MBNMAdose (version 0.5.0)

dpoly: Polynomial dose-response function

Description

Polynomial dose-response function

Usage

dpoly(
  degree = 1,
  beta.1 = "rel",
  beta.2 = "rel",
  beta.3 = "rel",
  beta.4 = "rel"
)

Value

An object of class("dosefun")

Arguments

degree

The degree of the polynomial - e.g. degree=1 for linear, degree=2 for quadratic, degree=3 for cubic.

beta.1

Pooling for the 1st polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

beta.2

Pooling for the 2nd polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

beta.3

Pooling for the 3rd polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

beta.4

Pooling for the 4th polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

Dose-response parameters

Argument	Model specification
"rel"	Implies that relative effects should be pooled for this dose-response parameter separately for each agent in the network.
"common"	Implies that all agents share the same common effect for this dose-response parameter.
"random"	Implies that all agents share a similar (exchangeable) effect for this dose-response parameter. This approach allows for modelling of variability between agents.
numeric()	Assigned a numeric value, indicating that this dose-response parameter should not be estimated from the data but should be assigned the numeric value determined by the user. This can be useful for fixing specific dose-response parameters (e.g. Hill parameters in Emax functions) to a single value.

When relative effects are modelled on more than one dose-response parameter, correlation between them is automatically estimated using a vague inverse-Wishart prior. This prior can be made slightly more informative by specifying the scale matrix omega and by changing the degrees of freedom of the inverse-Wishart prior using the priors argument in mbnma.run().

Details

• \(\beta_1\) represents the 1st coefficient.

• \(\beta_2\) represents the 2nd coefficient.

• \(\beta_3\) represents the 3rd coefficient.

• \(\beta_4\) represents the 4th coefficient.

Linear model: $$\beta_1{x}$$

Quadratic model: $$\beta_1{x} + \beta_2{x^2}$$

Cubic model: $$\beta_1{x} + \beta_2{x^2} + \beta_3{x^3}$$

Quartic model: $$\beta_1{x} + \beta_2{x^2} + \beta_3{x^3} + \beta_4{x^4}$$

References

Examples

# Linear model with random effects
dpoly(beta.1="rel")

# Quadratic model dose-response function
# with an exchangeable (random) absolute parameter estimated for the 2nd coefficient
dpoly(beta.1="rel", beta.2="random")