Title:	Analyze Multiple Exposure Realizations in Association Studies
Version:	0.2.0
Depends:	R (≥ 4.1.0), stats, nimble
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0), ggplot2, dplyr, tidyr, scales, patchwork
Description:	Analyze association studies with multiple realizations of a noisy or uncertain exposure. These can be obtained from e.g. a two-dimensional Monte Carlo dosimetry system (Simon et al 2015 <doi:10.1667/RR13729.1>) to characterize exposure uncertainty. The implemented methods are regression calibration (Carroll et al. 2006 <doi:10.1201/9781420010138>), extended regression calibration (Little et al. 2023 <doi:10.1038/s41598-023-42283-y>), Monte Carlo maximum likelihood (Stayner et al. 2007 <doi:10.1667/RR0677.1>), frequentist model averaging (Kwon et al. 2023 <doi:10.1371/journal.pone.0290498>), and Bayesian model averaging (Kwon et al. 2016 <doi:10.1002/sim.6635>). Supported model families are Gaussian, binomial, multinomial, Poisson, proportional hazards, and conditional logistic.
License:	MIT + file LICENSE
Imports:	Rcpp (≥ 1.0.10), RcppEigen, coda, numDeriv, mvtnorm, methods, MCMCvis, tidyselect, lifecycle
LinkingTo:	Rcpp, RcppEigen
NeedsCompilation:	yes
VignetteBuilder:	knitr
Config/testthat/edition:	3
Author:	Sander Roberti [aut, cre], William Wheeler [aut], Deukwoo Kwon [aut], Ruth Pfeiffer [ctb], NCI [cph, fnd]
Maintainer:	Sander Roberti <sander.roberti@nih.gov>
URL:	https://ameras.sanderroberti.com, https://github.com/sanderroberti/ameras
BugReports:	https://github.com/sanderroberti/ameras/issues
Packaged:	2026-04-26 17:36:27 UTC; robertis2
Repository:	CRAN
Date/Publication:	2026-04-26 18:00:02 UTC

Analyze multiple exposure realizations in association studies

Description

Analyze association studies with multiple realizations of a noisy or uncertain exposure. These can be obtained from e.g. a two-dimensional Monte Carlo dosimetry system (Simon et al 2015 <doi:10.1667/RR13729.1>) to characterize exposure uncertainty. Methods include regression calibration (Carroll et al. 2006 doi:10.1201/9781420010138), extended regression calibration (Little et al. 2023 doi:10.1038/s41598-023-42283-y), Monte Carlo maximum likelihood (Stayner et al. 2007 doi:10.1667/RR0677.1), frequentist model averaging (Kwon et al. 2023 doi:10.1371/journal.pone.0290498), and Bayesian model averaging (Kwon et al. 2016 doi:10.1002/sim.6635). Supported model families are Gaussian, binomial, multinomial, Poisson, proportional hazards, and conditional logistic.

Details

The function used to fit models is ameras. To attach confidence/credible intervals, use the method confint. To visualize the exposure uncertainty in the dose realizations, use ecdfplot.

Author(s)

Sander Roberti <sander.roberti@nih.gov>, William Wheeler <WheelerB@imsweb.com>, Ruth Pfeiffer <pfeiffer@mail.nih.gov>, and Deukwoo Kwon <DKwon@uams.edu

References

Roberti, S., Kwon D., Wheeler W., Pfeiffer R. (in preparation). ameras: An R Package to Analyze Multiple Exposure Realizations in Association Studies

Analyze multiple exposure realizations

Description

Fit regression models accounting for exposure uncertainty using multiple Monte Carlo exposure realizations. Six outcome model families are supported. The first is the Gaussian family for continuous outcomes,

Y_i \sim N(\mu_i, \sigma^2),

with \mu_i = \alpha_0 + \bm X_i^T \bm \alpha +\beta_1 D_i+\beta_2 D_i^2 + \bm M_i^T \bm \beta_{m1}D_i + \bm M_i^T \bm \beta_{m2}D_i^2. Here \bm X_i are covariates, D_i is the exposure with measurement error, and \bm M_i are binary effect modifiers. The quadratic exposure terms and effect modification are optional.

