The purpose of this vignette is to provide users with a step-by-step guide for performing and interpreting the results of a time varying mediation analysis with three treatment (exposure) groups and a continuous outcome. Please note, that this package has been built considering the structure of panel data, where each subject/participant has repeated responses (collected over time) for the outcome and mediator variables. We do not address dynamic treatment regimens in this package. Therefore, we assume the scenario where the treatment (exposure) is time-invariant (i.e., does not change over time). For more details, refer to Cai et al., 2020 (the paper can be obtained at https://arxiv.org/abs/2008.11797).
For illustration, we rely on an example dataset, simulated based on the Wisconsin Smokers’ Health Study 2 data (Baker et. al., 2016) which includes 1086 individuals assigned to one of three treatment conditions. One-third of participants received only a nicotine patch
; another one-third received varenicline
, and the final third of participants received a combination nicotine replacement therapy (NRT)
which included nicotine patch + nicotine mini-lozenge. The outcome of interest is cessation fatigue
; that is, how tired a participant felt of trying to quit smoking (7-point Likert scale). In addition, mediator variables were measured by asking participants if they felt a negative mood in the last fifteen minutes
, and whether they wanted to smoke in the last 15 minutes
, also recorded on a 7-point Likert scale. Both the outcome and mediator variables were assessed two times per day for the first two weeks post-quit day (rendering 30 time points of response since assessments start on day 0 post target quit day), and every other day (2x per day) for weeks 3 and 4 (rendering 14 time points of response).
A traditional approach to analyzing this type of data would be to use mediation analysis in which the effects are assumed to not vary as a function of time. First, a single (i.e., time-invariant) direct effect would be calculated by regressing the outcome on the treatment condition and mediator. Next, a time-invariant indirect effect would be computed by multiplying the effect of treatment condition on the mediator by the effect of the mediator on the outcome. However, this method potentially misses important information about the dynamic effect that a mediator may have over time. Specifically, we hypothesize that mood changes across and within days and thus, its mediating effect on one’s success of quitting smoking is likely to vary over time. We therefore propose a time varying mediation analysis which estimates the mediation effect as a function that varies over time.
To use the time varying mediation analysis package in R, you must first install the package and load it. Before that, make sure you have R version 4.0.3
or greater. There are two ways to install the package from the CRAN (Comprehensive R Archive Network) repository, by using install.packages
or the devtools
function.
install.packages("tvmediation", dependencies = TRUE)
library(tvmediation)
The equivalent code using devtools
is:
::install_cran("tvmediation", dependencies = TRUE)
devtoolslibrary(tvmediation)
If you do not have devtools
installed and loaded, you can do so using the following code:
install.packages("devtools", dependencies = TRUE)
library(devtools)
Alternatively, if you want to install the package directly from the GitHub repository to access new or revised functions in development, use the following code:
::install_github("dcoffman/tvmediation", dependencies = TRUE)
devtoolslibrary(tvmediation)
tvma_3trt
functionOnce installed, you can type ?tvmediation
in the console to view the package documentation, as well as links to the important functions and data included in the package. The time-varying mediation analysis for continuous outcomes and three exposure groups, relies on two user functions tvma_3trt
and LongToWide
as well as a number of internal functions of the tvmediation
package.
The tvma_3trt
function has five required and six optional arguments.
T1
A vector indicating assignment to treatment 1T2
A vector indicating assignment to treatment 2t.seq
The numeric vector of the time sequence of the measuresmediator
The matrix of mediator values in wide formatoutcome
The matrix of outcome values in wide formatThe optional arguments are:
t.est
The time sequence for estimation. This is by default equal to t.seq
.plot
TRUE or FALSE for plotting the mediation effect. The default value is “FALSE”.CI
“none” or “boot” method of deriving confidence intervals (CIs). The default value is “boot”.replicates
Number of replicates for bootstrapping CIs. The default value is 1000.grpname
Name of the treatment (exposure) groups to be displayed in the results. The default value is “T”.verbose
TRUE or FALSE for printing results to screen. The default value is “FALSE”.The dataset we will use for our illustration is named smoker
and is included in the package.
