Effect of Ozone Therapy on Diabetes-related Foot Ulcer Outcomes: A Systematic Review and Meta-analysis.

PURPOSE: This study aimed to assess the effectiveness of ozone therapy in treating Diabetes-related Foot Ulcer (DFU) and its outcomes. METHODS: A systematic search was conducted in PubMed/MEDLINE, Scopus, Web of Science, and ProQuest databases for published studies evaluating the use of ozone as an adjunct treatment for DFU, from inception to December 21, 2022. The primary outcome measure was the change in wound size after the intervention compared to pretreatment. Secondary outcomes included time to complete ulcer healing, number of healed patients, adverse events, amputation rates, and hospital length of stay. Quantitative data synthesis for the meta-analysis was performed using a random-effects model and generic inverse variance method, while overall heterogeneity analysis was conducted using a fixed-effects model. Interstudy heterogeneity was assessed using the I2 index (<50%) and the Cochrane Q statistic test. Sensitivity analysis was performed using the leave-one-out method. RESULTS: The meta-analysis included 11 studies comprising 960 patients with DFU. The results demonstrated a significant positive effect of ozone therapy on reducing foot ulcer size (Standardized Mean Difference (SMD): -25.84, 95% CI: -51.65 to -0.04, p = 0.05), shortening mean healing time (SMD: -38.59, 95% CI: -51.81 to -25.37, p < 0.001), decreasing hospital length of stay (SMD: -8.75, 95% CI: -14.81 to -2.69, p < 0.001), and reducing amputation rates (Relative Risk (RR): 0.46, 95% CI: 0.30-0.71, p < 0.001), compared to standard treatment. CONCLUSION: This meta-analysis indicates that ozone therapy has additional benefits in expediting complete DFU healing, reducing the amputation rates, and decreasing hospital length of stay, though its effects do not differ from standard treatments for complete ulcer resolution. Further research is needed to address the heterogeneity among studies and to better understand the potential beneficial effects of ozone therapy.

A joint normal-ordinal (probit) model for ordinal and continuous longitudinal data.

In biomedical studies, continuous and ordinal longitudinal variables are frequently encountered. In many of these studies it is of interest to estimate the effect of one of these longitudinal variables on the other. Time-dependent covariates have, however, several limitations; they can, for example, not be included when the data is not collected at fixed intervals. The issues can be circumvented by implementing joint models, where two or more longitudinal variables are treated as a response and modeled with a correlated random effect. Next, by conditioning on these response(s), we can study the effect of one or more longitudinal variables on another. We propose a normal-ordinal(probit) joint model. First, we derive closed-form formulas to estimate the model-based correlations between the responses on their original scale. In addition, we derive the marginal model, where the interpretation is no longer conditional on the random effects. As a consequence, we can make predictions for a subvector of one response conditional on the other response and potentially a subvector of the history of the response. Next, we extend the approach to a high-dimensional case with more than two ordinal and/or continuous longitudinal variables. The methodology is applied to a case study where, among others, a longitudinal ordinal response is predicted with a longitudinal continuous variable.

Random effects models of tumour growth for investigating interval breast cancer.

In Nordic countries and across Europe, breast cancer screening participation is high. However, a significant number of breast cancer cases are still diagnosed due to symptoms between screening rounds, termed "interval cancers". Radiologists use the interval cancer proportion as a proxy for the screening false negative rate (ie, 1-sensitivity). Our objective is to enhance our understanding of interval cancers by applying continuous tumour growth models to data from a study involving incident invasive breast cancer cases. Building upon previous findings regarding stationary distributions of tumour size and growth rate distributions in non-screened populations, we develop an analytical expression for the proportion of interval breast cancer cases among regularly screened women. Our approach avoids relying on estimated background cancer rates. We make specific parametric assumptions concerning tumour growth and detection processes (screening or symptoms), but our framework easily accommodates alternative assumptions. We also show how our developed analytical expression for the proportion of interval breast cancers within a screened population can be incorporated into an approach for fitting tumour growth models to incident case data. We fit a model on 3493 cases diagnosed in Sweden between 2001 and 2008. Our methodology allows us to estimate the distribution of tumour sizes at the most recent screening for interval cancers. Importantly, we find that our model-based expected incidence of interval breast cancers aligns closely with observed patterns in our study and in a large Nordic screening cohort. Finally, we evaluate the association between screening interval length and the interval cancer proportion. Our analytical expression represents a useful tool for gaining insights into the performance of population-based breast cancer screening programs.

Flagging unusual clusters based on linear mixed models using weighted and self-calibrated predictors.

