Causal Inference with Continuous (Multiple Time Point) Interventions

Description

This package facilitates the estimation of counterfactual outcomes for multiple values of continuous interventions at different time points, and allows plotting of causal dose-response curves.

It implements the standard g-methods approach using the (semi-)parametric g-formula, as described in the Schomaker et al. (2024) reference listed below. Weighted dose-response curves that address positivity violations, and are fitted via sequential g-computation, are currently only available on GitHub and are not (yet) integrated in this package.

The main function of the package is currently gformula.

Details

Author(s)

Michael Schomaker

Maintainer: Michael Schomaker <michael.schomaker@stat.uni-muenchen.de>

References

Schomaker M, McIlleron H, Denti P, Diaz I. (2024) Causal Inference for Continuous Multiple Time Point Interventions, Statistics in Medicine, 43:5380-5400, see also https://arxiv.org/abs/2305.06645.

Pharmacoepidemiological HIV treatment data

Description

A hypothetical, simulated dataset which is line with the data-generating process of Schomaker et al. (2024) and inspired by the data of Bienczak et al. (2017); see references below.

Usage

data(EFV)

Format

A data frame with 5000 observations on the following variables:

sex

The patient's sex

metabolic

Metabolism status (slow, intermediate, extensive) related to the single nucleotide polymorphisms in the CYP2B6 gene, which is relevant for metabolizing evafirenz and directly affects its concentration in the body.

log_age

log(age) at baseline

NRTI

Nucleoside reverse transcriptase inhibitor (NRTI) component of HIV treatment, i.e. abacavir, stavudine or zidovudine.

weight.0

log(weight) at time 0 (baseline)

efv.0

Efavirenz concentration at time 0 (baseline)

VL.0

Elevated viral load (viral failure) at time 0 (baseline)

adherence.1

Adherence at time 1 (if 0, then signs of non-adherence)

weight.1

log(weight) at time 1

efv.1

Efavirenz concentration at time 1

VL.1

Elevated viral load (viral failure) at time 1

adherence.2

Adherence at time 2 (if 0, then signs of non-adherence)

weight.2

log(weight) at time 2

efv.2

Efavirenz concentration at time 2

VL.2

Elevated viral load (viral failure) at time 2

adherence.3

Adherence at time 3 (if 0, then signs of non-adherence)

weight.3

log(weight) at time 3

efv.3

Efavirenz concentration at time 3

VL.3

Elevated viral load (viral failure) at time 3

adherence.4

Adherence at time 4 (if 0, then signs of non-adherence)

weight.4

log(weight) at time 4

efv.4

Efavirenz concentration at time 4

VL.4

Elevated viral load (viral failure) at time 4

References

Schomaker M, McIlleron H, Denti P, Diaz I. (2024) Causal Inference for Continuous Multiple Time Point Interventions, Statistics in Medicine, 43:5380-5400, see also https://arxiv.org/abs/2305.06645.

Bienczak et al. (2017) Determinants of virological outcome and adverse events in African children treated with paediatric nevirapine fixed-dose-combination tablets, AIDS, 31:905-915

Examples

data(EFV)
str(EFV)

Pharmacoepidemiological HIV treatment data

Description

A hypothetical, simulated dataset which is line with the data-generating process of Schomaker et al. (2024) and inspired by the data of Bienczak et al. (2017); see references below. Compared to the dataset EFV, it contains all variables of the DAG in Figure 3 of Schomaker et al. (2023), also those which are not needed for identification of the counterfactual quantity of interest; that is, the expected viral suppression (VL) under a specific intervention on efavirenz concentrations (efv.0, efv.1, ...).

Usage

data(EFVfull)

Format

A data frame with 5000 observations on the following variables:

sex

The patient's sex

metabolic

Metabolism status (slow, intermediate, extensive) related to the single nucleotide polymorphisms in the CYP2B6 gene, which is relevant for metabolizing evafirenz and directly affects its concentration in the body.

log_age

log(age) at baseline

NRTI

Nucleoside reverse transcriptase inhibitor (NRTI) component of HIV treatment, i.e. abacavir, stavudine or zidovudine.

weight.0

log(weight) at time 0 (baseline)

comorbidity.0

Presence of co-morbidities at time 0 (baseline)

dose.0

Dose of efavirenz administered at time 0 (basline)

efv.0

Efavirenz concentration at time 0 (baseline)

