ursa function

Model function for the universal response surface approach (URSA) for the quantitative assessment of drug interaction

URSA provides a parametric approach for modelling the joint action of several agents. The model allows quantification of synergistic effects through a single parameter. 1.1

ursa(fixed = rep(NA, 7), names = c("b1", "b2", "c", "d", "e1", "e1", "f"), 
  ssfct = NULL)

Arguments

• fixed: numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
• names: a vector of character strings giving the names of the parameters. The default is reasonable.
• ssfct: a self starter function to be used (optional).

Details

The model function is defined implicitly through an appropriate equation. More details are provided by Greco et al (1990, 1995).

Returns

A list containing the nonlinear function, the self starter function, and the parameter names.

References

Greco, W. R. and Park H. S. and Rustum, Y. M. (1990) Application of a New Approach for the Quantitation of Drug Synergism to the Combination of cis-Diamminedichloroplatinum and 1-beta-D-Arabinofuranosylcytosine, Cancer Research, 50 , 5318--5327.

Greco, W. R. Bravo, G. and Parsons, J. C. (1995) The Search for Synergy: A Critical Review from a Response Surface Perspective, Pharmacological Reviews, 47 , Issue 2, 331--385.

Author(s)

Christian Ritz after an idea by Hugo Ceulemans.

See Also

Other models for fitting mixture data are the Hewlett and Voelund models mixture.

Examples

## Here is the complete statistical analysis of the data 
##  from Greco et al. (1995) by means of the URSA model
if (FALSE)
{
d1 <- c(0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 10, 20, 50, 2, 2, 2, 
2, 2, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 20, 20, 20, 20, 
20, 50, 50, 50, 50, 50)

d2 <- c(0, 0, 0, 0.2, 0.5, 1, 2, 5, 0, 0, 0, 0, 0, 0.2, 
0.5, 1, 2, 5, 0.2, 0.5,  1, 2, 5, 0.2, 0.5, 1, 2, 5, 0.2, 
0.5, 1, 2, 5, 0.2, 0.5, 1, 2, 5)

effect <- c(106.00, 99.20, 115.00, 79.20, 70.10, 49.00, 
21.00, 3.83, 74.20, 71.50,48.10, 30.90, 16.30, 76.30, 
48.80, 44.50, 15.50, 3.21, 56.70, 47.50, 26.80, 16.90, 
3.25, 46.70, 35.60, 21.50, 11.10, 2.94, 24.80, 21.60, 
17.30, 7.78, 1.84, 13.60, 11.10, 6.43, 3.34, 0.89)

greco <- data.frame(d1, d2, effect)

greco.m1 <- drm(effect ~ d1 + d2, data = greco, fct = ursa(fixed = c(NA, NA, 0, NA, NA, NA, NA)))

plot(fitted(greco.m1), residuals(greco.m1)) # wedge-shaped

summary(greco.m1)
 
## Transform-both-sides approach using a logarithm transformation
greco.m2 <- drm(effect ~ d1 + d2, data = greco, fct = ursa(fixed = c(NA, NA, 0, NA, NA, NA, NA)), 
bcVal = 0, control = drmc(relTol = 1e-12))

plot(fitted(greco.m2), residuals(greco.m2))  # looks okay

summary(greco.m2)
# close to the estimates reported by Greco et al. (1995)
}