Package 'smoothedIPW' reference manual

Title:	Time-Smoothed Inverse Probability Weighting for Repeatedly Measured Outcomes
Description:	Implements several methods to estimate effects of generalized time-varying treatment strategies on the mean of an outcome at one or more selected follow-up times of interest. Specifically, the package implements the time-smoothed inverse probability weighted estimators described in McGrath et al. (2025) <doi:10.48550/arXiv.2509.13971>. Outcomes may be repeatedly, non-monotonically, informatively, and sparsely measured in the data source. The package also supports settings where outcomes are truncated by death, i.e. some individuals die during follow-up which renders the outcome of interest undefined at the follow-up time of interest.
Authors:	Sean McGrath [aut, cre] (ORCID: <https://orcid.org/0000-0002-7281-3516>), Takuya Kawahara [aut], Jessica Young [aut] (ORCID: <https://orcid.org/0000-0002-2758-6932>)
Maintainer:	Sean McGrath <[email protected]>
License:	GPL (>= 3)
Version:	0.1.1
Built:	2026-06-03 09:10:17 UTC
Source:	https://github.com/stmcg/smoothedipw

Example dataset with null treatment effects

Description

A dataset consisting of 25,000 observations on 1,000 individuals over 25 time points. Each row in the dataset corresponds to the record of one individual at one time point.

Usage

data_null
data_null

Format

A data table with 25,000 rows and 7 variables:

time: Time index.
id: Unique identifier for each individual.
L: Binary time-varying covariate.
Z: Medication initiated at baseline.
A: Binary indicator of adhering to medication initiated at baseline.
R: Indicator if the outcome of interest is measured.
Y: Continuous outcome of interest.

Example dataset with null treatment effects and deaths (continuous outcome)

Description

A dataset consisting of 21,713 observations on 1,000 individuals over 25 time points. Each row in the dataset corresponds to the record of one individual at one time point.

Usage

data_null_deaths
data_null_deaths

Format

A data table with 21,713 rows and 8 variables:

time: Time index.
id: Unique identifier for each individual.
L: Binary time-varying covariate.
Z: Medication initiated at baseline.
A: Binary indicator of adhering to medication initiated at baseline.
R: Indicator if the outcome of interest is measured.
Y: Continuous outcome of interest.
D: Indicator if death occurred.

Example dataset with null treatment effects and deaths (binary outcome)

Description

A dataset consisting of 21,674 observations on 1,000 individuals over 25 time points. Each row in the dataset corresponds to the record of one individual at one time point.

Usage

data_null_deaths_binary
data_null_deaths_binary

Format

A data table with 21,674 rows and 8 variables:

time: Time index.
id: Unique identifier for each individual.
L: Binary time-varying covariate.
Z: Medication initiated at baseline.
A: Binary indicator of adhering to medication initiated at baseline.
R: Indicator if the outcome of interest is measured.
Y: Binary outcome of interest.
D: Indicator if death occured.

Bootstrap-based confidence intervals

Description

This function applies nonparametric bootstrap to construct confidence intervals around the counterfactual mean/probability estimates obtained by ipw.

Usage

get_CI(
  ipw_res,
  data,
  n_boot,
  conf_level = 0.95,
  reference_z_value,
  contrast_type = "difference",
  show_progress = TRUE
)
get_CI(
  ipw_res,
  data,
  n_boot,
  conf_level = 0.95,
  reference_z_value,
  contrast_type = "difference",
  show_progress = TRUE
)

Arguments

ipw_res

Output from the ipw function.

data

Data table containing the observed data

n_boot

Numeric scalar specifying the number of bootstrap replicates to use

conf_level

Numeric scalar specifying the confidence level for the confidence intervals. The default is 0.95.

reference_z_value

Scalar specifying the value of $z$ considered as the reference level when forming contrasts. See also argument contrast_type.

contrast_type

Character string specifying the type of contrast. The options are "difference" (for the difference of means/probabilities) and "ratio" (for the ratio of means/probabilities).

show_progress

Logical scalar specifying whether to show a progress bar.