VL.0

Elevated viral load (viral failure) at time 0 (baseline)

adherence.1

Adherence at time 1 (if 0, then signs of non-adherence)

weight.1

log(weight) at time 1

comorbidity.1

Presence of co-morbidities at time 1

dose.1

Dose of efavirenz administered at time 1

efv.1

Efavirenz concentration at time 1

VL.1

Elevated viral load (viral failure) at time 1

adherence.2

Adherence at time 2 (if 0, then signs of non-adherence)

weight.2

log(weight) at time 2

comorbidity.2

Presence of co-morbidities at time 2

dose.2

Dose of efavirenz administered at time 2

efv.2

Efavirenz concentration at time 2

VL.2

Elevated viral load (viral failure) at time 2

adherence.3

Adherence at time 3 (if 0, then signs of non-adherence)

weight.3

log(weight) at time 3

comorbidity.3

Presence of co-morbidities at time 3

dose.3

Dose of efavirenz administered at time 3

efv.3

Efavirenz concentration at time 3

VL.3

Elevated viral load (viral failure) at time 3

adherence.4

Adherence at time 4 (if 0, then signs of non-adherence)

weight.4

log(weight) at time 4

comorbidity.4

Presence of co-morbidities at time 4

dose.4

Dose of efavirenz administered at time 4

efv.4

Efavirenz concentration at time 4

VL.4

Elevated viral load (viral failure) at time

References

Schomaker M, McIlleron H, Denti P, Diaz I. (2024) Causal Inference for Continuous Multiple Time Point Interventions, Statistics in Medicine, 43:5380-5400, see also https://arxiv.org/abs/2305.06645.

Bienczak et al. (2017) Determinants of virological outcome and adverse events in African children treated with paediatric nevirapine fixed-dose-combination tablets, AIDS, 31:905-915

Examples

data(EFVfull)
str(EFVfull)

Counterfactual contrast from the parametric or sequential g-formula for continuous multiple time point interventions

Description

Estimation of a contrast between counterfactual outcomes under different values of (continuous) interventions, or across different time points, using the parametric or sequential g-formula.

Usage

contrast(X, abar, nodes, contrastType = "difference", measure = mean,
         cond = NULL, cilevel = 0.95, ...)

Arguments

Details

Causal effects are defined as contrasts between the distributions of counterfactual variables under different interventions, across different time points or across different covariate strata. The counterfactual distributions to compare must be uniquely determined, by either specifying two values of abar at a single nodes or two nodes at a single intervention level abar or the natural course scenario with abar = 'natural' or two covariate strata cond. If the natural course scenario is selected and two nodes are specified, the natural intervention is compared across the two nodes. If one nodes is specified, the natural and observed scenarios are compared at a single node.

By default, the difference between the expectations of the two counterfactual outcome distributions is calculated. The difference can be exchanged for a ratio, odds ratio or custom contrast in the contrastType argument, and expectations can be exchanged for custom measures in the measure argument. Conditional measures can be specified through the cond argument. Custom contrasts, including those comparing more than two counterfactuals, can be defined by passing a function to contrastType.

Confidence intervals are based on the nonparametric bootstrap with B samples.

Value

Returns a list of class contrastResult:

See Also

gformula and sgf for estimating expected counterfactual outcomes under multiple intervention values and custom.measure for measures other than expectations.

Examples

## Not run: 
data(EFV)
gf1 <- gformula(
  X = EFV, Anodes = c("efv.0", "efv.1", "efv.2", "efv.3", "efv.4"),
  Ynodes = c("VL.0", "VL.1", "VL.2", "VL.3", "VL.4"),
  Lnodes = c("adherence.1", "weight.1", "adherence.2", "weight.2",
             "adherence.3", "weight.3", "adherence.4", "weight.4"),
  abar = seq(1, 5), B = 10, ret = TRUE
)

# compare outcomes at last time point under (1,...,1) and (5,...,5) 
contrast(gf1, abar = c(1, 5), nodes = "VL.4")

# compare outcomes at different time points, for same intervention (2,...)
contrast(gf1, abar = 2, nodes = c("VL.3", "VL.2"))

# compare own measure (rel. risk reduction) instead of mean
# ... and conditional on subset
relativeRiskReduction <- function(k, l){(k - l) / k}

contrast(
  gf1, abar = c(1, 2), nodes = "VL.4",
  contrastType = relativeRiskReduction,
  cond = quote(sex == 1)
)

# Instead of the mean, any other measure can be taken,
# and - of course - applied also to counterfactual Lnodes
contrast(
  gf1, abar = 2, nodes = c("weight.3", "weight.2"),
  measure = median
)

## End(Not run)

Custom estimands after applying gformula

Description

The default estimate returned by gformula is the expected outcome under the respective intervention strategies abar. custom.measure takes an object of class gformula and enables estimation of other estimands based on the counterfactual datasets produced by gformula (if the option ret=TRUE had been chosen), for example estimands conditional on baseline variables, quantiles instead of expectations, and others.

Usage

custom.measure(X, fun = NULL, cond = NULL, verbose = TRUE, with.se = FALSE,
               cilevel = 0.95, ...)

Arguments

Details

In settings with censoring, it will often be needed to pass on the option na.rm=T, e.g. for the mean, median, quantiles, and others.

Calculation of the bootstrap standard error (i.e., with.se=T) is typically not needed; but, for example, necessary for the calculations after multiple imputation and hence used by mi.boot.