Statistical models incorporating cluster-specific intercepts are commonly used in hierarchical settings, for example, observations clustered within patients or patients clustered within hospitals. Predicted values of these intercepts are often used to identify or "flag" extreme or outlying clusters, such as poorly performing hospitals or patients with rapid declines in their health. We consider a variety of flagging rules, assessing different predictors, and using different accuracy measures. Using theoretical calculations and comprehensive numerical evaluation, we show that previously proposed rules based on the 2 most commonly used predictors, the usual best linear unbiased predictor and fixed effects predictor, perform extremely poorly: the incorrect flagging rates are either unacceptably high (approaching 0.5 in the limit) or overly conservative (eg, much <0.05 for reasonable parameter values, leading to very low correct flagging rates). We develop novel methods for flagging extreme clusters that can control the incorrect flagging rates, including very simple-to-use versions that we call "self-calibrated." The new methods have substantially higher correct flagging rates than previously proposed methods for flagging extreme values, while controlling the incorrect flagging rates. We illustrate their application using data on length of stay in pediatric hospitals for children admitted for asthma diagnoses.

Multilevel superposition for deciphering the conformational variability of protein ensembles.

The dynamics and variability of protein conformations are directly linked to their functions. Many comparative studies of X-ray protein structures have been conducted to elucidate the relevant conformational changes, dynamics and heterogeneity. The rapid increase in the number of experimentally determined structures has made comparison an effective tool for investigating protein structures. For example, it is now possible to compare structural ensembles formed by enzyme species, variants or the type of ligands bound to them. In this study, the author developed a multilevel model for estimating two covariance matrices that represent inter- and intra-ensemble variability in the Cartesian coordinate space. Principal component analysis using the two estimated covariance matrices identified the inter-/intra-enzyme variabilities, which seemed to be important for the enzyme functions, with the illustrative examples of cytochrome P450 family 2 enzymes and class A $\beta$-lactamases. In P450, in which each enzyme has its own active site of a distinct size, an active-site motion shared universally between the enzymes was captured as the first principal mode of the intra-enzyme covariance matrix. In this case, the method was useful for understanding the conformational variability after adjusting for the differences between enzyme sizes. The developed method is advantageous in small ensemble-size problems and hence promising for use in comparative studies on experimentally determined structures where ensemble sizes are smaller than those generated, for example, by molecular dynamics simulations.

Conditioning on the Pre-Test versus Gain Score Modelling: Revisiting the Controversy in a Multilevel Setting.

We consider estimating the effect of a treatment on a given outcome measured on subjects tested both before and after treatment assignment in observational studies. A vast literature compares the competing approaches of modelling the post-test score conditionally on the pre-test score versus modelling the difference, namely, the gain score. Our contribution lies in analyzing the merits and drawbacks of two approaches in a multilevel setting. This is relevant in many fields, such as education, where students are nested within schools. The multilevel structure raises peculiar issues related to contextual effects and the distinction between individual-level and cluster-level treatments. We compare the two approaches through a simulation study. For individual-level treatments, our findings align with existing literature. However, for cluster-level treatments, the scenario is more complex, as the cluster mean of the pre-test score plays a key role. Its reliability crucially depends on the cluster size, leading to potentially unsatisfactory estimators with small clusters.

Meta-analysis prediction intervals are under reported in sport and exercise medicine.

AIM: Prediction intervals are a useful measure of uncertainty for meta-analyses that capture the likely effect size of a new (similar) study based on the included studies. In comparison, confidence intervals reflect the uncertainty around the point estimate but provide an incomplete summary of the underlying heterogeneity in the meta-analysis. This study aimed to estimate (i) the proportion of meta-analysis studies that report a prediction interval in sports medicine; and (ii) the proportion of studies with a discrepancy between the reported confidence interval and a calculated prediction interval. METHODS: We screened, at random, 1500 meta-analysis studies published between 2012 and 2022 in highly ranked sports medicine and medical journals. Articles that used a random effect meta-analysis model were included in the study. We randomly selected one meta-analysis from each article to extract data from, which included the number of estimates, the pooled effect, and the confidence and prediction interval. RESULTS: Of the 1500 articles screened, 866 (514 from sports medicine) used a random effect model. The probability of a prediction interval being reported in sports medicine was 1.7% (95% CI = 0.9%, 3.3%). In medicine the probability was 3.9% (95% CI = 2.4%, 6.6%). A prediction interval was able to be calculated for 220 sports medicine studies. For 60% of these studies, there was a discrepancy in study findings between the reported confidence interval and the calculated prediction interval. Prediction intervals were 3.4 times wider than confidence intervals. CONCLUSION: Very few meta-analyses report prediction intervals and hence are prone to missing the impact of between-study heterogeneity on the overall conclusions. The widespread misinterpretation of random effect meta-analyses could mean that potentially harmful treatments, or those lacking a sufficient evidence base, are being used in practice. Authors, reviewers, and editors should be aware of the importance of prediction intervals.