For non-Gaussian families, three relative risk models for the main exposure are supported, the usual exponential RR_i=\exp(\beta_1 D_i+\beta_2 D_i^2+ \bm M_i^T \bm \beta_{m1}D_i + \bm M_i^T \bm \beta_{m2} D_i^2) and the linear excess relative risk (ERR) model RR_i= 1+\beta_1 D_i+\beta_2 D_i^2 + \bm M_i^T \bm \beta_{m1}D_i + \bm M_i^T \bm \beta_{m2}D_i^2, where the quadratic and effect modification terms are optional. Finally, the linear-exponential relative risk model RR_i= 1+(\beta_1 + \bm{M}_i^T \bm{\beta}_{m1}) D_i \exp\{(\beta_2+ \bm{M}_i^T \bm{\beta}_{m2})D_i\} is supported.

The second supported family is logistic regression for binary outcomes, with probabilities

p_i/(1-p_i)=RR_i\exp(\alpha_0+\bm X_i^T \bm \alpha).

Third is Poisson regression for counts,

Y_i \sim \text{Poisson}(\mu_i),

where \mu_i=RR_i \exp(\alpha_0 +\bm X_i^T \bm \alpha)\times \text{offset}_i with optional offset.

Fourth is proportional hazards regression for time-to-event data, with hazard function

h(t) = h_0(t)RR_i\exp(\bm X_i^T \bm \alpha),

with h_0 the baseline hazard.

Fifth is multinomial logistic regression for a categorical outcome with Z>2 outcome categories, with the last category as the referent category (i.e., \alpha_{0,Z}=\bm \alpha_{Z}=\beta_{1,Z}=\beta_{2,Z}=\bm \beta_{m1,Z} = \bm \beta_{m2,Z}=0):

P(Y_i=z)=RR_i\exp(\alpha_{0,z}+\bm X_i^T \bm \alpha_{z})/\{1+\sum_{s=1}^{Z-1} RR_i\exp(\alpha_{0,s}+\bm X_i^T \bm \alpha_{s})\}

Sixth is conditional logistic regression for matched case control data, for which

P\left(Y_i = 1, Y_k = 0 \forall k \neq i \bigg| \sum_{i \in \mathcal{R}} Y_i = 1\right) = RR_i\exp(\bm X_i^T \bm \alpha)/\{\sum_{k \in \mathcal{R}}RR_k\exp(\bm X_k^T \bm \alpha)\},

where \mathcal{R} is the matched set corresponding to individual i.

Methods include regression calibration (Carroll et al. 2006 doi:10.1201/9781420010138), extended regression calibration (Little et al. 2023 doi:10.1038/s41598-023-42283-y), Monte Carlo maximum likelihood (Stayner et al. 2007 doi:10.1667/RR0677.1), frequentist model averaging (Kwon et al. 2023 doi:10.1371/journal.pone.0290498), and Bayesian model averaging (Kwon et al. 2016 doi:10.1002/sim.6635).

Usage

ameras(formula=NULL, data, family="gaussian", methods="RC", 
  Y=NULL, dosevars=NULL, doseRRmod=NULL, deg=NULL,
  M=NULL, X=NULL, offset=NULL, entry=NULL, exit=NULL,
  setnr=NULL,
  CI=NULL, params.profCI=NULL,
  maxit.profCI=NULL, tol.profCI=NULL,
  transform=NULL,
  transform.jacobian=NULL, inpar=NULL, loglim=1e-30, MFMA=100000, 
  prophaz.numints.BMA=10, ERRprior.BMA="doubleexponential", nburnin.BMA=5000, 
  niter.BMA=20000, nchains.BMA=2, thin.BMA=10, included.replicates.BMA=NULL, 
  optim.method="Nelder-Mead", control=NULL, keep.data=TRUE, ... )