Value

An object of class gformula. See gformula for details.

See Also

see also gformula

Examples

data(EFV)

est <- gformula(X=EFV,
                Lnodes  = c("adherence.1","weight.1",
                            "adherence.2","weight.2",
                            "adherence.3","weight.3",
                            "adherence.4","weight.4"
                ),
                Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                abar=seq(0,2,1), ret=TRUE
)

est
custom.measure(est, fun=prop,categ=1) # identical
custom.measure(est, fun=prop,categ=0)
custom.measure(est, fun=prop, categ=0, cond="sex==1")
# note: metabolic has been recoded internally (see output above)
custom.measure(est, fun=prop, categ=0, cond="metabolic==0") 
# does not make sense here, just for illustration (useful for metric outcomes)
custom.measure(est, fun=quantile, probs=0.1) 

Estimate Feasible Intervention Strategies

Description

Estimate a family of feasible intervention strategies for a continuous treatment (and optionally time-varying covariates). The method returns, for each intervention strategy, the corresponding “feasible” intervention values and a summary of overlap and positivity-violation diagnostics.

Usage

feasible(
  X, Anodes = NULL, Ynodes = NULL, Lnodes = NULL, Cnodes = NULL,
  abar = NULL,
  alpha = 0.95, grid.size = 0.5, tol = 1e-2,
  left.boundary = NULL, right.boundary = NULL,
  screen = FALSE, survival = FALSE,
  d.method = c("hazardbinning", "binning", "parametric", "hal_density"),
  verbose = TRUE, ...
)

Arguments

Details

The main steps of the algorithm are:

1. Model specification: Treatment models for each time point are constructed via helper routines from CICI. If screen = TRUE, a screening step updates the treatment formulas before density estimation (only recommended to address computational constraints).

2. Grid construction: A grid of treatment values, query_abar, is formed by combining:

   • observed treatment values in X[, Anodes],

   • the target values in abar, and

   • a regular grid from left.boundary to right.boundary with spacing grid.size (when grid.size is not NULL).

   If grid.size = NULL, the grid is restricted to the unique values in abar (only allowed when abar is a vector).

3. Density estimation: For each time point, the conditional treatment density is evaluated on the grid for each observation using the specified d.method. The resulting matrices are normalised so that each row integrates to one over the grid (accounting for bin width).

4. Feasibility threshold: For each observation and time point, a density threshold f_\alpha is computed such that the cumulative mass below the sorted densities first exceeds 1 - alpha. Cells with density below f_\alpha are flagged as “infeasible”.

5. Feasible mapping: For each grid cell with density below f_\alpha, the algorithm finds the closest grid cell with density at or above f_\alpha (in terms of grid index) and maps its value to that cell. This defines a “feasible” intervention that avoids low-density regions.

6. Summary: For each time point t and each intervention strategy (row of abar), the method collects:

   • the mean feasible value across individuals (column Feasible),

   • the proportion of cells below the density threshold (column Low, interpreted as %infeasible in the associated S3 methods),

   • the corresponding target value Abar at time t, and

   • the strategy index Strategy.

   These are combined into a data frame stored as the "summary" attribute of the returned object.

Plotting and printing methods are available for visual and tabular diagnostics; see plot.feasible, print.feasible, and summary.feasible.

Value

An object of class "feasible" with the following components:

• feasible: a list of length equal to the number of strategies (rows of abar). Each element is a matrix with one column per time point, containing the feasible intervention values for that strategy and time point across observations.

• low_matrix: a list of length equal to the number of time points. Each element is a logical matrix indicating, on the internal grid, which cells were marked as below the density threshold.

The object additionally has a "summary" attribute, a data frame with at least the columns time, Strategy, Abar, Feasible, and Low, which is accessed and formatted by summary.feasible and print.feasible.

See Also

plot.feasible, print.feasible, summary.feasible

Examples

data(EFV)


Lnodes <- c("adherence.1","weight.1",
            "adherence.2","weight.2",
            "adherence.3","weight.3",
            "adherence.4","weight.4")
Ynodes <- c("VL.0","VL.1","VL.2","VL.3","VL.4")
Anodes <- c("efv.0","efv.1","efv.2","efv.3","efv.4")

## ------------------------------------------------------------------
## Example 1: Hazard binning with default grid
## Static grid of targets (vector abar) over the full support of efv.*
## ------------------------------------------------------------------

abar_static <- seq(0, 10, by = 1)

m_hazard <- feasible(
  X      = EFV,
  Anodes = Anodes,
  Lnodes = Lnodes,
  Ynodes = Ynodes,
  d.method      = "hazardbinning", # long computation, but appropriate
  abar          = abar_static,
  grid.size     = 0.5,
  left.boundary = 0,
  right.boundary = 10
)


