Package 'tvmediation' reference manual

Title:	Time Varying Mediation Analysis
Description:	Provides functions for estimating mediation effects that vary over time as described in Cai X, Coffman DL, Piper ME, Li R. Estimation and inference for the mediation effect in a time-varying mediation model. BMC Med Res Methodol. 2022;22(1):1-12.
Authors:	Donna Coffman [aut, cre] , Xizhen Cai [aut] , Yajnaseni Chakraborti [aut] , Harry Zobel [ctb]
Maintainer:	Donna Coffman <[email protected]>
License:	GPL-3
Version:	1.1.0
Built:	2025-02-04 04:04:25 UTC
Source:	https://github.com/dcoffman/tvmediation

Bootstrap function for computing CIs for coefficients for a continuous outcome and two treatment groups

Description

Part of the set of internal functions for estimating bootstrapped CIs for the coefficients of the mediation model for continuous outcome and two treatment groups.

Usage

bootci_coeff_2trt(trt, t.seq, M, Y, t.est, deltat, replicates)
bootci_coeff_2trt(trt, t.seq, M, Y, t.est, deltat, replicates)

Arguments

`trt`	a vector indicating treatment group
`t.seq`	a vector of time points for each observation
`M`	matrix of mediator values in wide format
`Y`	matrix of outcome values in wide format
`t.est`	time points at which to make the estimation. Default = t.seq
`deltat`	a small constant which controls the time-lag of the effect of the mediator on the outcome.
`replicates`	number of replicates for bootstrapping confidence intervals. Default = 1000

Value

`CI.upper.alpha`	CI upper limit for coefficient hat.alpha
`CI.lower.alpha`	CI lower limit for coefficient hat.alpha
`CI.upper.gamma`	CI upper limit for coefficient hat.gamma
`CI.lower.gamma`	CI lower limit for coefficient hat.gamma
`CI.upper.beta`	CI upper limit for coefficient hat.beta
`CI.lower.beta`	CI lower limit for coefficient hat.beta
`CI.upper.tau`	CI upper limit for coefficient hat.tau
`CI.lower.tau`	CI lower limit for coefficient hat.tau

Bootstrap samples to estimate confidence intervals for coefficients for a continuous outcome and three treatment groups.

Description

Part of the set of internal functions for estimating bootstrapped confidence intervals for the coefficients of the mediation model for a continuous outcome and three treatment groups.

Usage

bootci_coeff_3trt(
  T1,
  T2,
  t.seq,
  mediator,
  outcome,
  t.est,
  original.coeff,
  boot.sample = 1000
)
bootci_coeff_3trt(
  T1,
  T2,
  t.seq,
  mediator,
  outcome,
  t.est,
  original.coeff,
  boot.sample = 1000
)

Arguments

`T1`	a vector indicating assignment to treatment 1
`T2`	a vector indicating assignment to treatment 2
`t.seq`	a vector of time points for each observation
`mediator`	matrix of mediator values in wide format
`outcome`	matrix of outcome values in wide format
`t.est`	time points at which to make the estimation. Default = t.seq
`original.coeff`	a list of the estimated coefficients.
`boot.sample`	number of replicates for bootstrapping confidence intervals. Default = 1000.

Value

`alw1`	CI lower limit for estimated Treatment 1 effect on mediator
`aup1`	CI upper limit for estimated Treatment 1 effect on mediator
`alw2`	CI lower limit for estimated Treatment 2 effect on mediator
`aup2`	CI upper limit for estimated Treatment 2 effect on mediator
`glw1`	CI lower limit for estimated Treatment 1 direct effect on outcome
`gup1`	CI upper limit for estimated Treatment 1 direct effect on outcome
`glw2`	CI lower limit for estimated Treatment 2 direct effect on outcome
`gup2`	CI upper limit for estimated Treatment 2 direct effect on outcome
`tlw1`	CI lower limit for estimated Treatment 1 total effect on outcome
`tup1`	CI upper limit for estimated Treatment 1 total effect on outcome
`tlw2`	CI lower limit for estimated Treatment 2 total effect on outcome
`tup2`	CI upper limit for estimated Treatment 2 total effect on outcome
`blw`	CI lower limit for estimated effect of mediator on outcome
`bup`	CI upper limit for estimated effect of mediator on outcome

Bootstrap samples to estimate confidence intervals for binary outcome coefficients.

Description

Internal function for estimating bootstrapped confidence intervals for the coefficients of the mediation model for a binary outcome.

