Dear Forum users,
I am planning to perform a systematic search in the literature to assess the percentage of pharyngeal cancers that are positive on a certain virus (human papilloma virus, HPV) among all pharyngeal cancers. The aim is to be able to present a result such as “32% (95% CI …) of all pharyngeal cancers are associated with HPV”.
I presented data from an initial search to my supervisor. To obtain an estimate, I had simply pooled the data from 9 studies, adding up all the reported numbers of cancers as denominator and the reported number of HPV+ cancers as numerator.
My supervisor said this approach gives a biased result and said I need to do a meta-analysis. However, he was not able to explain really well why my approach was flawed. He just said that the meta-analysis would consider the size of the study and give more weight to larger studies. However, my approach basically does the same as larger studies contribute a higher number of cancers to my estimate.
I did not find a clear answer to my question in literature. I found that meta-analysis weights the study by the inverse of the squared standard error, which in turn is a function of sample size and variance. So, I understand why a meta-analysis gives more weight to larger studies (=smaller SE, higher weight). But the variance of a proportion (np(1-p)) close to 0 (or to 1, but this does not apply to my data) is smaller than the variance of a proportion close to 0.5. So, if my understanding is correct, studies in which there was a very low proportion of HPV+ tumors have more weight than equally large studies with a higher proportion. I am concerned that this would bias (rather than prevent bias) the results towards a lower estimated proportion.
I greatly appreciate your opinion on whether (and why) my approach is flawed, and whether a meta-analysis is required.
Thank you and best regards,