## Individual-level feasible values (one matrix per strategy):
## rows = individuals, columns = time points
feasible_matrix <- m_hazard$feasible # pass on to gofrmula/sgf
lapply(feasible_matrix, head)

## Inspect feasability of strategies
m_hazard             # see also ?print.feasible
summary(m_hazard)    # see also ?summary.feasible


## ------------------------------------------------------------------
## Example 2: Parametric density, using abar as the grid
## Here grid.size = NULL, so only the target values are used as grid
## ------------------------------------------------------------------

abar_param <- seq(0, 10, by = 2)

m_param <- feasible(
  X      = EFV,
  Anodes = Anodes,
  Lnodes = Lnodes,
  Ynodes = Ynodes,
  # fast, but useful for reasonably symmetric distributions
  d.method      = "parametric", 
  abar          = abar_param,
  grid.size     = NULL,
  left.boundary = 0,
  right.boundary = 10
)

## Inspect feasability of strategies
m_param             # see also ?print.feasible
summary(m_param)    # see also ?summary.feasible


## ------------------------------------------------------------------
## Example 3: Matrix abar with non-constant strategies over time
## Each row is a strategy, each column corresponds to efv.0, ..., efv.4
## ------------------------------------------------------------------

abar_matrix <- rbind(
  c(0, 2, 4, 6, 8),  # strategy 1
  c(9, 6, 2, 1, 0),  # strategy 2
  c(1, 3, 5, 7, 9)   # strategy 3
)

m_matrix <- feasible(
  X      = EFV,
  Anodes = Anodes,
  Lnodes = Lnodes,
  Ynodes = Ynodes,
  d.method      = "parametric",
  abar          = abar_matrix,
  grid.size     = 1,
  left.boundary = 0,
  right.boundary = 10
)

## Inspect feasability of strategies
m_matrix             # see also ?print.feasible
summary(m_matrix)    # see also ?summary.feasible

Fit models after screening

Description

Fits the models that have been generated with screening using model.formulas.update.

Usage

fit.updated.formulas(formulas, X)

Arguments

Details

Fits generalized (additive) linear models based on the screened model formula list generated by model.formulas.update.

Value

Returns a list of length 2:

See Also

model.formulas.update

Examples

data(EFV)

# first: generate generic model formulas
m <- make.model.formulas(X=EFV,
                         Lnodes  = c("adherence.1","weight.1",
                                     "adherence.2","weight.2",
                                     "adherence.3","weight.3",
                                     "adherence.4","weight.4"
                                    ),
                         Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                         Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                         evaluate=FALSE) 
                         
# second: update these model formulas based on variable screening with LASSO
glmnet.formulas <-  model.formulas.update(m$model.names, EFV)
glmnet.formulas 

# then: fit and inspect the updated models
fitted.models <- fit.updated.formulas(glmnet.formulas, EFV)
fitted.models$all.summaries
fitted.models$all.summaries$Ynames[1] # first outcome model

Parametric g-formula for continuous multiple time point interventions

Description

Estimation of counterfactual outcomes for multiple values of continuous interventions at different time points using the g-formula.

Usage

gformula(X, Anodes, Ynodes, Lnodes = NULL, Cnodes = NULL,
         abar = NULL, cbar = "uncensored",
         survivalY = FALSE, 
         Yform = "GLM", Lform = "GLM", Aform = "GLM", Cform = "GLM",
         calc.support = FALSE, B = 0, ret = FALSE, ncores = 1, 
         verbose = TRUE, seed = NULL, prog = NULL, cilevel = 0.95, ...)

Arguments

Details

By default, expected counterfactual outcomes (specified under Ynodes) under the intervention abar are calculated. Other estimands can be specified via custom.measure.

If abar is a vector, then each vector component is used as the intervention value at each time point; that is, interventions which are constant over time are defined. If abar is a matrix (of size 'number interventions' x 'time points'), then each row of the length of Anodes refers to a particular time-varying intervention strategy. The natural intervention can be picked by setting abar='natural'.

The fitted outcome and confounder models are based on generalized additive models (GAMs) as implemented in the mgcv package. Model families are picked automatically and reported in the output if verbose=TRUE (see manual for modifications, though they hardly ever make sense). The model formulas are standard GLMs or GAMs (with penalized splines for continuous covariates), conditional on the past, unless specific formulae are given. It is recommended to use customized formulae to reduce the risk of model mis-specification and to ensure that the models make sense (e.g., not too many splines are used when this is computationally not meaningful). This can be best facilitated by using objects generated through make.model.formulas, followed by model.formulas.update and/or model.update (see examples for those functions).

For survival settings, it is required that i) survivalY=TRUE and ii) after a Cnode/Ynode is 1, every variable thereafter is set to NA. See manual for an example. By default, the package intervenes on Cnodes, i.e. calculates counterfactual outcomes under no censoring.

