Sensitivity Analysis for Irregular Assessment Times
Version: 0.1.1
Description: Sensitivity analysis for trials with irregular and informative assessment times, based on a new influence function-based, augmented inverse intensity-weighted estimator.
Language: en-US
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.2
Imports: assertthat, dplyr, glue, KernSmooth, MASS, methods, orthogonalsplinebasis, pracma, purrr, Rcpp (≥ 1.0.12), rlang, splines, stats, survival, tibble, tidyr, utils
Suggests: dfoptim, inline, progress, spelling, testthat (≥ 3.0.0)
Config/testthat/edition: 3
Depends: R (≥ 4.4.0)
LazyData: true
LinkingTo: Rcpp
SystemRequirements: C++17
URL: https://github.com/UofUEpiBio/SensIAT
BugReports: https://github.com/UofUEpiBio/SensIAT/issues
NeedsCompilation: yes
Packaged: 2024-11-15 23:24:00 UTC; u0092104
Author: Andrew Redd ORCID iD [aut, cre], Yujing Gao [aut], Shu Yang [aut], Bonnie Smith [aut], Agatha Mallett [ctb, ctr], Daniel Scharfstein ORCID iD [pdr, aut], University of Utah [cph]
Maintainer: Andrew Redd <andrew.redd@hsc.utah.edu>
Repository: CRAN
Date/Publication: 2024-11-17 16:30:02 UTC

SensIAT: Sensitivity Analysis for Irregular Assessment Times

Description

Sensitivity analysis for trials with irregular and informative assessment times, based on a new influence function-based, augmented inverse intensity-weighted estimator.

Author(s)

Maintainer: Andrew Redd andrew.redd@hsc.utah.edu (ORCID)

Authors:

Other contributors:

See Also

Useful links:

Estimate Subject Predicted Mean Outcome

Description

This function is used to get a subject's predicted mean outcome under a given sensitivity parameter value alpha. It is specific to the outcome model that we used on the ARC data (which was negative binomial), and specific to the tilting function alpha*Y(t), so would need to be changed if using a different outcome model or different tilting function.

Usage

Cond_mean_fn(mu, theta, alpha)

Arguments

mu

mean

theta

size

alpha

sensitivity

Value

a list containing \frac{E[ Y exp(\alpha Y) ]}{E[ exp(\alpha Y)]} and ⁠$E[ exp(\alpha Y) ]$⁠ for Y a (truncated version of) a negative binomial having mean mu and size theta.

SensIAT Example Data

Description

A simulated dataset for use in the SensIAT tutorial, testing and documentation.

Usage

SensIAT_example_data

Format

A data frame with 779 rows and 4 variables consisting of 200 simulated patients. Each row in the data represents a visit for the patient. The columns are:

Subject_ID

A unique identifier for each patient.

Visit

The ordinal number of the visit for the patient. Baseline observation is 0.

Time

The time of the visit in days, since baseline.

Outcome

The outcome of interest.

Estimate response with jackknife resampling

Description

Estimate response with jackknife resampling

Usage

SensIAT_jackknife(original.object, time, ...)

Arguments

original.object

A SensIAT_within_group_model object.

time

Time points for which to estimate the response.

...

currently ignored.

Value

A tibble with columns alpha, time, jackknife_mean, and jackknife_var, where jackknife_mean is the mean of the jackknife estimates and jackknife_var is the estimated variances of the response at the given time points for the specified alpha values.

Examples

## Not run: 
original.object <-
fit_SensIAT_within_group_model(
    group.data = SensIAT_example_data,
    outcome_modeler = SensIAT_sim_outcome_modeler,
    alpha = c(-0.6, -0.3, 0, 0.3, 0.6),
    id.var = Subject_ID,
    outcome.var = Outcome,
    time.var = Time,
    intensity.bandwidth = 30,
    knots = c(60,60,60,60,260,460,460,460,460),
    End = 830
)
jackknife.estimates <- SensIAT_jackknife(original.object, time = c(90, 180, 270, 360, 450))

## End(Not run)

Outcome Modeler for SensIAT Single Index Model.

Description

Outcome Modeler for SensIAT Single Index Model.

Usage

SensIAT_sim_outcome_modeler(
  formula,
  data,
  kernel = "K2_Biweight",
  method = "nmk",
  id = ..id..,
  ...
)

Arguments

formula

The outcome model formula

data

The data to fit the outcome model to. Should only include follow-up data, i.e. time > 0.

kernel

The kernel to use for the outcome model.

method

The optimization method to use for the outcome model, either "optim", "nlminb", or "nmk".

id

The patient identifier variable for the data.

...

Currently ignored, included for future compatibility.

