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

Description

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

Usage

ursa(fixed = rep(NA, 7), names = c("b1", "b2", "c", "d", "e1", "e1", "f"), 
  ssfct = NULL)
  
  genursa(fixed = rep(NA, 13), 
  names = c("b1", "b2", "c1", "c2", "d", "e1", "e2", "f1", "f2", "e3", "f3", "b3", "c3"), 
  ssfct = NULL)
  
  actimL(fixed = rep(NA, 14), names = 
  c("b1", "b2", "c1", "c2", "d", "e1", "e2", "f1", "f2", "e3", "f3", "b3", "c3", "g"), 
  ssfct = NULL)
  
  genLoewe(fixed = rep(NA, 8), names = 
  c("b1", "b2", "c", "d", "e1", "e2", "f1", "f2"), ssfct = NULL)
  
  genLoewe2(fixed = rep(NA, 9), names = 
  c("b1", "b2", "c1", "c2", "d", "e1", "e2", "f1", "f2"), ssfct = NULL)
  
  iceLoewe.1(fixed = rep(NA, 7), names = 
  c("b1", "b2", "c", "d", "e1", "e2", "f"), ssfct = NULL)
  
  iceLoewe2.1(fixed = rep(NA, 8), names = 
  c("b1", "b2", "c1", "c2", "d", "e1", "e2", "f"), ssfct = NULL)
  
  genBliss(fixed = rep(NA, 8), names = 
  c("b1", "b2", "c", "d", "e1", "e2", "f1", "f2"), ssfct = NULL)

  genBliss2(fixed = rep(NA, 9), names = 
  c("b1", "b2", "c1", "c2", "d", "e1", "e2", "f1", "f2"), 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).

Value

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

Details

The model function is defined implicitly through an appropriate equation. The details are found in Syracuse and Greco (1986), Greco et al (1990, 1995).

References

Finney, D. J. (1979) Bioassay and the Practise of Statistical Inference, Int. Statist. Rev., 47, 1--12. Syracuse, K. C. and Greco, W. R. (1986) Comparison between the method of Chou and Talalay and a new method for the assessment of the combined effects of drugs: A Monte-Carlo simulation study, Proceedings of the Biopharmaceutical Section of the American Statistical Association, 127--132. 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.

Examples

Run this code

## Note that all R lines below are commented out with one # (takes too long to compile for CRAN)
##  but they are still mostly working fine

## Data from Greco et al (1995)
#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)

## Fitting a Loewe additivity model with common maximum and lower limit 0
#greco.m0a <- drm(effect~d1, data=greco, fct=genLoewe(fixed=c(NA,NA,0,NA,NA,NA,1,1)),
#pmodels=list(~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1))
#summary(greco.m0a)
# not working any longer

#greco.m0a <- drm(effect~d1+d2, data=greco, fct=genLoewe(fixed=c(NA,NA,0,NA,NA,NA,1,1)))
#summary(greco.m0a)

## Fitting a generalized Loewe additivity model with common maximal response
#greco.m0b <- drm(effect~d1, data=greco, fct=genLoewe(fixed=c(NA,NA,NA,NA,NA,NA,NA,NA)), 
#pmodels=list(~1,~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1,~1,~1))

#greco.m0b <- drm(effect~d1+d2, data=greco, fct=genLoewe(fixed=c(NA,NA,0,NA,NA,NA,NA,NA)))
#summary(greco.m0b)
# with NAs

### Checking the model fit
#plot(fitted(greco.m0b), residuals(greco.m0b))

## Fitting reduced model with lower limit c equal to 0
#greco.m0c <- drm(effect~d1, data=greco, fct=genLoewe(fixed=c(NA,NA,0,NA,NA,NA,NA,NA)), 
#pmodels=list(~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1,~1,~1))

## Comparing models by means of an F-test
#anova(greco.m0c, greco.m0b)

## Looking at the summary output
#summary(greco.m0c)

## Below commented out to make faster check on CRAN
## Fitting a generalized Loewe additivity model with different maxima
#greco.m0d <- drm(effect~d1, data=greco, fct=genLoewe2(fixed=c(NA,NA,NA,NA,NA,NA,NA,NA,NA)), 
#pmodels=list(~1,~1,~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1,~1,~1))

