Package 'inlamemi'

Extract random effects from formula

Description

Extract random effects from formula

Usage

extract_random_effects(formula)

Arguments

formula

an object of class "formula", either the formula for the model of interest, the imputation model or the missingness model.

Value

A list containing "reff_vars", the random effect variables, and "reff", the entire random effect term.

---

Extract and group variables from formulas

Description

Helper function that takes in the formulas for the model of interest and the imputation model, and groups them into responses, covariates, covariate with error and covariate(s) without error, for both sub-models.

Usage

extract_variables_from_formula(
  formula_moi,
  formula_imp,
  formula_mis = NULL,
  error_variable = NULL
)

Arguments

formula_moi	an object of class "formula", describing the main model to be fitted.
formula_imp	an object of class "formula", describing the imputation model for the mismeasured and/or missing observations.
formula_mis	an object of class "formula", describing the missingness model. Does not need to have a response variable, since this will always be a binary missingness indicator.
error_variable	character vector with the name(s) of the variable(s) with error.

Value

A list containing the names of the different variables of the model. The names of the elements in the list are "response_moi" (the response for the moi), "covariates_moi" (all covariates in the moi), "error_variable" (the name of the variable with error or missing data), "covariates_error_free" (the moi covariates without error), "response_imp" (imputation model response), "covariates_imp" (imputation model covariates).

Examples

extract_variables_from_formula(formula_moi = y ~ x + z,
                               formula_imp = x ~ z)

---

Fit model for measurement error and missing data in INLA

Description

A wrapper function around "INLA::inla()", providing the necessary structure to fit the hierarchical measurement error model that adjusts coefficient estimates to account for biases due to measurement error and missing data.

Usage

fit_inlamemi(
  formula_moi,
  formula_imp = NULL,
  formula_mis = NULL,
  family_moi,
  data,
  error_type = "classical",
  error_variable = NULL,
  repeated_observations = FALSE,
  classical_error_scaling = NULL,
  prior.prec.moi = NULL,
  prior.prec.berkson = NULL,
  prior.prec.classical = NULL,
  prior.prec.imp = NULL,
  prior.beta.error = NULL,
  prior.gamma.error = NULL,
  initial.prec.moi = NULL,
  initial.prec.berkson = NULL,
  initial.prec.classical = NULL,
  initial.prec.imp = NULL,
  control.family.moi = NULL,
  control.family.berkson = NULL,
  control.family.classical = NULL,
  control.family.imp = NULL,
  control.family = NULL,
  control.predictor = NULL,
  ...
)

Arguments

formula_moi	an object of class "formula", describing the main model to be fitted.
formula_imp	an object of class "formula", describing the imputation model for the mismeasured and/or missing observations.
formula_mis	an object of class "formula", describing the missingness model. Does not need to have a response variable, since this will always be a binary missingness indicator.
family_moi	a string indicating the likelihood family for the model of interest (the main model).
data	an object of class data.frame or list containing the variables in the model.
error_type	type of error (one or more of "classical", "berkson", "missing")
error_variable	character vector with the name(s) of the variable(s) with error.
repeated_observations	Does the variable with measurement error and/or missingness have repeated observations? If so, set this to "TRUE". In that case, when specifying the formula, use the name of the variable without any numbers, but when specifying the data, make sure that the repeated measurements end in a number, i.e "sbp1" and "sbp2".
classical_error_scaling	can be specified if the classical measurement error varies across observations. Must be a vector of the same length as the data.
prior.prec.moi	a string containing the parameters for the prior for the precision of the residual term for the model of interest.
prior.prec.berkson	a string containing the parameters for the prior for the precision of the error term for the Berkson error model.
prior.prec.classical	a string containing the parameters for the prior for the precision of the error term for the classical error model.
prior.prec.imp	a string containing the parameters for the precision of the latent variable x, which is the variable being described in the imputation model.
prior.beta.error	parameters for the Gaussian prior for the coefficient of the error prone variable.
prior.gamma.error	parameters for the Gaussian prior for the coefficient of the variable with missingness in the missingness model.
initial.prec.moi	the initial value for the precision of the residual term for the model of interest.
initial.prec.berkson	the initial value for the precision of the residual term for the Berkson error term.
initial.prec.classical	the initial value for the precision of the residual term for the classical error term.
initial.prec.imp	the initial value for the precision of the residual term for the latent variable r.
control.family.moi	control.family component for model of interest. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments, or in the cases when other hyperparameters are needed for the model of interest, see for instance survival models.
control.family.berkson	control.family component Berkson model. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments. Useful in the cases when more flexibility is needed, for instance if one wants to specify a different prior distribution than Gamma.
control.family.classical	control.family component for classical model. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments. Useful in the cases when more flexibility is needed, for instance if one wants to specify a different prior distribution than Gamma.
control.family.imp	control.family component for imputation model. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments. Useful in the cases when more flexibility is needed, for instance if one wants to specify a different prior distribution than Gamma.
control.family	control.family for use in inla (can be provided directly instead of passing the "prior.prec...." and "initial.prec..." arguments. If this is specified, any other "control.family..." or "prior.prec..." arguments provided will be ignored.
control.predictor	control.predictor for use in inla.
...	other arguments to pass to 'inla'.

