Meta-analysis of paired count data

[rollanders]

I am analysing the impact of the change in the management of appendicitis during the covid pandemic. I have paired data from 31 reports comparing the number of operations for perforated and nonperforated appendicitis during the lockdown period and the same time period in 2019. So essentially I have data with 5 columns - author, number of perforated and nonperforated patients during the precovid and during lockdown.

A common conclusion in these reports is that the proportion of perforations increased during the lockdown and assumes that this indicates that the delay has caused more appendices to perforate.

However, in many cases the number of perforations is very similar in both periods or even lower during lockdown, but the number of non-perforated appendices are often much reduced. The increased proportion of perforations is thus explained by the reduced denominator and not an increased numerator. An explanation could be that more cases of non-complicated appendicitis were allowed to heal spontaneously.

How can I show that the increased proportion of perforations is explained by the decrease of nonperforated cases? And can I estimate the effect of the lockdown on the two types of appendicitis in some way? Unfortunately I have no data on the catchment population otherwise I could refer to that as the denominator.
The reports are from small and large hospitals so the numbers show large range.

From a non-statisticians point I wonder if I could use the change in the proportion of perforations as outcome and use the difference of the counts of perforated and nonperforated appendicitis as regressors? I guess there must be better ways.

[Tiago Pereira]

Rollanders, I think your question is very difficult to address via meta-analysis. You will end up with a set results which carry a lot of confounding. You can try a meta-regression model having the dependent variable some sort of transformation of the calculated proportion (logit, arcsine) and as moderator the year of publication.

In Stata, you can start here

https://journals.sagepub.com/doi/pdf...867X0800800403

help metareg

There are many more references, of course.

[rollanders]

Thanks Tiago Pereira

During the lockdown a common observation is that the ratio of perforated/all appendicitis has increased. Most interpret an increase in the proportion of perforation as bad as they assume that it is due to more patients had perforation, but if the increase is due to a decrease in all appendicitis it is good, as it suggests that spontaneous resolution was allowed.

I look at this explanation of the maths.

"You start with a numerator and denominator, N/D, then change N to N+n and change D to D+d. The total change is then (N+n)/(D+d) – N/D. The result from only the change in the numerator is n/D. The result from only the change in denominator is N/(D+d) – N/D. The difference between the total change and the sum of the two partial changes is –nd/D(D+d)."

So what I want is to determine the impact of n and d on the change in the ratio. But how? I will look at all the meta commands but am not sure I can sort it out.

[Tiago Pereira]

I don't think we will be able to address whether the incidence of perforation changed after lock-down. You can only examine whether the prevalence of perforation changed. There is a myriad of explanations. In Brazil, for example, we had a deterioration of many surgical indicators, simply because only the most serious cases were being surgically treated.

[rollanders]

I know this report from Brazil (Steinman American Journal of Emergency Medicine 42 (2021) 9–14) which showed an important decline in the number of appendectomies treated. This decline was present before the pandemic. But if the numer of appendectomies was reduced by 50%, what happened to them? Unfortunately Steinman does not report the number of perforations. There are reports showing small or no change in the number of perforations but large reductions in the number of nonperforated appendicitis with an increase in the proportion of perforations as a consequence.

[rollanders]

Another study from Brazil (Fonseca The American Surgeon 2020, Vol. 86(11) 1508–1512 ) compared 2 months covid period with the same period 2019 and found:

"Results: The number of appendectomies during the pandemic was 36, which represents a 56% reduction compared to the 82 patients operated during the same period in 2019.
The classification of appendicitis revealed a significant higher proportion of complicated cases than the previous year (33.3% vs. 15.2%, P = .04)."

However the underlying estimated numbers in the two periods were: perforated 12 vs 12 and non perforated 70 vs 24, eg precovid 12/82=14.6% and during covid 12/36=33.3%
So the doubled proportion of perforation was solely explained by the lower incidence of nonperforated appendicitis.

I need help to make the correct analysis of the impact of the numerator and denominator on the ratio.

[rollanders]

I have problems how to illustrate the problem but hope the linked graph will show the background for my message. The data are from reports for the meta-analysis. The X-axis is the change in proportion perforation between pre and covid periods. It has increased in most reports. The Y axis is the ratio of numbers of perforated and nonperforated percovid/precovid. A ratio=1 means same numbers during the Covid period as the year before. I have marked some results with an arrow that have an increase in the proportion of perforations but almost identical or even lower number of perforations, but in all cases a decrease in the number of non-perforated cases (suggesting spontaneous resolution). So parts of the change in proportion of perforations is due to decrease in nonperforated. How can I show this statistically?

https://app.box.com/s/tyfosjjoih72jfj1a30it8mga2pdmnc2

(I failed in uploading the graph)