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.

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.

Executive functions in psychopathy: a meta-analysis of inhibition, planning, shifting, and working memory performance.

Much research has focused on executive function (EF) impairments in psychopathy, a severe personality disorder characterized by a lack of empathy, antisocial behavior, and a disregard for social norms and moral values. However, it is still unclear to what extent EF deficits are present across psychopathy factors and, more importantly, which EF domains are impaired. The current meta-analysis answers these questions by synthesizing the results of 50 studies involving 5,694 participants from 12 different countries. Using multilevel random-effects models, we pooled effect sizes (Cohen's d) for five different EF domains: overall EF, inhibition, planning, shifting, and working memory. Moreover, differences between psychopathy factors were evaluated. Our analyses revealed small deficits in overall EF, inhibition, and planning performance. However, a closer inspection of psychopathy factors indicated that EF deficits were specific to lifestyle/antisocial traits, such as disinhibition. Conversely, interpersonal/affective traits, such as boldness, showed no deficits and in some cases even improved EF performance. These findings suggest that EF deficits are not a key feature of psychopathy per se, but rather are related to antisociality and disinhibitory traits. Potential brain correlates of these findings as well as implications for future research and treatment are discussed.

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.

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.

Postpartum pain and the risk of postpartum depression: A meta-analysis of observational studies.

OBJECTIVE: This meta-analysis of observational studies aimed to derive a more precise estimation of the relationship between postpartum pain and postpartum depression (PPD). METHODS: A systematic literature search was completed in the following databases from inception to September 26, 2022: PubMed, Embase, and Web of Science. Quality evaluation of each study was achieved through Newcastle-Ottawa scale (NOS) assessment. Heterogeneity across studies was evaluated by Cochran's Q test and I2 test. Pooled estimates of odds ratios (ORs) and corresponding 95% confidence intervals (CIs) were analyzed using fixed-effects model or random-effects model, according to heterogeneity. Subgroup analysis, sensitivity analysis, and Egger's test were also performed. RESULTS: From the identified 1884 articles, a total of 8 studies involving 3973 participants were included in the final meta-analysis. Seven of the 8 studies were evaluated as high-quality, with NOS scores ≥7. A significant heterogeneity was observed (I2 = 66.5%, p = 0.004) among eight studies. Therefore, the performed random-effect model suggested a significant association between postpartum pain and PPD risk (OR 1.29, 95% CI 1.10-1.52, p = 0.002). However, the subgroup analyses did not define the source of heterogeneity. Moreover, the sensitivity analysis showed the stability of the pooled results, but the significant publication bias was identified (p = 0.009). The trim and fill method was performed and resulted in an OR of 1.14 (95% CI 0.95-1.37, p = 0.162). CONCLUSIONS: This meta-analysis found a potential association between postpartum pain and PPD. Further researches are needed to provide more robust evidences.

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.

On the Q statistic with constant weights in meta-analysis of binary outcomes.

BACKGROUND: Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value (under an incorrect null distribution) is part of several popular estimators of the between-study variance, [Formula: see text]. Those applications generally do not account for use of the studies' estimated variances in the inverse-variance weights that define Q (more explicitly, [Formula: see text]). Importantly, those weights make approximating the distribution of [Formula: see text] rather complicated. METHODS: As an alternative, we are investigating a Q statistic, [Formula: see text], whose constant weights use only the studies' arm-level sample sizes. For log-odds-ratio (LOR), log-relative-risk (LRR), and risk difference (RD) as the measures of effect, we study, by simulation, approximations to distributions of [Formula: see text] and [Formula: see text], as the basis for tests of heterogeneity. RESULTS: The results show that: for LOR and LRR, a two-moment gamma approximation to the distribution of [Formula: see text] works well for small sample sizes, and an approximation based on an algorithm of Farebrother is recommended for larger sample sizes. For RD, the Farebrother approximation works very well, even for small sample sizes. For [Formula: see text], the standard chi-square approximation provides levels that are much too low for LOR and LRR and too high for RD. The Kulinskaya et al. (Res Synth Methods 2:254-70, 2011) approximation for RD and the Kulinskaya and Dollinger (BMC Med Res Methodol 15:49, 2015) approximation for LOR work well for [Formula: see text] but have some convergence issues for very small sample sizes combined with small probabilities. CONCLUSIONS: The performance of the standard [Formula: see text] approximation is inadequate for all three binary effect measures. Instead, we recommend a test of heterogeneity based on [Formula: see text] and provide practical guidelines for choosing an appropriate test at the .05 level for all three effect measures.