Usage

bootci_coeff_binary(
  treatment,
  t.seq,
  m,
  outcome,
  span = 0.75,
  replicates = 1000
)
bootci_coeff_binary(
  treatment,
  t.seq,
  m,
  outcome,
  span = 0.75,
  replicates = 1000
)

Arguments

`treatment`	a vector indicating treatment group
`t.seq`	a vector of unique time points for each observation
`m`	matrix of mediator values in wide format
`outcome`	matrix of outcome values in wide format
`span`	Numeric value of the span to be used for LOESS regression. Default = 0.75.
`replicates`	Number of replicates for bootstrapping confidence intervals. Default = 1000.

Value

`t.seq`	time points of estimation
`CI.lower.a`	CI lower limit for alpha_hat
`CI.upper.a`	CI upper limit for alpha_hat
`CI.lower.g`	CI lower limit for gamma_hat
`CI.upper.g`	CI upper limit for gamma_hat
`CI.lower.b`	CI lower limit for beta_hat
`CI.upper.b`	CI upper limit for beta_hat
`CI.lower.t`	CI lower limit for tau_hat
`CI.upper.t`	CI upper limit for tau_hat

Bootstrap samples to estimate confidence intervals for continuous outcome and three treatment groups.

Description

Internal function for estimating bootstrapped confidence intervals for the mediation effect of continuous outcome and three treatment groups when user argument CI="boot".

Usage

bootci_tvm_3trt(boot.sample, orig.data, t.est)
bootci_tvm_3trt(boot.sample, orig.data, t.est)

Arguments

`boot.sample`	number of replicates for bootstrapping confidence intervals. Default = 1000.
`orig.data`	a list of original data `T1`, `T2`, `mediator`, `outcome` and `t.seq`.
`t.est`	time points at which to make the estimation. Default = t.seq.

Value

`plw1`	CI lower limit for estimated mediation effect of T1
`pup1`	CI upper limit for estimated mediation effect of T1
`plw2`	CI lower limit for estimated mediation effect of T2
`pup2`	CI upper limit for estimated mediation effect of T2
`orig.se1.all`	estimated standard errors for the mediation effect of T1
`orig.se2.all`	estimated standard errors for the mediation effect of T2
`orig.mediation1`	time varying mediation effect for T1
`orig.mediation2`	time varying mediation effect for T2

Bootstrap samples to estimate confidence intervals for the mediation effect for a binary outcome.

Description

Part of the set of internal functions for estimating bootstrapped confidence intervals for the mediation effect for a binary outcome when user argument CI="boot".

Usage

bootci_tvmb(
  treatment,
  t.seq,
  m,
  outcome,
  coeff_data,
  span = 0.75,
  replicates = 1000
)
bootci_tvmb(
  treatment,
  t.seq,
  m,
  outcome,
  coeff_data,
  span = 0.75,
  replicates = 1000
)

Arguments

`treatment`	a vector indicating treatment group
`t.seq`	a vector of unique time points for each observation
`m`	matrix of mediator values in wide format
`outcome`	matrix of outcome values in wide format
`coeff_data`	a merged dataset of indirect and direct effects and CIs estimated from `bootci_coeff_binary`
`span`	Numeric value of the span to be used for LOESS regression. Default = 0.75.
`replicates`	number of replicates for bootstrapping CIs. Default = 1000.

Value

`timeseq`	time points of estimation
`alpha_hat`	time-varying treatment effect on the mediator
`CI.lower.a`	CI lower limit for estimated coefficient alpha_hat
`CI.upper.a`	CI upper limit for estimated coefficient alpha_hat
`gamma_hat`	time-varying treatment effect on the outcome (direct effect)
`CI.lower.g`	CI lower limit for estimated coefficient gamma_hat
`CI.upper.g`	CI upper limit for estimated coefficient gamma_hat
`beta_hat`	time-varying effect of the mediator on the outcome
`CI.lower.b`	CI lower limit for estimated coefficient beta_hat
`CI.upper.b`	CI upper limit for estimated coefficient beta_hat
`tau_hat`	time-varying treatment effect on outcome (total effect)
`CI.lower.t`	CI lower limit for estimated coefficient tau_hat
`CI.upper.t`	CI upper limit for estimated coefficient tau_hat
`medEffect`	time varying mediation effect
`CI.lower`	CI lower limit for medEffect
`CI.upper`	CI upper limit for medEffect

Function to estimate coefficients at time t

Description

Part of the set of internal functions called within the tvmcurve_3trt function to assist in the estimation of time varying mediation effect.