Value

An object of class inlamemi.

Examples

# Fit the model
simple_model <- fit_inlamemi(data = simple_data,
                           formula_moi = y ~ x + z,
                           formula_imp = x ~ z,
                           family_moi = "gaussian",
                           error_type = c("berkson", "classical"),
                           error_variable = "x",
                           prior.prec.moi = c(10, 9),
                           prior.prec.berkson = c(10, 9),
                           prior.prec.classical = c(10, 9),
                           prior.prec.imp = c(10, 9),
                           prior.beta.error = c(0, 1/1000),
                           initial.prec.moi = 1,
                           initial.prec.berkson = 1,
                           initial.prec.classical = 1,
                           initial.prec.imp = 1)

---

Framingham heart study data

Description

A data set with observations of heart disease status systolic blood pressure (SBP) and smoking status.

Usage

framingham

Format

## 'framingham' A data frame with 641 rows and 4 columns:

disease

A binary response, 1 if heart disease, 0 otherwise

sbp1

log(SBP - 50) at examination 1 (centered)

sbp2

log(SBP - 50) at examination 2 (centered)

smoking

Smoking status, 1 if smoking, 0 otherwise.

Source

MacMahon et al. (1990) <https://doi.org/10.1016/0140-6736(90)90878-9>

---

List the survival likelihoods in INLA

Description

List the survival likelihoods in INLA

Usage

inla_survival_families()

Value

List of survival models in INLA

---

Make "control.family" argument for passing to the "inla" function

Description

Make "control.family" argument for passing to the "inla" function

Usage

make_inlamemi_control.family(
  formula_mis = NULL,
  family_moi,
  error_type = "classical",
  prior.prec.moi = NULL,
  prior.prec.berkson = NULL,
  prior.prec.classical = NULL,
  prior.prec.imp = NULL,
  initial.prec.moi = NULL,
  initial.prec.berkson = NULL,
  initial.prec.classical = NULL,
  initial.prec.imp = NULL,
  control.family.moi = NULL,
  control.family.berkson = NULL,
  control.family.classical = NULL,
  control.family.imp = NULL,
  control.family = NULL
)

Arguments

formula_mis	an object of class "formula", describing the missingness model. Does not need to have a response variable, since this will always be a binary missingness indicator.
family_moi	a string indicating the likelihood family for the model of interest (the main model).
error_type	type of error (one or more of "classical", "berkson", "missing")
prior.prec.moi	a string containing the parameters for the prior for the precision of the residual term for the model of interest.
prior.prec.berkson	a string containing the parameters for the prior for the precision of the error term for the Berkson error model.
prior.prec.classical	a string containing the parameters for the prior for the precision of the error term for the classical error model.
prior.prec.imp	a string containing the parameters for the precision of the latent variable x, which is the variable being described in the imputation model.
initial.prec.moi	the initial value for the precision of the residual term for the model of interest.
initial.prec.berkson	the initial value for the precision of the residual term for the Berkson error term.
initial.prec.classical	the initial value for the precision of the residual term for the classical error term.
initial.prec.imp	the initial value for the precision of the residual term for the latent variable r.
control.family.moi	control.family component for model of interest. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments, or in the cases when other hyperparameters are needed for the model of interest, see for instance survival models.
control.family.berkson	control.family component Berkson model. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments. Useful in the cases when more flexibility is needed, for instance if one wants to specify a different prior distribution than Gamma.
control.family.classical	control.family component for classical model. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments. Useful in the cases when more flexibility is needed, for instance if one wants to specify a different prior distribution than Gamma.
control.family.imp	control.family component for imputation model. Can be specified here using the inla syntax instead of passing the "prior.prec..." and "initial.prec..." arguments. Useful in the cases when more flexibility is needed, for instance if one wants to specify a different prior distribution than Gamma.
control.family	control.family for use in inla (can be provided directly instead of passing the "prior.prec...." and "initial.prec..." arguments. If this is specified, any other "control.family..." or "prior.prec..." arguments provided will be ignored.