If calc.support=TRUE, conditional and crude support measures (i.e., diagnostics) are calculated as described in Section 3.4 of Schomaker et al. (2023). Another useful diagnostic for multiple time points is the natural course scenario, which can be evaluated under abar='natural' and cbar='natural'.

To parallelize computations automatically, it is sufficient to set ncores>1, as appropriate. To make estimates under parallelization reproducible, use the seed argument. To watch the progress of parallelized computations, set a path in the prog argument: then, a text file reports on the progress, which is particularly useful if lengthy bootstrapping computations are required.

Value

Returns an object of of class ‘gformula’:

Author(s)

Michael Schomaker

See Also

plot.gformula for plotting results as (causal) dose response curves, custom.measure for evaluating custom estimands and mi.boot for using gformula on multiply imputed data.

Examples

## Not run: 
data(EFV)
est <- gformula(X=EFV,
                      Lnodes  = c("adherence.1","weight.1",
                                  "adherence.2","weight.2",
                                  "adherence.3","weight.3",
                                  "adherence.4","weight.4"
                        ),
                        Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                        Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                        abar=seq(0,10,1)
)
est

## End(Not run)

Compose appropriate model formulas

Description

Function that generates generic model formulas for Y-/L-/A- and Cnodes, according to time ordering and to be used in gformula or model.formulas.update.

Usage

make.model.formulas(X, Ynodes = NULL, Lnodes = NULL, Cnodes = NULL, Anodes = NULL,
                    survival = FALSE, evaluate = FALSE)

Arguments

Details

This is a helper function to generate model formulas for Y-/L-/A- and Cnodes, according to the time ordering: i.e. to generate GLM/GAM model formulas for the respective nodes given all past variables. In survival settings, past censoring and outcome nodes are omitted from the formulae. If censoring is present without a survival setting (e.g. Cnodes describe drop-outs and Y is a continuous outcome), then survival should be set as FALSE.

Value

Returns a named list:

See Also

The generated generic model formulas can be updated manually with model.update or in an automated manner with screening using model.formulas.update.

Examples

data(EFV)

m <- make.model.formulas(X=EFV,
                         Lnodes  = c("adherence.1","weight.1",
                                     "adherence.2","weight.2",
                                     "adherence.3","weight.3",
                                     "adherence.4","weight.4"
                                    ),
                         Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                         Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                         evaluate=FALSE) # set TRUE to see fitted models
                         
m$model.names # all models potentially relevant for gformula(), given full past

Obtaining estimates from multiply imputed data

Description

Combines gformula estimates obtained from multiple imputed data sets according to the MI Boot and MI Boot pooled methods decribed in Schomaker and Heumann (2018, see reference section below)

Usage

mi.boot(x, fun, cond = NULL, pooled = FALSE, cilevel = 0.95, ...)

Arguments

Value

An object of class gformula. See gformula for details.

Author(s)

Michael Schomaker

References

Schomaker, M., Heumann, C. (2018) Bootstrap inference when using multiple imputation, Statistics in Medicine, 37:2252-2266

Examples

data(EFV)

# suppose the following subsets were actually multiply imputed data (M=2)
EFV_1 <- EFV[1:2500,]
EFV_2 <- EFV[2501:5000,]

# first: conduct analysis on each imputed data set. Set ret=T.
m1 <- gformula(X=EFV_1,
               Lnodes  = c("adherence.1","weight.1",
                           "adherence.2","weight.2",
                           "adherence.3","weight.3",
                           "adherence.4","weight.4"
               ),
               Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
               Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
               abar=seq(0,5,1), verbose=FALSE, ret=TRUE
        )

m2 <- gformula(X=EFV_2,
               Lnodes  = c("adherence.1","weight.1",
                           "adherence.2","weight.2",
                           "adherence.3","weight.3",
                           "adherence.4","weight.4"
               ),
               Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
               Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
               abar=seq(0,5,1), verbose=FALSE, ret=TRUE
)

# second combine results
m_imp <- mi.boot(list(m1,m2), mean) # uses MI rules & returns 'gformula' object
plot(m_imp)

# custom estimand: evaluate probability of suppression (Y=0), among females
m_imp2 <- mi.boot(list(m1,m2), prop, categ=0, cond="sex==1")
plot(m_imp2)

Update model formulas based on variable screening

Description

Wrapper function to facilitate variable screening on all models generated through make.model.formulas and return updated formulas in the appropriate format for gformula.

Usage

model.formulas.update(formulas, X, screening = screen.glmnet.cramer,
                      with.s = FALSE, by= NA, ...)

Arguments

Details

The default screening algorithm uses LASSO for variable screening (and Cramer's V for the categorized version of all variables if LASSO fails). It is possible to provide user-specific screening algorithms. User-specific algorithms should take the data as first argument, one model formula (i.e. one entry of the list in model.formulas) as second argument and return a vector of strings, containing the variable names that remain after screening. Another screening algorithm available in the package is screen.cramersv, which categorizes all variables, calculates their association with the outcome based on Cramer's V and selects the 4 variables with strongest associations (can be changed with option nscreen). The manual provides more information.