Details

This function applies nonparametric bootstrap resampling to construct confidence intervals around the counterfactual mean/probability estimates obtained by ipw. Bootstrap confidence intervals are constructed by resampling individuals (with replacement) from the original data set, applying the ipw function to each bootstrap sample, and computing percentile-based confidence intervals from the distribution of bootstrap estimates.

Value

An object of class "ipw_ci". This object is a list that includes the following components:

res_boot

res_boot_contrast

A list where each component corresponds to a different medication $z$ level. Each component of the list is a data frame containing the estimates and confidence intervals for the contrast (difference or ratio) counterfactual outcome mean/probability under the treatment regime indexed by $z$ compared to the counterfactual outcome mean/probability under the treatment regime indexed by the reference value.

res_boot_all

A three dimensional array containing all the bootstrap replicates. The first dimension corresponds to the bootstrap replicate; The second dimension corresponds to the time interval; The third dimension corresponds to the medication $z$ level.

outcome_type

Character string indicating whether the outcome is "continuous" or "binary".

outcome_times

Numeric vector of outcome times.

n_boot

Number of bootstrap replicates used.

conf_level

Confidence level used.

reference_z_value

Reference value of Z used for contrasts.

contrast_type

Type of contrast ("difference" or "ratio").

Examples


set.seed(1234)
data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res_est <- ipw(data = data_null_processed,
               time_smoothed = TRUE,
               outcome_times = c(6, 12, 18, 24),
               A_model = A ~ L + Z,
               R_model_numerator = R ~ L_baseline + Z,
               R_model_denominator = R ~ L + A + Z,
               Y_model = Y ~ L_baseline * (time + Z))
res_ci <- get_CI(ipw_res = res_est, data = data_null_processed, n_boot = 10)
res_ci



set.seed(1234)
data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res_est <- ipw(data = data_null_processed,
               time_smoothed = TRUE,
               outcome_times = c(6, 12, 18, 24),
               A_model = A ~ L + Z,
               R_model_numerator = R ~ L_baseline + Z,
               R_model_denominator = R ~ L + A + Z,
               Y_model = Y ~ L_baseline * (time + Z))
res_ci <- get_CI(ipw_res = res_est, data = data_null_processed, n_boot = 10)
res_ci

Time-smoothed inverse probability weighting

Description

This function applies the time-smoothed inverse probability weighted (IPW) approach described by McGrath et al. (2025) to estimate effects of generalized time-varying treatment strategies on the mean of an outcome at one or more selected follow-up times of interest. Binary and continuous outcomes are supported.

Usage

ipw(
  data,
  time_smoothed = TRUE,
  smoothing_method = "nonstacked",
  outcome_times,
  A_model,
  R_model_numerator = NULL,
  R_model_denominator,
  Y_model,
  truncation_percentile = NULL,
  truncation_value = NULL,
  include_baseline_outcome,
  return_model_fits = TRUE,
  return_weights = TRUE,
  trim_returned_models = FALSE
)
ipw(
  data,
  time_smoothed = TRUE,
  smoothing_method = "nonstacked",
  outcome_times,
  A_model,
  R_model_numerator = NULL,
  R_model_denominator,
  Y_model,
  truncation_percentile = NULL,
  truncation_value = NULL,
  include_baseline_outcome,
  return_model_fits = TRUE,
  return_weights = TRUE,
  trim_returned_models = FALSE
)

Arguments

data

Data table (or data frame) containing the observed data. See "Details".

time_smoothed

Logical scalar specifying whether the time-smoothed or non-smoothed IPW method is applied. The default is TRUE, i.e., the time-smoothed IPW method.

smoothing_method

Character string specifying the time-smoothed IPW method when there are deaths present. The options include "nonstacked" and "stacked". The default is "nonstacked".

outcome_times

Numeric vector specifying the follow-up time(s) of interest for the counterfactual outcome mean/probability

A_model

Model statement for the treatment variable

R_model_numerator

(Optional) Model statement for the indicator variable for the measurement of the outcome variable, used in the numerator of the IP weights. The default is NULL, i.e., a numerator of 1 is used in the IP weights.

