IrregLong

https://epullenayegum.github.io/IrregLong/
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The IrregLong package provides functions for handling longitudinal data subject to irregular...
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### Install IrregLong Package from GitHub

Source: https://epullenayegum.github.io/IrregLong/index.html

Use this command to install the development version of the IrregLong package directly from its GitHub repository.

```r
devtools::install_github("epullenayegum/Irreglong")
```

--------------------------------

### Example of Multiple Outputation with GEE

Source: https://epullenayegum.github.io/IrregLong/reference/mo.html

Demonstrates using the mo() function with geeglm for analyzing longitudinal data. It includes data preparation, weight calculation using iiw.weights, and defining a regression function for analysis. Note the caveat regarding sandwich variance estimates with small outputations.

```R
library(nlme)
data(Phenobarb)
library(survival)
library(geepack)
library(data.table)

Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb
data <- data[data$event==1,]
data$id <- as.numeric(data$Subject)
data <- data[data$time<16*24,]
i <- iiw.weights(Surv(time.lag,time,event)~I(conc.lag>0 & conc.lag<=20) +
I(conc.lag>20 & conc.lag<=30) + I(conc.lag>30)+ cluster(id),
id="id",time="time",event="event",data=data, invariant="id",lagvars=c("time","conc"),maxfu=16*24,
         lagfirst=c(0,0),first=TRUE)
wt <- i$iiw.weight
wt[wt>quantile(i$iiw.weight,0.95)] <- quantile(i$iiw.weight,0.95)
data$wt <- wt
reg <- function(data){
est <- summary(geeglm(conc~I(time^3) + log(time), id=id,data=data))$coefficients[,1:2]
est <- data.matrix(est)
return(est)
}

mo(20,reg,data,wt,singleobs=FALSE,id="id",time="time",keep.first=FALSE)
```

--------------------------------

### Create an Abacus Plot with Sample Data

Source: https://epullenayegum.github.io/IrregLong/reference/abacus.plot.html

Example of creating an abacus plot using the Phenobarb dataset. Ensure the 'event' column is correctly defined and filtered before plotting. Customize point character and color for clarity.

```R
library(nlme)
data(Phenobarb)
Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb[Phenobarb$event==1,]
abacus.plot(n=20,time="time",id="Subject",data=data,tmin=0,tmax=16*24,
xlab.abacus="Time in hours",pch=16,col.abacus=gray(0.8))
```

--------------------------------

### Calculate Extent of Irregularity

Source: https://epullenayegum.github.io/IrregLong/reference/extent.of.irregularity.html

Demonstrates how to use the extent.of.irregularity function with sample data. Requires the nlme and survival packages. The example is time-consuming and marked with \dontrun{}.

```R
if (FALSE) { # \dontrun{
# time-consuming so not run in R package build
library(nlme)
library(survival)
data(Phenobarb)
Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb
data <- data[data$event==1,]
data$id <- as.numeric(data$Subject)
counts <- extent.of.irregularity(data,time="time",id="id",scheduledtimes=NULL,
cutpoints=NULL,ncutpts=10, maxfu=16*24,plot=TRUE,legendx=NULL,legendy=NULL,
formula=Surv(time.lag,time,event)~1,tau=16*24)
counts$counts
counts$auc
} # } 

```

--------------------------------

### Create Outputted Dataset

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Use `outputation()` to create an outputted dataset specifically formatted for use with multiple outputation procedures. This prepares data for analysis with functions like `mo()`.

```r
outputation()
```

--------------------------------

### Get Best Model Adjusted R-squared

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Retrieves the adjusted R-squared value of the best fitting model identified in the previous step.

```r
rsq1[which.max(rsq1)]
```

--------------------------------

### Prepare Phenobarb Dataset

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Prepares the Phenobarb dataset for analysis by creating an event indicator, filtering data, assigning IDs, and ordering by time. The analysis is restricted to time points with concentration measurements and within the first 16 days of life.

```r
data(Phenobarb)
Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb
data <- data[data$event==1,]
data$id <- as.numeric(data$Subject)
data <- data[data$time<16*24,]
data <- data[order(data$id,data$time),]
head(data)
```