Usage

coeff(j, T1, T2, x, y)
coeff(j, T1, T2, x, y)

Arguments

`j`	a number indicating time point of observation
`T1`	a vector indicating assignment to treatment 1
`T2`	a vector indicating assignment to treatment 2
`x`	matrix of mediator values in wide format
`y`	matrix of outcome outcomes in wide format

Value

`coeff.est`	estimated coefficients of the mediation model
`nomissing.index`	index of complete cases

Bootstrapping samples to estimate mediation effects confidence intervals for continuous outcome and two treatment (exposure) groups.

Description

Part of the set of internal functions for estimating bootstrapped confidence intervals for continuous outcome and two treatment groups when user argument CI="boot".

Usage

estBootCIs(trt, t.seq, M, Y, t.est, deltat, replicates)
estBootCIs(trt, t.seq, M, Y, t.est, deltat, replicates)

Arguments

`trt`	a vector indicating treatment group
`t.seq`	a vector of time points at each obs
`M`	matrix of mediator values
`Y`	matrix of outcome values
`t.est`	time points at which to make the estimation
`deltat`	a small constant which controls the time-lag of the effect of the mediator on the outcome, half the time between two time points
`replicates`	number of replicates for bootstrapping confidence intervals.

Value

boot.sebootstrapped standard error for the estimated mediation effect

CI.upperpercentile bootstrapped CI upper limit for the estimated mediation effect

CI.lowerpercentile bootstrapped CI lower limit for the estimated mediation effect

Function to estimate coefficients at time t.

Description

Part of the set of internal functions called within the tvma function to assist in the estimation of the time varying mediation effect.

Usage

estCoeff(newMO.j.est)
estCoeff(newMO.j.est)

Arguments

newMO.j.est

a list containing mean centered mediators and outcomes

Value

coeff.est

estimated coefficients of the mediation model

Function to transpose the data from long to wide format

Description

Transposing a dataset with repeated measurements/responses for each subject from longitudinal to wide format.

Usage

LongToWide(subject.id, time.sequence, outcome, verbose = FALSE)
LongToWide(subject.id, time.sequence, outcome, verbose = FALSE)

Arguments

`subject.id`	a column of subject identifiers
`time.sequence`	a column of time points
`outcome`	a column to be transposed
`verbose`	TRUE or FALSE (default = FALSE) prints output to screen (OPTIONAL INPUT)

Details

If data is not sorted by subject.id, a warning message will appear. The function will then sort the data by subject.id. It is recommended that the user sorts the data prior to using this function.

Value

mat.wide

a matrix in wide format, in which each column is the outcome for each subject and each row is the time sequence

Examples

# CREATING A TRANSPOSED MATRIX FOR MEDIATOR `WantToSmokeLst15min`
data(smoker)
mat.wide <- LongToWide(smoker$SubjectID,
                       smoker$timeseq,
                       smoker$WantToSmokeLst15min)

# CREATING A TRANSPOSED MATRIX FOR MEDIATOR `WantToSmokeLst15min`
data(smoker)
mat.wide <- LongToWide(smoker$SubjectID,
                       smoker$timeseq,
                       smoker$WantToSmokeLst15min)

Function to compute new Mediator and Outcome using time t and t-1 mean centered on the individual.

Description

Part of the set of internal functions called within the tvma function to assist in the estimation of time varying mediation effect.

Usage

newMediatorOutcome(trt, M, Y)
newMediatorOutcome(trt, M, Y)

Arguments

`trt`	numeric binary treatment group indicator for each individual
`M`	(t.seq x N) matrix where N = number of observations. Column 1 is mediator at time t-1. Column 2 is mediator at time t.
`Y`	(Nx1) matrix were N = number of observations. Column 1 is outcome at time t-1.

Value

newMO

list containing new mediators, outcomes, and index of complete cases

Wisconsin Smokers' Health Study 2

Description

The dataset is simulated based on the Wisconsin Smokers' Health Study 2.

Usage

data(smoker)data(smoker)

Format

A data frame with 40,130 observations on 12 variables.