R_model_denominator

Model statement for the indicator variable for the measurement of the outcome variable, used in the denominator of the IP weights

Y_model

Model statement for the outcome variable

truncation_percentile

Numerical scalar specifying the percentile by which to truncate the IP weights. The default is NULL, i.e., no truncation. Only one of truncation_value and truncation_percentile may be specified.

truncation_value

Numerical scalar specifying the value at which to truncate the IP weights. The default is NULL, i.e., no truncation. Only one of truncation_value and truncation_percentile may be specified.

include_baseline_outcome

Logical scalar indicating whether to include the time interval indexed by 0 in fitting the time-smoothed outcome model and outcome measurement models. By default, this argument is set to TRUE if data has any non-missing outcome values in the time interval indexed by 0 and is otherwise set to FALSE.

return_model_fits

Logical scalar specifying whether to include the fitted models in the output. The default is TRUE.

return_weights

Logical scalar specifying whether to return the estimated inverse probability weights. The default is TRUE.

trim_returned_models

Logical scalar specifying whether to only return the estimated coefficients (and corresponding standard errors, z scores, and p-values) of the fitted models (e.g., treatment model) rather than the full fitted model objects. This reduces the size of the object returned by the ipw function when return_model_fits is set to TRUE, especially when the observed data set is large. By default, this argument is set to FALSE.

Details

Treatment strategies

Users can estimate effects of treatment strategies with the following components:

Initiate treatment $z$ at baseline
Follow a user-specified time-varying adherence protocol for treatment $z$
Ensure an outcome measurement at the follow-up time of interest.

The time-varying adherence protocol is specified by indicating in data when an individual deviates from their adherence protocol. The function prep_data facilitates this step. See also "Formatting data".

Formatting data

The input data set data must be a data table (or data frame) in a "long" format, where each row represents one time interval for one individual. The data frame should contain the following columns:

id: A unique identifier for each participant.
time: The follow-up time index, starting from 0 and increasing in increments of 1 in consecutive rows.
Covariate columns: One or more columns for baseline and time-varying covariates.
Z: The treatment initiated at baseline.
A: An indicator for adherence to the treatment protocol at each time point.
R: An indicator of whether the outcome was measured at that time point (1 for measured, 0 for not measured/censored).
Y: The outcome variable, which can be binary or continuous.

To specify the intervention, the data set should additionally have the following columns:

C_artificial: An indicator specifying when an individual should be artificially censored from the data due to violating the adherence protocol.
A_model_eligible: An indicator specifying which records should be used for fitting the treatment adherence model.

The prep_data function facilitates adding these columns to the data set. Users may optionally include the following column for fitting the outcome measurement model:

R_model_denominator_eligible: An indicator specifying which records should be used for fitting the outcome measurement model R_model_denominator_eligible.

Otherwise, the R_model_denominator_eligible is fit on all records on the artificially censored data set.

Specifying the models

Users must specify model statements for the treatment (A_model), outcome measurement (R_model_numerator and R_model_denominator), and outcome variable (Y_model). The package uses pooled-over-time generalized linear models that are fit over the relevant time points (see "Formatting data"), where logistic regression is used for binary variables and linear regression is used for continuous variables.

For stabilized weights, the outcome measurement model R_model_numerator should only include baseline covariates, treatment initiated Z, and time as predictors. It must not include time-varying covariates as predictors. The outcome model Y_model should also only depend on baseline covariates, treatment initiated Z, and time (if using time smoothing).

A note on the outcome definition at baseline

In some settings, the outcome may not be defined in the baseline time interval. The ipw function can accommodate such settings in two ways:

Users can set a value of NA in the column Y in the input data set data in rows corresponding to time 0. In this case, users should ensure that include_baseline_outcome is set to FALSE.
Users can specify the value of $Y_{t+1}$ (rather than $Y_t$ ) in the column Y in the input data set data in rows corresponding to time $t$ . That is, the value supplied for Y in the input data set data at time 0 is $Y_1$ . In this case, users should ensure that include_baseline_outcome is set to TRUE. Users should also set outcome_times accordingly.