--------------------------------

### Load Required Libraries

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Loads essential R packages for data manipulation, survival analysis, and generalized estimating equations.

```r
library(IrregLong)
library(nlme)
library(survival)
library(geepack)
library(data.table)
```

--------------------------------

### create.bootstrapped.dataset

Source: https://epullenayegum.github.io/IrregLong/reference/create.bootstrapped.dataset.html

Creates a single bootstrap sample for clustered data by sampling subjects with replacement.

```APIDOC
## create.bootstrapped.dataset

### Description
Create a single bootstrap sample for clustered data. For clustered data, create a bootstrapped sample by sampling, with replacement, the same number of clusters as in the original dataset.

### Usage
```R
create.bootstrapped.dataset(data, idname)
```

### Arguments

*   **data** (data.frame or similar) - The dataset to be resampled.
*   **idname** (character) - A character indicating which column of the data contains subject identifiers.

### Details
This function is designed to assist in computing bootstrap standard errors when working with longitudinal data. Given longitudinal data with multiple rows per subject, it will sample subjects, with replacement, n times, where n is the number of subjects in the original dataset. In the bootstrapped dataset, each resample has its own id.
```

--------------------------------

### View Fitted Visit Intensity Model Summary

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Display the summary of the fitted visit intensity model from the iiwgee object. This provides details on the model used for inverse-intensity weighting.

```R
summary(iiwgee$phfit)
```

--------------------------------

### Create Bootstrapped Dataset for Clustered Data

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Use `create.bootstrapped.dataset()` to generate a single bootstrap sample for clustered data. This involves sampling clusters with replacement to create a new dataset for resampling-based analysis.

```r
create.bootstrapped.dataset()
```

--------------------------------

### Perform Outputation with Weighted Data

Source: https://epullenayegum.github.io/IrregLong/reference/outputation.html

This snippet shows how to use the `outputation` function with pre-calculated weights. It is applied to a dataset where `singleobs` is set to `FALSE`, indicating that multiple observations per subject are expected.

```R
data.output1 <-   outputation(data,data$weight,singleobs=FALSE,
id="id",time="time",keep.first=FALSE)
head(data.output1)
#> Grouped Data: conc ~ time | Subject
#>    Subject  Wt Apgar ApgarInd  time dose conc event id weight
#> 2        1 1.4     7     >= 5   2.0   NA 17.3     1 32  1.000
#> 12       1 1.4     7     >= 5 112.5   NA 31.0     1 32  0.478
#> 14       2 1.5     9     >= 5   2.0   NA  9.7     1 38  1.000
#> 20       2 1.5     9     >= 5  63.5   NA 24.6     1 38  1.000
#> 27       2 1.5     9     >= 5 135.5   NA 33.0     1 38  0.478
#> 29       3 1.5     6     >= 5   1.5   NA 18.0     1 11  1.000
```

```R
data.output2 <-   outputation(data,data$weight,singleobs=FALSE,
id="id",time="time",keep.first=FALSE)
head(data.output2)
#> Grouped Data: conc ~ time | Subject
#>    Subject  Wt Apgar ApgarInd  time dose conc event id weight
#> 2        1 1.4     7     >= 5   2.0   NA 17.3     1 32  1.000
#> 14       2 1.5     9     >= 5   2.0   NA  9.7     1 38  1.000
#> 20       2 1.5     9     >= 5  63.5   NA 24.6     1 38  1.000
#> 27       2 1.5     9     >= 5 135.5   NA 33.0     1 38  0.478
#> 29       3 1.5     6     >= 5   1.5   NA 18.0     1 11  1.000
#> 36       3 1.5     6     >= 5  83.5   NA 23.8     1 11  1.000
```

```R
data.output3 <-   outputation(data,data$weight,singleobs=FALSE,
id="id",time="time",keep.first=FALSE)
head(data.output3)
#> Grouped Data: conc ~ time | Subject
#>    Subject  Wt Apgar ApgarInd  time dose conc event id weight
#> 2        1 1.4     7     >= 5   2.0   NA 17.3     1 32  1.000
#> 12       1 1.4     7     >= 5 112.5   NA 31.0     1 32  0.478
#> 14       2 1.5     9     >= 5   2.0   NA  9.7     1 38  1.000
#> 20       2 1.5     9     >= 5  63.5   NA 24.6     1 38  1.000
#> 29       3 1.5     6     >= 5   1.5   NA 18.0     1 11  1.000
#> 36       3 1.5     6     >= 5  83.5   NA 23.8     1 11  1.000
```