To load the simulated dataset smoker.rda
, type:
data(smoker)
The smoker
data frame is organized in long format with SubjectID
repeating over multiple rows for each participant. The tvma_3trt
function requires that the data be in wide format to estimate the time varying coefficients. The tvmediation
package includes a useful function LongToWide
to help users properly format their data for analysis.
LongToWide
has three required arguments and a fourth optional argument.
subject.id
specifies the column of subject identifiers.time.sequences
specifies the column of measurement times.outcome
specifies the column for the variable (either the outcome or the mediator) that will be transposed.verbose
is an optional argument that if “TRUE” prints the output of LongToWide
to the console. The default value is “FALSE”.The output of LongToWide
is a matrix of data in wide format where columns represent the subjects and rows represent the time sequence. Thus, each cell contains the j-th subject’s response at the i-th time point.
The tvma_3trt
function requires two matrices, one for the mediator, and one for the outcome. Thus, we use the LongToWide
function twice as illustrated below:
<- LongToWide(smoker$SubjectID, smoker$timeseq,
mediator $NegMoodLst15min)
smoker<- LongToWide(smoker$SubjectID, smoker$timeseq, smoker$cessFatig) outcome
class(mediator)
## [1] "matrix" "array"
1:16, 1:10] mediator[
## 1 2 3 4 5 6 7 8 9 10
## 0 7 1 1 1 1 NA 4 1 1 3
## 0.5 2 1 1 6 1 NA NA 1 1 1
## 1 1 1 2 NA NA 1 3 1 1 1
## 1.5 1 1 1 1 1 1 2 1 NA 1
## 2 1 1 1 1 NA 1 1 1 1 1
## 2.5 3 1 1 1 1 3 1 1 1 1
## 3 1 6 NA 1 1 1 1 2 NA 1
## 3.5 1 1 2 6 3 7 1 6 1 1
## 4 1 1 1 1 1 1 1 1 2 4
## 4.5 1 1 1 5 1 5 2 NA 1 3
## 5 4 1 2 1 NA 5 2 1 1 1
## 5.5 1 1 2 1 1 2 NA 1 1 2
## 6 2 1 1 4 1 7 1 NA 2 3
## 6.5 1 1 1 1 1 1 1 5 3 1
## 7 1 2 1 NA 1 1 NA 1 1 4
## 7.5 2 2 1 1 1 NA 1 1 1 6
class(outcome)
## [1] "matrix" "array"
1:16, 1:10] outcome[
## 1 2 3 4 5 6 7 8 9 10
## 0 1 6 1 2 1 NA 1 6 7 3
## 0.5 1 3 1 1 1 NA NA 1 7 1
## 1 1 1 1 NA NA 1 1 7 7 1
## 1.5 6 7 6 1 1 6 6 4 NA 7
## 2 7 7 1 1 NA 1 7 1 1 1
## 2.5 1 2 1 7 1 6 1 2 1 7
## 3 4 1 NA 1 7 2 1 4 NA 5
## 3.5 5 3 7 7 6 1 1 7 5 1
## 4 6 3 5 4 7 2 7 5 7 5
## 4.5 7 7 1 7 7 1 7 NA 4 1
## 5 7 7 1 1 NA 1 1 7 1 1
## 5.5 6 5 1 1 1 3 NA 5 7 1
## 6 1 1 1 7 5 1 7 NA 2 1
## 6.5 5 7 5 7 7 1 1 1 7 7
## 7 1 1 1 NA 7 1 NA 1 7 7
## 7.5 5 1 2 1 1 NA 1 1 1 7
If your data are already in wide format, there is no need to use the LongToWide
function and you can simply subset your dataset. However, mediator
and outcome
must be of class matrix
; hence make sure you convert the class of the subsetted mediator
and outcome
objects to matrix
before proceeding. This can be done using the R function as.matrix
.