Value

the "control.family" argument to be passed to inla, a list of "control.family" arguments for each model in the hierarchical measurement error model.

Examples

make_inlamemi_control.family(
  family_moi = "gaussian",
  error_type = c("berkson", "classical"),
  prior.prec.moi = c(10, 9),
  prior.prec.berkson = c(10, 9),
  prior.prec.classical = c(10, 9),
  prior.prec.imp = c(10, 9),
  initial.prec.moi = 1,
  initial.prec.berkson = 1,
  initial.prec.classical = 1,
  initial.prec.imp = 1)

make_inlamemi_control.family(
  family_moi = "weibull.surv",
  error_type = c("classical", "missing"),
  control.family.moi =
    list(hyper = list(alpha = list(param = 0.01,
                                   initial = log(1.4),
                                   fixed = FALSE))),
  prior.prec.classical = c(0.5, 0.5),
  prior.prec.imp = c(0.5, 0.5),
  initial.prec.classical = 2.8,
  initial.prec.imp = 1)

---

Make vector of likelihood families

Description

Make vector of likelihood families

Usage

make_inlamemi_families(family_moi, inlamemi_stack)

Arguments

family_moi	a string indicating the likelihood family for the model of interest (the main model).
inlamemi_stack	object of type inla.stack

Value

A vector specifying the likelihood family for each model level.

Examples

simple_stack <- make_inlamemi_stacks(formula_moi = y ~ x + z,
                                     formula_imp = x ~ z,
                                     data = simple_data,
                                     error_type = c("classical"))
make_inlamemi_families(family_moi = "gaussian",
                       inlamemi_stack = simple_stack)

---

Make formula for measurement error and missing data model

Description

Make formula for measurement error and missing data model

Usage

make_inlamemi_formula(
  formula_moi,
  formula_imp,
  formula_mis = NULL,
  family_moi = "gaussian",
  error_type = "classical",
  error_variable = NULL,
  prior.beta.error,
  prior.gamma.error = NULL,
  vars = NULL
)

Arguments

formula_moi	an object of class "formula", describing the main model to be fitted.
formula_imp	an object of class "formula", describing the imputation model for the mismeasured and/or missing observations.
formula_mis	an object of class "formula", describing the missingness model. Does not need to have a response variable, since this will always be a binary missingness indicator.
family_moi	a string indicating the likelihood family for the model of interest (the main model).
error_type	type of error (one or more of "classical", "berkson", "missing")
error_variable	character vector with the name(s) of the variable(s) with error.
prior.beta.error	parameters for the Gaussian prior for the coefficient of the error prone variable.
prior.gamma.error	parameters for the Gaussian prior for the coefficient of the variable with missingness in the missingness model.
vars	Results from a call to "extract_variables_from_formula" function. If this is not passed as an argument, it is called inside the function.

Value

An object of class "formula".

Examples

make_inlamemi_formula(formula_moi = y ~ x + z,
                      formula_imp = x ~ z,
                      error_type = "classical",
                      prior.beta.error = c(0, 1/1000)
                      )

---

Construct scaling vector to scale the precision of correctly observed observations

Description

Construct scaling vector to scale the precision of correctly observed observations

Usage

make_inlamemi_scaling_vector(
  inlamemi_stack,
  error_type,
  classical_error_scaling = NULL,
  vars
)

Arguments

inlamemi_stack	an object of class inlamemi.data.stack containing data structured
error_type	type of error (one or more of "classical", "berkson", "missing")
classical_error_scaling	can be specified if the classical measurement error varies across observations. Must be a vector of the same length as the data.
vars	Results from a call to "extract_variables_from_formula" function. If this is not passed as an argument, it is called inside the function.

