Description Usage Format Details Examples

A simulated dataset for longitudinal data analysis.

1 | ```
data("longDat")
``` |

A data frame with 540 observations on the following 4 variables.

`sid`

subject id

`time`

time points. A factor with levels

`time1`

`time2`

`time3`

`time4`

`time5`

`time6`

`y`

numeric. outcome variable

`grp`

subject group. A factor with levels

`grp1`

`grp2`

`grp3`

The dataset is generated from the following mixed effects model for repeated measures:

*
yij=beta0i+beta1*tj + beta2*grp2i +
beta3*grp3i + beta4*(tj*grp2i)
+ beta5*(tj*grp3i)+epsilonij,
*

where *yij* is the outcome value for the *i*-th subject
measured at *j*-th time point *tj*,
*grp2i* is a dummy variable indicating if the *i*-th subject
is from group 2,
*grp3i* is a dummy variable indicating if the *i*-th subject
is from group 3,
*
beta0i ~ N(beta0, sigmab^2)
*,
*
epsilonij ~ N(0, sigmae^2)
*, *i=1, ..., n, j=1, ..., m*,
*n* is the number of subjects, and *m* is the number of time points.

When *t_j=0*, the expected outcome value is

*
E(yij)=beta0+beta2*dose2i + beta3*dose3i.
*

Hence, we have at baseline

*
E(yij)=beta0, for dose 1 group.
*

*
E(yij)=beta0+beta2, for dose 2 group.
*

*
E(yij)=beta0+beta2, for dose 3 group.
*

For dose 1 group, the expected outcome values across time is

*
E(yij)=beta0+beta1*tj.
*

We also can get the expected difference of outcome values between dose 2 group and dose 1 group, between dose 3 group and dose 1 group, and between dose 3 group and dose 2 group:

*
E(yij - yi'j) =beta2+beta4*tj, for subject i in dose 2 group and subject i' in dose 1 group,
*

*
E(ykj - yi'j) =beta3+beta5*tj, for subject k in dose 3 group and subject i' in dose 1 group,
*

*
E(ykj - yij) =(beta3-beta2)+(beta5-beta4)*tj, for subject k in dose 3 group and subject i in dose 2 group.
*

We set *n=90*, *m=6*,
*beta0=5*,
*beta1=0*,
*beta2=0*,
*beta3=0*,
*beta4=2*,
*beta5=-2*,
*sigmae=1*,
*sigmab=0.5*,
and
*tij=j, j=1, ..., m*.

That is, the trajectories for dose 1 group are horizontal with mean intercept at *5*, the trajectories for dose 2 group are linearly increasing with slope *2* and mean intercept *5*, and the trajectories for dose 3 group are linearly decreasing with slope *-2* and mean intercept *5*.

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