The fitted models of the updated models can be evaluated with fit.updated.formulas.

Value

A list of length 4 containing the updated model formulas:

See Also

make.model.formulas, model.update, fit.updated.formulas

Examples

data(EFV)

# first: generate generic model formulas
m <- make.model.formulas(X=EFV,
                         Lnodes  = c("adherence.1","weight.1",
                                     "adherence.2","weight.2",
                                     "adherence.3","weight.3",
                                     "adherence.4","weight.4"
                                    ),
                         Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                         Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                         evaluate=FALSE) 
                         
# second: update these model formulas based on variable screening with LASSO
glmnet.formulas <-  model.formulas.update(m$model.names, EFV)
glmnet.formulas 


# third: use these models for estimation
est <- gformula(X=EFV,
                Lnodes  = c("adherence.1","weight.1",
                            "adherence.2","weight.2",
                            "adherence.3","weight.3",
                            "adherence.4","weight.4"
                ),
                Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                Yform=glmnet.formulas$Ynames, Lform=glmnet.formulas$Lnames,
                abar=seq(0,2,1)
)
est

Update GAM models

Description

A wrapper to simplify the update of GAM models

Usage

model.update(gam.object, form)

Arguments

Details

The gam object needs to be fitted with the option control=list(keepData=T), otherwise the function can not access the data that is needed to update the model fit. Note that both fit.updated.formulas and make.model.formulas with option evaluate=T produce results that are based on this option.

Value

An object of class ‘gam’, ‘glm’ and ‘lm’.

Examples

data(EFV)

m <- make.model.formulas(X=EFV,
                         Lnodes  = c("adherence.1","weight.1",
                                     "adherence.2","weight.2",
                                     "adherence.3","weight.3",
                                     "adherence.4","weight.4"
                         ),
                         Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                         Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                         evaluate=TRUE) # set TRUE for model.update()

# update first confounder model of weight manually
model.update(m$fitted.models$fitted.L$m_weight.1, .~s(weight.0, by=sex))

# manual update of model formula
m$model.names$Lnames[2] <- "weight.1 ~ s(weight.0, by=sex)" 

Plot Method for feasible objects

Description

Generate diagnostic plots for objects of class "feasible", returned by feasible. One can display either (i) mean feasible vs. target interventions, or (ii) the non-overlap ratio.

Usage

## S3 method for class 'feasible'
plot(x, x.axis = c("strategy", "time"),
                        which  = c("feasible", "nonoverlap"),
                        facet  = c("none", "time", "strategy"), ...)

Arguments

Details

Both plot types are drawn with ggplot2. To reduce overplotting, lines and points use transparency (alpha) and slightly smaller widths/sizes by default. Faceting by time or strategy can further improve readability when many series are present.

The "summary" attribute of a "feasible" object is expected to contain (at least) the following columns:

• time: discrete time index.

• Strategy: strategy index (row index of the intervention design).

• Abar: target value (intervention level) for that strategy at that time.

• Feasible: mean feasible value under the estimated feasible intervention.

• Low: non-overlap ratio (proportion of mass below the density threshold).

Interpretation of abar:

• In feasible, the abar argument may be either a numeric vector (static grid of targets) or a numeric matrix (dynamic interventions).

• If abar is a vector, each distinct value defines a strategy that is constant over time; in this case each strategy represents the same target value at every time-point.

• If abar is a matrix, rows index intervention strategies and columns index time-points. In the summary, Strategy identifies the row, and Abar is the entry of that row at the corresponding time-point.

Plot types:

1. Feasible vs Target (which = "feasible"):

   • Y-axis: mean feasible intervention (Feasible).

   • X-axis: controlled by x.axis:

     • x.axis = "time": x-axis shows time; colors represent Targets (Abar) when each strategy has the same target at all time-points, or represent strategies when targets vary over time within a strategy.

     • x.axis = "strategy": x-axis shows strategy index; if each strategy corresponds to a single target value at all time-points and this relationship is consistent, the x-axis is relabelled to show Abar (Targets) instead.

   • Reference line and ticks:

   • When the x-axis is on the Target scale (strategies are constant over time with respect to Abar), the plot includes a dashed 1:1 reference line \text{Feasible} = \text{Target} and aligns the x- and y-axis limits to the range of Abar, when plausible (i.e., when the feasible values lie within the range of Abar).

   • When x.axis = "time", short horizontal ticks at each time-point indicate the Abar values for each strategy (or Target when strategies are constant over time), using the same color mapping as the series.

   • When x.axis = "strategy" and strategies do not correspond to a single target over all time-points, ticks are drawn at each strategy to indicate the Abar values across time.

