Fit a MuSyC Synergy Model — MuSyC

The MuSyC synergy model is a bivariate functional form with Bliss and Loewe synergy models models as special cases described in (Meyer, et al., 2019) and (Wooten, et al., 2021).

The functional form is


    <response> ~ MuSyC(
      <treatment 1> - <logd1scale>,
      <treatment 2> - <logd2scale>,
      logE0,
      logC1, logE1, h1,
      logC2, logE2, h2,
      logE3, logalpha)

See MuSyC_robust() for the full mathematical description of the MuSyC function. By default the observed data (and therefore should be columns in the input data data.frame) are

<treatment 1>: logd1, the log10 of the dose as a molar concentration of treatment 1
<treatment 2>: logd2, the log10 of the dose as a molar concentration of treatment 2
<response>: response, with unspecified units

The logd1scale and logd2scale are used to center <treatment 1> and <treatment 2> to make fitting more numerically stable. If they are not in the input data, then they are taken to be the mean of <treatment 1> and <treatment 2> respectively.

The modeled parameters are

logE0: the log(<response>) when <treatment 1> = 0 and <treatment 2> = 0
logC1: the log(<treatment 1>) where when <treatment 2> = 0, the <response> is halfway between E0 and E1
logE1: the log(response) when <treatment 1> => Inf and <treatment 2> = 0
h1: the hill slope of the response with respect to <treatment 1> when <treatment 1> = C1 and <treatment 2> = 0. See MuSyC_hi_to_si() and MuSyC_si_to_hi() for converting between the slope (si) and hill slope (hi).
logC2: the log(<treatment 2>) where when <treatment 1> = 0, the <response> is halfway between E0 and E2
logE2: the log(response) when <treatment 2> => Inf and <treatment 1> = 0
h2: the hill slope of the response with respect to <treatment 2> when <treatment 2> = C2 and <treatment 1> = 0. See MuSyC_hi_to_si() and MuSyC_si_to_hi() for converting between the slopec(si) and hill slope (hi).
logE3: the log(response) when <treatment1 1> => Inf and <treatment 2> => Inf, modeling the synergistic efficacy
logalpha: the log of the synergistic potency alpha. When alpha > 1 the treatments are synergistic so that <treatment 1>`` shifts the response due to <treatment 2>to lower doses and visa versa. Whenalpha < 1the treatments are antagonistic so that<treatment 1>shifts the response to<treatment 2>` to higher doses and vise versa

Usage

MuSyC_model(
  data,
  prior = MuSyC_prior(),
  init = MuSyC_init(),
  formula = MuSyC_formula(),
  control = list(adapt_delta = 0.99, max_treedepth = 12),
  stanvars = c(MuSyC_stanvar(), MuSyC_genquant()),
  expose_functions = TRUE,
  ...
)

Arguments

data: data.frame of observed data. It must contain columns for the treatment, response and any additional predictors specified in the formula. See sigmoid_agonist_formula() for more details.
prior: brms::brmsprior() for the model parameters. To create a prior for the MuSyC model, use the MuSyC_prior() function.
init: function giving the initial values for the parameters. To specify the initial values, use the MuSyC_init() function.
formula: bpformula object. To create a formula for the MuSyC model, use the MuSyC_formula() function.
control: a named list of arguments to control the sampler's behavior. Adding max_treedepth and giving a greater value than 10 can improve model convergence.
stanvars: stanvars code for the MuSyC model.
expose_functions: logical. Expose the sigmoid function used in the model. This is needed e.g. for brms::loo_compare()
...: additional arguments passed to brms::brm()

References

Meyer, D.J., Wooten, D.J., Paudel B.B., Bauer, J., Hardeman, K.N., Westover, D., Lovly, C.M., Harris, L.A., Tyson D.R., Quaranta, V., Quantifying Drug Combination Synergy along Potency and Efficacy Axes, Cell Syst. 8, 2 (2019). https://doi.org/10.1016/j.cels.2019.01.003

Wooten, D.J., Meyer, C.T., Lubbock, A.L.R. et al. MuSyC is a consensus framework that unifies multi-drug synergy metrics for combinatorial drug discovery. Nat Commun 12, 4607 (2021). https://doi.org/10.1038/s41467-021-24789-z