To simulate longitudinal data, we start with a ‘cross-sectional’ data
set and convert it to a time-dependent data set. The original
cross-sectional data set may or may not include time-dependent data in
the columns. In the next example, we measure outcome `Y`

once
before and twice after intervention `T`

in a randomized
trial:

```
<- defData(varname = "T", dist = "binary", formula = 0.5)
tdef <- defData(tdef, varname = "Y0", dist = "normal", formula = 10, variance = 1)
tdef <- defData(tdef, varname = "Y1", dist = "normal", formula = "Y0 + 5 + 5 * T",
tdef variance = 1)
<- defData(tdef, varname = "Y2", dist = "normal", formula = "Y0 + 10 + 5 * T",
tdef variance = 1)
set.seed(483726)
<- genData(500, tdef)
dtTrial dtTrial
```

```
## id T Y0 Y1 Y2
## 1: 1 0 10.42 14.2 20.9
## 2: 2 1 9.36 21.9 25.4
## 3: 3 1 8.25 19.1 23.9
## 4: 4 0 10.86 16.5 20.4
## 5: 5 1 11.29 21.7 25.9
## ---
## 496: 496 1 11.87 22.6 26.6
## 497: 497 1 10.62 19.5 24.9
## 498: 498 1 10.13 22.2 26.1
## 499: 499 0 11.88 17.9 23.0
## 500: 500 0 11.92 18.4 22.5
```

Longitudinal data are created with a call to
** addPeriods**. If the cross-sectional data
includes time-dependent data, then the number of periods

`nPeriods`

must be the same as the number of time-dependent
columns. If a variable is not declared as one of the
`timevars`

, it will be repeated each time period. In this
example, the treatment indicator `T`

is not specified as a
time-dependent variable. (Note: if there are two time-dependent
variables, it is best to create two data sets and merge them. This will
be shown later in the vignette).```
<- addPeriods(dtTrial, nPeriods = 3, idvars = "id", timevars = c("Y0", "Y1",
dtTime "Y2"), timevarName = "Y")
dtTime
```

```
## id period T Y timeID
## 1: 1 0 0 10.42 1
## 2: 1 1 0 14.15 2
## 3: 1 2 0 20.93 3
## 4: 2 0 1 9.36 4
## 5: 2 1 1 21.90 5
## ---
## 1496: 499 1 0 17.94 1496
## 1497: 499 2 0 23.05 1497
## 1498: 500 0 0 11.92 1498
## 1499: 500 1 0 18.39 1499
## 1500: 500 2 0 22.50 1500
```

This is what the longitudinal data look like:

It is also possible to generate longitudinal data with varying
numbers of measurement periods as well as varying time intervals between
each measurement period. This is done by defining specific variables in
the data set that define the number of observations per subject and the
average interval time between each observation. `nCount`

defines the number of measurements for an individual;
`mInterval`

specifies the average time between intervals for
a subject; and `vInterval`

specifies the variance of those
interval times. If `vInterval`

is set to 0 or is not defined,
the interval for a subject is determined entirely by the mean interval.
If `vInterval`

is greater than 0, time intervals are
generated using a gamma distribution with mean and dispersion
specified.

In this simple example, the cross-sectional data generates individuals with a different number of measurement observations and different times between each observation. Data for two of these individuals is printed:

```
<- defData(varname = "xbase", dist = "normal", formula = 20, variance = 3)
def <- defData(def, varname = "nCount", dist = "noZeroPoisson", formula = 6)
def <- defData(def, varname = "mInterval", dist = "gamma", formula = 30, variance = 0.01)
def <- defData(def, varname = "vInterval", dist = "nonrandom", formula = 0.07)
def
<- genData(200, def)
dt %in% c(8, 121)] # View individuals 8 and 121 dt[id
```

```
## id xbase nCount mInterval vInterval
## 1: 8 18.0 4 28.1 0.07
## 2: 121 22.7 6 33.2 0.07
```

The resulting longitudinal data for these two subjects can be
inspected after a call to `addPeriods`

. Notice that no
parameters need to be set since all information resides in the data set
itself:

```
<- addPeriods(dt)
dtPeriod %in% c(8, 121)] # View individuals 8 and 121 only dtPeriod[id
```

```
## id period xbase time timeID
## 1: 8 0 18.0 0 41
## 2: 8 1 18.0 29 42
## 3: 8 2 18.0 51 43
## 4: 8 3 18.0 104 44
## 5: 121 0 22.7 0 691
## 6: 121 1 22.7 46 692
## 7: 121 2 22.7 81 693
## 8: 121 3 22.7 117 694
## 9: 121 4 22.7 154 695
## 10: 121 5 22.7 180 696
```

If a time-sensitive measurement is added to the data set …

```
<- defDataAdd(varname = "Y", dist = "normal", formula = "15 + .1 * time", variance = 5)
def2 <- addColumns(def2, dtPeriod) dtPeriod
```

… a plot of five randomly selected individuals looks like this: