deviationSurface: Non-interacting Reference Surfaces

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

Non-interacting Reference Surfaces

Description

Estimate the best fitting non-interacting reference surface according to multiple methods, including Loewe, Bliss, and HSA

Usage

deviationSurface(concs, act, method = "Bliss", ...)

referenceSurface(concs, act, method = "Bliss", ...)

blissDeviation(concs, act, range, clip = "none")

blissReference(concs, act, range, clip = "none")

hsaDeviation(concs, act, increasing)

hsaReference(concs, act, increasing)

loeweDeviation(concs, act, weights = NULL, limits = c(NA, NA))

loeweReference(concs, act, weights = NULL, limits = c(NA, NA))

zipDeviation(concs, act, range, weights = NULL, limits = c(NA, NA))

zipReference(concs, act, range, weights = NULL, limits = c(NA, NA))

zipSmoothed(concs, act, range, weights = NULL, limits = c(NA, NA))

Arguments

concs	A width-two array of concentrations representing all measured dose pairs
act	A vector of measured activity or effect values
method	A string specifying which model of non-interaction should be used; possible values are "Bliss" (the default), "HSA", "Loewe", and "ZIP"
...	Additional parameters to be passed to the method-specific deviation or reference surface functions
range	For Bliss calculations, the range of effects assumed by Bliss independence; a two-element numeric vector containing the minimal effect and the maximal effect, in that order. For ZIP calculations, the initial estimate of the minimal and maximal effects used in fitting the individual dose response curves.
clip	Clipping method for Bliss reference and deviation calculations. Possible values are "pre", "post", and "none". See details for specifics.
increasing	For HSA calculations, is the effect increasing (TRUE) meaning the "highest" single agent activity is numerically greater; or decreasing (FALSE), meaning the "highest" single agent activity is numerically lower. The latter may be appropriate when the modeled response is target growth or survival.
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	For Loewe and ZIP calculations, 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.

Details

This collection of functions can be used to implement a family of combination analysis methods known as "deviation" methods. The details of the methods differ, but the core strategy is common to all of them: estimate what a given response measurement would be based on individual behaviors and some model of non-interaction, and use the deviation of the measured response from that expected response as a measure of the degree of synergy or antagonism.

Bliss independence is the most widely used of these, and can be described as the assumption that any response represents a fraction of the target population being unaffected, and that a combined response corresponds to the product of these fractions for both drugs (Bliss, 1939). It is extremely simple to calculate, and relies on the intuitive model of probabilisticalyly independent events. Because it treats responses as a scaled representation of probabilities, it requires that all values be expressed relative to two limiting values: the response seen when all targets are unaffected (the minimal effect) and the response seen when none of the targets remain unaffected (the maximal effect). For a Bliss independent surface to be estimated, these two values must be provided, using the parameter range. Further, because values outside of this range would represent proportions above 1 or below 0, most Bliss calculations involve some adjustment of the data to ensure they always lie within the specified range. The Bliss functions support two ways of doing this to generate a reference surface: "pre" will clip all values to the range immediately; "post" will clip all calculated responses to the given range after they have been combined. A third option, "none", performs no clipping at all, and allows for proportions outside of the 0 to 1 range.

The highest-single-agent, or HSA model, is even simpler than Bliss. The effect of a combined pair of doses is simply the "greater" of the individual effects produced by the two drugs at those levels. The word "greater" is placed in quotes here as taking the larger response value is only appropriate when a numerically larger measurement corresponds to greater activity. For survival or growth inhibition studies, the reverse may be true; the parameter increasing allows the user to specify this directionality.

Loewe additivity is one of the oldest models of non-interaction, and the inspiration for BRAID additivity (Loewe and Muischnek, 1926). According to Loewe additivity, the combined response to a pair of doses the the effect such that the two individual doses represent complementary fractions of the individual doses of both drugs that produce the same effect in isolation. It is considered the gold standard of non-interaction by many researchers, but = has several significant pragmatic disadvantages. It requires that the full dose response behavior of both drugs is known, and that they produce an identical range of effects. The loeweReference and loeweDeviation functions perform basic dose response fitting with the additional constraint of matching minimal and maximal effects, either fixed by the limits parameter or estimated directly from the data.

The zero-interaction potency, or ZIP, model is a variant of Bliss independence that uses smoothing to give more robust values (Wooten et al. 2015). The reference surface is calculated by fitting the dose response of the individual drugs and then combining them using Bliss independence; the method then adds additional robustness and smooths the measured surface itself by fitting each constant-dose set of data points as its own dose response curve, constrained to match the other drug's effect when the first drug is zero. Fitting these partial dose-response curves in either direction produces a smoothed version of the original measurements (which can be accessed directly using the function zipSmoothed), from which the reference surface is subtracted to get the deviation (or "delta") surface.

Value

For the deviation functions (deviationSurface, blissDeviation, hsaDeviation, loeweDeviation, and zipDeviation), a vector of values the same length as act and/or concs representing the deviation of the measurement from the specified reference surface. For the reference functions (referenceSurface, blissReference, hsaReference, loeweReference, and zipReferences), a vector of values the same length as act and/or concs containing the appropriate non-interacting reference surface itself. For zipSmoothed, the smoothed measurement surface given by ZIP's dose-response-based smoothing method (see Details).

References

Bliss, Chester I. 1939. “The Toxicity of Poisons Applied Jointly 1.” Annals of Applied Biology 26 (3): 585–615.

Loewe, S, and H Muischnek. 1926. “Uber Kombinationswirkungen.” Naunyn. Schmiedebergs. Arch. Pharmacol. 114: 313–26.

Yadav, Bhagwan, Krister Wennerberg, Tero Aittokallio, and Jing Tang. 2015. “Searching for Drug Synergy in Complex Dose–Response Landscapes Using an Interaction Potency Model.” Computational and Structural Biotechnology Journal 13: 504–13.

Examples

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

sum(deviationSurface(concs1,act1,"Bliss",range=c(0,1)))
sum(deviationSurface(concs1,act1,"Loewe"))
surface$hsa <- hsaReference(concs1,act1,increasing=TRUE)

surface <- synergisticExample
concs2 <- cbind(surface$concA,surface$concB)
act2 <- surface$measure

sum(deviationSurface(concs2,act2,"ZIP",range=c(0,1)))
sum(deviationSurface(concs2,act2,"Loewe"))
surface$smooth <- zipSmoothed(concs2,act2,range=c(0,1))

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