estimateCombinationIndices: Combination Index

In braidrm: Fitting Combined Action with the BRAID Response Surface Model

Combination Index

Description

Estimates the combination index using the median effet method of Chou and Talalay (1984) or the more robust method of non-linear optimization.

Usage

estimateCombinationIndices(
  concs,
  act,
  level,
  weights = NULL,
  limits = c(NA, NA)
)

estimateCombinationIndex(dr1, dr2, drc, ratio, level, limits = c(NA, NA))

estimateChouIndices(concs, act, level, range, excess = "clip")

estimateChouIndex(dr1, dr2, drc, ratio, level, range, excess = "clip")

Arguments

concs	A width-two array of concentrations representing all measured dose pairs
act	A vector of measured activity or effect values
level	A numeric vector of one or more effect levels at which to estimate the combination index
weights	A vector of weights (between 0 and 1) the same length as the data which determines the weight with which each measurement will impact the the sum of squared errors. Weights will be multiplied by errors before squaring. If NULL (the default) all weights will be set to 1. Can be a numeric vector, or the name of a column in data if formula is a symbolic formula
limits	The fixed values of the minimal and maximal effects of the drugs and the combination. By default, both values are set to NA; any value set to NA will fit from the data.
dr1	A data frame with two columns, conc and act reflecting the dose response behavior of the first drug alone
dr2	A data frame with two columns, conc and act reflecting the dose response behavior of the second drug alone
drc	A data frame with two columns, conc and act reflecting the dose response behavior of a constant ratio combination; conc should be the combined concentrations of the two drugs
ratio	The ratio of the two drugs in the constant ratio combination (dose A to dose B)
range	The range of effects assumed by the median effect model; a two-element numeric vector containing the minimal effect and the maximal effect, in that order.
excess	For estimateChouIndices and estimateChouIndex, what should be done with values outside the expected range. If "clip" (the default), values will be clipped to 0.1% and 99.9% of the expected range; if "drop", values outside the range will be dropped

Details

The combination index is a peculiar method, as it does not produce values corresponding to each measurement (as the deviation methods do), nor does it produce a value shared by the entire surface (as response surface methods do). It instead, produces a value associated with a particular effect level and a particular dose ratio. This makes implementing the method consistently for a wide range of possible data sources quite tricky; nevertheless, we have attempted to do so here. In brief, the combination index method involves fitting the dose response of both individual drugs and and a constant ratio combination of the drugs (treated as a virtual third drug). It the compares the potency of the constant-ratio combination (estimated a particular effect level) with the expected potency according to Loewe additivity, and returns the degree to which the combination is more potent (with a combination index less than 1) or less potent (with a combination greater than one) than expected by additivity. This method is also in turns known as the sum of fractional inhibitory coefficients (FICs), observed-over-expected, or originally as Berenbaum's interaction index.

Because the method was originally built for three distinct sets of dose response measurements, we have included the estimateCombinationIndex and estimateChouIndex functions which operate on three separate data frames. However, in most cases, it will be easier to use the estimateCombinationIndices and estimateChouIndices functions, which operate on an array of concentrations and a vector of responses, just like the numerous other functions in this package, and generate a set of combination index values with level and ratio information included.

The only difference between the ⁠estimateCombination*⁠ and ⁠estimateChou*⁠ functions is the way in which they perform dose response fitting. The ⁠estimateCombination*⁠ functions use non-linear least squares optimization (based on the package basicdrm) to estimate dose-response parameters. The ⁠estimateChou*⁠ functions use the median-effect method described by Chou and Talalay in their 1984 paper, which linearized all measurements and performs linear regression. We do not recommend using these methods, as they are much less reliable than the non-linear optimization approach and extremely susceptible to noise at extreme values.

Value

For estimateCombinationIndices and estimateChouIndices, a data frame with the following columns:

• ratio: The ratio of doses (dose A to dose B) along which the index was estimated

• level: The effect level at which the index was estimated

• ci: The estimated combination index at that dose ratio and effect level

Combination index estimates will be included for all provided effect levels and all dose ratios present. For estimateCombinationIndex and estimateChouIndex, a vector of estimated combinatoin indices the same length as level.

References

Berenbaum, MC. 1978. “A Method for Testing for Synergy with Any Number of Agents.” Journal of Infectious Diseases 137 (2): 122–30.

Berenbaum, MC. 1989. “What Is Synergy.” Pharmacol Rev 41: 93–141.

Chou, Ting-Chao, and Paul Talalay. 1984. “Quantitative Analysis of Dose-Effect Relationships: The Combined Effects of Multiple Drugs or Enzyme Inhibitors.” Advances in Enzyme Regulation 22: 27–55.

Examples

surface <- synergisticExample
concs1 <- cbind(surface$concA, surface$concB)
act1 <- surface$measure

estimateCombinationIndices(concs1,act1,c(0.5))

dr1 <- surface[surface$concB==0, c("concA","measure")]
names(dr1) <- c("conc","act")
dr2 <- surface[surface$concA==0, c("concB","measure")]
names(dr2) <- c("conc","act")
drc <- surface[surface$concA==surface$concB,]
drc$conc <- drc$concA+drc$concB
drc <- drc[,c("conc","measure")]
names(drc) <- c("conc","act")

estimateChouIndex(dr1,dr2,drc,ratio=1,
                  level=c(0.5,0.9,0.99),
                  range=c(0,1))

braidrm documentation built on Sept. 30, 2024, 9:40 a.m.