Nodal Heterogeneity can Induce Ghost Triadic Effects in Relational Event Models.

Temporal network data is often encoded as time-stamped interaction events between senders and receivers, such as co-authoring scientific articles or communication via email. A number of relational event frameworks have been proposed to address specific issues raised by complex temporal dependencies. These models attempt to quantify how individual behaviour, endogenous and exogenous factors, as well as interactions with other individuals modify the network dynamics over time. It is often of interest to determine whether changes in the network can be attributed to endogenous mechanisms reflecting natural relational tendencies, such as reciprocity or triadic effects. The propensity to form or receive ties can also, at least partially, be related to actor attributes. Nodal heterogeneity in the network is often modelled by including actor-specific or dyadic covariates. However, comprehensively capturing all personality traits is difficult in practice, if not impossible. A failure to account for heterogeneity may confound the substantive effect of key variables of interest. This work shows that failing to account for node level sender and receiver effects can induce ghost triadic effects. We propose a random-effect extension of the relational event model to deal with these problems. We show that it is often effective over more traditional approaches, such as in-degree and out-degree statistics. These results that the violation of the hierarchy principle due to insufficient information about nodal heterogeneity can be resolved by including random effects in the relational event model as a standard.

Profit efficiency among kenyan maize farmers.

The profit efficiency (PE) of maize farming and its determinants are estimated using the true random effect (TRE) approach. A survey of maize farmers was conducted in Uasin Gishu, one of Kenya's top maize-producing regions. Clearly, maize farmers can increase their profits based on the mean PE of 0.62. In terms of profitability, maize farming is elastically affected by the price of maize, but inelastically affected by the price of inputs. In households where the head of household is male, household sizes are larger, and farm sizes are larger, inefficiencies of profit are significantly reduced. Despite this, factors such as the distance between home and the maize farm, soil characteristics, maize diseases, along with natural disasters significantly increase profit inefficiency. According to the findings of the study, maize prices are more effective targets for developing supportive policies than input prices. To significantly increase PE, farmers would benefit from programs designed to improve their production and management skills to preserve soil health and minimize damage caused by disease and natural disasters. Furthermore, increase in PE would be achieved by improving farm size through land-use policies.

Accounting for informative observation process in transition models of binary longitudinal outcome: Application to medical record data.

When extracting medical record data to form a retrospective cohort, investigators typically focus on a pre-specified study window, and select subjects who had hospital visits during that study window. However, such data extraction may suffer from an informative observation process, since sicker patients may have hospital visits more frequently. For example, Consecutive Pregnancy Study is a retrospective cohort study of women with multiple pregnancies in 23 Utah hospitals from 2003 to 2010, where the interest is to understand the risk factors of recurrent pregnancy outcomes, such as preterm birth. The observation process is informative in the sense that, women with adverse pregnancy outcomes may be less likely/willing/able to endure subsequent pregnancies. We proposed a three-part joint model with shared random effects structure to address this analytic complication. Particularly, a first-order transition model is used to model the longitudinal binary outcome; a gamma regression model is assumed for the inter-pregnancy intervals; a continuation ratio model specifies the probability of continuing with more births in the future. We note that the latter two parts give rise to a parametric cure-rate survival model. The performance of the proposed method was examined in extensive simulation studies, with both correctly and mis-specified models. The analyses of Consecutive Pregnancy Study data further demonstrate the inadequacies of fitting the transition model alone ignoring the informative observation process.

A Bayesian nonparametric meta-analysis model for estimating the reference interval.

A reference interval represents the normative range for measurements from a healthy population. It plays an important role in laboratory testing, as well as in differentiating healthy from diseased patients. The reference interval based on a single study might not be applicable to a broader population. Meta-analysis can provide a more generalizable reference interval based on the combined population by synthesizing results from multiple studies. However, the assumptions of normally distributed underlying study-specific means and equal within-study variances, which are commonly used in existing methods, are strong and may not hold in practice. We propose a Bayesian nonparametric model with more flexible assumptions to extend random effects meta-analysis for estimating reference intervals. We illustrate through simulation studies and two real data examples the performance of our proposed approach when the assumptions of normally distributed study means and equal within-study variances do not hold.

Regression analysis of multivariate recurrent event data allowing time-varying dependence with application to stroke registry data.