The tvma_3trt
function requires three more variables that we have not yet created:
T1
A binary numeric vector with treatment1 scheduleT2
A binary numeric vector with treatment2 schedulet.seq
A numeric vector of the time sequence of the measuresWhen there are three treatment groups, we can create two dummy variables NRT1
and NRT2
corresponding to the treatment (exposure) groups other than the placebo or, in this case, the nicotine patch
only standard of care. NRT1 = 1
indicates that the participant has been given varenicline
and NRT1 = 0
for no varenicline
. Similarly, NRT2 = 1
indicates that the participant received combination NRT
and NRT2 = 0
indicates that the participant did not receive the combination treatment (comboNRT)
. Naturally, NRT1 = 1
and NRT2 = 1
are mutually exclusive; that is, a participant cannot have NRT1 = 1
and NRT2 = 1
simultaneously. If NRT1 = 1
then for that participant NRT2
must be equal to 0
. However, NRT1 = 0
and NRT2 = 0
are not mutually exclusive. When NRT1 = 0
and NRT2 = 0
then the participant has received the placebo or the standard of care, in this case nicotine patch
only. Thus if there are three treatment groups, two dummy variables need to be created indicating NRT1
or treatment1
and NRT2
or treatment2
. In the smoker.rda
dataset, three columns indicating the assignment of the three treatments are present, such that we can use any two of the columns and the omitted column becomes the reference group.
We create two dummy variables to indicate whether a participant was given varenicline
or combination NRT
. Because treatment
is time-invariant, we need only one instance of each subject’s response for the treatment group (e.g. varenicline
or combination NRT
). We then convert it to a numeric value and subtract 1 to yield a vector of zeros and ones, as shown below.
# Step 1: Since each subject has multiple rows of data, extract the unique response of each subject to receiving varenicline. The data is still in dataframe format.
<- unique(smoker[ , c("SubjectID","varenicline")])
trtv 1:10,] trtv[
## SubjectID varenicline
## 1 1 No
## 2 2 Yes
## 3 3 Yes
## 4 4 No
## 5 5 Yes
## 6 6 Yes
## 7 7 Yes
## 8 8 Yes
## 9 9 Yes
## 10 10 Yes
# Step 2: `2` to those subjects who received varenicline and `1` to the rest. The data is now in vector format.
<- as.numeric(trtv[ , 2])
trtv2 1:10] trtv2[
## [1] 2 1 1 2 1 1 1 1 1 1
# Step 3: subtract 1 from these numeric responses and procure a vector of zeros and ones
<- trtv2 -1
NRT1 1:10] NRT1[
## [1] 1 0 0 1 0 0 0 0 0 0
# Step 1: Since each subject has multiple rows of data, extract the unique response of each subject to receiving comboNRT. The data is still in dataframe format.
<- unique(smoker[ , c("SubjectID","comboNRT")])
trtc 1:10,] trtc[
## SubjectID comboNRT
## 1 1 Yes
## 2 2 No
## 3 3 Yes
## 4 4 Yes
## 5 5 No
## 6 6 Yes
## 7 7 Yes
## 8 8 Yes
## 9 9 Yes
## 10 10 Yes
# Step 2: `2` to those subjects who received comboNRT and `1` to the rest. The data is now in vector format.
<- as.numeric(trtc[ , 2])
trtc2 1:10] trtc2[
## [1] 1 2 1 1 2 1 1 1 1 1
# Step 3: subtract 1 from these numeric responses and procure a vector of zeros and ones
<- trtc2 -1
NRT2 1:10] NRT2[
## [1] 0 1 0 0 1 0 0 0 0 0
This steps can be alternatively collated into a single step and written as follows:
<- as.numeric(unique(smoker[ ,c("SubjectID","varenicline")])[,2])-1
NRT1 <- as.numeric(unique(smoker[ ,c("SubjectID","comboNRT")])[,2])-1
NRT2 1:10] NRT1[
## [1] 1 0 0 1 0 0 0 0 0 0
1:10] NRT2[
## [1] 0 1 0 0 1 0 0 0 0 0
To generate t.seq
we found the unique instance of each time point and then sorted from smallest to largest. There are 44 unique time points in the dataset where 0
after the decimal indicates the morning measurement and 5
after the decimal indicates the evening measurement recorded for that day.
