2.3. Statistical analysis

First, we extracted the absolute number of PLHIV reported by the selected studies for quantitative synthesis and grouped data by the type of HIV and comorbidities (diabetes, HPT, CVD, RD and CKD), and HIV monoinfection. We then collected information on the number of and the type of severe COVID‐19 outcome, which were defined as: mortality, hospitalization, severe and critical outcomes. Hospitalization was coded as a fact, and included the following outcomes: mortality; hospitalized but not requiring supplemental oxygen, hospitalized but requiring supplemental oxygen, hospitalized with non‐invasive ventilation and hospitalized on invasive mechanical ventilation. Severe outcome was defined as fever or suspected respiratory infection plus respiratory rate greater than 30 breaths per min, oxygen saturation of 93% or less on room air, or acute severe respiratory distress [acute lung infiltrate in chest imaging and ratio of partial pressure of arterial oxygen to fractional concentration of oxygen in inspired air (PaO₂/FiO₂) of ≤300]. Critical outcome was defined as rapid disease progression and respiratory failure with need for mechanical ventilation or organ failure that requires monitoring in an intensive care unit. Lastly, we re‐calculated the odds ratio (OR) of severe COVID‐19 outcomes between HIV monoinfections and HIV infections with the respective comorbidities through our meta‐analysis, instead of extracting the original relative risks, ORs or hazard ratios reported in the original studies.

In the classical frequentist approach, we used a random‐effects model and the DerSimonian–Laird method to estimate the model on a log‐OR scale. The DerSimonian–Laird Q test and I ² values were used to assess heterogeneity, with low, moderate and high heterogeneity corresponding to I ² values of 25%, 50% and 75%. In addition, heterogeneity τ was assessed in this study. We investigated a publication bias by inspecting funnel plots. To test the funnel plot asymmetry, we used both mixed‐effects meta‐regression model and rank correction test. The statistical analysis was carried out using R (version R 3.6.2) using the Metafor package v.2.4‐0 [25].

To better estimate the between‐study variance in a context of limited numbers of studies to be included in the meta‐analysis, applying a Bayesian meta‐analysis increases the robustness of the model in the context of all sources of uncertainty, and incorporates external evidence on heterogeneity in the analysis [26]. Bayesian probability, contrary to the frequentist model, belongs to the category of evidential probabilities. It interprets probability as a reasonable expectation based on so‐called priors and compares them against so‐called posterior probabilities (evidence based). Choosing the adequate prior is thus essential in the Bayesian inference process. In sum, the Bayesian framework introduces a formal combination of a prior probability distribution (with a likelihood distribution of the pooled effect based on the observed data) to obtain a posterior probability distribution of the pooled effect [26]. An informative prior is necessary to precisely estimate heterogeneity [26]. Thus, we applied the half‐normal distribution with scale 0.5 as a prior for the analysis presented here, as this is recommended for log‐OR endpoints [27, 28]. Different prior distributions (half‐normal distribution with scale of 1.0 and half‐Cauchy distribution with scale of 0.5) were also applied for the purpose of the sensitivity analysis. Results were shown as the posterior distribution of the fixed effect μ on a log‐OR scale, heterogeneity τ and posterior knowledge of a “future” observation (prediction distribution). Both estimated fixed effects and random effects with 95% credible interval (CrI) were pitted against the estimates from the classical frequentist approach. The Bayesian meta‐analysis was carried out with the Bayesmeta package v.2.6 [28].