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The authors conclude that:
"Development of robust evidence of the putative effectiveness of the non-mainstream treatments being used should be a priority given that they are being used by carers."
This reads as a call for studies based on confirmation bias. The purpose of research is to test a hypothesis, not to develop an evidence base to support a belief.
"... paediatric doctors are increasingly turning to more natural treatments"
No evidence to support this claim is presented, either in the study data or via references. Longitudinal data were not collected. There is nothing natural about homeopathy, as its claimed mode of action violates laws of physics and chemistry.