Separating Measurement Error and Signal in Environmental Data: Use of Replicates to Address Uncertainty.

Measurement uncertainty has long been a concern in the characterizing and interpreting environmental and toxicological measurements. We compared statistical analysis approaches when there are replicates: a Naïve approach that omits replicates, a Hybrid approach that inappropriately treats replicates as independent samples, and a Measurement Error Model (MEM) approach in a random effects analysis of variance (ANOVA) model that appropriately incorporates replicates. A simulation study assessed the effects of sample size and levels of replication, signal variance, and measurement error on estimates from the three statistical approaches. MEM results were superior overall with confidence intervals for the observed mean narrower on average than those from the Naïve approach, giving improved characterization. The MEM approach also featured an unparalleled advantage in estimating signal and measurement error variance separately, directly addressing measurement uncertainty. These MEM estimates were approximately unbiased on average with more replication and larger sample sizes. Case studies illustrated analyzing normally distributed arsenic and log-normally distributed chromium concentrations in tap water and calculating MEM confidence intervals for the true, latent signal mean and latent signal geometric mean (i.e., with measurement error removed). MEM estimates are valuable for study planning; we used simulation to compare various sample sizes and levels of replication.

Heterogeneity in health funding and disparities in health outcome: a comparison between high focus and non-high focus states in India.

BACKGROUND: The Central Government of India introduced the National Health Mission (NHM) in 2005 to improve health outcomes by enhancing publicly financed (government) health expenditure and health infrastructure at the state level. This study aims to examine the effects of the state-level heterogeneity in publicly financed spending on health services on major health outcomes such as life expectancy, infant mortality rate, child mortality rate, the incidence of malaria, and immunization coverage (i.e., BCG, Polio, Measles, and Tetanus). METHODS: This study investigates the relationships between publicly financed health expenditure and health outcomes by controlling income and infrastructure levels across 28 Indian States from 2005 to 2016. Along with all states, the empirical analysis has also been carried out for high-focus and non-high-focus states as per the NHM fund flow criteria. It has applied panel fixed-effects and random effects model wherever required based on the Hausman test. RESULTS: The empirical results show that publicly financed health expenditure reduces infant mortality, child mortality, and malaria cases. At the same time, it improves life expectancy and immunization coverage in India. It also finds that the relationship between publicly financed health expenditure and health outcomes is weak, especially in the high-focus states. CONCLUSIONS: Given the healthcare need for achieving desirable health outcomes, Indian States should enhance publicly financed expenditure on health services. This study augments essential guidance for implementing public health policies in developing countries.

Outlier identification and monitoring of institutional or clinician performance: an overview of statistical methods and application to national audit data.