Arguments

Details

Models are specified through formulas of the form Y~dose(dose_expression, model="ERR", deg=1, modifier=M1+M2)+X1+X2. Here dose_expression specifies the dose realization columns and is parsed by eval_select from the tidyselect package. Useful examples are D1:D1000 if the doses are in a sequence of columns with sequential names such as D1-D1000, and all_of(dosevars) where dosevars is a vector with the names of all dose columns. Further, model specifies, for non-Gaussian families, whether to use the exponential dose-response model (model="EXP"), the linear-exponential model (model="LINEXP") or the linear ERR model (model="ERR"). Next, deg is used to specify whether a quadratic dose term should (deg=2) or should not (deg=1) be estimated for the exponential or linear ERR dose-response model. The modifier term is optional and used to specify binary effect modification variables. Note that interactions in the modifier term are not allowed, e.g. M1*M2. When deg, modifier, and model are not supplied, the defaults are deg=1, no effect modifiers, and model="ERR". Finally, X1 and X2 above represent optional additional covariates, which can include factor variables and interactions such as X1*X2. The matched set variable setnr required for conditional logistic regression is specified on the right-hand side of the formula through a term strata(setnr), and an optional offset variable offset for Poisson regression similarly through a term offset(offset). For proportional hazards regression, the left-hand side of the formula should have the form Surv(exit, status) or Surv(entry, exit, status).

A transformation can be used to reparametrize parameters internally (i.e., such that the likelihoods are evaluated at transform(parameters), where parameters are unconstrained), and should be specified when fitting linear excess relative risk and linear-exponential models to ensure nonnegative odds/risk/hazard. The included function transform1 applies an exponential transformation to the desired parameters, see ?transform1. When supplying a function to transform, this should be a function of the full parameter vector, returning a full (transformed) parameter vector. In particular, the full parameter vector contains parameters in the following order: \alpha_0, \bm \alpha, \beta_1, \beta_2, \bm \beta_{m1}, \bm \beta_{m2}, \sigma, where \bm \alpha, \bm\beta_{m1} and \bm \beta_{m2} can be vectors, with lengths matching \bm X and \bm M, respectively. \sigma is only included for the linear model (Gaussian family), and no intercept is included for the proportional hazards and conditional logistic models. For the multinomial model, the full parameter vector is the concatenation of Z-1 parameter vectors in the order as given above, where Z is the number of outcome categories, with the last category chosen as the referent category. See vignette("transformations", package="ameras") for an example of how to specify a custom transformation function.

When no transformation is specified and the linear ERR model is used, transform1 is used for ERR parameters \beta_1 and \beta_2 by default, with lower limits -1/max(D) for \beta_1 in the linear dose-response and (0,-1/max(D^2)) for (\beta_1,\beta_2) in the linear-quadratic dose-response, respectively. For the linear-exponential model, a lower limit of 0 is used for \beta_1, and no transformation is used for \beta_2. If effect modifiers M are specified, no transformation is used for those parameters. When negative RRs are obtained during optimization, an error will be generated and a different transformation or bounds should be used. All output is returned in the original parametrization. The Jacobian of the transformation (transform.jacobian) is required when using a transformation. For transform1, the Jacobian is given by transform1.jacobian. No transformations are used in BMA, and FMA is applied on the parameters using the parametrization as given in above with variances obtained using the delta method with the provided Jacobian function.

For BMA, a prior distribution for exposure-response parameters can be chosen when using linear or linear-exponential exposure-response model. The options are normal, horshoe, and double exponential priors, and the same priors truncated at 0 to yield positive values. In particular:

• Normal: \beta_j \sim N(0,1000) for all exposure-response parameters \beta_j

• Horseshoe (shrinkage prior): \tau \sim \text{Cauchy}(0,1)^+; \lambda_j \sim \text{Cauchy}(0,1)^+; \beta_j \sim N(0, \tau^2 \lambda_j^2). Here \tau is shared across all parameters

• Double exponential (shrinkage prior): \lambda_j \sim \text{Cauchy}(0,1)^+; \beta_j \sim \text{DoubleExponential}(0,\lambda_j)

For all other parameters, and when using the exponential exposure-response model or the Gaussian outcome family, the prior is N(0, 1000). For the parameter \sigma in the Gaussian family, this prior is truncated at 0.

