The impact of studies with no events in both arms on meta-analysis of rare events: a simulation study using generalized linear mixed model

ObjectiveThe common approach to meta-analysis with double-zero studies is to remove such studies. Our previous work has confirmed that exclusion of these studies may impact the results. In this study, we undertook extensive simulations to investigate how the results of meta-analyses would be impacted in relation to the proportion of such studies.MethodsTwo standard generalized linear mixed models (GLMMs) were employed for the meta-analysis. The statistical properties of the two GLMMs were first examined in terms of percentage bias, mean squared error, and coverage. We then repeated all the meta-analyses after excluding double-zero studies. Direction of estimated effects and p-values for including against excluding double-zero studies were compared in nine ascending groups classified by the proportion of double-zero studies within a meta-analysis.ResultsBased on 50,000 simulated meta-analyses, the two GLMMs almost achieved unbiased estimation and reasonable coverage in most of the situations. When excluding double-zero studies, 0.00% to 4.47% of the meta-analyses changed the direction of effect size, and 0.61% to 8.78% changed direction of the significance of p-value. When the proportion of double-zero studies increased in a meta-analysis, the probability of the effect size changed the direction increased; when the proportion was about 40% to 60%, it has the largest impact on the change of p-values.ConclusionDouble-zero studies can impact the results of meta-analysis and excluding them may be problematic. The impact of such studies on meta-analysis varies by the proportion of such studies within a meta-analysis.

Meta-analysis with zero-event studies: a comparative study with application to COVID-19 data

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.

Meta-analysis With Zero-event Studies: A Comparative Study With Application to COVID-19 Data

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.

Vigor difference during storage and germination in Indian mustard explained by reactive oxygen species and antioxidant enzymes

Canola-type genotypes in Indian mustard (Brassica juncea) are a new kind of quality resource developed for their low levels of erucic acid (<2%) and glucosinolate (<30 μmole/g defatted meal) contents. Single-zero (low erucic acid) and double-zero (low erucic acid and glucosinolate content) genotypes of Indian mustard have less vigor. Conventional genotypes (high erucic acid and glucosinolate contents) havea significantly higher seedling vigor index-II (SVI-II) and single-zero genotypes have a significantly higher SVI-I, whereas double-zero genotypes have been observed to have a significantly lower SVI-I and SVI-II. To know the possible reasons for the differences in vigor, the seed quality parameters, reactive oxygen species (ROS) contents (superoxide radicals (O2−·) and hydrogen peroxide), lipid peroxidation, and antioxidant enzyme activity were examined. In the dry seeds, the conventional genotypes revealed lower ROS contents and higher catalase and peroxidase enzyme activity. This trend was reversed in the double-zero genotypes, which could be the reason why they were more susceptible to oxidative damage. During seed germination, an increase in the ROS contents, and corresponding increase in antioxidant enzyme activity, was noticed, which was highest in the conventional genotypes, followed by the single-zero genotypes. Double-zero genotypes showed the lowest increase in ROS contents and antioxidant enzyme activity during this period. This meant that the required attributes were met for maintaining oxidative balance within the cells and triggering physiological activities to reach high vigor. This study proposed 2 causes for the poor vigor of the double-zero genotypes; first, in the dry seeds, the ROS remained high due to low antioxidant activity (ROS scavengers) and the second was less generation of O2−· during germination.

Double-zero-event studies matter: a re-evaluation of physical distancing, face masks, and eye protection for preventing person-to-person transmission of COVID-19 and its policy impact

Objectives: High-quality meta-analyses on COVID-19 are in urgent demand for evidence-based decision making. However, conventional approaches exclude double-zero-event studies (DZS) from meta-analyses. We assessed whether including such studies impacts the conclusions in a recent systematic urgent review on prevention measures for preventing person-to-person transmission of COVID-19. Study designs and settings: We extracted data for meta-analyses containing DZS from a recent review that assessed the effects of physical distancing, face masks, and eye protection for preventing person-to-person transmission. A bivariate generalized linear mixed model was used to re-do the meta-analyses with DZS included. We compared the synthesized relative risks (RRs) of the three prevention measures, their 95% confidence intervals (CI), and significance tests (at the level of 0.05) including and excluding DZS. Results: The re-analyzed COVID-19 data containing DZS involved a total of 1,784 participants who were not considered in the original review. Including DZS noticeably changed the synthesized RRs and 95% CIs of several interventions. For the meta-analysis of the effect of physical distancing, the RR of COVID-19 decreased from 0.15 (95% CI, 0.03 to 0.73) to 0.07 (95% CI, 0.01 to 0.98). For several meta-analyses, the statistical significance of the synthesized RR was changed. The RR of eye protection with a physical distance of 2 m and the RR of physical distancing when using N95 respirators were no longer statistically significant after including DZS. Conclusions: DZS may contain useful information. Sensitivity analyses that include DZS in meta-analysis are recommended.

Bogdanov–Takens Bifurcation in a Neutral Delayed Hopfield Neural Network with Bidirectional Connection

In this paper, a neutral Hopfield neural network with bidirectional connection is considered. In the first step, by choosing the connection weights as parameters bifurcation, the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system. In the second step, we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root, all the other roots of the characteristic equation have real parts that are negative. Moreover, we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation. In the third step, the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form. Furthermore, for the demonstration of our results, we have given a numerical example.

Pulse Reshaping in Double-zero-index Photonic Crystals with Dirac-like-cone Dispersion

Triply-degenerate Dirac-like cone at the Brillouin zone center attracts much research interest in recent years. Whether the linear dispersion in such a Dirac-like cone reflects the same physics to Dirac cones at the Brillouin zone boundaries is still under investigation. In this manuscript, through microwave experiments and numerical simulations, we observe intriguing pulse reshaping phenomena in double-zero-index photonic crystals, which cannot be fully understood from their close-to-zero effective parameters. A reshaped pulse, with frequency components close to the Dirac frequency filtered, is propagating at a constant group velocity while part of these filtered frequencies appears at a much later time. In time domain measurements, we find a way to separate the effect between the linear dispersion and the extra flat band in Dirac-like cone to have a better understanding of the underneath physics. We succeed in obtaining the group velocity inside a double-zero-index photonic crystal and good consistence can be found between experiments, numerical simulations and band diagram calculations.