--------------------------------

### Low-level functions

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Functions for constructing the inverse-intensity weights manually.

```APIDOC
## addcensoredrows()

### Description
Add rows corresponding to censoring times to a longitudinal dataset.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

```APIDOC
## lagfn()

### Description
Create lagged versions of the variables in data.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

--------------------------------

### R: Execute Multiple Simulations and Summarize Results

Source: https://epullenayegum.github.io/IrregLong/reference/Liang.html

Executes a specified number of simulation runs (controlled by 'n') and aggregates the results into a matrix for summary statistics. This is used to replicate the paper's findings.

```r
# change n to 500 to replicate results of Liang et al.
n <- 10
 s <- lapply(1:n,sim1,nsubj=200)
 smat <- matrix(unlist(s),byrow=TRUE,ncol=4)
 apply(smat,2,mean)
 
```

--------------------------------

### Create Outputted Dataset with outputation()

Source: https://epullenayegum.github.io/IrregLong/reference/outputation.html

Use this function to create a single outputted dataset for use with multiple outputation methods. It's designed for longitudinal data with irregular observation times and can handle clustered data by ensuring only one observation per subject is retained.

```R
outputation(data, weights, singleobs, id, time, keep.first)
```

--------------------------------

### Fit GEE and Proportional Hazards Model for Irregular Follow-up

Source: https://epullenayegum.github.io/IrregLong/reference/iiwgee.html

Use this snippet to fit a GEE model and a proportional hazards model simultaneously for longitudinal data with irregular and informative follow-up. Ensure necessary libraries (nlme, survival, geepack, data.table) are loaded and data is preprocessed correctly, including defining event status and cluster IDs.

```R
library(nlme)
data(Phenobarb)
library(survival)
library(geepack)
library(data.table)
Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb
data <- data[data$event==1,]
data$id <- as.numeric(data$Subject)
data <- data[data$time<16*24,]
miiwgee <- iiwgee(conc ~ I(time^3) + log(time),
Surv(time.lag,time,event)~I(conc.lag>0 & conc.lag<=20) +
I(conc.lag>20 & conc.lag<=30) + I(conc.lag>30)+ cluster(id),
id="id",time="time",event="event",data=data,
invariant="id",lagvars=c("time","conc"),maxfu=16*24,lagfirst=0,first=TRUE)
summary(miiwgee$geefit)
```

```R
summary(miiwgee$phfit)
```

--------------------------------

### Fit GEE Model with Transformed Variables

Source: https://epullenayegum.github.io/IrregLong/reference/iiwgee.html

This snippet shows how to transform time variables and fit a GEE model using geeglm. It includes printing the model summary.

```r
data$time3 <- (data$time^3)/mean(data$time^3)
data$logtime <- log(data$time)
m <- geeglm(conc ~ time3 + logtime , id=Subject, data=data); print(summary(m))
```

