A statistical framework for defining synergistic anticancer drug interactions

A statistical framework to detect significant drug combination synergies in cancer. Using reference null distributions across various synergy metrics and tissue tissues, we provide empirical p-values to standardize synergy detection, uncover novel effects, and enable rigorous evaluation of drug combinations.

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Quick start: Direct application of tissue-specific reference (null) distributions for synergy scores

# Load all required libraries (PS: Install if any is missing).
pkgs <- c("dplyr", "readxl", "openxlsx","ggplot2")  
to_install <- setdiff(pkgs, rownames(installed.packages()))
if (length(to_install)) install.packages(to_install)
invisible(lapply(pkgs, library, character.only = TRUE))

# Load reference distributions (example structure: Drug.combination, Synergy.score, Method (optional), cell, type)
zip_results   <- readxl::read_excel("Data/ZIP_results.xlsx")
bliss_results <- readxl::read_excel("Data/Bliss_results.xlsx")
hsa_results   <- readxl::read_excel("Data/HSA_results.xlsx")
loewe_results <- readxl::read_excel("Data/Loewe_results.xlsx")

# Load example dataset (example structure: Drug.combination, Synergy.score, Method (optional), cell, type)
example_results <- readxl::read_excel("Data/example_results.xlsx")

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Example dataset input

# Reference datasets in list format to use in the main helper function
refs <- list(ZIP = zip_results, BLISS = bliss_results, HSA = hsa_results, LOEWE = loewe_results)

# Empirical p-value (one-sided)
compute_empirical_p <- function(scores, score) {
  s <- scores[is.finite(scores)]
  N <- length(s)
  if (!is.finite(score) || N == 0L) return(NA_real_)
  if (score >= 0) {
    p.val <- sum(s >= score) / N
  } else {
    p.val <- sum(s <= score) / N
  }
  if (p.val == 0) p.val <- 1 / N
  p.val
}

# Helper function to directly input synergy model, type, and synergy scores
calculate_pval <- function(refs, method, type, scores) {
  ref_df  <- refs[[toupper(method)]]
  ref_vec <- ref_df$Synergy.score[trimws(ref_df$type) == type]
  ref_vec <- ref_vec[is.finite(ref_vec)]
  vapply(scores, function(x) compute_empirical_p(ref_vec, x), numeric(1))
}

# Example of usage
methods <- c("ZIP", "BLISS", "HSA", "LOEWE")
type <- c("Breast", "Colon", "Pancreas")

chosen_method <- "ZIP"
chosen_type <- "Breast"

# 1) Direct synergy scores in vector format

example_scores <- c(-21.1, -14.9, -9.6, -7, 7, -4.3, -0.6, 0, 0.2, 2.4, 8.9, 10.1, 15.9, 25.3)
pvals <- calculate_pval(refs, method = chosen_method, type = chosen_type, scores = example_scores)

results <- data.frame(score = example_scores, pval = pvals, log10_pval = -log10(pvals))
print(results)

# 2) Apply directly with example dataset

example_results$pval <- calculate_pval(refs, method = "ZIP",type = "Breast",scores = example_results$Synergy.score)

example_results$log10_pval <- -log10(example_results$pval)

# Volcano plotting: Average within each (Drug.combination, cell)
combo_summary <- example_results %>%
  mutate(log10_pval = dplyr::coalesce(log10_pval, -log10(pval))) %>%
  summarise(
    synergy_cell = mean(Synergy.score, na.rm = TRUE),
    log10_cell   = mean(log10_pval, na.rm = TRUE),
    .by = c(Drug.combination, cell)
  ) %>%
  summarise(
    mean_synergy = mean(synergy_cell, na.rm = TRUE), mean_log10 = mean(log10_cell,   na.rm = TRUE),
    n_cells = dplyr::n_distinct(cell),
    .by = Drug.combination
  )

# Color the top synergists and antagonists
top15 <- combo_summary %>%
  slice_max(mean_synergy, n = 15, with_ties = FALSE) %>%
  transmute(Drug.combination, cat = "Top 15 synergists")

bot15 <- combo_summary %>%
  slice_min(mean_synergy, n = 15, with_ties = FALSE) %>%
  transmute(Drug.combination, cat = "Top 15 antagonists")

combo_summary <- combo_summary %>%
  left_join(bind_rows(top15, bot15), by = "Drug.combination") %>%
  mutate(cat = tidyr::replace_na(cat, "Other"))

# Volcano synergistic plot
col_volcano_synergy <- c("Top 15 synergists" = "#B2182B", "Top 15 antagonists" = "#2166AC", "Other" = "#C1C1C1")

volcano_plot <- ggplot(combo_summary, aes(mean_synergy, mean_log10)) +
  geom_point(aes(colour = cat, size = n_cells), shape = 19, alpha = 0.9) +
  geom_hline(yintercept = 2,   linetype = "dashed", color = "grey20", linewidth = 1) +
  geom_vline(xintercept = -10, linetype = "dashed", color = "grey20", linewidth = 1) +
  geom_vline(xintercept =  10, linetype = "dashed", color = "grey20", linewidth = 1) +
  scale_colour_manual(values = col_volcano_synergy, guide = "none") +
  scale_size_continuous(range = c(3, 8)) +
  labs(x = "Average synergy",
       y = "Average -log10 (P-value)",
       size = "cells (n)") +
  theme_classic(base_family = "Arial") +
  theme(
    axis.title = element_text(size = 24, color = "black"),
    axis.text  = element_text(size = 22, color = "black"),
    axis.ticks = element_line(size = 1.1),
    axis.ticks.length = unit(.40, "cm")
  )

print(volcano_plot)

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Example output

For implementation details, see:

https://github.com/dias-dio/defining-synergy/blob/main/R/apply_reference.R

Contact information

For questions or inquiries, please contact:

• Diogo Dias — diogo.dias@helsinki.fi
• Tero Aittokallio — tero.aittokallio@helsinki.fi

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Copyright and license

This project is licensed under the MIT License See the LICENSE for details.

Repository: https://github.com/dias-dio/defining-synergy/