longDat {statVisual}

A Simulated Dataset for Longitudinal Data Analysis

Description

A simulated dataset for longitudinal data analysis.

Usage

data("longDat")

Format

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

Details

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

y_{ij}=\beta_{0i}+\beta_1 t_{j} + \beta_2 grp_{2i} + \beta_3 grp_{3i} + \beta_4 \times\left(t_{j}\times grp_{2i}\right) + \beta_5 \times\left(t_{j}\times grp_{3i}\right) +\epsilon_{ij},

where y_{ij} is the outcome value for the i-th subject measured at j-th time point t_{j}, grp_{2i} is a dummy variable indicating if the i-th subject is from group 2, grp_{3i} is a dummy variable indicating if the i-th subject is from group 3, \beta_{0i}\sim N\left(\beta_0, \sigma_b^2\right), \epsilon_{ij}\sim N\left(0, \sigma_e^2\right), i=1,\ldots, n, j=1, \ldots, 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\left(y_{ij}\right)=\beta_0+\beta_2 dose_{2i} + \beta_3 dose_{3i}.

Hence, we have at baseline

E\left(y_{ij}\right)=\beta_0,\; \mbox{for dose 1 group}.

E\left(y_{ij}\right)=\beta_0 + \beta_2,\; \mbox{for dose 2 group}.

E\left(y_{ij}\right)=\beta_0 + \beta_3,\; \mbox{for dose 3 group}.

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

E\left(y_{ij}\right)=\beta_0+\beta_1 t_{j}.

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\left(y_{ij} - y_{i'j}\right) =\beta_2+\beta_4 t_{j},\;\mbox{for subject $i$ in dose 2 group and subject $i'$ in dose 1 group},

E\left(y_{kj} - y_{i'j}\right) =\beta_3+\beta_5 t_{j},\;\mbox{for subject $k$ in dose 3 group and subject $i'$ in dose 1 group},

E\left(y_{kj} - y_{ij}\right) =\left(\beta_3-\beta_2\right)+\left(\beta_5-\beta_4\right) t_{j},\;\mbox{for subject $i$ in dose 3 group and subject $i$ in dose 2 group}.

We set n=90, m=6, \beta_0=5, \beta_1=0, \beta_2=0, \beta_3=0, \beta_4=2, \beta_5=-2, \sigma_e=1, \sigma_b=0.5, and t_{ij}=j, j=1, \ldots, 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.

Examples

data(longDat)

print(dim(longDat))
print(longDat[1:3,])

print(table(longDat$time, useNA = "ifany"))
print(table(longDat$grp, useNA = "ifany"))
print(table(longDat$sid, useNA = "ifany"))

print(table(longDat$time, longDat$grp))