2. Non-overlap Ratio (which = "nonoverlap"):

   • Y-axis: non-overlap ratio Low (bounded between 0 and 1), plotted with fixed limits c(0, 1).

   • X-axis: same choice of x.axis as for the feasible plot.

Terminology: Throughout the plots, “Target” refers to the intervention values passed as the abar argument to feasible (stored as column Abar in the object's summary). When strategies are constant over time with respect to Abar and this structure is consistent across time, each Target corresponds to an identical intervention pattern at all time-points. This is reflected in both the x-axis labelling and the legend.

Value

Invisibly returns the ggplot2 object that is drawn (either the feasible plot or the non-overlap plot).

Author(s)

Han Bao, Michael Schomaker

See Also

feasible, summary.feasible

Examples

data(EFV)


Lnodes <- c("adherence.1","weight.1",
            "adherence.2","weight.2",
            "adherence.3","weight.3",
            "adherence.4","weight.4")
Ynodes <- c("VL.0","VL.1","VL.2","VL.3","VL.4")
Anodes <- c("efv.0","efv.1","efv.2","efv.3","efv.4")

## ------------------------------------------------------------------
## Example 1: Static grid of Targets (vector abar)
## Each strategy uses the same target value at every time-point
## ------------------------------------------------------------------

abar_static <- seq(0, 10, by = 2)

m_static <- feasible(X = EFV,
                     Anodes = Anodes,
                     Lnodes = Lnodes,
                     Ynodes = Ynodes,
                     d.method = "parametric",
                     abar = abar_static,
                     grid.size = NULL,
                     left.boundary = 0,
                     right.boundary = 10)

## Feasible vs Target with time on x-axis (default).
## Colors indicate Targets (Abar), and short ticks show Abar at each time.
plot(m_static, which = "feasible")

## Feasible vs Target with time on x-axis.
plot(m_static, x.axis = "time", which = "feasible")

## Non-overlap ratio 
plot(m_static, which = "nonoverlap")

## Facet by time to reduce overplotting
plot(m_static, which = "feasible", facet = "time")


## ------------------------------------------------------------------
## Example 2: Non-constant intervention strategies (matrix abar)
## Strategies can have different target values at different time-points
## ------------------------------------------------------------------

## Here rows define strategies and columns define time-points.
abar_matrix <- rbind(
  c(0, 2, 4, 6, 8),  # strategy 1
  c(9, 6, 2, 1, 0),  # strategy 2
  c(1, 3, 5, 7, 9)   # strategy 3
)

set.seed(456)
m_matrix <- feasible(X = EFV,
                     Anodes = Anodes,
                     Lnodes = Lnodes,
                     Ynodes = Ynodes,
                     d.method = "parametric",
                     abar = abar_matrix,
                     grid.size = 1,
                     left.boundary = 0,
                     right.boundary = 10)

## Feasible vs Target with time on the x-axis.
## Colors represent strategies; short ticks at each time show
## the corresponding Abar for each strategy.
plot(m_matrix,
     x.axis = "time",
     which  = "feasible",
     facet  = "none")

## Feasible vs Target with strategy on the x-axis.
## Strategies no longer use the same target at all time-points,
## so the x-axis stays on the strategy index, and ticks at each
## strategy indicate the Abar values across time.
plot(m_matrix,
     x.axis = "strategy",
     which  = "feasible",
     facet  = "none")

## Non-overlap ratio for these non-constant strategies,
## shown over time and faceted by strategy for clarity.
plot(m_matrix,
     x.axis = "time",
     which  = "nonoverlap",
     facet  = "strategy")

Plot dose-response curves

Description

Function to plot dose-response curves based on results returned from gformula

Usage

## S3 method for class 'gformula'
plot(x, msm.method = c("line","loess", "gam", "none"), 
                        CI = FALSE, time.points = NULL, 
                        cols = NULL, weight = NULL, xaxis=NULL,
                        variable = "psi", difference = FALSE, ...)

Arguments

Details

Time points and variable names should be specified according to the labeling of the results table returned by gformula.

Value

Draws an object of class ‘ggplot’.

Examples

data(EFV)
est <- gformula(X=EFV,
                Lnodes  = c("adherence.1","weight.1",
                            "adherence.2","weight.2",
                            "adherence.3","weight.3",
                            "adherence.4","weight.4"
                ),
                Ynodes  = c("VL.0","VL.1","VL.2","VL.3","VL.4"),
                Anodes  = c("efv.0","efv.1","efv.2","efv.3","efv.4"),
                abar=seq(0,10,1)
)


plot(est)
plot(est, time.points=c(1,5))

Printing a contrastResult object

Description

Generic S3 function to print the results of a contrastResult object created with contrast.

Usage

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

Arguments

Value

No return value, called for printing the results of an object of class contrastResult.

Print method for feasible objects

Description

Produces a concisey summary of a feasible intervention object. The printout summarizes information jointly over time and strategy, using tables with strategies as rows and time points as columns. Separate tables are printed for the proportion of infeasible mass (%infeasible) and the mean feasible value (Feasible).