--------------------------------

### Liangint Simulation and Estimation

Source: https://epullenayegum.github.io/IrregLong/reference/Liangint.html

This R code block simulates survival data and then uses the Liangint function to estimate model parameters. It's designed to replicate simulation results from Liang et al. by estimating intercept and time terms. Ensure necessary libraries like 'data.table' and 'survival' are loaded.

```r
if (FALSE) { # \dontrun{
library(data.table)
library(survival)
datasimi <- function(id){
X1 <- runif(1,0,1)
X2 <- rbinom(1,1,0.5)
Z <- rgamma(1,1,1)
Z1 <- rnorm(1,Z-1,1)
gamma <- c(0.5,-0.5)
beta <- c(1,-1)
hazard <- Z*exp(X1/2 - X2/2)
C <- runif(1,0,5.8)
t <- 0
tlast <- t
y <- t + X1-X2 + Z1*X2 + rnorm(1,0,1)
wait <- rexp(1,hazard)
while(tlast+wait<C){
  tnew <- tlast+wait
    y <- c(y,tnew + X1-X2 + Z1*X2 + rnorm(1,0,1))
    t <- c(t,tnew)
    tlast <- tnew
    wait <- rexp(1,hazard)
 }
 datai <- list(id=rep(id,length(t)),t=t,y=y,
      X1=rep(X1,length(t)),X2=rep(X2,length(t)),C=rep(C,length(t)))
 return(datai)
 }
sim1 <- function(it,nsubj){
 data <- lapply(1:nsubj,datasimi)
 data <- as.data.frame(rbindlist(data))
 data$event <- 1
 C <- tapply(data$C,data$id,mean)
 tapply(data$C,data$id,sd)
 maxfu <- cbind(1:nsubj,C)
 maxfu <- as.data.frame(maxfu)
 res <- Liangint(data=data, id="id",time="t",Yname="y",
            Xnames=c("t","X1","X2"),
            Wnames=c("X2"),Znames=c("X1","X2"), formulaobs=Surv(t.lag,t,event)~X1
            + X2+ frailty(id),invariant=c
            ("id","X1","X2"),lagvars="t",lagfirst=NA,maxfu=maxfu,
            baseline=1)
 return(res)
 }
 # change n to 500 to replicate results of Liang et al.
n <- 10
s <- lapply(1:n,sim1,nsubj=200)
smat <- matrix(unlist(s),byrow=TRUE,ncol=4)
apply(smat,2,mean)
 } # }
```

--------------------------------

### Create Abacus Plot

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Use `abacus.plot()` to create an abacus plot, which visually depicts subject visits over time. This helps in understanding the pattern of observations.

```r
abacus.plot()
```

--------------------------------

### Multiple Outputation

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Functions for performing multiple outputation.

```APIDOC
## mo()

### Description
Multiple outputation for longitudinal data subject to irregular observation.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

```APIDOC
## outputation()

### Description
Create an outputted dataset for use with multiple outputation.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

--------------------------------

### Create Bootstrapped Dataset Function Signature

Source: https://epullenayegum.github.io/IrregLong/reference/create.bootstrapped.dataset.html

This is the function signature for creating a bootstrapped dataset. It requires the dataset and the name of the column containing subject identifiers.

```R
create.bootstrapped.dataset(data, idname)
```

--------------------------------

### Fit Inverse-Intensity Weighted GEE Model

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

This snippet prepares data by creating log-transformed time and scaled cubic time variables. It then fits an inverse-intensity weighted GEE model using the 'iiwgee' function, specifying the outcome formula, inverse intensity weight formula, and other parameters like cluster ID, time, and event variables.

```r
data$logtime <- log(data$time)
data$time3 <- (data$time^3)/(mean(data$time^3))
iiwgee <- iiwgee(conc ~ time + time3 + logtime,Surv(time.lag,time,event)~I(conc.lag>0 & conc.lag<=20) + 
                I(conc.lag>20 & conc.lag<=30) + I(conc.lag>30) +cluster(id),
        formulanull=NULL,id="id",time="time",event="event",data=data,
        invariant=c("id","Wt"),lagvars=c("time","conc"),maxfu=16*24,lagfirst=c(0,0),first=FALSE)
```

--------------------------------

### Plotting Data and Model Fits

Source: https://epullenayegum.github.io/IrregLong/reference/iiwgee.html

This snippet plots the raw data points and overlays the fitted lines from both unweighted and weighted GEE models. A legend is included to differentiate the lines.

```r
plot(data$time,data$conc,xlim=c(0,200),pch=16)
lines(time,unweighted,type="l")
lines(time,weighted,col=2)
legend (0,60,legend=c("Unweighted","Inverse-intensity weighted"),col=1:2,bty="n",lty=1)
```