<- sort(unique(smoker$timeseq))
t.seq t.seq
## [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
## [16] 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5
## [31] 16.0 16.5 18.0 18.5 20.0 20.5 22.0 22.5 24.0 24.5 26.0 26.5 28.0 28.5
We are now ready to perform the time varying mediation analysis.
tvma_3trt
functionAs discussed earlier, the tvma_3trt
function has five required and six optional arguments.
T1
A vector indicating assignment to treatment 1T2
A vector indicating assignment to treatment 2t.seq
The numeric vector of the time sequence of the measuresmediator
The matrix of mediator values in wide formatoutcome
The matrix of outcome values in wide formatThe optional arguments are:
t.est
The time sequence for estimation. This is by default equal to t.seq
.plot
TRUE or FALSE for plotting the mediation effect. The default value is “FALSE”.CI
“none” or “boot” method of deriving CIs. The default value is “boot”.replicates
Number of replicates for bootstrapping CIs. The default value is 1000.grpname
Name of the treatment (exposure) groups to be displayed in the results. The default value is “T”.verbose
TRUE or FALSE for printing results to screen. The default value is “FALSE”.The argument grpname
is important if the user wants the results from the bootstrapped CIs for the mediation effects to be displayed with a particular name in the Estimates
dataframe and plots. For example, if the user defines grpname = "exposure"
, instead of the default value T
, the effect of this choice will be reflected in the column names; CI.upper.T1
will be CI.upper.exposure1
and so forth. The plot titles will also change accordingly. For our illustration we use NRT
since the example is drawn from a Nicotine Replacement Therapy study.
We will call the function with additional optional arguments plot=TRUE
and replicates = 250
. We decreased the number of bootstrap replicates so that this vignette compiles faster but we suggest using at least 500 replicates in an actual analysis. The remaining optional arguments are left to their respective default values.
<- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome, plot = TRUE,
results_tvma_3trt replicates = 250, grpname = "NRT")
The tvma_3trt
function returns a list of results that include:
hat.alpha1
estimated time-varying effect of treatment 1 on the mediatorCI.lower.alpha1
CI lower limit for hat.alpha1
CI.upper.alpha1
CI upper limit for hat.alpha1
hat.alpha2
estimated time-varying effect of treatment 2 on the mediatorCI.lower.alpha2
CI lower limit for hat.alpha2
CI.upper.alpha2
CI upper limit for hat.alpha2
hat.gamma1
estimated time-varying direct effect of treatment 1 on the outcomeCI.lower.gamma1
CI lower limit for hat.gamma1
CI.upper.gamma1
CI upper limit for hat.gamma1
hat.gamma2
estimated time-varying direct effect of treatment 2 on the outcomeCI.lower.gamma2
CI lower limit for hat.gamma2
CI.upper.gamma2
CI upper limit for hat.gamma2
hat.tau1
estimated time-varying total effect of treatment 1 on the outcomeCI.lower.tau1
CI lower limit for hat.tau1
CI.upper.tau1
CI upper limit for hat.tau1
hat.tau2
estimated time-varying total effect of treatment 2 on the outcomeCI.lower.tau2
CI lower limit for hat.tau2
CI.upper.tau2
CI upper limit for hat.tau2
hat.beta
estimated time-varying effect of the mediator on the outcomeCI.lower.beta
CI lower limit for hat.beta
CI.upper.beta
CI upper limit for hat.beta
hat.mediation1
time varying mediation effect of treatment 1 on the outcomehat.mediation2
time varying mediation effect of treatment 2 on the outcomeOptional returns based on argument CI = "boot"
include:
CI.lower.T1
CI lower limit for the time varying mediation effect of treatment 1CI.upper.T1
CI upper limit for the time varying mediation effect of treatment 1CI.lower.T2
CI lower limit for the time varying mediation effect of treatment 2CI.upper.T2
CI upper limit for the time varying mediation effect of treatment 2SE_MedEff1
estimated standard error of the time varying mediation effect for treatment 1SE_MedEff2
estimated standard error of the time varying mediation effect for treatment 2The above estimates are compiled in a single dataframe which can be accessed using nameOfStoredResultsObj$Estimates
. The following line of code displays only the estimates at the first 6 time-points.
