A conservative method of testing whether combination analgesics produce additive or synergistic effects using evidence from acute pain and migraine.

Fixed-dose combination analgesics are used widely, and available both on prescription and over-the-counter. Combination drugs should provide more analgesia than with any single drug in the combination, but there is no evidence in humans about whether oral combinations have just additive effects, or are synergistic or even subadditive. We suggest that the measured result for the combination would be the summation of the absolute benefit increase (effect of active drug minus effect of placebo) of each component of a combination if effects were (merely) additive, and greater than the sum of the absolute benefits if they were synergistic. We tested measured effects of combination analgesics against the sum of the absolute benefits in acute pain and migraine using meta-analysis where individual components and combinations were tested against placebo in the same trials, and verified the result with meta-analyses where individual components and combinations were tested against placebo in different trials. Results showed that expected numbers needed to treat (NNT) for additive effects were generally within the 95% confidence interval of measured NNTs. This was true for combinations of paracetamol plus ibuprofen and paracetamol plus opioids in acute pain, and naproxen plus sumatriptan in migraine, but not where efficacy was very low or very high, nor combinations of paracetamol plus dextropropoxyphene. There was no evidence of synergy, defined as supra-additive effects.