--------------------------------

### Compare Unweighted and Weighted GEE Models

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Fit an unweighted GEE model and compare its predictions to the inverse-intensity weighted GEE model. This helps visualize the impact of weighting on the fitted trajectories.

```R
m <- geeglm(conc ~ time + I(time^3) + log(time) , id=Subject, data=data)
time <- (2:200)
unweighted <- cbind(rep(1,199),time,time^3,log(time))%*%m$coefficients
weighted <- cbind(rep(1,199),time,time^3/mean(data$time^3),log(time))%*%iiwgee$geefit$coefficients
plot(data$time,data$conc,xlim=c(0,199),ylim=c(min(unweighted,weighted,data$conc),max(unweighted,weighted,data$conc)),pch=16,xlab="Time",ylab="Serum phenobarbital concentration")
lines(time,unweighted,type="l")
lines(time,weighted,col=2)
legend (0,60,legend=c("Unweighted","Inverse-intensity weighted"),bty="n",lty=1)
```

--------------------------------

### outputation Function

Source: https://epullenayegum.github.io/IrregLong/reference/outputation.html

Creates a single outputted dataset for use in multiple outputation. This function is crucial for handling data where observations are not uniformly spaced or where clusters have informative sizes.

```APIDOC
## outputation

### Description
Creates a single outputted dataset for use with multiple outputation. Multiple outputation is a procedure whereby excess observations are repeatedly randomly sampled and discarded. The method was originally developed to handle clustered data where cluster size is informative, for example when studying pups in a litter. In this case, analysis that ignores cluster size results in larger litters being over-represented in a marginal analysis. Multiple outputation circumvents this problem by randomly selecting one observation per cluster. Multiple outputation has been further adapted to handle longitudinal data subject to irregular observation; here the probability of being retained on any given outputation is inversely proportional to the visit intensity.

### Usage
```R
outputation(data, weights, singleobs, id, time, keep.first)
```

### Arguments 

*   **data** (data.frame or similar)
    The original dataset on which multiple outputation is to be performed.

*   **weights** (numeric vector)
    The weights to be used in the outputation, i.e. the inverse of the probability that a given observation will be selected in creating an outputted dataset. Ignored if `singleobs=TRUE`.

*   **singleobs** (logical)
    Logical variable indicating whether a single observation should be retained for each subject.

*   **id** (character string)
    Character string indicating which column of the data identifies subjects.

*   **time** (character string)
    Character string indicating which column of the data contains the time at which the visit occurred.

*   **keep.first** (logical)
    Logical variable indicating whether the first observation should be retained with probability 1. This is useful if the data consists of an observation at baseline followed by follow-up at stochastic time points.
```

--------------------------------

### Summarize GEE Fit

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

This code displays the summary of the inverse-intensity weighted GEE fit obtained from the 'iiwgee' function. It provides detailed statistics for the fitted model.

```r
summary(iiwgee$geefit)
```

--------------------------------

### Using inverse-intensity weighting

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Using inverse-intensity weighting to account for irregular and informative observation times.

```APIDOC
## iiw.weights()

### Description
Compute inverse-intensity weights.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

```APIDOC
## iiwgee()

### Description
Fit an inverse-intensity weighted GEE.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

```APIDOC
## iiw()

### Description
Given a proportional hazards model for visit intensities, compute inverse-intensity weights.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

--------------------------------

### Access Model Estimates

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Retrieves the estimated coefficients and variance from the fitted Liang model. The output includes coefficients for covariates, the frailty variance, and potentially other model parameters.

```R
m.moLiang$est
```

--------------------------------

### R: Run Liang Simulation and Analysis

Source: https://epullenayegum.github.io/IrregLong/reference/Liang.html

Simulates data for multiple subjects and then applies the Liang function for survival analysis. This function orchestrates the simulation and analysis for a single simulation run.

