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The study, 'Paracetamol prescribing in primary care: Too little and too much?', published in the British Journal of Clinical Pharmacology, looked at medical data from nearly 40,000 children up to the age of 12.
Researchers from the universities of Aberdeen and Edinburgh found nearly one in 20 children had been prescribed an excessive dose by GPs. When they restricted it to children under three years old, the incidence rose to one in four.
About a quarter of children aged between six and 12 years old were under-dosed, while one in eight prescriptions failed to include any dosage instructions at all.
The researchers concluded, 'Both overdosing in young children and underdosing in older children, together with their associated risks of toxicity or under treatment, occur relatively frequently.'
Under-dosing may result in insufficient pain relief and over-dosing can damage the liver.
James McLay, a senior member of the research team, said, 'This is the first study to describe the patterns of paracetamol prescribing by primary care physicians in the community, and it is worrying to discover that just over half of the prescriptions failed to comply with current British National Formulary for Children recommendations.
'Getting the dose right can become even more complicated when parents also give their children additional paracetamol that they have bought over the counter.
'We know from other studies that around half of parents do not understand official dosage recommendations for medicines such as paracetamol, and not taking care over dosing instructions can leave parents in a state of confusion, or strengthen the public perception that paracetamol is harmless.'