Not my area, but this looks like an interesting place to look up the strengths (estimation of treatment effects) and weaknesses (estimation of between-study variances) of the DSL procedure and its alternatives.

https://www.sciencedirect.com/science/article/abs/pii/S0378375809003073

The choice between logistic regression and the DerSimonian-Laird method for meta-analysis of proportions depends on several factors, including the characteristics of your data and the assumptions you are willing to make. Let's briefly discuss both methods and their suitability for meta-analysis of proportions with high heterogeneity.

Logistic Regression:

Logistic regression is a statistical method used to model the relationship between a binary outcome variable (e.g., success/failure) and one or more predictor variables. In the context of meta-analysis of proportions, you could use logistic regression to model the relationship between the binary outcome (e.g., the proportion of success) and study-specific characteristics or covariates.

Pros of Logistic Regression:

It allows for the incorporation of study-specific covariates, which may help explain some of the observed heterogeneity between studies.

It can be useful when you have additional information beyond just the proportions, such as sample size or other study characteristics.

Cons of Logistic Regression:

It assumes a specific functional form for the relationship between the predictor variables and the log odds of the proportion, which may not always hold.

In the presence of high heterogeneity, logistic regression may still not fully account for all sources of variation between studies.

DerSimonian-Laird Method:

The DerSimonian-Laird method is a commonly used approach for performing random-effects meta-analysis. It estimates the between-study variance, which accounts for the heterogeneity between studies in addition to the within-study variance. The method produces a pooled proportion estimate, taking into account the variability both within and between studies.

Pros of DerSimonian-Laird Method:

It provides a straightforward way to estimate the pooled proportion while considering the between-study heterogeneity.

It is robust and widely used in meta-analyses.

Cons of DerSimonian-Laird Method:

It assumes that the observed heterogeneity is due to a random variation between studies and not because of systematic differences among the studies. This assumption might not always hold.

Given that you have performed both methods and obtained varying results, it suggests that there might be substantial heterogeneity between the included studies. In such cases, it is essential to interpret the results carefully.

Here are some steps you can take to handle the situation:

Consider the underlying assumptions: Reflect on whether the assumptions of both methods are met in your data. For instance, logistic regression assumes a specific relationship between covariates and log odds, while DerSimonian-Laird assumes random-effects variability. Assess the appropriateness of these assumptions for your data.

Check for model adequacy: Evaluate the goodness-of-fit of your logistic regression model. Ensure that the model adequately explains the observed variation in proportions across studies.

Explore sources of heterogeneity: Try to identify potential sources of heterogeneity between studies. Conduct sensitivity analyses to see how different factors influence the results.

Report both results: Considering the variability in results, it is good practice to report both the logistic regression and DerSimonian-Laird estimates in your study. Be transparent about the methods used and their limitations.

Seek expert advice: If you are uncertain about the results or the best approach for your specific study, consider seeking advice from a statistician or an expert in meta-analysis.

Neither is ideal. See this paper:

Article Meta-analysis of prevalence