```r
sim1 <- function(it,nsubj){
 data <- lapply(1:nsubj,datasimi)
 data <- as.data.frame(rbindlist(data))
 data$event <- 1
 C <- tapply(data$C,data$id,mean)
 tapply(data$C,data$id,sd)
 maxfu <- cbind(1:nsubj,C)
 maxfu <- as.data.frame(maxfu)
 res <- Liang(data=data, id="id",time="t",Yname="y",
            Xnames=c("X1","X2"),
            Wnames=c("X2"),Znames=c("X1","X2"), formulaobs=Surv(t.lag,t,event)~X1
            + X2+ frailty(id),invariant=c
            ("id","X1","X2"),lagvars="t",lagfirst=NA,maxfu=maxfu,
            baseline=1)
 return(res)
 }
```

--------------------------------

### Evaluate Fractional Polynomial Models for Time

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Calculates and compares the adjusted R-squared for linear models of serum concentration against various fractional polynomial transformations of time. This helps in selecting the best functional form for time in the model.

```R
rsq1 <- array(dim=8)
rsq1[1] <- summary(lm(conc~time,data=data))$adj.r.squared
rsq1[2] <- summary(lm(conc~I((time)^0.5),data=data))$adj.r.squared
rsq1[3] <- summary(lm(conc~I((time)^2),data=data))$adj.r.squared
rsq1[4] <- summary(lm(conc~I((time)^3),data=data))$adj.r.squared
rsq1[5] <- summary(lm(conc~log(time),data=data))$adj.r.squared
rsq1[6] <- summary(lm(conc~I((time)^(-0.5)),data=data))$adj.r.squared
rsq1[7] <- summary(lm(conc~I((time)^(-1)),data=data))$adj.r.squared
rsq1[8] <- summary(lm(conc~I((time)^(-2)),data=data))$adj.r.squared
which.max(rsq1)
```

```R
rsq1[which.max(rsq1)]
```

--------------------------------

### Multiple Outputation with Weighted GEE

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Performs multiple outputation using inverse-intensity weights and analyzes each outputted dataset with an unweighted GEE. Truncates large weights and uses a subset of time variables for analysis due to potential collinearity in smaller outputted datasets. Employs a small sample sandwich variance correction for GEE.

```R
library(geesmv)


reg <- function(data){
  m <- geeglm(conc~time + I(time^3), id=id,data=data)
  est <- summary(m)$coefficients[,1:2]
  if(max(table(data$id))>1) est[,2] <- GEE.var.md(conc~time + I(time^3) , id=id,data=data)$cov.beta
  est <- data.matrix(est)
  return(est)
}
set.seed(301031)
wt <- i$iiw.weight
wt[wt>quantile(i$iiw.weight,0.95)] <- quantile(i$iiw.weight,0.95)
m.mogee <- mo(20,reg,data,wt, singleobs=FALSE,id="id",time="time",keep.first=FALSE,var=TRUE)
m.mogee
```

--------------------------------

### Fit Inverse-Intensity Weighted GEE

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Use `iiwgee()` to fit a Generalized Estimating Equation (GEE) model using inverse-intensity weighting. This method accounts for irregular and informative observation times.

```r
iiwgee()
```

--------------------------------

### Generate Unweighted and Weighted Predictions

Source: https://epullenayegum.github.io/IrregLong/reference/iiwgee.html

This code generates predictions from both an unweighted and a weighted GEE model for plotting. It requires the 'geefit' object from a weighted model.

```r
time <- (1:200)
unweighted <- cbind(rep(1,200),time^3/mean(data$time^3),log(time))%*%m$coefficients
weighted <- cbind(rep(1,200),time^3/mean(data$time^3),log(time))%*%miiwgee$geefit$coefficients
```

--------------------------------

### Multiple Outputation Function Signature

Source: https://epullenayegum.github.io/IrregLong/reference/mo.html

Defines the signature for the mo() function, outlining its parameters for performing multiple outputation on longitudinal data.

```R
mo(
  noutput,
  fn,
  data,
  weights,
  singleobs,
  id,
  time,
  keep.first,
  var = TRUE,
  ...
)
```

--------------------------------

### Plot Serum Concentration vs. Time

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Generates a scatter plot of serum concentration against time. This is a preliminary step to visualize the relationship before modeling.

```R
plot(data$time,data$conc,xlim=c(0,200),pch=16, xlab="Time in hours", ylab="Concentration")
```

--------------------------------

### Perform Multiple Outputation

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Use `mo()` for multiple outputation of longitudinal data that is subject to irregular observation times. This function helps in handling missing data patterns common in such datasets.