Note that these two approaches involve different assumptions. For example, the first approach allows the outcome at time $t$ to depend on time-varying covariates up to and including time $t$ , whereas the second approach only allows the outcome at time $t$ to depend on covariates up to and including time $t-1$ .

Value

An object of class "ipw". This object is a list that includes the following components:

est

A data frame containing the counterfactual mean/probability estimates for each medication at each time interval.

model_fits

A list containing the fitted models for the treatment, outcome measurement, and outcome (if return_model_fits is set to TRUE). If the nonstacked time-smoothed approach is used, the $i$ th element in model_fits is a list of fitted models for the $i$ th outcome time in outcome_times. If the stacked time-smoothed approach is used, the $i$ th element in model_fits is a list of fitted models for the outcome time $i+1$ in the data set data. The last element in model_fits contains the fitted outcome model.

data_weights

(A list containing) the artificially censored data set with columns for the estimated weights. The column "weights" contains the (final) inverse probability weight, and the columns "weights_A" and "weights_R" contain the inverse probability weights for treatment and outcome measurement, respectively. If no deaths are present in the data, this object will be a data frame. If deaths are present in the data and either the non-smoothed IPW method is applied or the time-smoothed non-stacked IPW method is applied, this object will be a list of length length(outcome_times) where each element corresponds to the artificially censored data set for each outcome time in outcome_times. If deaths are present in the data and the time-smoothed stacked IPW method is applied, this object will be a data frame with the stacked, artificially censored data.

args

A list containing the arguments supplied to ipw, except the observed data set.

References

McGrath S, Kawahara T, Petimar J, Rifas-Shiman SL, Díaz I, Block JP, Young JG. (2025). Time-smoothed inverse probability weighted estimation of effects of generalized time-varying treatment strategies on repeated outcomes truncated by death. arXiv e-prints arXiv:2509.13971.

Examples


## Time-smoothed IPW without deaths (continuous outcome)
data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res <- ipw(data = data_null_processed,
           time_smoothed = TRUE,
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
res

## Time-smoothed IPW with deaths, nonstacked smoothing method (continuous outcome)
data_null_deaths_processed <- prep_data(data = data_null_deaths, grace_period_length = 2,
                                        baseline_vars = 'L')
res <- ipw(data = data_null_deaths_processed,
           time_smoothed = TRUE,
           smoothing_method = 'nonstacked',
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
res

## Time-smoothed IPW with deaths, stacked smoothing method (binary outcome)

data_null_deaths_binary_processed <- prep_data(data = data_null_deaths_binary,
                                               grace_period_length = 2,
                                               baseline_vars = 'L')
res <- ipw(data = data_null_deaths_binary_processed,
           time_smoothed = TRUE,
           smoothing_method = 'stacked',
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
res$est


## Time-smoothed IPW without deaths (continuous outcome)
data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res <- ipw(data = data_null_processed,
           time_smoothed = TRUE,
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
res

## Time-smoothed IPW with deaths, nonstacked smoothing method (continuous outcome)
data_null_deaths_processed <- prep_data(data = data_null_deaths, grace_period_length = 2,
                                        baseline_vars = 'L')
res <- ipw(data = data_null_deaths_processed,
           time_smoothed = TRUE,
           smoothing_method = 'nonstacked',
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
res

## Time-smoothed IPW with deaths, stacked smoothing method (binary outcome)

data_null_deaths_binary_processed <- prep_data(data = data_null_deaths_binary,
                                               grace_period_length = 2,
                                               baseline_vars = 'L')
res <- ipw(data = data_null_deaths_binary_processed,
           time_smoothed = TRUE,
           smoothing_method = 'stacked',
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
res$est

Prepare data set for inverse probability weighting

Description

This function adds columns to the input data set to assist with inverse probability weighting. See details.

