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Background Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. Methods We sequentially remove pairs of “centrosymmetric” cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. Results We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in “hot-spots” in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. Conclusions Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs.

Background Staircase designs are incomplete stepped wedge designs that, unlike standard stepped wedge designs, require clusters to contribute data for only a limited number of trial periods. Previous work has provided formulae based on asymptotic results for the calculation of the power of staircase designs to detect treatment effects of interest. Methods We conduct a simulation study to assess the finite sample performance of these formulae, and the impact of misspecifying the correlation structure when analysing data from staircase designs on inference for the treatment effect, under a range of realistic trial settings. This study focuses on basic staircase designs with one control period followed by one intervention period in each sequence. We simulate staircase trial datasets with continuous outcomes and a repeated cross-sectional measurement scheme under exchangeable and block-exchangeable intracluster correlation structures, and then fit linear mixed models with linear and categorical time period effects. For settings with a small number of clusters, Kenward-Roger and Satterthwaite small-sample corrections are applied. Comparisons are made between nominal and observed Type I error rates, and theoretically-derived study power and empirical power. The impact on inference for the treatment effect when misspecifying the intracluster correlation structure is assessed through considering performance metrics including bias and 95% confidence interval coverage. Results Data analysis assuming an exchangeable correlation structure and application of the Satterthwaite correction controls Type I error well when the correlation structure is correctly specified, and there are a sufficient number of clusters. For the true block-exchangeable model, when fitting the correct model with the Satterthwaite correction, the observed Type I error (empirical power) can be higher (lower) than the nominal (i.e., theoretical) value when there is only 1 cluster per sequence, but otherwise, it aligns well with the nominal (theoretical) value. Misspecification of the correlation structure (fitting an exchangeable model when the true structure is block-exchangeable) can lead to inflated Type I error and poor confidence interval coverage. Conclusions Staircase designs with one cluster per sequence should be used with caution. Additionally, using a correlation structure that allows for decay is preferable for making valid inferences for the estimation of the treatment effect.

Background Stepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials. Methods We conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect. Results Both REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias. Conclusions The use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

Background Child stunting due to chronic malnutrition is a major problem in low- and middle-income countries due, in part, to inadequate nutrition-related practices and insufficient access to services. Limited budgets for nutritional interventions mean that available resources must be targeted in the most cost-effective manner to have the greatest impact. Quantitative tools can help guide budget allocation decisions. Methods The Optima approach is an established framework to conduct resource allocation optimization analyses. We applied this approach to develop a new tool, ‘ Optima Nutrition’, for conducting allocative efficiency analyses that address childhood stunting. At the core of the Optima approach is an epidemiological model for assessing the burden of disease; we use an adapted version of the Lives Saved Tool (LiST). Six nutritional interventions have been included in the first release of the tool: antenatal micronutrient supplementation, balanced energy-protein supplementation, exclusive breastfeeding promotion, promotion of improved infant and young child feeding (IYCF) practices, public provision of complementary foods, and vitamin A supplementation. To demonstrate the use of this tool, we applied it to evaluate the optimal allocation of resources in 7 districts in Bangladesh, using both publicly available data (such as through DHS) and data from a complementary costing study. Results Optima Nutrition can be used to estimate how to target resources to improve nutrition outcomes. Specifically, for the Bangladesh example, despite only limited nutrition-related funding available (an estimated $0.75 per person in need per year), even without any extra resources, better targeting of investments in nutrition programming could increase the cumulative number of children living without stunting by 1.3 million (an extra 5%) by 2030 compared to the current resource allocation. To minimize stunting, priority interventions should include promotion of improved IYCF practices as well as vitamin A supplementation. Once these programs are adequately funded, the public provision of complementary foods should be funded as the next priority. Programmatic efforts should give greatest emphasis to the regions of Dhaka and Chittagong, which have the greatest number of stunted children. Conclusions A resource optimization tool can provide important guidance for targeting nutrition investments to achieve greater impact.

It has been highlighted that the original manuscript [1] contains a typesetting error in the name of Meera Shekar. This had been incorrectly captured as Meera Shekhar in the original article which has since been updated.

Models for cluster randomized trials conducted over multiple time periods should account for underlying temporal trends. However, in practice there is often limited knowledge or data available to inform the choice of time parameterization of these trends, or to anticipate the implications of this choice on trial planning. In this article, we establish a sufficient condition for when the choice of time parameterization does not affect the form of the variance of the treatment effect estimator, thereby simplifying the planning of these trials.

