Documentation |
Define relationship between parameters and covariates
The Expression property is a string or cell array of strings, where each string 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 string must be in the form:
parameterName = relationship |
This example of an expression string 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 expression strings are valid MATLAB^{®} code.
Each expression string is linear with a transformation.
There is exactly one expression string for each parameter.
In each expression string, a covariate is used in at most one term.
In each expression string, there is at most one random effect (eta)
Fixed effect (theta) and random effect (eta) names are unique within and across expression strings. 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 | String or cell array of strings |
Data values | parameterName = relationship |
Access | Read/write |