head(results_tvma_3trt$Estimates)
## timeseq hat.alpha1 CI.lower.alpha1 CI.upper.alpha1 hat.alpha2 CI.lower.alpha2
## 1 0.0 -0.7157486 -0.4737295 -1.1250982 -0.8871672 -0.3263855
## 2 0.5 -0.7000508 -0.4793805 -0.9592556 -0.7883056 -0.3891667
## 3 1.0 -0.6924259 -0.5339295 -0.8747141 -0.7115165 -0.4572214
## 4 1.5 -0.6913309 -0.5706236 -0.8181397 -0.6621873 -0.5053024
## 5 2.0 -0.6949645 -0.5864469 -0.7899621 -0.6423338 -0.5178458
## 6 2.5 -0.7014576 -0.6204193 -0.7776869 -0.6489869 -0.5475813
## CI.upper.alpha2 hat.gamma1 CI.lower.gamma1 CI.upper.gamma1 hat.gamma2
## 1 -1.2391513 0.5192259 0.8417433 0.02158184 0.6184312
## 2 -1.0387556 0.5979069 0.8577297 0.25797668 0.6632065
## 3 -0.8786651 0.6577964 0.8452876 0.43418577 0.6978976
## 4 -0.7912214 0.6981700 0.8496592 0.54920643 0.7219649
## 5 -0.7522936 0.7199237 0.8482852 0.59725258 0.7358780
## 6 -0.7417643 0.7253630 0.8444562 0.61209312 0.7408749
## CI.lower.gamma2 CI.upper.gamma2 hat.tau1 CI.lower.tau1 CI.upper.tau1
## 1 0.8835678 0.2723078 -0.271779695 0.07342616 -1.2035293
## 2 0.8555217 0.4031040 -0.174314576 0.09232692 -0.9369578
## 3 0.8569076 0.5000175 -0.097974873 0.12396106 -0.6221263
## 4 0.8718653 0.5799488 -0.042454107 0.17282037 -0.3785643
## 5 0.8557381 0.6132280 -0.006592278 0.17755868 -0.2111034
## 6 0.8513722 0.6315880 0.011546099 0.17519121 -0.1271759
## hat.tau2 CI.lower.tau2 CI.upper.tau2 hat.beta CI.lower.beta
## 1 -0.379043226 0.2352917 -0.8929108 0.1854940 0.2763794
## 2 -0.258942738 0.1434451 -0.6782298 0.1919473 0.2576013
## 3 -0.149034271 0.1220041 -0.4756705 0.1949410 0.2500705
## 4 -0.057886622 0.1544505 -0.2943409 0.1965561 0.2461197
## 5 0.008665267 0.1886272 -0.1673289 0.1983277 0.2442402
## 6 0.048551637 0.2303431 -0.1051564 0.2012113 0.2466614
## CI.upper.beta hat.mediation1 SE_MedEff1 CI.lower.NRT1 CI.upper.NRT1
## 1 0.08180988 -0.1327670 0.04486634 -0.2253446 -0.05091982
## 2 0.12391649 -0.1343729 0.03023095 -0.1970266 -0.08124524
## 3 0.14569337 -0.1349822 0.02156411 -0.1786543 -0.09905334
## 4 0.15695781 -0.1358853 0.01704610 -0.1677488 -0.10611347
## 5 0.16345260 -0.1378307 0.01496486 -0.1653311 -0.10765707
## 6 0.16958086 -0.1411412 0.01416942 -0.1672116 -0.10959277
## hat.mediation2 SE_MedEff2 CI.lower.NRT2 CI.upper.NRT2
## 1 -0.1645642 0.05248490 -0.2553042 -0.06603817
## 2 -0.1513131 0.03489355 -0.2131060 -0.08326861
## 3 -0.1387037 0.02403887 -0.1879364 -0.09289220
## 4 -0.1301569 0.01835298 -0.1667433 -0.09594698
## 5 -0.1273926 0.01578373 -0.1573869 -0.09571622
## 6 -0.1305835 0.01450536 -0.1594585 -0.10194035
At each time point of interest timeseq = t.est
, which in this case is equal to t.seq
