Epidemiological evidence suggests non-steroidal anti-inflammatory drugs reduce the risk of Alzheimer's disease. However, clinical trials have found no evidence of non-steroidal anti-inflammatory drug efficacy. This incongruence may be due to the wrong non-steroidal anti-inflammatory drugs being tested in robust clinical trials or the epidemiological findings being caused by confounding factors. Therefore, this study used logistic regression and the innovative approach of negative binomial generalized linear mixed modelling to investigate both prevalence and cognitive decline, respectively, in the Alzheimer's Disease Neuroimaging dataset for each commonly used non-steroidal anti-inflammatory drug and paracetamol. Use of most non-steroidal anti-inflammatories was associated with reduced Alzheimer's disease prevalence yet no effect on cognitive decline was observed. Paracetamol had a similar effect on prevalence to these non-steroidal anti-inflammatory drugs suggesting this association is independent of the anti-inflammatory effects and that previous results may be due to spurious associations. Interestingly, diclofenac use was significantly associated with both reduce incidence and slower cognitive decline warranting further research into the potential therapeutic effects of diclofenac in Alzheimer's disease.