Value

A vector reflecting the scaling factor for the residual terms in each model level.

Examples

stacks <- make_inlamemi_stacks(data = simple_data,
                             formula_moi = y ~ x + z,
                             formula_imp = x ~ z,
                             error_type = c("classical", "berkson"))
vars <- extract_variables_from_formula(formula_moi = y ~ x + z,
                                       formula_imp = x ~ z)
make_inlamemi_scaling_vector(stacks,
                           error_type = c("classical", "berkson"),
                           vars = vars)

---

Make data stacks for joint model specification in INLA

Description

Make data stacks for joint model specification in INLA

Usage

make_inlamemi_stacks(
  formula_moi,
  formula_imp,
  formula_mis = NULL,
  family_moi = "gaussian",
  data,
  error_type = "classical",
  error_variable = NULL,
  repeated_observations = FALSE,
  vars = NULL
)

Arguments

formula_moi	an object of class "formula", describing the main model to be fitted.
formula_imp	an object of class "formula", describing the imputation model for the mismeasured and/or missing observations.
formula_mis	an object of class "formula", describing the missingness model. Does not need to have a response variable, since this will always be a binary missingness indicator.
family_moi	a string indicating the likelihood family for the model of interest (the main model).
data	an object of class data.frame or list containing the variables in the model.
error_type	type of error (one or more of "classical", "berkson", "missing")
error_variable	character vector with the name(s) of the variable(s) with error.
repeated_observations	Does the variable with measurement error and/or missingness have repeated observations? If so, set this to "TRUE". In that case, when specifying the formula, use the name of the variable without any numbers, but when specifying the data, make sure that the repeated measurements end in a number, i.e "sbp1" and "sbp2".
vars	Results from a call to "extract_variables_from_formula" function. If this is not passed as an argument, it is called inside the function.

Value

An object of class inla.stack with data structured according to specified formulas and error models.

Examples

make_inlamemi_stacks(formula_moi = y ~ x + z,
                   formula_imp = x ~ z,
                   data = simple_data,
                   error_type = "classical")

---

Simulated data with observation missing at random (MAR)

Description

A simulated dataset to demonstrate how to set up a model in the case where there are two variables with measurement error.

Usage

mar_data

Format

## 'mar_data' A data frame with 1000 rows and 5 columns:

y

Response variable

x

Observed value of covariate, with almost 20 percent missing

x_true

Correct version of x, without missingness

z1

Covariate correlated with x

z2

Covariate correlated with the missingness of x

Source

The dataset is simulated.

---

Survival data with repeated systolic blood pressure measurements

Description

A dataset containing a repeated blood pressure measurement along with some other variables for participants in the Third National Health and Nutrition Survey (NHANES III), merged with data from the US National Death Index by Ruth H. Keogh and Jonathan Bartlett. For the illustration purposes in this package, we have left out observations where smoking status is missing.

Usage

nhanes_survival

Format

## 'nhanes_survival' A data frame with 3433 rows and 8 columns:

sbp1

systolic blood pressure (standardized), first measurement

sbp2

systolic blood pressure (standardized), second measurement

sex

sex (0 = female, 1 = male)

age

age (standardized)

smoke

smoking status (0 = no, 1 = yes)

diabetes

diabetes status (0 = no, 1 = yes)

d

censoring status (0 = censored, 1 = observed death due to cardiovascular disease)

t

time until death due to cardiovascular disease occurs

Source

https://github.com/ruthkeogh/meas_error_handbook

---

Plot model summary

Description

Plot model summary

Usage

## S3 method for class 'inlamemi'
plot(
  x,
  plot_moi = TRUE,
  plot_imp = TRUE,
  plot_mis = TRUE,
  plot_intercepts = TRUE,
  error_variable_highlight = FALSE,
  greek = FALSE,
  palette = NULL,
  ...
)

Arguments

x	the model returned from the fit_inlamemi function.
plot_moi	should the posterior mean for the coefficients of the model of interest be plotted? Defaults to TRUE.
plot_imp	should the posterior mean for the coefficients of the imputation model be plotted? Defaults to TRUE.
plot_mis	should the posterior mean for the coefficients of the missingness model be plotted? Defaults to TRUE.
plot_intercepts	should the posterior mean for the intercept(s) be plotted? Defaults to TRUE.
error_variable_highlight	should the coefficient(s) of the variable(s) with error be highlighted? (circled in black) Defaults to FALSE.
greek	make the coefficient names into greek letters with the covariate name as subscript. Defaults to FALSE.
palette	either a number (between 1 and 5), indicating the number of the color palette to be used, or a vector of the colors to be used.
...	other arguments

Value

An object of class "ggplot2" that plots the posterior mean and 95 % credible interval for each coefficient in the model. The coefficients are colored to indicate if they belong to the main or imputation model, and the variable with error is also highlighted.