SubjectID: Subject ID
treatment: Treatment group (2 = patch, 3 = varenicline, 4 = combination nicotine replacement therapy)
patch: Received patch (0 = No, 1 = Yes)
varenicline: Received varenicline (0 = No, 1 = Yes)
comboNRT: Received combination nicotine replacement therapy (0 = No, 1 = Yes)
DaysFromTQD: Number of days from quit date
time.of.day: Time of day (0 = am, 1 = pm)
timeseq: Number of days from quit date (.5 indicates pm)
WantToSmokeLst15min: How did you feel in the last 15 min: wanting to smoke (1 = not at all, 7 = extremely)
NegMoodLst15min: How did you feel in the last 15 min: Negative mood (1 = not at all, 7 = extremely)
cessFatig: Cessation fatigue - I am tired of trying to quit smoking (1 = strongly disagree, 7 = strongly agree)
CigCount: Cigarettes smoked over entire day
smoke_status: Did you smoke (0 = No, 1 = Yes)

Examples

data(smoker)
data(smoker)

Function to compute local polynomial estimation using rule of thumb for bandwidth selection

Description

Part of the set of internal functions called within the tvma function to assist in the estimation of the time varying mediation effect.

Usage

smoothest(t.seq, t.coeff, t.est, deltat)
smoothest(t.seq, t.coeff, t.est, deltat)

Arguments

`t.seq`	a vector of time points at each observation
`t.coeff`	estimated coefficients
`t.est`	time points at which to make the estimation
`deltat`	a small constant which controls the time-lag of the effect of the mediator on the outcome, half the time between two time points

Value

`bw_alpha`	a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for alpha coefficient.
`bw_gamma`	a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for gamma coefficient.
`bw_beta`	a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for beta coefficient.
`bw_beta`	a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for tau coefficient.
`hat.alpha`	estimated treatment effect on mediator
`hat.gamma`	estimated treatment effect on outcome, adjusted for mediator
`hat.beta`	estimated mediator effect on outcome
`hat.tau`	estimated treatment effect on outcome, not adjusting for mediator
`est.M`	estimated mediation effect, product of hat.alpha and hat.beta

Time Varying Mediation Function: Continuous Outcome and Two Treatment Groups

Description

Function to estimate the time-varying mediation effect and bootstrap standard errors for two treatment groups and a continuous outcome.

Usage

tvma(
  treatment,
  t.seq,
  mediator,
  outcome,
  t.est = t.seq,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  verbose = FALSE
)
tvma(
  treatment,
  t.seq,
  mediator,
  outcome,
  t.est = t.seq,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  verbose = FALSE
)

Arguments

`treatment`	a vector indicating treatment group
`t.seq`	a vector of time points for each observation
`mediator`	matrix of mediator values in wide format
`outcome`	matrix of outcome values in wide format
`t.est`	a vector of time points at which to estimate. Default = t.seq (OPTIONAL ARGUMENT)
`plot`	TRUE or FALSE for producing plots. Default = "FALSE" (OPTIONAL ARGUMENT)
`CI`	"none" or "boot" method of deriving confidence intervals. Default = "boot" (OPTIONAL ARGUMENT)
`replicates`	number of replicates for bootstrapping confidence intervals. Default = 1000 (OPTIONAL ARGUMENT)
`verbose`	TRUE or FALSE for printing results to screen. Default = "FALSE" (OPTIONAL ARGUMENT)

Value

`hat.alpha`	estimated time-varying treatment effect on mediator
`CI.lower.alpha`	CI lower limit for estimated coefficient hat.alpha
`CI.upper.alpha`	CI upper limit for estimated coefficient hat.alpha
`hat.gamma`	estimated time-varying treatment effect on outcome (direct effect)
`CI.lower.gamma`	CI lower limit for estimated coefficient hat.gamma
`CI.upper.gamma`	CI upper limit for estimated coefficient hat.gamma
`hat.beta`	estimated time-varying effect of the mediator on outcome
`CI.lower.beta`	CI lower limit for estimated coefficient hat.beta
`CI.upper.beta`	CI upper limit for estimated coefficient hat.beta
`hat.tau`	estimated time-varying treatment effect on outcome (total effect)
`CI.lower.tau`	CI lower limit for estimated coefficient hat.tau
`CI.upper.tau`	CI upper limit for estimated coefficient hat.tau
`est.M`	time varying mediation effect
`boot.se.m`	estimated standard error for est.M
`CI.lower`	CI lower limit for est.M
`CI.upper`	CI upper limit for est.M

Plot Returns

Alpha_CI plot for hat.alpha with CIs over t.est
Gamma_CI plot for hat.gamma with CIs over t.est
Beta_CI plot for hat.beta with CIs over t.est
Tau_CI plot for hat.tau with CIs over t.est
MedEff plot for est.M over t.est
MedEff_CI plot for est.M with CIs over t.est

Note

** IMPORTANT ** An alternate way of formatting the data and calling the function is documented in detail in the tutorial for the tvmb() function.

