Three types of covariate effects can be added to structural parameters. They are continuous, categorical, and occasion. Each type has its own set of options, and affect the structural parameters and the model differently.
Select the COVARIATES tab.
Click + to add a covariate.
Each covariate effect added creates a new fixed effect in the Fixed Effects tab.
In the Covariate field, enter the name of the covariate column.
From the Type pulldown, select the covariate type: Continuous, Categorical, Occasion.
If Continuous is selected:
From the Direction pulldown, select the method of curve fitting if the covariate value changes between observations for a subject.
Forward holds the first value between covariate observations.
Interpolate linearly interpolates the covariate between covariate observations. Only available for continuous covariate types.
Backward holds the last value between covariate observations.
Covariates can also be added based on available columns in the input source. See “Considerations when modeling with covariates” for additional information on covariate direction.
From the Effects pulldown, check the boxes for all structural parameters that this covariate influences.
Checking a box adds covariate effects to that parameter by updating the code with an additional term. For example, if the effects of the covariate wgt are added to the structural parameter V, a new fixed effect parameter is created called dVdwgt and the term wt^dVdwgt is added). dVdwgt is also added to the Fixed Effects tab, and users can enter initial, lower, and upper values for the fixed effects parameter, In this example, dVdwgt is the derivative of the parameter value with respect to weight. dV is the increment of volume divided by dwgt, the increment of weight.
From the Center pulldown, select the centering value for the covariate: Mean, Median, Value, or None. (If Value is selected, enter the value to use in the field that displays.)
If Categorical is selected:
In the Levels field, type a comma-separated list of values representing the different categories.
A minimum of two categories is required. It is typically best to use consecutive integers for categorical variables, starting at zero.
In the Labels field, enter a comma-separated list of categorical labels that correspond to the values entered in the Levels field.
If Occasion is selected:
In the Levels field, type a comma-separated list of values representing the different occasions.
A minimum of two occasions is required. It is typically best to use consecutive integers for occasion variables, starting at zero.
In the Labels field, enter a comma-separated list of occasion labels that correspond to the values entered in the Levels field.
Use the Diagonal checkbox to set the interoccasion covariance to a diagonal structure (box is checked) or block structure (box is unchecked).
Adding an occasion covariate creates a copy of each selected structural parameter random effect in the Random Effects tab. For example, if V is a structural parameter, and an occasion covariate is added to it, then nV is added to the Random Effects tab, where n stands for eta, or random effect, and V stands for volume. If three occasion covariate effects are added for V, they are named nV, nV2, and nV3.
To remove a covariate from the model, click the corresponding “—” button.
Note: Covariate effects can be specified in population modeling as well as in individual modeling, however, care must be taken not to over-parameterize the individual model. For example, suppose body weight W affects volume V. Then the model for V might be V=tvV+W*dVdW. In this case, if W is constant for the individual, the model is over-parameterized, because tvV and dVdW are redundant. However, if W is time-varying, the model is not over-parameterized. Covariates can also be useful if the data are pooled, or all subjects are modeled together.
Other covariates can be included in the individual model, even though they may not affect any structural parameters, because they may appear in secondary parameters, such as AUC.
Columns mapped as covariates (including categorical or occasion covariates) can only be numeric. However, a label can be assigned to the numeric categorical covariate, for example, and the label will be displayed in graphs even if the underlying data is numeric.
Considerations when modeling with covariates
It should be cautioned that Macro or Macro1 parameterization models can give incorrect results if time-varying covariate effects are present. Covariates may also have apparent incorrect covariate values being propagated (contrary to observed data), because of forward/backward/interpolate, for time-varying covariates. This raises several significant issues to consider when modeling:
Covariates have a direction of propagation that is forward in time, backward in time, or linearly interpolated.
The propagation occurs over records with missing covariate values, which is not consistent with some other tools. Be aware that, if an observation has a missing covariate value, the covariate will take on a propagated value, rather than a zero value.
Regardless of covariate direction, the value of the covariate applies during all other dose or observation events occurring on the same input data row. For example, if the data looks like this:
time CObs age weight
…
14 99.7 17 50
…
and if there is any doafter code associated with observable CObs, the age and weight have the value 17 and 50 in that code, regardless of forward or backward covariate direction.