Value

Object of class SensIAT::Single-index-outcome-model which contains the outcome model portion.

Examples


model <-
    fit_SensIAT_within_group_model(
        group.data = SensIAT_example_data,
        outcome_modeler = SensIAT_sim_outcome_modeler,
        alpha = c(-0.6, -0.3, 0, 0.3, 0.6),
        id.var = Subject_ID,
        outcome.var = Outcome,
        time.var = Time,
        End = 830,
        knots = c(60,60,60,60,260,460,460,460,460),
    )

Produce fitted model for group (treatment or control)

Description

Produces a fitted model that may be used to produce estimates of mean and variance for the given group.

Usage

fit_SensIAT_fulldata_model(data, trt, ...)

fit_SensIAT_within_group_model(
  group.data,
  outcome_modeler,
  knots,
  id.var,
  outcome.var,
  time.var,
  alpha = 0,
  intensity.covariates = ~.,
  outcome.covariates = ~. - 1,
  End = max({
     {
         time.var
     }
 }, na.rm = TRUE) + 1,
  integration.tolerance = .Machine$double.eps^(1/3),
  intensity.bandwidth = NULL,
  ...,
  influence.args = list()
)

Arguments

data

the full data set.

trt

an expression that determine what is treated as the treatment. Everything not treatment is considered control.

...

add parameters as needed or use this to pass forward into the outcome_modeler.

group.data

The data for the group that is being analyzed. Preferably passed in as a single tibble that internally is subsetted/filtered as needed.

outcome_modeler

A separate function that may be swapped out to switch between negative-binomial, single index model, or another we will dream up in the future.

knots

knot locations for defining the spline basis.

id.var

The variable that identifies the patient.

outcome.var

The variable that contains the outcome.

time.var

The variable that contains the time.

alpha

The sensitivity parameter.

intensity.covariates

A formula representing modifications to the intensity model.

outcome.covariates

A formula representing modifications to the outcome model. The default removes the intercept term.

End

The end time for this data analysis, we need to set the default value as the max value of the time

integration.tolerance

The tolerance for the integration.

intensity.bandwidth

The bandwidth for the intensity model kernel.

influence.args

A list of additional arguments to pass to the influence function.

Details

This function should be agnostic to whether it is being provided a treatment or control group.

Value

a list with class SensIAT-fulldata-fitted-model with two components, control and treatment, each of which is an independently fitted SensIAT-within-group-fitted-model fit with the fit_within_group_model function.

Should return everything needed to define the fit of the model. This can then be used for producing the estimates of mean, variance, and in turn treatment effect. For the full data model a list with two models one each for the treatment and control groups.

Functions

Examples


model <-
    fit_SensIAT_within_group_model(
        group.data = SensIAT_example_data,
        outcome_modeler = SensIAT_sim_outcome_modeler,
        alpha = c(-0.6, -0.3, 0, 0.3, 0.6),
        id.var = Subject_ID,
        outcome.var = Outcome,
        time.var = Time,
        End = 830,
        knots = c(60,60,60,60,260,460,460,460,460),
    )

Compute Conditional Means

Description

Compute Conditional Means

Usage

pcori_conditional_means(model, alpha = 0, new.data = model.frame(model), ...)

Arguments

model

An object of class SensIAT::outcome-model

alpha

Sensitivity parameter

new.data

Data to compute conditional means for, defaults to the model frame for the fitted model.

...

passed onto methods.

Details

Compute the conditional expectations needed for predictions in the models. Three additional values/expectations are computed:

Value

The new.data frame with additional columns E_Y_past, and E_exp_alphaY appended.

Control Parameters for Fitting the within Group Model

Description

Control Parameters for Fitting the within Group Model

Usage

pcori_control(
  integration.method = c("quadvcpp", "quadv", "linear", "numerical", "piecewise"),
  intensity.bandwidth = NULL,
  resolution = 1000,
  resolution.within.period = 50,
  tol = .Machine$double.eps^(1/4),
  ...
)

Arguments

integration.method

Method for integration when computing the second influence term.

intensity.bandwidth

The bandwidth for the intensity model.

resolution

The number of points to use for numerical integration.

resolution.within.period

The number of points to use for numerical integration within a period.

tol

The tolerance for numerical integration.

...

Currently ignored.

Value

a list of control parameters.

Runs an optimized implementation of the "NW" function.

Description

Runs an optimized implementation of the "NW" function.

Usage

pcoriaccel_NW(Xb, Y, xb, y_seq, h, kernel = "K2_Biweight")

Arguments

Xb

a vector (expected to be about 500 elements)

Y

a vector (same size as Xb)

xb

a vector

y_seq

a vector

h

a scalar, the bandwidth of kernel

kernel

a string, denoting the kernel function to use, either "dnorm", "K2_Biweight", or "K4_Biweight"

Value

A matrix of the same size as xb by y_seq.

