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# Theophylline data set

## Theophylline data set

The data considered here are courtesy of Dr. Robert A. Upton of the University of California, San Francisco. Theophylline is a methylxanthine drug used in therapy for respiratory diseases such as chronic obstructive pulmonary disease (COPD) and asthma under a variety of brand names. Theophylline was administered orally to 12 subjects whose serum concentrations were measured at 11 times over the next 25 hours. This is an example of a laboratory pharmacokinetic study characterized by many observations on a moderate number of individuals. The data set can be seen here, and the corresponding Datxplore project here (notice that both file should be in the same folder to be correctly linked). A representation of the concentration over time for each subject is presented on the following figure (notice, that this figure was generated using Datxplore).

The purpose of this page is to see the construction, the definition and the use of such a data set in Datxplore and Monolix. For sake of simplicity, the focus will be done on only one subject of ID 1.

## Simplified data set

The data set for subject one can be defined as follows

ID AMT TIME    CONC    WEIGHT  SEX
1   4.02    0   .   79.6    M
1   .   0.25    2.84    79.6    M
1   .   0.57    6.57    79.6    M
1   .   1.12    10.5    79.6    M
1   .   2.02    9.66    79.6    M
1   .   3.82    8.58    79.6    M
1   .   5.1 8.36    79.6    M
1   .   7.03    7.47    79.6    M
1   .   9.05    6.89    79.6    M
1   .   12.12   5.94    79.6    M
1   .   24.37   3.28    79.6    M

#### Interpretation

One can see the following columns

• ID: the subject ID.
• AMT: the amount of drug provided to this subject.
• TIME: the time of the event.
• CONC: the measured concentration.
• WEIGHT: Weight of the subject.
• SEX: Sex of the subject.

Several points can be noticed.

1. The first line corresponds to a dose, while the other ones are measurements. This explains the dot in the CONC column for the first line and the dots in the AMT column for the other ones.
2. The covariates columns (the continuous WEIGHT and the categorical SEX) are filled with the same values. Even though it is not necessary, we encourage the user to fill the columns for readability and usage reasons.
3. Finally, notice that no initial washout is needed at the beginning as by default, the null initial condition is used for parameter estimation.

In Mlxtran, the data set writes

[FILEINFO]
file = './theophylline_data.txt'
delimiter = tab
header = {ID, AMT, TIME, CONC, WEIGHT, SEX}

[CONTENT]
ID = {use=identifier}
AMT = {use=amount}
TIME = {use=time}
CONC = {use=observation, name=concentration, ytype=1, type=continuous}
WEIGHT = {use=covariate, type=continuous}
SEX = {use=covariate, type=categorical}


## Censored data set

#### Data set

In the following example, some measurements are censored. This means that the value of the measurement (typically coming from a sensor) is wrong. In the presented case, the sensor can not measure a concentration under .25. However, this value can not be under a limit which is 0 in that case. The data set for subject one can be defined as follows

ID AMT TIME    CONC    LIMIT   CENS    WEIGHT  SEX
1   4.02    0   .   .   0   79.6    M
1   .   0.25    3   0   1   79.6    M
1   .   0.57    6.57    .   0   79.6    M
1   .   1.12    10.5    .   0   79.6    M
1   .   2.02    9.66    .   0   79.6    M
1   .   3.82    8.58    .   0   79.6    M
1   .   5.1 8.36    .   0   79.6    M
1   .   7.03    7.47    .   0   79.6    M
1   .   9.05    6.89    .   0   79.6    M
1   .   12.12   5.94    .   0   79.6    M
1   .   24.37   3.28    .   0   79.6    M

#### Interpretation

One can see the following additional columns

• CENS: it says if the data is censored or not.
• LIMIT: providing the under bound of the measurement.

The LIMIT information is very important for parameter estimation. Indeed, if no additional information is added, one can not known if the value is in ]-Infinity, .25] or [0, .25].

In Mlxtran, the data set writes

[FILEINFO]
file = './theophylline_cens1_data.txt'
delimiter = tab
header = {ID, AMT, TIME, CONC, LIMIT, CENS, WEIGHT}

[CONTENT]
ID = {use=identifier}
AMT = {use=amount}
TIME = {use=time}
CONC= {use=observation, name=concentration, ytype=1, type=continuous}
LIMIT = {use=limit}
CENS = {use=censored}
SEX = {use=covariate, type=categorical}