In multivariate recurrent event data, each patient may repeatedly experience more than one type of event. Analysis of such data gets further complicated by the time-varying dependence structure among different types of recurrent events. The available literature regarding the joint modeling of multivariate recurrent events assumes a constant dependency over time, which is strict and often violated in practice. To close the knowledge gap, we propose a class of flexible shared random effects models for multivariate recurrent event data that allow for time-varying dependence to adequately capture complex correlation structures among different types of recurrent events. We developed an expectation-maximization algorithm for stable and efficient model fitting. Extensive simulation studies demonstrated that the estimators of the proposed approach have satisfactory finite sample performance. We applied the proposed model and the estimating method to data from a cohort of stroke patients identified in the University of Texas Houston Stroke Registry and evaluated the effects of risk factors and the dependence structure of different types of post-stroke readmission events.

Identifiability and estimability of Bayesian linear and nonlinear crossed random effects models.

Crossed random effects models (CREMs) are particularly useful in longitudinal data applications because they allow researchers to account for the impact of dynamic group membership on individual outcomes. However, no research has determined what data conditions need to be met to sufficiently identify these models, especially the group effects, in a longitudinal context. This is a significant gap in the current literature as future applications to real data may need to consider these conditions to yield accurate and precise model parameter estimates, specifically for the group effects on individual outcomes. Furthermore, there are no existing CREMs that can model intrinsically nonlinear growth. The goals of this study are to develop a Bayesian piecewise CREM to model intrinsically nonlinear growth and evaluate what data conditions are necessary to empirically identify both intrinsically linear and nonlinear longitudinal CREMs. This study includes an applied example that utilizes the piecewise CREM with real data and three simulation studies to assess the data conditions necessary to estimate linear, quadratic, and piecewise CREMs. Results show that the number of repeated measurements collected on groups impacts the ability to recover the group effects. Additionally, functional form complexity impacted data collection requirements for estimating longitudinal CREMs.

Risk factors for herpes zoster infections: a systematic review and meta-analysis unveiling common trends and heterogeneity patterns.

PURPOSE: The burden of herpes zoster (HZ) is substantial and numerous chronic underlying conditions are known as predisposing risk factors for HZ onset. Thus, a comprehensive study is needed to synthesize existing evidence. This study aims to comprehensively identify these risk factors. METHODS: A systematic literature search was done using MEDLINE via PubMed, EMBASE and Web of Science for studies published from January 1, 2003 to January 1, 2023. A random-effects model was used to estimate pooled Odds Ratios (OR). Heterogeneity was assessed using the I2 statistic. For sensitivity analyses basic outlier removal, leave-one-out validation and Graphic Display of Heterogeneity (GOSH) plots with different algorithms were employed to further analyze heterogeneity patterns. Finally, a multiple meta-regression was conducted. RESULTS: Of 6392 considered records, 80 were included in the meta-analysis. 21 different conditions were identified as potential risk factors for HZ: asthma, autoimmune disorders, cancer, cardiovascular disorders, chronic heart failure (CHF), chronic obstructive pulmonary disorder (COPD), depression, diabetes, digestive disorders, endocrine and metabolic disorders, hematological disorders, HIV, inflammatory bowel disease (IBD), mental health conditions, musculoskeletal disorders, neurological disorders, psoriasis, renal disorders, rheumatoid arthritis (RA), systemic lupus erythematosus (SLE) and transplantation. Transplantation was associated with the highest risk of HZ (OR = 4.51 (95% CI [1.9-10.7])). Other risk factors ranged from OR = 1.17-2.87, indicating an increased risk for all underlying conditions. Heterogeneity was substantial in all provided analyses. Sensitivity analyses showed comparable results regarding the pooled effects and heterogeneity. CONCLUSIONS: This study showed an increased risk of HZ infections for all identified factors.

Appropriateness of conducting and reporting random-effects meta-analysis in oncology.

A random-effects model is often applied in meta-analysis when considerable heterogeneity among studies is observed due to the differences in patient characteristics, timeframe, treatment regimens, and other study characteristics. Since 2014, the journals Research Synthesis Methods and the Annals of Internal Medicine have published a few noteworthy papers that explained why the most widely used method for pooling heterogeneous studies-the DerSimonian-Laird (DL) estimator-can produce biased estimates with falsely high precision and recommended to use other several alternative methods. Nevertheless, more than half of studies (55.7%) published in top oncology-specific journals during 2015-2022 did not report any detailed method in the random-effects meta-analysis. Of the studies that did report the methodology used, the DL method was still the dominant one reported. Thus, while the authors recommend that Research Synthesis Methods and the Annals of Internal Medicine continue to increase the publication of its articles that report on specific methods for handling heterogeneity and use random-effects estimates that provide more accurate confidence limits than the DL estimator, other journals that publish meta-analyses in oncology (and presumably in other disease areas) are urged to do the same on a much larger scale than currently documented.