Because the proportional hazards model is not available in nimble, ameras uses a piecewise constant baseline hazard for Bayesian model averaging. The interval min(entry), max(exit)) is divided into prophaz.numints.BMA subintervals with cutpoints obtained as quantiles of the distribution of event times among cases, and a baseline hazard parameter is estimated for each subinterval.

Value

The output is an object of class amerasfit. General components are call (the function call to ameras), formula (the formula object specifying the model), num.rows (the number of rows in data), num.replicates (the number of dose replicates provided), transform (the used transformation function, if applicable), transform.jacobian (the used Jacobian function for the transformation, if applicable), other.args (any other arguments passed to ...), model (a list containing the specified model components parsed from the formula), CI.computed (logical, whether confidence intervals have been attached by confint), and data (either the data frame used for model fitting when keep.data=TRUE or NULL otherwise).

For each method supplied to methods, the output contains a list with components:

For RC, ERC, and MCML the following additional output is included:

For RC and ERC, the output additionally contains:

For BMA the output additionally contains:

Finally, for FMA the output additionally contains:

The class amerasfit supports the methods print, coef, confint, summary, and traceplot.

References

Roberti, S., Kwon D., Wheeler W., Pfeiffer R. (in preparation). ameras: An R Package to Analyze Multiple Exposure Realizations in Association Studies

See Also

confint for computing confidence intervals, summary for a summary of the fitted model including confidence intervals if computed, coef for extracting coefficients.

Examples

  data(data, package="ameras")
  ameras(Y.gaussian~dose(V1:V10, modifier=M1+M2)+X1+X2, data=data, family="gaussian") 

Estimated coefficients for an amerasfit object

Description

Returns a data frame with all the parameters of a fitted amerasfit object. The resulting object has a column for every method supplied to 'methods' when calling 'ameras', with rows corresponding to parameters.

Usage

## S3 method for class 'amerasfit'
coef(object, ...)

Arguments

Value

Data frame with estimated model parameters. Column names correspond to the 'methods' used in the 'ameras' call, and row names correspond to parameter names.

See Also

ameras for model fitting, summary for a summary of the fitted model including confidence intervals if computed.

Examples

data("data", package = "ameras")
dosevars <- paste0("V", 1:10)

## Fit the model
fit <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial", 
methods = c("RC","ERC"))
## Full matrix
coef(fit)

## Vector with RC parameters
coef(fit)$RC

Confidence intervals for an amerasfit object

Description

Computes confidence intervals for the parameters of a fitted amerasfit object. This is a separate step from model fitting, i.e., ameras fits the model and confint computes intervals and attaches them to the fitted object.

Usage

## S3 method for class 'amerasfit'
confint(object, parm="dose", level=0.95, 
        type=c("proflik","percentile"), maxit.profCI=20, 
        tol.profCI=1e-2, data=NULL, ...)

Arguments

Details

For (extended) regression calibration and Monte Carlo maximum likelihood, Wald and profile likelihood intervals can be obtained. When a parameter transformation \bm\theta = h(\bm\eta) is used, type="wald.transformed" yields the CI at significance level \alpha of h(\bm\eta \pm z_{1-\alpha/2} \bm V) where z_{1-\alpha/2} is the 1-\alpha/2-quantile of the standard normal distribution and \bm V is the vector of standard deviations estimated using the inverse Hessian matrix, and type="wald.orig" uses the delta method to obtain the CI h(\bm\eta)\pm z_{1-\alpha/2} \bm V_* where \bm V_* is the vector of standard deviations estimated using J H^{-1} J^T with J the Jacobian of the transformation and H is the Hessian. When no transformation is used, type="wald.orig" should be used. The third option is proflik, which uses the profile likelihood to compute confidence bounds.

For FMA and BMA, the options for confidence/credible intervals are type="percentile" which uses percentiles, and type="hpd" which computes highest posterior density intervals using HPDinterval from the coda package, both using the FMA samples or Bayesian posterior samples.

