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Cluster randomized trials (CRTs) are commonly used to evaluate the causal effects of educational interventions, where the entire clusters (e.g., schools) are randomly assigned to treatment or control conditions. This study introduces statistical methods for designing and analyzing two-level (e.g., students nested within schools) and three-level (e.g., students nested within classrooms nested within schools) CRTs. Specifically, we utilize hierarchical linear models (HLMs) to account for the dependency of the intervention participants within the same clusters, estimating the average treatment effects (ATEs) of educational interventions and other effects of interest (e.g., moderator and mediator effects). We demonstrate methods and tools for sample size planning and statistical power analysis. Additionally, we discuss common challenges and potential solutions in the design and analysis phases, including the effects of omitting one level of clustering, non-compliance, threats to external validity, and cost-effectiveness of the intervention. We conclude with some practical suggestions for CRT design and analysis, along with recommendations for further readings. 

Cost-effectiveness analysis studies in education often prioritize descriptive statistics of cost-effectiveness measures, such as the point estimate of the incremental cost-effectiveness ratio (ICER), while neglecting inferential statistics like confidence intervals (CIs). Without CIs, it becomes impossible to make meaningful comparisons of alternative educational strategies, as there is no basis for assessing the uncertainty of point estimates or the plausible range of ICERs. This study is designed to evaluate the relative performance of five methods of constructing CIs for ICERs in randomized controlled trials with cost-effectiveness analyses. We found that the Monte Carlo interval method based on summary statistics consistently performed well regarding coverage, width, and symmetry. It yielded estimates comparable to the percentile bootstrap method across multiple scenarios. In contrast, Fieller’s method did not work well with small sample sizes and treatment effects. Further, Taylor’s method and the Box method performed least well. We discussed two-sided and one-sided hypothesis testing based on ICER CIs, developed tools for calculating these ICER CIs, and demonstrated the calculation using an empirical example. We concluded with suggestions for applications and extensions of this work. 

Cometabolic bioremediation is trending for the treatment of 1,4-dioxane (dioxane) and other emerging contaminants to meet stringent regulatory goals ( e.g. , <10 μg L −1 ) since biodegradation activities can be fueled by the supplementation of auxiliary substrates. In this study, we compared and investigated the effectiveness of two types of common auxiliary substrates, short-chain alkane gases ( e.g. , propane and butane) and primary alcohols ( e.g. , 1-propanol, 1-butanol, and ethanol), for dioxane removal in diverse environmental matrices with Azoarcus sp. DD4 as the inoculum. Physicochemical characterization at the pure culture level revealed that propane and 1-propanol are advantageous for stimulating cell growth and dioxane biodegradation by DD4. Parallel microcosm assays were conducted to assess the compatibility of DD4 bioaugmentation in diverse microbiomes recovered from five different environmental samples, including shallow and deep aquifer groundwater, contaminated river sediment, and municipal activated sludge. Propane was effective in sustaining efficient dioxane removal and the dominance of DD4 across all environmental matrices. Notably, amendment with 1-propanol promoted superior dioxane degradation in the deep aquifer groundwater, in which low pre-treatment biomass and post-treatment diversity were observed, suggesting its potential for intrinsic field applications. The combination of microbial community analysis and differential ranking identified that Ochrobactrum and several other indigenous bacteria were boosted by the inoculation of DD4, implying their commensal or mutualistic relationship. Collectively, propane and 1-propanol can be effective auxiliary substrate alternatives tailored for in situ bioaugmentation and their effectiveness is affected by the density and structure of environmental microbiomes. 

Cometabolic degradation plays a prominent role in bioremediation of commingled groundwater contamination (e.g., chlorinated solvents and the solvent stabilizer 1,4-dioxane [dioxane]). In this study, we untangled the diversity and catalytic functions of multi-component monooxygenases in Azoarcus sp. DD4, a gram-negative propanotroph that is effective in degrading dioxane and 1,1-dichloroethylene (1,1-DCE). Using a combination of knockout mutagenesis and heterologous expression, a toluene monooxygenase (MO) encoded by the tmoABCDEF gene cluster was unequivocally proved as the key enzyme responsible for the cometabolism of both dioxane and 1,1-DCE. Interestingly, in addition to utilizing toluene as a primary substrate, this toluene MO can also oxidize propane into 1-propanol. Expression of this toluene MO in DD4 appears inducible by both substrates (toluene and propane) and their primary hydroxylation products (m-cresol, p-cresol, and 1-propanol). These findings coherently explain why DD4 can grow on propane and express toluene MO for active co-oxidation of dioxane and 1,1-DCE. Furthermore, upregulation of tmo transcription by 1-propanol underlines the implication potential of using 1-propanol as an alternative auxiliary substrate for DD4 bioaugmentation. The discovery of this toluene MO in DD4 and its degradation and induction versatility renders broad applications spanning from environmental remediation and water treatment to biocatalysis in green chemistry. Importance Toluene MOs have been well recognized given their robust abilities to degrade a variety of environmental pollutants. Built upon previous research efforts, this study ascertained the untapped capability of a toluene MO in DD4 for effective co-oxidation of dioxane and 1,1-DCE, two of the most prevailing yet challenging groundwater contaminants. This report also aligns the induction of a toluene MO with non-toxic and commercially accessible chemicals (e.g., propane and 1-propanol), extending its implication values in the field of environmental microbiology and beyond.