Categorical observation block

Use the Categorical Observation block to model multinomial data. The data should be given as integer (whole) number values, such as 0, 1, 2, etc. A key feature of the Categorical Observation block is the ability to use model variables to affect the probability of observing data in a particular category. For instance, the Categorical Observation block could be used to link the probability of a patient reporting adverse effects of a given type to the administered dose or even drug concentration.

The default settings for the Categorical Observation block give a 50% chance of a zero or one output when the input value is zero. The probability of a one output increases as the input value increases from zero.

Insert a Categorical Observation block by selecting Insert > Observation > Categorical.

The Categorical Observation block can be connected to any PK compartment, observation block, PD block, or parameter block. See the Continuous Observation block section for instructions on adding and deleting a connection.

To specify categorical observation options

Use the pointer to select a Categorical Observation block.
In the Mtn field, enter a name for the Categorical Observation block or use the default name.
Check the Inhibitory checkbox to set the output values to decrease as the input increases.
In the Link menu, select the inverse link function.

This function determines the shape of the demarcation between output values as a function of inputs. This is the inverse of the link function sometimes used in fitting data. In the equations listed below, i is the input variable value, o is the offset between a given set of outputs such as zero or one, and p is the probability of getting a specific output, given i and o.

Inverse link functions include:

Logit: Inverse of the sigmoid function. p=e^i+o/(1+e^i+o)
Probit: Inverse cumulative distribution function. p=G(i+o) where G is the cumulative normal distribution.
Log-log: Logarithmic function. p=exp(–e^–i+o)
CLog-log: Complementary logarithmic function. p=i+o (truncated to the interval [0,1])
In the Slope field, type the slope expression.
In the N outcomes menu, click (-) to decrease the number of outcomes, and click (+) to increase the number of outcomes.

N outcomes corresponds to the number of categorical output values. For example, if N outcomes is three, the output could equal zero, one, or two, depending on the input value. The minimum number of outcomes is two.
In the Icept field, type the intercept expression.

Enter an expression representing the negative value of the input value that gives a 50% probability of outputting either of the adjacent output values. This is the negative of the offset between outputs. Because it is the negative, the values should be entered in descending numerical order. Use the syntax for expressions, described under “Expression block”.

Each extra outcome that is added to the categorical observation adds an extra Icept field. The first Icept field is labeled Icept10. The second Icept field is labeled Icept21. Each extra Icept field is labeled Icept32, Icept43, Icept54, and so forth.

For more information on the use of the Categorical Observation block, see “Multi statement for Categorical models”.

Make sure the Model Text tab shows an entry for the observation in the Column Definition Text field. It is displayed as “obs([block name]<-[“column name”]). If there is no entry, type it in the User-Provided Extra Column Definition Text field.