Profile likelihood intervals (type="proflik") require re-evaluating the likelihood repeatedly and can be time-consuming. The parm argument can be used to restrict computation to dose parameters only (the default) when intervals for the other parameters are not of interest.

When the model was fitted with keep.data=FALSE and type="proflik" is used for confint, the original data must be supplied via the data argument. Wald intervals do not require the data and can always be computed from the stored Hessian and parameter estimates alone.

Value

The original amerasfit object with a CI element added to each fitted method result. For RC, ERC, and MCML the CI element is a data frame with columns:

lower

Lower confidence bound.

upper

Upper confidence bound.

When type = "proflik", four additional columns are included:

pval.lower

P-value at the lower bound, should be close to 1 - level.

pval.upper

P-value at the upper bound, should be close to 1 - level.

iter.lower

Number of iterations used by the root-finding algorithm for the lower bound.

iter.upper

Number of iterations used by the root-finding algorithm for the upper bound.

For FMA and BMA the CI element is a data frame with columns lower and upper.

See Also

ameras for model fitting, summary for a summary of the fitted model including confidence intervals if computed, confint for the generic function.

Examples

data("data", package = "ameras")

## Fit the model
fit <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial",
               methods = "RC")

## Wald intervals (fast)
fit <- confint(fit, type = "wald.orig")
summary(fit)

## Profile likelihood intervals for dose parameters only (slower)

fit <- confint(fit, type = "proflik", parm = "dose")
summary(fit)


## With keep.data = FALSE, supply data explicitly for proflik

fit2 <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial",
               methods = "RC", keep.data = FALSE)
fit2 <- confint(fit2, type = "proflik", data = data)


## FMA and BMA with percentile intervals

fit3 <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial", 
               methods = c("FMA", "BMA"))
fit3 <- confint(fit3, type = "percentile")
summary(fit3)

Example data

Description

Data includes outcomes of all six supported types in the appropriately named columns. For proportional hazards regression, the observed exit time is time and event status is event. For conditional logistic regression, the matched set variable is setnr. The data has 10 exposure replicates in columns V1-V10.

Examples

 data(data, package="ameras")

 # Display a few rows of the data
 data[1:5, ]

Visualize multiple dose realizations

Description

Create a descriptive figure to visualize the distribution of dose and its uncertainty.

Usage

ecdfplot(data, dosevars, xlab="Dose", 
  ylab="Cumulative distribution", log.xaxis=TRUE)

Arguments

Details

In the left panel, the empirical cumulative distribution function (ECDF) is plotted for each dose realization. In other words, each curve shows one distribution of dose across individuals. The spread within individual curves reflects the dose range across individuals, while the spread between curves reflects between-realization variation on the cohort level.

In the right panel, ECDFs are plotted for each individual, showing distributions within individuals. A wide spread within individual curves is indicative of large within-individual variation, while the spread between curves reflects between-individual variation.

When using a log-scale for the x-axis, any zero dose values are excluded before plotting.

Examples

## Not run: 
   data(data, package="ameras")
   ecdfplot(data,  dosevars=paste0("V", 1:10))

## End(Not run)

Simple summary for an amerasfit object

Description

Prints a simple summary of a fitted amerasfit object.

Usage

## S3 method for class 'amerasfit'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Value

Prints the 'ameras' call, number of rows and dose replicates in the data, runtime, and model coefficients.

See Also

ameras for model fitting, summary for a more detailed summary of the fitted models including confidence intervals if computed.

Examples

data("data", package = "ameras")

## Fit the model
fit <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial", 
              methods = c("RC","ERC"))

## Default print
fit
print(fit)

## More digits
print(fit, digits=5)

Summarize an amerasfit object

Description

Produces a summary of a fitted amerasfit object, including parameter estimates, standard errors, and confidence intervals if computed via confint.

Usage

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

## S3 method for class 'summary.amerasfit'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Details

summary.amerasfit collects results from all estimation methods present in the fitted object into a single summary table. Columns for confidence intervals are only printed if they have been computed by confint. When BMA results are present in the fitted object, the summary table includes columns Rhat and n.eff, with NA values for all other methods.