Multi-trait analysis of gene-by-environment interactions in large-scale genetic studies.

Identifying genotype-by-environment interaction (GEI) is challenging because the GEI analysis generally has low power. Large-scale consortium-based studies are ultimately needed to achieve adequate power for identifying GEI. We introduce Multi-Trait Analysis of Gene-Environment Interactions (MTAGEI), a powerful, robust, and computationally efficient framework to test gene-environment interactions on multiple traits in large data sets, such as the UK Biobank (UKB). To facilitate the meta-analysis of GEI studies in a consortium, MTAGEI efficiently generates summary statistics of genetic associations for multiple traits under different environmental conditions and integrates the summary statistics for GEI analysis. MTAGEI enhances the power of GEI analysis by aggregating GEI signals across multiple traits and variants that would otherwise be difficult to detect individually. MTAGEI achieves robustness by combining complementary tests under a wide spectrum of genetic architectures. We demonstrate the advantages of MTAGEI over existing single-trait-based GEI tests through extensive simulation studies and the analysis of the whole exome sequencing data from the UKB.

Individual Mobility across Clusters: The Impact of Ignoring Cross-Classified Data Structures in Discrete-Time Survival Analysis.

A multilevel-discrete time survival model may be appropriate for purely hierarchical data, but when data are non-purely hierarchical due to individual mobility across clusters, a cross-classified discrete time survival model may be necessary. The purpose of this research was to investigate the performance of a cross-classified discrete-time survival model and assess the impact of ignoring a cross-classified data structure on the model parameters of a conventional discrete-time survival model and a multilevel discrete-time survival model. A Monte Carlo simulation was used to examine the performance of three discrete-time survival models when individuals are mobile across clusters. Simulation factors included the value of the between-clusters variance, number of clusters, within-cluster sample size, Weibull scale parameter, and mobility rate. The results suggest that substantial relative parameter bias, unacceptable coverage of the 95% confidence intervals, and severely biased standard errors are possible for all model parameters when a discrete-time survival model is used that ignores the cross-classified data structure. The findings presented in this study are useful for methodologists and practitioners in educational research, public health, and other social sciences where discrete-time survival analysis is a common methodological technique for analyzing event-history data.

Go Multivariate: Recommendations on Bayesian Multilevel Hidden Markov Models with Categorical Data.

The multilevel hidden Markov model (MHMM) is a promising method to investigate intense longitudinal data obtained within the social and behavioral sciences. The MHMM quantifies information on the latent dynamics of behavior over time. In addition, heterogeneity between individuals is accommodated with the inclusion of individual-specific random effects, facilitating the study of individual differences in dynamics. However, the performance of the MHMM has not been sufficiently explored. We performed an extensive simulation to assess the effect of the number of dependent variables (1-8), number of individuals (5-90), and number of observations per individual (100-1600) on the estimation performance of a Bayesian MHMM with categorical data including various levels of state distinctiveness and separation. We found that using multivariate data generally alleviates the sample size needed and improves the stability of the results. Moreover, including variables only consisting of random noise was generally not detrimental to model performance. Regarding the estimation of group-level parameters, the number of individuals and observations largely compensate for each other. However, only the former drives the estimation of between-individual variability. We conclude with guidelines on the sample size necessary based on the level of state distinctiveness and separation and study objectives of the researcher.

When Space and Time Matter in Environmental Injustice: A Bayesian Analysis of the Association between Socio-economic Disadvantage and Air Pollution in Greater Mexico City.

Environmental injustice refers to the unequal burden of pollutants on groups with lower socioeconomic status. An increasing number of studies have identified associations between high levels of pollution and socioeconomic disadvantage. However, few studies have controlled adequately for spatio-temporal variations in pollution. This study uses a Bayesian approach to explore the association between socioeconomic disadvantage and pollution in Mexico City Metropolitan Area. We quantify the association of socioeconomic disadvantage with PM10 and ozone and evaluate the impact of accounting for spatio-temporal structure of the pollution data. We find a significant positive association between socio-economic disadvantage and pollution for levels of PM10, but not ozone. The inclusion of the spatio-temporal element in the modeling results in improved weaker estimates of this association but this does not alter results substantially. These findings confirm the robustness of previous studies that found signs of environmental injustice where spatio-temporal variations have not been explicitly considered, confirming that targeted policies to reduce pollution in socio-economically disadvantaged areas are required.