Runs a basic implementation of the "NW" function with the "K2_Biweight" kernel, just as a proof-of-concept.

Description

Runs a basic implementation of the "NW" function with the "K2_Biweight" kernel, just as a proof-of-concept.

Usage

pcoriaccel_NW_basic(Xb, Y, xb, y_seq, h)

Arguments

Xb

a vector (expected to be about 500 elements)

Y

a vector (same size as Xb)

xb

a vector

y_seq

a vector

h

a scalar, the bandwidth of kernel

Value

A matrix of the same size as xb by y_seq.

Runs an optimized implementation of the compute_influence_term_2_quadv_sim_via_matrix function.

Description

Runs an optimized implementation of the compute_influence_term_2_quadv_sim_via_matrix function.

Usage

pcoriaccel_compute_influence_term_2_quadv_sim_via_matrix(
  X,
  Y,
  times,
  individual_X,
  x_slope,
  alpha,
  beta,
  spline_basis,
  bandwidth,
  tol = 0.0001220703,
  kernel = "K2_Biweight"
)

Arguments

X

Matrix of all covariates, transformed as necessary by model

Y

Vector of all outcomes (same length as a column of X)

times

Vector of observation times for individual

individual_X

Matrix of covariates for individual rows correspond to times prepared for inferences for integration.

x_slope

Vector of numeric(length(beta)) indicating how

alpha

Vector of sensitivity parameters

beta

Vector of coefficients of the outcome model

spline_basis

Spline basis object (orthogonalsplinebasis::SplineBasis)

bandwidth

Bandwidth for the kernel density estimate of the outcome model.

tol

Tolerance for integration

kernel

Kernel function to use for the kernel density estimate

Value

integration result

Directly estimate the probability mass function of Y.

Description

Directly estimate the probability mass function of Y.

Usage

pcoriaccel_estimate_pmf(Xb, Y, xi, y_seq, h, kernel = "K2_Biweight")

Arguments

Xb

Numeric vector of individual linear predictors from the data

Y

Numeric vector of individual responses from the data

xi

value of the individuals linear predictor at the point of estimation

y_seq

Numeric vector of unique values of Y.

h

bandwidth of the kernel

kernel

character string specifying the kernel to use, either "dnorm", "K2_Biweight", or "K4_Biweight"

Compiled version of evaluate_basis() function

Description

Compiled version of evaluate_basis() function

Usage

pcoriaccel_evaluate_basis(spline_basis, x)

Arguments

spline_basis

The spline basis, S4 class orthogonalsplinebasis::SplineBasis

x

The point to evaluate

Value

Vector of the basis functions evaluated at x.

Integrate function using adaptive Simpson quadrature.

Description

Integrate function using adaptive Simpson quadrature.

Usage

pcoriaccel_integrate_simp(integrand, lo, hi, tol = 1.490116e-08)

Arguments

integrand

The integrand, must take scalar argument, may return scalar, vector, or matrix.

lo

Lower integration bound

hi

Upper integration bound

tol

Tolerance for integration, default .Machine$double.eps^(1/2)

Value

integration result, list with elements ⁠$Q⁠ (the integral estimate), ⁠$fcnt⁠ (the number of function evaluations), and ⁠$estim.prec⁠ (a (pessimistic) estimate of the precision).

Predict mean and variance of the outcome for a SensIAT within-group model

Description

Predict mean and variance of the outcome for a SensIAT within-group model

Usage

## S3 method for class 'SensIAT_fulldata_model'
predict(object, time, ...)

## S3 method for class 'SensIAT_within_group_model'
predict(object, time, include.var = TRUE, ..., base = object$base)

Arguments

object

SensIAT_within_group_model object

time

Time points of interest

...

Currently ignored.

include.var

Logical. If TRUE, the variance of the outcome is also returned

base

A SplineBasis object used to evaluate the basis functions.

Value

If include.var is TRUE, a tibble with columns time, mean, and var is returned. otherwise if include.var is FALSE, only the mean vector is returned.

Functions

Examples


model <-
    fit_SensIAT_within_group_model(
        group.data = SensIAT_example_data,
        outcome_modeler = SensIAT_sim_outcome_modeler,
        alpha = c(-0.6, -0.3, 0, 0.3, 0.6),
        id.var = Subject_ID,
        outcome.var = Outcome,
        time.var = Time,
        End = 830,
        knots = c(60,60,60,60,260,460,460,460,460),
    )
predict(model, time = c(90, 180))

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