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 Royston and Altman (1994)
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.

Value

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().

References

Royston P, Altman D (1994). “Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling.” Journal of the Royal Statistical Society: Series C, 43(3), 429-467.

Examples

# 1st order fractional polynomial a value of 0.5 for the power
dfpoly(beta.1="rel", power.1=0.5)
#> $name
#> [1] "fpoly"
#> 
#> $fun
#> ~beta.1 * ifelse(dose > 0, ifelse(power.1 == 0, log(dose), dose^power.1), 
#>     0)
#> <environment: 0x55c4668db670>
#> 
#> $params
#> [1] "beta.1"  "power.1"
#> 
#> $nparam
#> [1] 2
#> 
#> $jags
#> [1] "s.beta.1[agent[i,k]] * ifelse(dose[i,k]>0, ifelse(s.beta.2[agent[i,k]]==0, log(dose[i,k]), dose[i,k]^s.beta.2[agent[i,k]]), 0)"
#> 
#> $apool
#>  beta.1 power.1 
#>   "rel"   "0.5" 
#> 
#> $bname
#>   beta.1  power.1 
#> "beta.1" "beta.2" 
#> 
#> attr(,"class")
#> [1] "dosefun"

# 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)
#> $name
#> [1] "fpoly"
#> 
#> $fun
#> ~beta.1 * ifelse(dose > 0, ifelse(beta.3 == 0, log(dose), dose^beta.3), 
#>     0) + (beta.2 * ifelse(beta.4 == beta.3, ifelse(dose > 0, 
#>     ifelse(beta.4 == 0, log(dose)^2, (dose^beta.4) * log(dose)), 
#>     0), ifelse(dose > 0, ifelse(beta.4 == 0, log(dose), dose^beta.4), 
#>     0)))
#> <environment: 0x55c466758fb8>
#> 
#> $params
#> [1] "beta.1"  "beta.2"  "power.1" "power.2"
#> 
#> $nparam
#> [1] 4
#> 
#> $jags
#> [1] "s.beta.1[agent[i,k]] * ifelse(dose[i,k]>0, ifelse(s.beta.3[agent[i,k]]==0, log(dose[i,k]), dose[i,k]^s.beta.3[agent[i,k]]), 0) + (s.beta.2[agent[i,k]] * ifelse(s.beta.4[agent[i,k]]==s.beta.3[agent[i,k]], ifelse(dose[i,k]>0, ifelse(s.beta.4[agent[i,k]]==0, log(dose[i,k])^2, (dose[i,k]^s.beta.4[agent[i,k]]) * log(dose[i,k])), 0), ifelse(dose[i,k]>0, ifelse(s.beta.4[agent[i,k]]==0, log(dose[i,k]), dose[i,k]^s.beta.4[agent[i,k]]), 0)))"
#> 
#> $apool
#>  beta.1  beta.2 power.1 power.2 
#>   "rel"   "rel"  "-0.5"     "2" 
#> 
#> $bname
#>   beta.1   beta.2  power.1  power.2 
#> "beta.1" "beta.2" "beta.3" "beta.4" 
#> 
#> attr(,"class")
#> [1] "dosefun"