Introduction With limited funds available, meeting global health targets requires countries to both mobilize and prioritize their health spending. Within this context, countries have recognized the importance of allocating funds for HIV as efficiently as possible to maximize impact. Over the past six years, the governments of 23 countries in Africa, Asia, Eastern Europe and Latin America have used the Optima HIV tool to estimate the optimal allocation of HIV resources. Methods Each study commenced with a request by the national government for technical assistance in conducting an HIV allocative efficiency study using Optima HIV. Each study team validated the required data, calibrated the Optima HIV epidemic model to produce HIV epidemic projections, agreed on cost functions for interventions, and used the model to calculate the optimal allocation of available funds to best address national strategic plan targets. From a review and analysis of these 23 country studies, we extract common themes around the optimal allocation of HIV funding in different epidemiological contexts. Results and discussion The optimal distribution of HIV resources depends on the amount of funding available and the characteristics of each country's epidemic, response and targets. Universally, the modelling results indicated that scaling up treatment coverage is an efficient use of resources. There is scope for efficiency gains by targeting the HIV response towards the populations and geographical regions where HIV incidence is highest. Across a range of countries, the model results indicate that a more efficient allocation of HIV resources could reduce cumulative new HIV infections by an average of 18% over the years to 2020 and 25% over the years to 2030, along with an approximately 25% reduction in deaths for both timelines. However, in most countries this would still not be sufficient to meet the targets of the national strategic plan, with modelling results indicating that budget increases of up to 185% would be required. Conclusions Greater epidemiological impact would be possible through better targeting of existing resources, but additional resources would still be required to meet targets. Allocative efficiency models have proven valuable in improving the HIV planning and budgeting process.

With limited funds available, meeting global health targets requires countries to both mobilize and prioritize their health spending. Within this context, countries have recognized the importance of allocating funds for HIV as efficiently as possible to maximize impact. Over the past six years, the governments of 23 countries in Africa, Asia, Eastern Europe and Latin America have used the Optima HIV tool to estimate the optimal allocation of HIV resources. Each study commenced with a request by the national government for technical assistance in conducting an HIV allocative efficiency study using Optima HIV. Each study team validated the required data, calibrated the Optima HIV epidemic model to produce HIV epidemic projections, agreed on cost functions for interventions, and used the model to calculate the optimal allocation of available funds to best address national strategic plan targets. From a review and analysis of these 23 country studies, we extract common themes around the optimal allocation of HIV funding in different epidemiological contexts. The optimal distribution of HIV resources depends on the amount of funding available and the characteristics of each country's epidemic, response and targets. Universally, the modelling results indicated that scaling up treatment coverage is an efficient use of resources. There is scope for efficiency gains by targeting the HIV response towards the populations and geographical regions where HIV incidence is highest. Across a range of countries, the model results indicate that a more efficient allocation of HIV resources could reduce cumulative new HIV infections by an average of 18% over the years to 2020 and 25% over the years to 2030, along with an approximately 25% reduction in deaths for both timelines. However, in most countries this would still not be sufficient to meet the targets of the national strategic plan, with modelling results indicating that budget increases of up to 185% would be required. Greater epidemiological impact would be possible through better targeting of existing resources, but additional resources would still be required to meet targets. Allocative efficiency models have proven valuable in improving the HIV planning and budgeting process.

In stepped wedge cluster randomized trials (SW-CRTs), interventions are sequentially rolled out to clusters over multiple periods. It is common practice to analyze data from SW-CRTs using linear mixed models that treat time as discrete. However, a recent systematic review found that 95.1% of cross-sectional SW-CRTs recruit individuals continuously over time. Despite the high prevalence of such continuous recruitment designs, there has been limited guidance on how to draw model-robust inference when analyzing such SW-CRTs. In this article, we investigate through simulations the implications of using such discrete-time linear mixed models in the case of continuous recruitment designs with a continuous outcome. Specifically, in the data-generating process, we characterize continuous recruitment using a continuous-time exponential decay correlation structure in the presence or absence of a fixed continuous period effect, addressing scenarios both with and without a random or exposure-time-dependent intervention effect. We then analyze the simulated data under three popular discrete-time working correlation structures: simple exchangeable, nested exchangeable, and discrete-time exponential decay, with a robust sandwich variance estimator. Our results demonstrate that discrete-time analysis often yields negligible bias and that the robust variance estimator with the Mancl and DeRouen correction consistently achieves nominal coverage and type I error rate. One important exception occurs when recruitment patterns vary systematically between control and intervention periods, where discrete-time analysis leads to slightly biased estimates. Finally, we illustrate these findings by reanalyzing a completed SW-CRT.

Oncostatin M (OSM) is a pleiotropic, interleukin-6 family inflammatory cytokine that plays an important role in inflammatory diseases, including inflammatory bowel disease, rheumatoid arthritis, and cancer progression and metastasis. Recently, elevated OSM levels have been found in the serum of COVID-19 patients in intensive care units. Multiple anti-OSM therapeutics have been investigated, but to date no OSM small molecule inhibitors are clinically available. To pursue a high-throughput screening and structure-based drug discovery strategy to design a small molecule inhibitor of OSM, milligram quantities of highly pure, bioactive OSM are required. Here, we developed a reliable protocol to produce highly pure unlabeled and isotope enriched OSM from E. coli for biochemical and NMR studies. High yields (ca. 10 mg/L culture) were obtained in rich and minimal defined media cultures. Purified OSM was characterized by mass spectrometry and circular dichroism. The bioactivity was confirmed by induction of OSM/OSM receptor signaling through STAT3 phosphorylation in human breast cancer cells. Optimized buffer conditions yielded 1 H, 15 N HSQC NMR spectra with intense, well-dispersed peaks. Titration of 15 N OSM with a small molecule inhibitor showed chemical shift perturbations for several key residues with a binding affinity of 12.2 ± 3.9 μM. These results demonstrate the value of bioactive recombinant human OSM for NMR-based small molecule screening.