dfpoly function

Fractional polynomial dose-response function

dfpoly(degree = 1, beta.1 = "rel", beta.2 = "rel", power.1 = 0, power.2 = 0)

Arguments

• degree: The degree of the fractional polynomial as defined in \insertCite royston1994;textualMBNMAdose
• beta.1: Pooling for the 1st fractional polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
• beta.2: Pooling for the 2nd fractional polynomial coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
• power.1: Value for the 1st fractional polynomial power ($\gamma_1$). Must take any numeric value in the set -2, -1, -0.5, 0, 0.5, 1, 2, 3.
• power.2: Value for the 2nd fractional polynomial power ($\gamma_2$). Must take any numeric value in the set -2, -1, -0.5, 0, 0.5, 1, 2, 3.

Returns

An object of class("dosefun")

Details

• $\beta_1$ represents the 1st coefficient.
• $\beta_2$ represents the 2nd coefficient.
• $\gamma_1$ represents the 1st fractional polynomial power
• $\gamma_2$ represents the 2nd fractional polynomial power

For a polynomial of degree=1:

$${\beta_1}x^{\gamma_1}$$

For a polynomial of degree=2:

$${\beta_1}x^{\gamma_1}+{\beta_2}x^{\gamma_2}$$

$x^{\gamma}$ is a regular power except where $\gamma=0$, where $x^{(0)}=ln(x)$. If a fractional polynomial power $\gamma$ repeats within the function it is multiplied by another $ln(x)$.

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().

Examples

# 1st order fractional polynomial a value of 0.5 for the power
dfpoly(beta.1="rel", power.1=0.5)

# 2nd order fractional polynomial with relative effects for coefficients
# and a value of -0.5 and 2 for the 1st and 2nd powers respectively
dfpoly(degree=2, beta.1="rel", beta.2="rel",
  power.1=-0.5, power.2=2)

References

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