, the effects of the treatment on the mediator, the treatment on the outcome (adjusted and not adjusted for mediator), and the mediator on the outcome are estimated along with the respective 95% CIs. The CIs are computed via a non-parametric bootstrap method (Efron and Tibshirani, 1986), drawing samples of size 1086 from the original sample with replacement, estimating the sample mean and then applying the percentile method to compute the 95% CIs. Note that the CIs for the alpha
, gamma
, beta
and tau
coefficients (hat.alpha.1, hat.alpha.2, hat.gamma1, hat.gamma2, hat.tau1, hat.tau2, hat.beta)
are computed regardless of the value of CI
argument in the function. hat.mediation1
and hat.mediation2
are the estimated mediation effects of NRT1 (varenicline)
and NRT2 (combination NRT)
compared to the placebo (nicotine patch only)
that varies over t.est
. For CI = "boot"
(which is the default option unless the user chooses otherwise) the standard errors of the estimated mediation effects and 95% CIs are estimated via a similar bootstrapping technique described earlier for the coefficients.
If plot = TRUE
, the results will also include the following figures:
plot1_a1
plot for hat.alpha1
with 95% CIs across timeseq
plot2_a2
plot for hat.alpha2
with 95% CIs across timeseq
plot3_g1
plot for hat.gamma1
with 95% CIs across timeseq
plot4_g2
plot for hat.gamma2
with 95% CIs across timeseq
plot5_t1
plot for hat.tau1
with 95% CIs across timeseq
plot6_t2
plot for hat.tau2
with 95% CIs across timeseq
plot7_b
plot for hat.beta
with 95% CIs across timeseq
MedEff_T1
plot for hat.mediation1
across timeseq
MedEff_T2
plot for hat.mediation2
across timeseq
MedEff_CI_T1
plot for hat.mediation1
with 95% CIs across timeseq
MedEff_CI_T2
plot for hat.mediation2
with 95% CIs across timeseq
We recommend using the plots to interpret your findings as it may be difficult to derive meaning from the numerical values alone. To display the plots, use nameOfStoredResultsObj$
followed by the name of the plot to access the required plot accordingly. For example:
$plot1_a1 results_tvma_3trt
In the above plot, the effect of varenicline
on subjects’ feeling of negative mood in the last fifteen minutes
varies somewhat over time. The effect is negative compared to the effect of nicotine patch
only. That is, those assigned to varenicline
have a less negative mood in the last 15 min. compared to those assigned to the nicotine patch
only group.
$plot2_a2 results_tvma_3trt
In the above plot, the effect of combination NRT
on subjects’ feeling of negative mood in the last fifteen minutes
varies over time. The effect is negative compared to the effect of nicotine patch
only. That is, those assigned to combination NRT
have a less negative mood in the last 15 min. compared to those assigned to the nicotine patch
only group.
