Spline dose-response functions — dspline • MBNMAdose

Used to fit B-splines, natural cubic splines, and piecewise linear splines(Perperoglu et al. 2019) .

dspline(
  type = "bs",
  knots = 1,
  degree = 1,
  beta.1 = "rel",
  beta.2 = "rel",
  beta.3 = "rel",
  beta.4 = "rel",
  beta.5 = "rel",
  beta.6 = "rel"
)

Arguments

type: The type of spline. Can take "bs" (B-spline), "ns" (natural cubic spline), or "ls" (piecewise linear spline)
knots: The number/location of spline internal knots. If a single number is given it indicates the number of knots (they will be equally spaced across the range of doses for each agent). If a numeric vector is given it indicates the location of the knots.
degree: The degree of the piecewise B-spline polynomial - e.g. degree=1 for linear, degree=2 for quadratic, degree=3 for cubic.
beta.1: Pooling for the 1st coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
beta.2: Pooling for the 2nd coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
beta.3: Pooling for the 3rd coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
beta.4: Pooling for the 4th coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
beta.5: Pooling for the 5th coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).
beta.6: Pooling for the 6th coefficient. Can take "rel", "common", "random" or be assigned a numeric value (see details).

Value

An object of class("dosefun")

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

Perperoglu A, Sauerbrei W, Abrahamowicz M, Schmid M (2019). “A review of spline function procedures in R.” BMC Medical Research Methodology, 19(46), 1-16. doi:10.1186/s12874-019-0666-3 .

Examples

# Second order B spline with 2 knots and random effects on the 2nd coefficient
dspline(type="bs", knots=2, degree=2,
  beta.1="rel", beta.2="rel")
#> $name
#> [1] "bs"
#> 
#> $fun
#> ~beta.1 * spline.1 + beta.2 * spline.2 + beta.3 * spline.3 + 
#>     beta.4 * spline.4
#> <environment: 0x55e2699242b0>
#> 
#> $params
#> [1] "beta.1" "beta.2" "beta.3" "beta.4"
#> 
#> $nparam
#> [1] 4
#> 
#> $knots
#> $knots[[1]]
#> [1] 2
#> 
#> 
#> $degree
#> [1] 2
#> 
#> $jags
#> [1] "s.beta.1[agent[i,k]] * spline[i,k,1] + s.beta.2[agent[i,k]] * spline[i,k,2] + s.beta.3[agent[i,k]] * spline[i,k,3] + s.beta.4[agent[i,k]] * spline[i,k,4]"
#> 
#> $apool
#> beta.1 beta.2 beta.3 beta.4 
#>  "rel"  "rel"  "rel"  "rel" 
#> 
#> $bname
#>   beta.1   beta.2   beta.3   beta.4 
#> "beta.1" "beta.2" "beta.3" "beta.4" 
#> 
#> attr(,"class")
#> [1] "dosefun"

# Piecewise linear spline with knots at 0.1 and 0.5 quantiles
# Single parameter independent of treatment estimated for 1st coefficient
#with random effects
dspline(type="ls", knots=c(0.1,0.5),
  beta.1="random", beta.2="rel")
#> $name
#> [1] "ls"
#> 
#> $fun
#> ~beta.1 * spline.1 + beta.2 * spline.2 + beta.3 * spline.3
#> <environment: 0x55e26ad4c970>
#> 
#> $params
#> [1] "beta.1" "beta.2" "beta.3"
#> 
#> $nparam
#> [1] 3
#> 
#> $knots
#> $knots[[1]]
#> [1] 0.1 0.5
#> 
#> 
#> $degree
#> [1] 1
#> 
#> $jags
#> [1] "s.beta.1[agent[i,k]] * spline[i,k,1] + s.beta.2[agent[i,k]] * spline[i,k,2] + s.beta.3[agent[i,k]] * spline[i,k,3]"
#> 
#> $apool
#>   beta.1   beta.2   beta.3 
#> "random"    "rel"    "rel" 
#> 
#> $bname
#>   beta.1   beta.2   beta.3 
#> "beta.1" "beta.2" "beta.3" 
#> 
#> attr(,"class")
#> [1] "dosefun"