Background Meta-analysis is a statistical method to synthesize evidence from a number of independent studies, including those from clinical studies with binary outcomes. In practice, when there are zero events in one or both groups, it may cause statistical problems in the subsequent analysis. Methods In this paper, by considering the relative risk as the effect size, we conduct a comparative study that consists of four continuity correction methods and another state-of-the-art method without the continuity correction, namely the generalized linear mixed models (GLMMs). To further advance the literature, we also introduce a new method of the continuity correction for estimating the relative risk. Results From the simulation studies, the new method performs well in terms of mean squared error when there are few studies. In contrast, the generalized linear mixed model performs the best when the number of studies is large. In addition, by reanalyzing recent coronavirus disease 2019 (COVID-19) data, it is evident that the double-zero-event studies impact the estimate of the mean effect size. Conclusions We recommend the new method to handle the zero-event studies when there are few studies in a meta-analysis, or instead use the GLMM when the number of studies is large. The double-zero-event studies may be informative, and so we suggest not excluding them.
According to Davey et al. (2011) with a total of 22,453 meta-analyses from the January 2008 Issue of the Cochrane Database of Systematic Reviews, the median number of studies included in each meta-analysis is only three. In other words, about a half or more of meta-analyses conducted in the literature include only two or three studies. While the common-effect model (also referred to as the fixed-effect model) may lead to misleading results when the heterogeneity among studies is large, the conclusions based on the random-effects model may also be unreliable when the number of studies is small. Alternatively, the fixedeffects model avoids the restrictive assumption in the common-effect model and the need to estimate the between-study variance in the random-effects model.We note, however, that the fixed-effects model is under appreciated and rarely used in practice until recently. In this paper, we compare all three models and demonstrate the usefulness of the fixed-effects model when the number of studies is small. In addition, we propose a new estimator for the unweighted average effect in the fixed-effects model. Simulations and real examples are also used to illustrate the benefits of the fixed-effects model and the new estimator.
The development of a heterogeneous catalyst for use in environmental remediation remains a challenging and attractive research endeavor. Specifically, for Fenton reactions, most research approaches have focused on the preparation of iron-containing heterostructures as photo-Fenton catalysts that utilize visible light for enhancing the degradation efficiency. Herein, the synthesis and novel application of C,N-doped iron borates are demonstrated as single-component heterogeneous photo-Fenton catalysts with high Fenton activity under visible light. Under the optimal conditions, 10 mg of the catalyst is shown to achieve effective degradation of 10 ppm methylene blue (MB) dye, Rhodamine B (RhB) dye, and tetracycline (TC) under simulated solar irradiation with a first-order rate constant of k = 0.218 min−1, 0.177 min−1, and 0.116 min−1, respectively. Using MB as a model system, the C,N-doped iron borate exhibits 10- and 26-fold increases in catalytic activity relative to that of the 50 nm hematite nanoparticles and that of the non-doped iron borate, respectively, in the presence of H2O2 under the simulated solar irradiation. Furthermore, the optimum reaction conditions used only 320 equivalents of H2O2 with respect to the concentration of dye, rather than the several thousand equivalents of H2O2 used in conventional heterogeneous Fenton catalysts. In addition, the as-prepared C,N-doped iron borate achieves 75% MB degradation after 20 min in the dark, thus enabling the continuous degradation of pollutants at night and in areas with poor light exposure. The stability and recyclability of C,N-doped iron borate for the oxidation of MB was demonstrated over three cycles with insignificant loss in photo-Fenton activity. The high Fenton activity of the C,N-doped iron borate is considered to be due to the synergistic action between the negatively-charged borate ligands and the metal center in promoting the Fenton reaction. Moreover, carbon and nitrogen doping are shown to be critical in modifying the electronic structure and increasing the conductivity of the catalyst. In view of its synthetic simplicity, high efficiency, low cost of reagents, and minimal cost of operation (driven by natural sunlight), the as-prepared heterogeneous single-component metal borate catalyst has potential application in the industrial treatment of wastewater.
Background: Meta-analysis is a statistical method to synthesize evidence from a number of independent studies, including those from clinical studies with binary outcomes. In practice, when there are zero events in one or both groups, it may cause statistical problems in the subsequent analysis. Methods: In this paper, by considering the relative risk as the effect size, we conduct a comparative study that consists of four continuity correction methods and another state-of-the-art method without the continuity correction, namely the generalized linear mixed models. To further advance the literature, we also introduce a new method of the continuity correction for estimating the relative risk. Results: From the simulation studies, the new method performs well in terms of mean squared error when there are few studies. In contrast, the generalized linear mixed model performs the best when the number of studies is large. In addition, by reanalyzing a recent COVID-19 data, it is evident that the double-zero-event studies impact on the estimate of the mean effect size.Conclusion: We recommend the new method to handle the zero-event studies when there are only few studies in the meta-analysis, or instead use the GLMM when the number of studies is large. The double-zero-event study may beinformative, and so we suggest not excluding them.
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