BACKGROUND: Institutions or clinicians (units) are often compared according to a performance indicator such as in-hospital mortality. Several approaches have been proposed for the detection of outlying units, whose performance deviates from the overall performance. METHODS: We provide an overview of three approaches commonly used to monitor institutional performances for outlier detection. These are the common-mean model, the 'Normal-Poisson' random effects model and the 'Logistic' random effects model. For the latter we also propose a visualisation technique. The common-mean model assumes that the underlying true performance of all units is equal and that any observed variation between units is due to chance. Even after applying case-mix adjustment, this assumption is often violated due to overdispersion and a post-hoc correction may need to be applied. The random effects models relax this assumption and explicitly allow the true performance to differ between units, thus offering a more flexible approach. We discuss the strengths and weaknesses of each approach and illustrate their application using audit data from England and Wales on Adult Cardiac Surgery (ACS) and Percutaneous Coronary Intervention (PCI). RESULTS: In general, the overdispersion-corrected common-mean model and the random effects approaches produced similar p-values for the detection of outliers. For the ACS dataset (41 hospitals) three outliers were identified in total but only one was identified by all methods above. For the PCI dataset (88 hospitals), seven outliers were identified in total but only two were identified by all methods. The common-mean model uncorrected for overdispersion produced several more outliers. The reason for observing similar p-values for all three approaches could be attributed to the fact that the between-hospital variance was relatively small in both datasets, resulting only in a mild violation of the common-mean assumption; in this situation, the overdispersion correction worked well. CONCLUSION: If the common-mean assumption is likely to hold, all three methods are appropriate to use for outlier detection and their results should be similar. Random effect methods may be the preferred approach when the common-mean assumption is likely to be violated.

Multilevel IRT models for the analysis of satisfaction for distance learning during the Covid-19 pandemic.

The Covid-19 pandemic played a relevant role in the diffusion of distance learning alternatives to "traditional" learning based on classroom activities, to allow university students to continue attending lessons during the most severe phases of the pandemic. In such a context, investigating the students' perspective on distance learning provides useful information to stakeholders to improve effective educational strategies, which could be useful also after the end of the emergency to favor the digital transformation in the higher educational setting. Here we focus on the satisfaction in distance learning for Italian university students. We rely on data comprising students enrolled in various Italian universities, which were inquired about several aspects related to learning distance. We explicitly take into account the hierarchical nature of data (i.e., students nested in universities) and the latent nature of the variable of interest (i.e., students' learning satisfaction) through a multilevel Item Response Theory model with students' and universities' covariates. As the main results of our study, we find out that distance learning satisfaction of students: (i) depends on the University where they study; (ii) is affected by some students' socio-demographic characteristics, among which psychological factors related to Covid-19; (iii) is affected by some observable university characteristics.

TWO-SIGMA: A novel two-component single cell model-based association method for single-cell RNA-seq data.

In this paper, we develop TWO-SIGMA, a TWO-component SInGle cell Model-based Association method for differential expression (DE) analyses in single-cell RNA-seq (scRNA-seq) data. The first component models the probability of "drop-out" with a mixed-effects logistic regression model and the second component models the (conditional) mean expression with a mixed-effects negative binomial regression model. TWO-SIGMA is extremely flexible in that it: (i) does not require a log-transformation of the outcome, (ii) allows for overdispersed and zero-inflated counts, (iii) accommodates a correlation structure between cells from the same individual via random effect terms, (iv) can analyze unbalanced designs (in which the number of cells does not need to be identical for all samples), (v) can control for additional sample-level and cell-level covariates including batch effects, (vi) provides interpretable effect size estimates, and (vii) enables general tests of DE beyond two-group comparisons. To our knowledge, TWO-SIGMA is the only method for analyzing scRNA-seq data that can simultaneously accomplish each of these features. Simulations studies show that TWO-SIGMA outperforms alternative regression-based approaches in both type-I error control and power enhancement when the data contains even moderate within-sample correlation. A real data analysis using pancreas islet single-cells exhibits the flexibility of TWO-SIGMA and demonstrates that incorrectly failing to include random effect terms can have dramatic impacts on scientific conclusions. TWO-SIGMA is implemented in the R package twosigma available at https://github.com/edvanburen/twosigma.

A unified method for improved inference in random effects meta-analysis.

