Example: Single experiment

In the R package, we’ve attached two example datasets from a large drug combination screening experiment on diffuse large B-cell lymphoma. We’ll use these to show some simple use cases of the main functions and how to interpret the results.

Let’s load in the first example and have a look at it

library(bayesynergy)
data("mathews_DLBCL")
y = mathews_DLBCL[[1]][[1]]
x = mathews_DLBCL[[1]][[2]]
head(cbind(y,x))

##      Viability ibrutinib ispinesib
## [1,] 1.2295618    0.0000         0
## [2,] 1.0376006    0.1954         0
## [3,] 1.1813851    0.7812         0
## [4,] 0.5882688    3.1250         0
## [5,] 0.4666700   12.5000         0
## [6,] 0.2869514   50.0000         0

We see that the the measured viability scores are stored in the vector y, while x is a matrix with two columns giving the corresponding concentrations where the viability scores were read off.

Fitting the regression model is simple enough, and can be done on default settings simply by running the following code (where we add the names of the drugs involved, the concentration units for plotting purposes, and calculate the bayes factor).

fit = bayesynergy(y,x, drug_names = c("ibrutinib", "ispinesib"),
                  units = c("nM","nM"),bayes_factor = T)

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## Calculating the Bayes factor

The resulting model can be summarised by running

summary(fit)

##                 mean  se_mean     sd      2.5%       50%  97.5% n_eff Rhat
## la_1[1]       0.3327 0.002030 0.0754  1.55e-01  3.43e-01  0.455  1379 1.00
## la_2[1]       0.3831 0.003669 0.0699  1.14e-01  3.96e-01  0.457   363 1.01
## log10_ec50_1  0.4842 0.004285 0.1588  2.46e-01  4.48e-01  0.868  1373 1.00
## log10_ec50_2 -1.0214 0.022533 1.0396 -3.35e+00 -8.64e-01  0.485  2129 1.00
## slope_1       2.0070 0.018769 0.9094  8.53e-01  1.79e+00  4.242  2348 1.00
## slope_2       1.4638 0.023353 1.1144  8.95e-02  1.20e+00  4.380  2277 1.00
## ell           3.0573 0.031525 1.4626  1.25e+00  2.74e+00  6.551  2153 1.00
## sigma_f       0.8230 0.015463 0.8064  1.70e-01  6.00e-01  2.767  2720 1.00
## s             0.0969 0.000283 0.0151  7.30e-02  9.49e-02  0.132  2851 1.00
## dss_1        33.4547 0.043492 2.9305  2.75e+01  3.35e+01 39.028  4540 1.00
## dss_2        59.4281 0.047148 2.7633  5.37e+01  5.95e+01 64.632  3435 1.00
## rVUS_f       82.7376 0.013881 0.8703  8.10e+01  8.27e+01 84.419  3931 1.00
## rVUS_p0      73.0236 0.035422 2.1692  6.84e+01  7.31e+01 77.097  3750 1.00
## VUS_Delta    -9.7139 0.036606 2.3281 -1.47e+01 -9.65e+00 -5.349  4045 1.00
## VUS_syn      -9.7625 0.036161 2.2869 -1.47e+01 -9.68e+00 -5.538  3999 1.00
## VUS_ant       0.0486 0.001903 0.1143  4.71e-06  8.53e-05  0.364  3607 1.00
## 
## log-Pseudo Marginal Likelihood (LPML) =  52.45587 
## Estimated Bayes factor in favor of full model over non-interaction only model:  31.65008

which gives posterior summaries of the parameters of the model.

In addition, the model calculates summary statistics of the monotherapy curves and the dose-response surface including drug sensitivity scores (DSS) for the two drugs in question, as well as the volumes that capture the notion of efficacy (rVUS_f), interaction (VUS_Delta), synergy (VUS_syn) and interaction (VUS_ant).

As indicated, the total combined drug efficacy is around 80% (rVUS_f), of which around 70 percentage points can be attributed to \(p_0\) (rVUS_p0), leaving room for 10 percentage points worth of synergy (VUS_syn). We can also note that the model is fairly certain of this effect, with a 95% credible interval given as (-14.688, -5.538). The certainty of this is also verified by the Bayes factor, which at 31.65 indicates strong evidence of an interaction effect present in the model.

Visualization

Monotherapy curves, 2D contour plots

We can also create plots by simply running

plot(fit, plot3D = F)

which produces monotherapy curves, monotherapy summary statistics, 2D contour plots of the dose-response function \(f\), the non-interaction assumption \(p_0\) and the interaction \(\Delta\). The last plot displays the \(rVUS\) scores as discussed previously, with corresponding uncertainty.

3D interactive plots

The package can also generate 3D interactive plots by setting plot3D = T. These are displayed as following using the plotly library (Plotly Technologies Inc. (2015)).

Dose-response

Non-interaction

Interaction

References

Plotly Technologies Inc. 2015. “Collaborative Data Science.” Montreal, QC: Plotly Technologies Inc. 2015. https://plot.ly.