```r
mo()
```

--------------------------------

### IrregLong Package Citation

Source: https://epullenayegum.github.io/IrregLong/authors.html

This is the recommended citation format for the IrregLong R package, version 0.4.1. It includes the title, author, year, version, and URL.

```bibtex
@Manual{
  title = {IrregLong: Analysis of Longitudinal Data with Irregular Observation Times},
  author = {Eleanor Pullenayegum},
  year = {2026},
  note = {R package version 0.4.1},
  url = {https://epullenayegum.github.io/IrregLong/},
}
```

--------------------------------

### Semi-parametric joint model

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Functions for fitting the Liang semi-parametric joint model.

```APIDOC
## Liang()

### Description
Fit a semi-parametric joint model.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

```APIDOC
## Liangint()

### Description
Fit a semi-parametric joint model, incorporating intercept estimation.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

```APIDOC
## create.bootstrapped.dataset()

### Description
Create a single bootstrap sample for clustered data. For clustered data, create a bootstrapped sample by sampling, with replacement, the same number of clusters as in the original dataset.

### Parameters
(No parameters explicitly documented)

### Response
(No response details explicitly documented)
```

--------------------------------

### abacus.plot

Source: https://epullenayegum.github.io/IrregLong/reference/abacus.plot.html

Creates an abacus plot, depicting visits per subject over time. This function is useful for visualizing the extent of irregularity in the visit process.

```APIDOC
## abacus.plot

### Description
Creates an abacus plot, depicting visits per subject over time.

### Usage
```R
abacus.plot(
  n,
  time,
  id,
  data,
  tmin,
  tmax,
  xlab.abacus = "Time",
  ylab.abacus = "Subject",
  pch.abacus = 16,
  col.abacus = 1
)
```

### Arguments

* **n** (numeric) - the number of subjects to randomly sample. Subjects are sampled without replacement and therefore n must be smaller than the total number of subjects in the dataset.
* **time** (character) - character string indicating which column of the data contains the time at which the visit occurred.
* **id** (character) - character string indicating which column of the data identifies subjects.
* **data** (data.frame) - data frame containing the variables in the model.
* **tmin** (numeric) - the smallest time to include on the x-axis.
* **tmax** (numeric) - the largest time to include on the x-axis.
* **xlab.abacus** (character, optional) - the label for the x-axis. Defaults to "Time".
* **ylab.abacus** (character, optional) - the label for the y-axis. Defaults to "Subject".
* **pch.abacus** (numeric, optional) - the plotting character for the points on the abacus plot. Defaults to 16.
* **col.abacus** (numeric, optional) - the colour of the rails on the abacus plot. Defaults to 1.

### Value
Produces a plot depicting observation times for each subject. No values are returned.

### Details
This function creates a plot for n randomly sampled individuals from the supplied dataset, with one row per subject and one point per visit. This can be useful for visualising the extent of irregularity in the visit process. For example, with perfect repeated measures data (i.e., no irregularity), the points will line up vertically. With greater irregularity, the points will be randomly scattered over time.

### Examples
```R
library(nlme)
data(Phenobarb)
Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb[Phenobarb$event==1,]
abacus.plot(n=20, time="time", id="Subject", data=data, tmin=0, tmax=16*24,
xlab.abacus="Time in hours", pch=16, col.abacus=gray(0.8))
```
```

--------------------------------

### Fit Weighted GEE Model

Source: https://epullenayegum.github.io/IrregLong/reference/iiw.weights.html

Use `geeglm` to fit a GEE model with specified weights. This is useful when observations have different variances. The `summary()` function provides model diagnostics.

```r
mw <- geeglm(conc ~ I(time^3) + log(time) , id=Subject, data=data, weights=weight)
summary(mw)
```

--------------------------------

### Compute Inverse-Intensity Weights from Model

Source: https://epullenayegum.github.io/IrregLong/reference/index.html

Use `iiw()` to compute inverse-intensity weights given a proportional hazards model for visit intensities. This function is part of the inverse-intensity weighting methodology.