Value

summary.amerasfit returns an object of class summary.amerasfit, which is a list containing the following elements:

call

The matched call from the original ameras invocation.

summary_table

A data frame with one row per parameter per method, containing columns:

Method

The estimation method (RC, ERC, MCML, FMA, or BMA).

Term

The parameter name.

Estimate

The parameter estimate.

SE

The standard error.

CI.lower

The lower confidence bound, if confidence intervals have been computed via confint.

CI.upper

The upper confidence bound, if confidence intervals have been computed via confint.

pval.lower

p-value associated with the lower bound of the profile likelihood CI, the assess validity of the obtained bound. Only included if profile likelihood confidence intervals were computed via confint.

pval.upper

p-value associated with the upper bound of the profile likelihood CI, the assess validity of the obtained bound. Only included if profile likelihood confidence intervals were computed via confint.

Rhat

The Gelman-Rubin convergence diagnostic, included only when BMA results are present. Values above 1.05 indicate potential convergence problems.

n.eff

The effective sample size, included only when BMA results are present.

runtime_table

A data frame with columns Method and Runtime, reporting the computation time in seconds for each method.

total_runtime_seconds

The total computation time in seconds across all methods.

CI.computed

Logical. TRUE if confidence intervals have been computed via confint, FALSE otherwise.

See Also

ameras for model fitting, confint for computing confidence intervals, print for a shorter printed summary, coef for extracting coefficients.

Examples

data("data", package = "ameras")

## Fit the model
fit <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial",
              methods = "RC")

## Summary without confidence intervals
summary(fit)

## Summary with confidence intervals
fit <- confint(fit, method = "wald.orig")
summary(fit)

## Access the summary table directly
s <- summary(fit)
s$summary_table

## Multiple methods
## Not run: 
fit2 <- ameras(Y.binomial~dose(V1:V10, model="ERR"), data = data, family = "binomial",
              methods = c("RC", "ERC", "MCML"))
fit2 <- confint(fit2, method = "wald.orig")
summary(fit2)

## End(Not run)

Traceplots for MCMC samples

Description

Produce MCMC traceplots for amerasfit objects.

Usage

traceplot(object, ...)

## S3 method for class 'amerasfit'
traceplot(object, iter = 5000, Rhat = TRUE, n.eff = TRUE, pdf = FALSE, ...)

Arguments

Details

Wrapper for MCMCvis::MCMCtrace to produce MCMC diagnostic plots. See ?MCMCtrace for more plotting options that can be provided through ....

Value

Traceplots and posterior density plots.

See Also

MCMCtrace

Examples

   data(data, package="ameras")
   fit <- ameras(Y.gaussian~dose(V1:V10), data, methods="BMA")
   traceplot(fit)

Exponential parameter transformation

Description

Applies exponential transformation f(\theta_i)=\exp(\theta_i)+L_i to one or multiple components of parameter vector \bm \theta, where L_i are lower limits that can be different for each component

Usage

transform1(params, index.t=1:length(params), lowlimit=rep(0,length(index.t)), 
  boundcheck=FALSE, boundtol=1e-3, ... )

Arguments

Value

Transformed parameter vector.

Examples

params <- c(.1, .5, 1)
transform1(params, lowlimit=c(0, -1, 1))

Inverse of exponential parameter transformation

Description

Inverse of transform1 for the purpose of deriving initial values.

Usage

transform1.inv(params, index.t=1:length(params), lowlimit=rep(0,length(index.t)), ... )

Arguments

Value

Transformed parameter vector.

Examples

params <- c(.1, .5, 1) # Desired initial values on original scale
transform1.inv(params, lowlimit=c(0, -1, 1)) # Initial values to use on transformed scale

Jacobian of the exponential parameter transformation

Description

Computes the Jacobian matrix of transform1. Note that lower limits do not need to be specified as the Jacobian is independent of those

Usage

transform1.jacobian(params, index.t=1:length(params), ... )

Arguments

Value

Jacobian matrix.

Examples

params <- c(.1, .5, 1)
transform1.jacobian(params)