$plot3_g1 results_tvma_3trt
The above plot shows the time-varying direct effect of varenicline
on the outcome cessation fatigue
is positive compared to the direct effect of nicotine patch
only. That is, those assigned to varenicline
have greater cessation fatigue (due to factors other than negative mood) compared to those in the nicotine patch
only group.
$plot4_g2 results_tvma_3trt
The above plot shows the time-varying direct effect of combination NRT
on the outcome cessation fatigue
is positive compared to the direct effect of nicotine patch
only. That is, those assigned to combination NRT
have greater cessation fatigue (due to factors other than negative mood) compared to those in the nicotine patch
only group.
$plot5_t1 results_tvma_3trt
The above plot shows the time-varying total effect of varenicline
on the outcome cessation fatigue
, which is not statistically significant over much of the time. The estimated 95% CI covers 0 (no effect), except during days 6-9.
$plot6_t2 results_tvma_3trt
The above plot shows the time-varying total effect of combination NRT
on the outcome cessation fatigue
, which is not statistically significant over time. The estimated 95% CI covers 0 (no effect).
$plot7_b results_tvma_3trt
In the above plot, the time-varying effect of subjects’ negative mood in the last fifteen minutes
on the outcome cessation fatigue
increases slightly until around day 6-7 (end of week 1) and then decreases beginning around day 20-21 (end of week 3).
$MedEff_T1 results_tvma_3trt
$MedEff_CI_T1 results_tvma_3trt
In the above plots, the time-varying effect of varenicline
on cessation fatigue
that is mediated by the negative mood in the last fifteen minutes
is negative indicating that in comparison to the nicotine patch
only group, varenicline
reduces cessation fatigue
due to a decrease in negative mood. This effect decreases during the first week, increases slightly from day 8-10, and then continues to weaken further until week 3. The effect increases after week 3 with a slight decrease around days 24-26. Given that the CIs do not cross zero, we can conclude that this effect is statistically significant.
$MedEff_T2 results_tvma_3trt
$MedEff_CI_T2 results_tvma_3trt
In the above plots, the effect of combination NRT
on cessation fatigue
that is mediated by the negative mood in the last fifteen minutes
is weaker than the effect of using the nicotine patch
only. This effect is sinusoidal over time, with occasional spikes at days 2, 11, 24 and 28. The effect takes a decreasing trend between week 2 and week 3. The effect increases after week 3 and continues its upward trend with occasional decrease. Given that the confidence intervals do not cross zero, we can conclude that this effect is statistically significant.
The tvma_3trt
function computes bootstrap confidence intervals by default. Therefore, if the user decides to not bootstrap CIs for the mediation effect by specifying CI = "none"
, but by mistake also specifies replicates = 500
, the function will not display an error, but will simply execute without computing the CIs for mediation effect. Note that the CIs for the effects of the treatment on the mediator and the mediator on the outcome, and for the direct and total effects are computed even if the user passes the argument CI = "none"
.
The tvmediation
package provides a set of functions for estimating mediation effects that vary over time for both binary and continuous time-varying outcomes. Currently, the package only allows for a time-invariant treatment. The mediator and outcome are assumed to be time-varying, such as intensive longitudinal measurements obtained via Ecological Momentary Assessment or via wearable and mobile devices. The development of this tool has widespread application for use in human behavior research, clinical trials, addiction research, and others by allowing specification of mediation effects that vary as a function of time.
Cai, X., Piper, M. E., Li, R., & Coffman, D. L. (2020). Estimation and inference for the mediation effect in a time-varying mediation model. https://arxiv.org/abs/2008.11797
Baker, T. B., Piper, M. E., Stein, J. H., Smith, S. S., Bolt, D. M., Fraser, D. L., & Fiore, M. C. (2016). Effects of nicotine patch vs varenicline vs combination nicotine replacement therapy on smoking cessation at 26 weeks: A randomized clinical trial. JAMA, 315(4), 371-379.}
Efron, B. & Tibshirani, R. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statist. Sci. 1 (1986), no. 1, 54–75.}