```r
iiw()
```

--------------------------------

### Summarize Events Per Subject

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Calculates and summarizes the total number of events for each subject in the dataset.

```R
summary(tapply(data$event,data$Subject,sum))
```

--------------------------------

### Fit Fractional Polynomials to Time Series Data

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Calculates adjusted R-squared values for linear models with various fractional polynomial transformations of time, including log(time) and interactions. Use this to identify the best functional form for concentration over time.

```R
rsq2 <- array(dim=8)
rsq2[1] <- summary(lm(conc~log(time)+ time,data=data))$adj.r.squared
rsq2[2] <- summary(lm(conc~log(time)+ I((time)^0.5),data=data))$adj.r.squared
rsq2[3] <- summary(lm(conc~log(time) + I((time)^2),data=data))$adj.r.squared
rsq2[4] <- summary(lm(conc~log(time)+ I((time)^3),data=data))$adj.r.squared
rsq2[5] <- summary(lm(conc~log(time)+ time:log(time),data=data))$adj.r.squared
rsq2[6] <- summary(lm(conc~log(time) + I((time)^(-0.5))*log(1+time),data=data))$adj.r.squared
rsq2[7] <- summary(lm(conc~log(time) + I((time)^(-1)),data=data))$adj.r.squared
rsq2[8] <- summary(lm(conc~log(time)+ I((time)^(-2)),data=data))$adj.r.squared
which.max(rsq2)
```

```R
rsq2[which.max(rsq2)]
```

--------------------------------

### Compute Inverse-Intensity Weights

Source: https://epullenayegum.github.io/IrregLong/reference/iiw.weights.html

Use this function to compute inverse-intensity weights, which are ordered by subject ID and time. Sorting the data beforehand is recommended. The `loess.stabilize` option helps avoid time trends in weights.

```R
iiw.weights(
  formulaph,
  formulanull = NULL,
  data,
  id,
  time,
  event,
  lagvars,
  invariant = NULL,
  maxfu,
  lagfirst = lagfirst,
  first,
  stabilize.loess = FALSE
)
```

--------------------------------

### Liangint Function Signature

Source: https://epullenayegum.github.io/IrregLong/reference/Liangint.html

This is the function signature for Liangint, detailing its arguments for fitting a semi-parametric joint model.

```R
Liangint(
  data,
  Yname,
  Xnames,
  Wnames,
  Znames = NULL,
  formulaobs = NULL,
  id,
  time,
  invariant = NULL,
  lagvars = NULL,
  lagfirst = NULL,
  maxfu,
  baseline,
  Xfn = NULL,
  Wfn = NULL,
  ...
)
```

--------------------------------

### Fit GEE Model with Independence Correlation

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

Fit a GEE model using the geeglm function with an independence correlation structure. This is useful for initial model fitting or when no specific correlation is assumed.

```R
geeglm(formula = formulagee, family = family, data = data, weights = useweight, 
    id = iddup, corstr = "independence")
```

--------------------------------

### Fit Linear Models with Time Transformations

Source: https://epullenayegum.github.io/IrregLong/articles/Irreglong-vignette.html

This snippet fits multiple linear regression models to 'conc' based on different transformations of 'time'. It calculates the adjusted R-squared for each model to compare their fit. The models include cubic, square root, squared, and logarithmic transformations of time, as well as interactions.

```r
rsq1 <- array(dim=8)
rsq1[1] <- summary(lm(conc~I((time)^3) +time,data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[2] <- summary(lm(conc~I((time)^3) +I((time)^0.5),data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[3] <- summary(lm(conc~I((time)^3) +I((time)^2),data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[4] <- summary(lm(conc~I((time)^3) + log(time):I(time^3),data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[5] <- summary(lm(conc~I((time)^3) +log(time),data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[6] <- summary(lm(conc~I((time)^3) +I((time)^(-0.5)),data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[7] <- summary(lm(conc~I((time)^3) +I((time)^(-1)),data=data,weight=i$iiw.weight))$adj.r.squared
rsq1[8] <- summary(lm(conc~I((time)^3) +I((time)^(-2)),data=data,weight=i$iiw.weight))$adj.r.squared
which.max(rsq1)
```
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