#greco.m0d <- drm(effect~d1+d2, data=greco, fct=genLoewe2(fixed=c(NA,NA,NA,NA,NA,NA,NA,1,1)))
#summary(greco.m0d)


## Checking the model fit
#plot(fitted(greco.m0d), residuals(greco.m0d))

## Looking at the summary output
#summary(greco.m0d)  # suboptimal fit!


## Fitting the URSA model
#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))
#summary(greco.m1)

## Fitting the URSA model using values from Greco et al (1995) (p. 364)
#greco.m2 <- drm(effect~d1+d2, data=greco, fct=ursa(fixed=c(NA,NA,0,NA,NA,NA,NA)), 
#start=c(-1.05, -2.04,95.1,11.1,1.07,0.52))
# same fit as above

## Fitting with weights
#greco.m2b <- drm(effect~d1, data=greco, fct=ursa(fixed=c(NA,NA,0,NA,NA,NA,NA)), 
#pmodels=list(~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1,~1), weights=1/residuals(greco.m1)^2, 
#start=coef(greco.m1))
#summary(greco.m2b)

## Adjusting for variance heterogeneity
#greco.m3 <- boxcox(greco.m2, method = "anova")

#plot(fitted(greco.m3), residuals(greco.m3))  # improved, not great
#summary(greco.m3)

## Getting closer to Greco's estimates
#greco.m4<-drm(effect~d1, data=greco, fct=ursa(fixed=c(NA,NA,0,NA,NA,NA,NA)), 
#pmodels=list(~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1,~1), bcVal=0)  # not perfect
#greco.m4 <- drm(effect~d1, data=greco, fct=ursa(fixed=c(NA,NA,0,NA,NA,NA,NA)), 
#pmodels=list(~1,~1,~1,~I(1/d1)-1,~I(1/d2)-1,~1), bcVal=0, 
#start=coef(greco.m3))

#plot(fitted(greco.m4), residuals(greco.m4))  # better!

#summary(greco.m4)

## Fitting the Bliss independence model (with common baseline and maximal response)
#greco.bliss.m0 <- drm(effect~d1+d2, data=greco, fct=genBliss(fixed = c(rep(NA, 6),1,1)))
#summary(greco.bliss.m0)

## Fitting the generalized Bliss independence model (with common baseline and maximal response)
#greco.bliss.m1 <- drm(effect~d1+d2, data=greco, fct=genBliss())
#summary(greco.bliss.m1)
# huge estimated f parameters!
# huge standard errors on e parameter!

# Likelihood ratio test comparing the two Bliss models
#anova(greco.bliss.m1, greco.bliss.m0)
# No need to assume that the f parameters are different from 1


## Fitting the generalized Bliss independence model (with different maximal responses)
#greco.bliss.m2 <- drm(effect~d1+d2, data=greco, fct=genBliss2())
#summary(greco.bliss.m2)
# huge estimated f parameters!
# huge standard errors on e parameter!

#greco.bliss.m3 <- drm(effect~d1+d2, data=greco, fct=genBliss2(fixed=c(rep(NA, 7),1,1)))
#summary(greco.bliss.m3)
# much more realistic estimated e parameters

# Likelihood ratio test comparing the two generalized Bliss models
#anova(greco.bliss.m3, greco.bliss.m2)
# No need to assume that the f parameters are different from 1



## Fitting the actimL model (needs some tweaking with the starting values)
#greco.actimL.m1 <- drm(effect~d1+d2, data=greco, 
#fct=actimL(fixed=c(rep(NA,7),1,1,NA,1,rep(NA,3))))
# now works (July 19 2011)

#greco.actimL.m2 <- drm(effect~d1+d2, data=greco, 
#fct=actimL(fixed=c(rep(NA,7),1,1,NA,1,rep(NA,3))), start=coef(greco.actimL.m1)+rnorm(11,0,0.1))
## perhaps some more tweaking with the starting values is needed to get the standard errors

#summary(greco.actimL.m2)

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