Define relationship between parameters and covariates
The Expression property is a character vector
or cell array of character vectors, where each character vector represents
the relationship between a parameter and one or more covariates. The Expression property
denotes fixed effects with the prefix theta, and
random effects with the prefix eta.
Each expression must be in the form:
parameterName = relationship |
This example of an expression defines the relationship between
a parameter (volume) and a covariate (weight),
with fixed effects, but no random effects:
CovModelObj.Expression = {'volume = theta1 + theta2*weight'}; |
This table illustrates expression formats for some common parameter-covariate relationships.
| Parameter-Covariate Relationship | Expression Format |
|---|---|
| Linear with random effect | Cl = theta1 + theta2*WEIGHT + eta1 |
| Exponential without random effect | Cl = exp(theta_Cl + theta_Cl_WT*WEIGHT) |
| Exponential, WEIGHT centered by mean, has random effect | Cl = exp(theta1 + theta2*(WEIGHT - mean(WEIGHT)) +
eta1) |
| Exponential, log(WEIGHT), which is equivalent to power model | Cl = exp(theta1 + theta2*log(WEIGHT) + eta1) |
| Exponential, dependent on WEIGHT and AGE, has random effect | Cl = exp(theta1 + theta2*WEIGHT + theta3*AGE + eta1) |
| Inverse of probit, dependent on WEIGHT and AGE, has random effect | Cl = probitinv(theta1 + theta2*WEIGHT + theta3*AGE
+ eta1) |
| Inverse of logit, dependent on WEIGHT and AGE, has random effect | Cl = logitinv(theta1 + theta2*WEIGHT + theta3*AGE
+ eta1) |
Tip
To simultaneously fit data from multiple dose levels, use a CovariateModel object
as an input argument to sbiofitmixed,
and omit the random effect (eta) from the Expression property
in the CovariateModel object.
The Expression property must meet the following
requirements:
The expressions are valid MATLAB® code.
Each expression is linear with a transformation.
There is exactly one expression for each parameter.
In each expression, a covariate is used in at most one term.
In each expression, there is at most one random effect
(eta)
Fixed effect (theta) and random
effect (eta) names are unique within and across
expressions. That is, each covariate has its own fixed effect.
Tip
Use the getCovariateData method
to view the covariate data when writing equations for the Expression property
of a CovariateModel object.
Tip
Use the verify method
to check that the Expression property of a CovariateModel object
meets the conditions described previously.
| Applies to | Object: CovariateModel |
| Data type | Character vector or cell array of character vectors |
| Data values | parameterName = relationship |
| Access | Read/write |