Research is an expanding area of Homeopathy and it is an area that I am interested in because of my science background. The Homeopathic Research Institute (HRI) has been set up and is dedicated to providing high-quality research on the efficacy of Homeopathy.
The most robust data on efficacy of homeopathy comes from a 2014 meta-analysis of placebo-controlled double-blind randomised controlled trials which found that homeopathic medicines, when prescribed during individualised treatment, are 1.5- to 2.0-times more likely to have a beneficial effect than placebo (Ref 1). This study is one of the four most recent comprehensive systematic reviews conducted by Dr Robert Mathie within a ten-year programme of work.
Ref 1. Mathie, R.T., Lloyd, S.M., Legg, L.A., Clausen, J., Moss,S. Davidson, J., Ford, I. (2014) Placebo-controlled trials of individualised homeopathic treatment: systematic review and meta-analysis. Systematic Reviews Vol 3. Pages 142. https://doi.org/10.1186/2046-4053-3-142
Here are a few more peer-reviewed papers.
Rossignol M, Beagud B, Engel P, Avouac B, Lert F, Rouillon F, Massol J, Duru G, Magnier AM, Guillemot D, Grimaldi-Bensouda L, Abenhaim L, EPI3-LA-SER groupn (2012). Impact of physician preferences for homeopathic or conventional medicines on patients with musculoskeletal disorders: results from the EPI3-MSD cohort. Pharmacoepidemiol. Drug Saf. Vol 21(1). Pages 1093–1101.
Headache frequency and intensity was lower in the homeopathy group than in controls. Compared with usual care, patients randomized to homeopathy used 35% less medication (P = 0.001) and had 45% fewer visits to general practitioners (P = 0.0001).
Sharma et al. (2013) Effect of homeopathy on chronic tension-type headache: a pragmatic, randomized controlled single blind trial. J Headache Pain. Vol 14 (Suppl 1): P56.