References

Fan, J. and Gijbels, I. Local polynomial modelling and its applications: Monographs on statistics and applied probability 66. CRC Press; 1996.
Fan J, Zhang W. Statistical Estimation in Varying Coefficient Models. The Annals of Statistics. 1999;27(5):1491-1518.
Fan J, Zhang JT. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(2):303-322.
Cai X, Coffman DL, Piper ME, Li R. Estimation and inference for the mediation effect in a time-varying mediation model. BMC Med Res Methodol. 2022;22(1):1-12.
Baker TB, Piper ME, Stein JH, et al. Effects of Nicotine Patch vs Varenicline vs Combination Nicotine Replacement Therapy on Smoking Cessation at 26 Weeks: A Randomized Clinical Trial. JAMA. 2016;315(4):371.
B. Efron, R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science. 1986;1(1):54-75.

Examples

## Not run: data(smoker)

# REDUCE DATA SET TO ONLY 2 TREATMENT CONDITIONS (EXCLUDING COMBINATION NRT)
smoker.sub <- smoker[smoker$treatment != 4, ]

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker.sub$SubjectID,
                       smoker.sub$timeseq,
                       smoker.sub$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker.sub$SubjectID,
                      smoker.sub$timeseq,
                      smoker.sub$cessFatig)

# GENERATE A BINARY TREATMENT VARIABLE
trt <- as.numeric(unique(smoker.sub[,c("SubjectID","varenicline")])[,2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker.sub$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvma(trt, t.seq, mediator, outcome)

# COMPUTE TIME VARYING MEDIATION ANALYSIS FOR SPECIFIED POINTS IN TIME USING 250 REPLICATES
results <- tvma(trt, t.seq, mediator, outcome,
                t.est = c(0.2, 0.4, 0.6, 0.8),
                replicates = 250)
## End(Not run)
## Not run: data(smoker)

# REDUCE DATA SET TO ONLY 2 TREATMENT CONDITIONS (EXCLUDING COMBINATION NRT)
smoker.sub <- smoker[smoker$treatment != 4, ]

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker.sub$SubjectID,
                       smoker.sub$timeseq,
                       smoker.sub$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker.sub$SubjectID,
                      smoker.sub$timeseq,
                      smoker.sub$cessFatig)

# GENERATE A BINARY TREATMENT VARIABLE
trt <- as.numeric(unique(smoker.sub[,c("SubjectID","varenicline")])[,2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker.sub$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvma(trt, t.seq, mediator, outcome)

# COMPUTE TIME VARYING MEDIATION ANALYSIS FOR SPECIFIED POINTS IN TIME USING 250 REPLICATES
results <- tvma(trt, t.seq, mediator, outcome,
                t.est = c(0.2, 0.4, 0.6, 0.8),
                replicates = 250)
## End(Not run)

Time Varying Mediation Function: Continuous Outcome and Three Treatment Groups

Description

Function to estimate the time-varying mediation effect and bootstrap standard errors for three treatment groups and a continuous outcome.

Usage

tvma_3trt(
  T1,
  T2,
  t.seq,
  mediator,
  outcome,
  t.est = t.seq,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  grpname = "T",
  verbose = FALSE
)
tvma_3trt(
  T1,
  T2,
  t.seq,
  mediator,
  outcome,
  t.est = t.seq,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  grpname = "T",
  verbose = FALSE
)

Arguments

`T1`	a vector indicating assignment to treatment 1
`T2`	a vector indicating assignment to treatment 2
`t.seq`	a vector of time points for each observation
`mediator`	matrix of mediator values in wide format
`outcome`	matrix of outcome values in wide format
`t.est`	a vector of time points at which to make the estimation. Default = t.seq. (OPTIONAL ARGUMENT)
`plot`	TRUE or FALSE for plotting mediation effect. Default = "FALSE". (OPTIONAL ARGUMENT)
`CI`	"none" or "boot" method of deriving confidence intervals. Default = "boot". (OPTIONAL ARGUMENT)
`replicates`	number of replicates for bootstrapping confidence intervals. Default = 1000. (OPTIONAL ARGUMENT)
`grpname`	name of the treatment arms (exposure groups) to be displayed in the results. Default = "T". (OPTIONAL ARGUMENT)
`verbose`	TRUE or FALSE for printing results to screen. Default = "FALSE". (OPTIONAL ARGUMENT)