Usage

## S3 method for class 'feasible'
print(x, digits = 3, strategies = "all", times = "all", ...)

Arguments

Details

The method extracts the data.frame stored in the "summary" attribute of x and optionally restricts it to the selected strategies and times. All reported values are based on this restricted data.

The summary data typically contains at least the following columns:

• time: time index t.

• Strategy: index of the intervention strategy.

• Abar: target intervention value at time t.

• %infeasible: proportion of mass (on the 0–1 scale) falling below the estimated density threshold for the targeted Abar.

• Feasible: mean of the mapped feasible values (after replacing low-density bins) for the targeted bin.

The output consists of:

• A short header showing how many strategies and time points exist in the underlying object, and how many are being displayed after subsetting via strategies and times.

• Table 1: %infeasible summarized by strategy (rows) and time (columns), printed as percentage.

• Table 2: Feasible (mean feasible value) summarized by strategy (rows) and time (columns), printed on the original scale.

• A compact display of the Abar targets by strategy and time.

Within the selected subset, the method also checks whether each strategy uses the same Abar at every selected time point. If that is the case, the printout notes that each selected strategy corresponds to the same intervention pattern over time. Otherwise, differences in Abar across time are made visible by the Abar-by-time display.

Value

Invisibly returns x.

See Also

feasible, summary.feasible, plot.feasible

Examples

data(EFV)


Lnodes <- c("adherence.1","weight.1",
            "adherence.2","weight.2",
            "adherence.3","weight.3",
            "adherence.4","weight.4")
Ynodes <- c("VL.0","VL.1","VL.2","VL.3","VL.4")
Anodes <- c("efv.0","efv.1","efv.2","efv.3","efv.4")

## ------------------------------------------------------------------
## Example 1: Static grid of targets (vector abar)
## Each strategy uses the same target value at every time point
## ------------------------------------------------------------------

abar_static <- seq(0, 10, by = 2)

set.seed(123)
m_static <- feasible(X = EFV,
                     Anodes = Anodes,
                     Lnodes = Lnodes,
                     Ynodes = Ynodes,
                     d.method = "parametric",
                     abar = abar_static,
                     grid.size = NULL,
                     left.boundary = 0,
                     right.boundary = 10)

## Full time x strategy summary
print(m_static)

## Use fewer digits in the numeric summaries
print(m_static, digits = 2)

## Focus on a subset of strategies (e.g., 1 and 3)
print(m_static, strategies = c(1, 3))

## Focus on early time points only (e.g., times 1, 2)
print(m_static, times = c(1, 2))

## Combine selection: only strategies 1 and 3 over times 1, 2, 3
print(m_static, strategies = c(1, 3), times = 1:3)

## ------------------------------------------------------------------
## Example 2: Non-constant intervention strategies (matrix abar)
## Strategies can have different target values at different time points
## ------------------------------------------------------------------

## Rows define strategies, columns define time points.
## The first row increases over time, the second decreases, the third increases.
abar_matrix <- rbind(
  c(0, 2, 4, 6, 8),  # strategy 1
  c(9, 6, 2, 1, 0),  # strategy 2
  c(1, 3, 5, 7, 9)   # strategy 3
)

set.seed(456)
m_matrix <- feasible(X = EFV,
                     Anodes = Anodes,
                     Lnodes = Lnodes,
                     Ynodes = Ynodes,
                     d.method = "parametric",
                     abar = abar_matrix,
                     grid.size = 1,
                     left.boundary = 0,
                     right.boundary = 10)

## Time x strategy summary where targets vary over time within strategies
print(m_matrix)

## Focus on strategies 1 and 3 over a subset of time points
print(m_matrix, strategies = c(1, 3), times = 1:3)

Printing the results of a gformula object

Description

Generic S3 function to print the results of an object created with gformula.

Usage

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

Arguments

Value

No return value, called for printing the results of an object of class class ‘gformula’.

Helper function to calculate proportions of categorical variables

Description

To be used as fun argument in custom.measure.

Arguments

Value

A scalar numeric value of the proportion of categ values in vec

Summarize a feasible object

Description

Displays the full summary of an object returned by feasible.

Usage

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

Arguments

Details

The method extracts the data frame stored in the "summary" attribute of the feasible object. This data frame contains (at least) the following columns:

• time: Time index t.

• Strategy: Index of the intervention strategy.

• Abar: The target intervention value at time t.

• Feasible: Mean of the mapped feasible values for the targeted bin.

• %infeasible: Proportion of observations falling below the estimated density threshold for the given Abar as targeted.

If the "summary" attribute is NULL, the method prints “No summary available.”

Value

A data frame containing the summary if available; otherwise NULL.

See Also

feasible, plot.feasible

Examples

# see ?feasible