Random effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations; for instance, coverage probabilities of confidence intervals can be substantially below the nominal level. The main reason is that these inference methods rely on large sample approximations even though the number of synthesized studies is usually small or moderate in practice. In this article, we solve this problem using a unified inference method based on Monte Carlo conditioning for broad application to random effects meta-analysis. The developed method provides improved confidence intervals with coverage probabilities that are closer to the nominal level than standard methods. As specific applications, we provide new inference procedures for three types of meta-analysis: conventional univariate meta-analysis for pairwise treatment comparisons, meta-analysis of diagnostic test accuracy, and multiple treatment comparisons via network meta-analysis. We also illustrate the practical effectiveness of these methods via real data applications and simulation studies.

Analysis of clustered interval-censored data using a class of semiparametric partly linear frailty transformation models.

A flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval-censored data, which arise naturally in complex diseases and dental research. This class of models features two nonparametric components, resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate. The dependence among failure times within a cluster is induced by a shared, unobserved frailty term. A sieve maximum likelihood estimation method based on piecewise linear functions is proposed. The proposed estimators of the regression, dependence, and transformation parameters are shown to be strongly consistent and asymptotically normal, whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence. An extensive simulation study is conducted to study the finite-sample performance of the proposed estimators. We provide an application to a dental study for illustration.

A penalization approach to random-effects meta-analysis.

Systematic reviews and meta-analyses are principal tools to synthesize evidence from multiple independent sources in many research fields. The assessment of heterogeneity among collected studies is a critical step when performing a meta-analysis, given its influence on model selection and conclusions about treatment effects. A common-effect (CE) model is conventionally used when the studies are deemed homogeneous, while a random-effects (RE) model is used for heterogeneous studies. However, both models have limitations. For example, the CE model produces excessively conservative confidence intervals with low coverage probabilities when the collected studies have heterogeneous treatment effects. The RE model, on the other hand, assigns higher weights to small studies compared to the CE model. In the presence of small-study effects or publication bias, the over-weighted small studies from a RE model can lead to substantially biased overall treatment effect estimates. In addition, outlying studies may exaggerate between-study heterogeneity. This article introduces penalization methods as a compromise between the CE and RE models. The proposed methods are motivated by the penalized likelihood approach, which is widely used in the current literature to control model complexity and reduce variances of parameter estimates. We compare the existing and proposed methods with simulated data and several case studies to illustrate the benefits of the penalization methods.

Assessing complier average causal effects from longitudinal trials with multiple endpoints and treatment noncompliance: An application to a study of Arthritis Health Journal.

Treatment noncompliance often occurs in longitudinal randomized controlled trials (RCTs) on human subjects, and can greatly complicate treatment effect assessment. The complier average causal effect (CACE) informs the intervention efficacy for the subpopulation who would comply regardless of assigned treatment and has been considered as patient-oriented treatment effects of interest in the presence of noncompliance. Real-world RCTs evaluating multifaceted interventions often employ multiple study endpoints to measure treatment success. In such trials, limited sample sizes, low compliance rates, and small to moderate effect sizes on individual endpoints can significantly reduce the power to detect CACE when these correlated endpoints are analyzed separately. To overcome the challenge, we develop a multivariate longitudinal potential outcome model with stratification on latent compliance types to efficiently assess multivariate CACEs (MCACE) by combining information across multiple endpoints and visits. Evaluation using simulation data shows a significant increase in the estimation efficiency with the MCACE model, including up to 50% reduction in standard errors (SEs) of CACE estimates and 1-fold increase in the power to detect CACE. Finally, we apply the proposed MCACE model to an RCT on Arthritis Health Journal online tool. Results show that the MCACE analysis detects significant and beneficial intervention effects on two of the six endpoints while estimating CACEs for these endpoints separately fail to detect treatment effect on any endpoint.

Meta-analysis Using Flexible Random-effects Distribution Models.