Examples

# Fit the model
simple_model <- fit_inlamemi(data = simple_data,
                           formula_moi = y ~ x + z,
                           formula_imp = x ~ z,
                           family_moi = "gaussian",
                           error_type = c("berkson", "classical"),
                           prior.prec.moi = c(10, 9),
                           prior.prec.berkson = c(10, 9),
                           prior.prec.classical = c(10, 9),
                           prior.prec.imp = c(10, 9),
                           prior.beta.error = c(0, 1/1000),
                           initial.prec.moi = 1,
                           initial.prec.berkson = 1,
                           initial.prec.classical = 1,
                           initial.prec.imp = 1)

plot(simple_model)

---

Visualize the model data structure as matrices

Description

Visualize the model data structure as matrices

Usage

show_data_structure(stack)

Arguments

stack

an object of class inla.stack returned from the function make_inlamemi_stacks, which describes the structure of the data for the measurement error and imputation model.

Value

A list containing data frames with the left hand side (response_df) and right hand side (effects_df), along with the latex code needed to visualize the matrices (matrix_string).

Examples

stack <- make_inlamemi_stacks(data = simple_data,
                   formula_moi = y ~ x + z,
                   formula_imp = x ~ z,
                   error_type = "classical")
show_data_structure(stack)

---

Simple simulated data

Description

A simulated dataset to demonstrate how to model different types of measurement error and missing data using the 'inlamemi' package.

Usage

simple_data

Format

## 'simple_data' A data frame with 1000 rows and 4 columns:

y

Response variable

x

Covariate measured with error, both Berkson and classical error and missing observations

x_true

Correct version of the covariate with error

z

Error free covariate, correlated with x

Source

The dataset is simulated.

---

Simplify the "raw" model summary for printing and plotting

Description

Simplify the "raw" model summary for printing and plotting

Usage

simplify_inlamemi_model_summary(inlamemi_model)

Arguments

inlamemi_model

the model returned from the fit_inlamemi function.

Value

A list of four data frames, containing the summaries for different components of the model. These are the coefficients of the model of interest, the coefficient of the variable with error, the coefficients of the imputation model, and the hyperparameters.

---

Summary method for inlamemi

Description

Takes a fitted 'inlamemi' object produced by 'fit_inlamemi' and produces a summary from it.

Usage

## S3 method for class 'inlamemi'
summary(object, ...)

## S3 method for class 'summary.inlamemi'
print(x, ...)

Arguments

object	model of class 'inlamemi'.
...	other arguments
x	object of class summary.inlamemi.

Value

'summary.inlamemi' returns an object of class 'summary.inlamemi', a list of components to print.

Examples

# Fit the model
simple_model <- fit_inlamemi(data = simple_data,
                           formula_moi = y ~ x + z,
                           formula_imp = x ~ z,
                           family_moi = "gaussian",
                           error_type = c("berkson", "classical"),
                           prior.prec.moi = c(10, 9),
                           prior.prec.berkson = c(10, 9),
                           prior.prec.classical = c(10, 9),
                           prior.prec.imp = c(10, 9),
                           prior.beta.error = c(0, 1/1000),
                           initial.prec.moi = 1,
                           initial.prec.berkson = 1,
                           initial.prec.classical = 1,
                           initial.prec.imp = 1)

summary(simple_model)

---

Simulated data with two covariates with classical measurement error

Description

A simulated dataset to demonstrate how to set up a model in the case where there are two variables with measurement error.

Usage

two_error_data

Format

## 'two_error_data' A data frame with 1000 rows and 5 columns:

y

Response variable

x1

Covariate measured with classical error, correlated with z

x2

Covariate measured with classical error

x1_true

Correct version of x1

x2_true

Correct version of x2

z

Error free covariate, correlated with x1

Source

The dataset is simulated.

---