Value

`hat.alpha1`	estimated Treatment 1 effect on mediator
`CI.lower.alpha1`	CI lower limit for estimated coefficient hat.alpha1
`CI.upper.alpha1`	CI upper limit for estimated coefficient hat.alpha1
`hat.alpha2`	estimated Treatment 2 effect on mediator
`CI.lower.alpha2`	CI lower limit for estimated coefficient hat.alpha2
`CI.upper.alpha2`	CI upper limit for estimated coefficient hat.alpha2
`hat.gamma1`	estimated Treatment 1 direct effect on outcome
`CI.lower.gamma1`	CI lower limit for estimated coefficient hat.gamma1
`CI.upper.gamma1`	CI upper limit for estimated coefficient hat.gamma1
`hat.gamma2`	estimated Treatment 2 direct effect on outcome
`CI.lower.gamma2`	CI lower limit for estimated coefficient hat.gamma2
`CI.upper.gamma2`	CI upper limit for estimated coefficient hat.gamma2
`hat.tau1`	estimated Treatment 1 total effect on outcome
`CI.lower.tau1`	CI lower limit for estimated coefficient hat.tau1
`CI.upper.tau1`	CI upper limit for estimated coefficient hat.tau1
`hat.tau2`	estimated Treatment 2 total effect on outcome
`CI.lower.tau2`	CI lower limit for estimated coefficient hat.tau2
`CI.upper.tau2`	CI upper limit for estimated coefficient hat.tau2
`hat.beta`	estimated mediator effect on outcome
`CI.lower.beta`	CI lower limit for estimated coefficient hat.beta
`CI.upper.beta`	CI upper limit for estimated coefficient hat.beta
`hat.mediation1`	time varying mediation effect for Treatment 1 on outcome
`SE_MedEff1`	estimated standard errors of hat.mediation1
`CI.upper.T1`	CI upper limit for hat.mediation1
`CI.lower.T1`	CI lower limit for hat.mediation1
`hat.mediation2`	time varying mediation effect for Treatment 2 on outcome
`SE_MedEff2`	estimated standard errors of hat.mediation2
`CI.upper.T2`	CI upper limit for hat.mediation2
`CI.lower.T2`	CI lower limit for hat.mediation2

Plot Returns

plot1_a1 plot for hat.alpha1 with CIs over t.est
plot2_a2 plot for hat.alpha2 with CIs over t.est
plot3_g1 plot for hat.gamma1 with CIs over t.est
plot4_g2 plot for hat.gamma2 with CIs over t.est
plot5_t1 plot for hat.tau1 with CIs over t.est
plot6_t2 plot for hat.tau2 with CIs over t.est
plot7_b plot for hat.beta with CIs over t.est
MedEff_T1 plot for hat.mediation1 over t.est
MedEff_T2 plot for hat.mediation2 over t.est
MedEff_CI_T1 plot for hat.mediation1 with CIs over t.est
MedEff_CI_T2 plot for hat.mediation2 with CIs over t.est

References

Fan, J. and Gijbels, I. Local polynomial modelling and its applications: Monographs on statistics and applied probability 66. CRC Press; 1996.
Fan J, Zhang W. Statistical Estimation in Varying Coefficient Models. The Annals of Statistics. 1999;27(5):1491-1518.
Fan J, Zhang JT. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(2):303-322.
Cai X, Coffman DL, Piper ME, Li R. Estimation and inference for the mediation effect in a time-varying mediation model. BMC Med Res Methodol. 2022;22(1):1-12.
Baker TB, Piper ME, Stein JH, et al. Effects of Nicotine Patch vs Varenicline vs Combination Nicotine Replacement Therapy on Smoking Cessation at 26 Weeks: A Randomized Clinical Trial. JAMA. 2016;315(4):371.
B. Efron, R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science. 1986;1(1):54-75.