BACKGROUND: In meta-analysis, the normal distribution assumption has been adopted in most systematic reviews of random-effects distribution models due to its computational and conceptual simplicity. However, this restrictive model assumption is possibly unsuitable and might have serious influences in practices. METHODS: We provide two examples of real-world evidence that clearly show that the normal distribution assumption is explicitly unsuitable. We propose new random-effects meta-analysis methods using five flexible random-effects distribution models that can flexibly regulate skewness, kurtosis and tailweight: skew normal distribution, skew t-distribution, asymmetric Subbotin distribution, Jones-Faddy distribution, and sinh-arcsinh distribution. We also developed a statistical package, flexmeta, that can easily perform these methods. RESULTS: Using the flexible random-effects distribution models, the results of the two meta-analyses were markedly altered, potentially influencing the overall conclusions of these systematic reviews. CONCLUSION: The restrictive normal distribution assumption in the random-effects model can yield misleading conclusions. The proposed flexible methods can provide more precise conclusions in systematic reviews.

Age Difference of the Relationship Between Cerebral Oxygen Saturation and Physiological Parameters in Pediatric Cardiac Surgery with Cardiopulmonary Bypass: Analysis Using the Random-Effects Model.

Recently, monitoring of cerebral oxygen saturation (ScO2) has become widespread in pediatric cardiac surgery. Our previous study reported that mean blood pressure (mBP) was the major contributor to ScO2 throughout cardiac surgery with cardiopulmonary bypass (CPB) in children weighing under 10 kg. We speculated that this result might be attributable to incomplete cerebral autoregulation in such young children. Accordingly, our hypothesis is that the relationship between ScO2 and the physiological parameters may change according to the growth of the children. ScO2 was measured with an INVOS 5100C (Somanetics, Troy, MI). Random-effects analysis was employed with ScO2 as a dependent variable, and seven physiological parameters (mBP, central venous pressure, nasopharyngeal temperature, SaO2, hematocrit, PaCO2, and pH) were entered as independent covariates. The analysis was performed during the pre-CPB, CPB, and post-CPB periods by dividing the patients into two groups: infants (Infant Group) and children who were more than 1 year old (Child Group). The Infant and Child Groups consisted of 28 and 21 patients. In the random-effects analysis, mBP was the major contributor to ScO2 during CPB in both groups. During the pre-CPB period, the effect of mBP was strongest in the Infant group. However, its effect was second to that of SaO2 in the Child Group. During the post-CPB period, SaO2 and mBP still affected ScO2 in the Infant group. However, the dominant contributors were unclear in the Child Group. Cerebral autoregulation may be immature in infants. In addition, it may be impaired during CPB even after 1 year of age.

Estimating intervention effectiveness in trials of malaria interventions with contamination.

BACKGROUND: In cluster randomized trials (CRTs) or stepped wedge cluster randomized trials (SWCRTs) of malaria interventions, mosquito movement leads to contamination between trial arms unless buffer zones separate the clusters. Contamination can be accounted for in the analysis, yielding an estimate of the contamination range, the distance over which contamination measurably biases the effectiveness. METHODS: A previously described analysis for CRTs is extended to SWCRTs and estimates of effectiveness are provided as a function of intervention coverage. The methods are applied to two SWCRTs of malaria interventions, the SolarMal trial on the impact of mass trapping of mosquitoes with odor-baited traps and the AvecNet trial on the effect of adding pyriproxyfen to long-lasting insecticidal nets. RESULTS: For the SolarMal trial, the contamination range was estimated to be 146 m ([Formula: see text] credible interval [Formula: see text] km), together with a [Formula: see text] ([Formula: see text] credible interval [Formula: see text]) reduction of Plasmodium infection, compared to the [Formula: see text] reduction estimated without accounting for contamination. The estimated effectiveness had an approximately linear relationship with coverage. For the AvecNet trial, estimated contamination effects were minimal, with insufficient data from the cluster boundary regions to estimate the effectiveness as a function of coverage. CONCLUSIONS: The contamination range in these trials of malaria interventions is much less than the distances Anopheles mosquitoes can fly. An appropriate analysis makes buffer zones unnecessary, enabling the design of more cost-efficient trials. Estimation of the contamination range requires information from the cluster boundary regions and trials should be designed to collect this.