Usage

prep_data(
  data,
  grace_period_length = 0,
  baseline_vars = NULL,
  lag_vars = NULL,
  n_lags = 1
)
prep_data(
  data,
  grace_period_length = 0,
  baseline_vars = NULL,
  lag_vars = NULL,
  n_lags = 1
)

Arguments

data

Data frame containing the observed data

grace_period_length

Numeric scalar indicating the length of the grace period, if applicable. The default is 0, indicating no grace period.

baseline_vars

Vector of character strings specifying the names of the baseline covariates that should be added to the observed data.

lag_vars

Vector of character strings specifying the names of the covariates whose lags should be added as columns to the observed data. The number of lags is controlled by the n_lags argument.

n_lags

Numeric scalar specifying the number of lags to use when computing the lagged values of lag_vars. Additional columns will be created for 1, ..., n_lags lags of the variables specified in lag_vars.

Details

This function performs the following tasks:

Adds a column C_artificial which indicates when an individual should be artificially censored from the data when applying inverse probability weighting.
Adds a column A_model_eligible which indicates what records should be used for fitting the treatment adherence model.
If baseline_vars is supplied, it adds columns corresponding to the baseline value of these variables. These columns have the name _baseline appended to them.
If lag_vars is supplied, it adds columns corresponding to the lagged value of these variables. For each of these variables, additional columns will be created for 1, ..., n_lags lags of the variable.

Value

A data table containing the observed data with the additional columns.

Examples

data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')


data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')

Print method for "ipw" objects

Description

Print method for objects of class "ipw".

Usage

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

Arguments

x

Object of class "ipw".

...

Other arguments.

Value

No value is returned.

Examples

data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res <- ipw(data = data_null_processed,
           time_smoothed = TRUE,
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
print(res)

data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res <- ipw(data = data_null_processed,
           time_smoothed = TRUE,
           outcome_times = c(6, 12, 18, 24),
           A_model = A ~ L + Z,
           R_model_numerator = R ~ L_baseline + Z,
           R_model_denominator = R ~ L + A + Z,
           Y_model = Y ~ L_baseline * (time + Z))
print(res)

Print method for "ipw_ci" objects

Description

Print method for objects of class "ipw_ci".

Usage

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

Arguments

x

Object of class "ipw_ci".

...

Other arguments.

Value

No value is returned.

Examples


set.seed(1234)
data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res_est <- ipw(data = data_null_processed,
               time_smoothed = TRUE,
               outcome_times = c(6, 12, 18, 24),
               A_model = A ~ L + Z,
               R_model_numerator = R ~ L_baseline + Z,
               R_model_denominator = R ~ L + A + Z,
               Y_model = Y ~ L_baseline * (time + Z))
res_ci <- get_CI(ipw_res = res_est, data = data_null_processed, n_boot = 10)
print(res_ci)


set.seed(1234)
data_null_processed <- prep_data(data = data_null, grace_period_length = 2,
                                 baseline_vars = 'L')
res_est <- ipw(data = data_null_processed,
               time_smoothed = TRUE,
               outcome_times = c(6, 12, 18, 24),
               A_model = A ~ L + Z,
               R_model_numerator = R ~ L_baseline + Z,
               R_model_denominator = R ~ L + A + Z,
               Y_model = Y ~ L_baseline * (time + Z))
res_ci <- get_CI(ipw_res = res_est, data = data_null_processed, n_boot = 10)
print(res_ci)

Package 'smoothedIPW'

Help Index

Example dataset with null treatment effects

Description

Usage

Format

Example dataset with null treatment effects and deaths (continuous outcome)

Description

Usage

Format

Example dataset with null treatment effects and deaths (binary outcome)

Description

Usage

Format

Bootstrap-based confidence intervals

Description

Usage

Arguments

Details

Value

Examples

Time-smoothed inverse probability weighting

Description

Usage

Arguments

Details

Value

References

Examples

Prepare data set for inverse probability weighting

Description

Usage

Arguments

Details

Value

Examples

Print method for "ipw" objects

Description

Usage

Arguments

Value

See Also

Examples

Print method for "ipw_ci" objects

Description

Usage

Arguments

Value

See Also

Examples