Examples

## Not run: data(smoker)

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker$SubjectID,
                        smoker$timeseq, 
                        smoker$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker$SubjectID,
                      smoker$timeseq,
                      smoker$cessFatig)

# GENERATE TWO BINARY TREATMENT VARIABLES
NRT1 <- as.numeric(unique(smoker[,c("SubjectID","varenicline")])[,2])-1
NRT2 <- as.numeric(unique(smoker[,c("SubjectID","comboNRT")])[,2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome)

# COMPUTE TIME VARYING MEDIATION ANALYSIS FOR SPECIFIED POINTS IN TIME USING 250 REPLICATES
results <- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome,
                     t.est = c(0.2, 0.4, 0.6, 0.8),
                     replicates = 250)
## End(Not run)

## Not run: data(smoker)

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker$SubjectID,
                        smoker$timeseq, 
                        smoker$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker$SubjectID,
                      smoker$timeseq,
                      smoker$cessFatig)

# GENERATE TWO BINARY TREATMENT VARIABLES
NRT1 <- as.numeric(unique(smoker[,c("SubjectID","varenicline")])[,2])-1
NRT2 <- as.numeric(unique(smoker[,c("SubjectID","comboNRT")])[,2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome)

# COMPUTE TIME VARYING MEDIATION ANALYSIS FOR SPECIFIED POINTS IN TIME USING 250 REPLICATES
results <- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome,
                     t.est = c(0.2, 0.4, 0.6, 0.8),
                     replicates = 250)
## End(Not run)

Time Varying Mediation Function: Binary Outcome and Two Treatment Groups

Description

Function to estimate the time-varying mediation effect and bootstrap standard errors, involving two treatment groups and binary outcome.

Usage

tvmb(
  treatment,
  t.seq,
  mediator,
  outcome,
  span = 0.75,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  verbose = FALSE
)
tvmb(
  treatment,
  t.seq,
  mediator,
  outcome,
  span = 0.75,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  verbose = FALSE
)

Arguments

`treatment`	a vector indicating treatment group
`t.seq`	a vector of unique time points for each observation
`mediator`	matrix of mediator values in wide format
`outcome`	matrix of outcome values in wide format
`span`	Numeric value of the span to be used for LOESS regression. Default = 0.75.
`plot`	TRUE or FALSE for producing plots. Default = "FALSE". (OPTIONAL ARGUMENT)
`CI`	"none" or "boot" method of deriving confidence intervals. Default = "boot". (OPTIONAL ARGUMENT)
`replicates`	Number of replicates for bootstrapping confidence intervals. Default = 1000. (OPTIONAL ARGUMENT)
`verbose`	TRUE or FALSE for printing results to screen. Default = "FALSE". (OPTIONAL ARGUMENT)

Value

`timeseq`	time points of estimation
`alpha_hat`	estimated treatment effect on mediator
`CI.lower.a`	CI lower limit for estimated coefficient alpha_hat
`CI.upper.a`	CI upper limit for estimated coefficient alpha_hat
`gamma_hat`	estimated treatment effect on outcome (direct effect)
`CI.lower.g`	CI lower limit for estimated coefficient gamma_hat
`CI.upper.g`	CI upper limit for estimated coefficient gamma_hat
`beta_hat`	estimated mediator effect on outcome
`CI.lower.b`	CI lower limit for estimated coefficient beta_hat
`CI.upper.b`	CI upper limit for estimated coefficient beta_hat
`tau_hat`	estimated treatment effect on outcome (total effect)
`CI.lower.t`	CI lower limit for estimated coefficient tau_hat
`CI.upper.t`	CI upper limit for estimated coefficient tau_hat
`medEffect`	time varying mediation effect
`CI.lower`	CI lower limit for medEffect
`CI.upper`	CI upper limit for medEffect

Plot Returns

plot1_a plot for alpha_hat with CIs over t.seq
plot2_g plot for gamma_hat with CIs over t.seq
plot3_b plot for beta_hat with CIs over t.seq
plot4_t plot for tau_hat with CIs over t.seq
MedEff plot for medEffect over t.seq
MedEff_CI plot for medEffect with CIs over t.seq
bootstrap plot for estimated medEffect from bootstrapped samples over t.seq

Note

Currently supports 2 treatment groups
** IMPORTANT ** An alternate way of formatting the data and calling the function is documented in detail in the tutorial for the tvmb() function.

References

Fan, J. and Gijbels, I. Local polynomial modelling and its applications: Monographs on statistics and applied probability 66. CRC Press; 1996.
Fan J, Zhang W. Statistical Estimation in Varying Coefficient Models. The Annals of Statistics. 1999;27(5):1491-1518.
Fan J, Zhang JT. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(2):303-322.
Baker TB, Piper ME, Stein JH, et al. Effects of Nicotine Patch vs Varenicline vs Combination Nicotine Replacement Therapy on Smoking Cessation at 26 Weeks: A Randomized Clinical Trial. JAMA. 2016;315(4):371.
B. Efron, R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science. 1986;1(1):54-75.

Examples

## Not run: data(smoker)

# REDUCE DATA SET TO ONLY 2 TREATMENT CONDITIONS (EXCLUDE COMBINATION NRT)
smoker.sub <- smoker[smoker$treatment != 4, ]

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker.sub$SubjectID,
                       smoker.sub$timeseq,
                       smoker.sub$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker.sub$SubjectID,
                      smoker.sub$timeseq,
                      smoker.sub$smoke_status)

# GENERATE A BINARY TREATMENT VARIABLE
trt <- as.numeric(unique(smoker.sub[, c("SubjectID","varenicline")])[, 2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker.sub$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvmb(trt, t.seq, mediator, outcome)
## End(Not run)

## Not run: data(smoker)

# REDUCE DATA SET TO ONLY 2 TREATMENT CONDITIONS (EXCLUDE COMBINATION NRT)
smoker.sub <- smoker[smoker$treatment != 4, ]

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker.sub$SubjectID,
                       smoker.sub$timeseq,
                       smoker.sub$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker.sub$SubjectID,
                      smoker.sub$timeseq,
                      smoker.sub$smoke_status)

# GENERATE A BINARY TREATMENT VARIABLE
trt <- as.numeric(unique(smoker.sub[, c("SubjectID","varenicline")])[, 2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker.sub$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvmb(trt, t.seq, mediator, outcome)
## End(Not run)

Main function for time varying mediation function for continuous outcome and three treatment arms (i.e., exposure groups).

Description

Part of the set of internal functions to estimate the time-varying mediation effect and bootstrap standard errors for three treatment groups and continuous outcome.

Usage

tvmcurve_3trt(T1, T2, t.seq, x, y, t.est)
tvmcurve_3trt(T1, T2, t.seq, x, y, t.est)

Arguments

`T1`	a vector indicating assignment to treatment 1
`T2`	a vector indicating assignment to treatment 2
`t.seq`	a vector of time points for each observation
`x`	matrix of mediator values in wide format
`y`	matrix of outcome values in wide format
`t.est`	time points at which to make the estimation. Default = t.seq

Value

`hat.alpha1`	estimated Treatment 1 effect on mediator
`hat.alpha2`	estimated Treatment 2 effect on mediator
`hat.gamma1`	estimated Treatment 1 direct effect on outcome
`hat.gamma2`	estimated Treatment 2 direct effect on outcome
`hat.tau1`	estimated Treatment 1 total effect on outcome
`hat.tau2`	estimated Treatment 2 total effect on outcome
`hat.beta`	estimated mediator effect on outcome
`hat.mediation1`	time varying mediation effect for Treatment 1 on outcome
`hat.mediation2`	time varying mediation effect for Treatment 2 on outcome

Package 'tvmediation'

Help Index

Bootstrap function for computing CIs for coefficients for a continuous outcome and two treatment groups

Description

Usage

Arguments

Value

Bootstrap samples to estimate confidence intervals for coefficients for a continuous outcome and three treatment groups.

Description

Usage

Arguments

Value

Bootstrap samples to estimate confidence intervals for binary outcome coefficients.

Description

Usage

Arguments

Value

Bootstrap samples to estimate confidence intervals for continuous outcome and three treatment groups.

Description

Usage

Arguments

Value

Bootstrap samples to estimate confidence intervals for the mediation effect for a binary outcome.

Description

Usage

Arguments

Value

Function to estimate coefficients at time t

Description

Usage

Arguments

Value

Bootstrapping samples to estimate mediation effects confidence intervals for continuous outcome and two treatment (exposure) groups.

Description

Usage

Arguments

Value

Function to estimate coefficients at time t.

Description

Usage

Arguments

Value

Function to transpose the data from long to wide format

Description

Usage

Arguments

Details

Value

Examples

Function to compute new Mediator and Outcome using time t and t-1 mean centered on the individual.

Description

Usage

Arguments

Value

Wisconsin Smokers' Health Study 2

Description

Usage

Format

See Also

Examples

Function to compute local polynomial estimation using rule of thumb for bandwidth selection

Description

Usage

Arguments

Value

Time Varying Mediation Function: Continuous Outcome and Two Treatment Groups

Description

Usage

Arguments

Value

Plot Returns

Note

References

Examples

Time Varying Mediation Function: Continuous Outcome and Three Treatment Groups

Description

Usage

Arguments

Value

Plot Returns