Cost and Affordability of Habitual and Recommended Diets in Welfare-Dependent Households in Australia.

It is crucial to ensure healthy diets are affordable in low socioeconomic groups, such as welfare-dependent households, who experience higher rates of diet-related disease than others. This study assessed the cost of habitual (unhealthy) and recommended (healthy) diets in six welfare-dependent and six other, comparable Australian households, using either popular branded products or the cheapest available alternatives. It also assessed diet affordability in welfare-dependent households, before and after modest increases in government welfare payments introduced in early September 2023. Results confirmed that recommended diets were less expensive than habitual diets in all households unless the cheapest available products were included. This strategy reduced habitual diet costs by 35-37% and recommended diet costs by 30-32%. The lower cost differential could aid perceptions that healthy foods are more expensive than unhealthy foods. In April 2023, 23-37% of the income of welfare-dependent households with children was required to purchase recommended diets; this reduced only to 20-35% in September 2023. Hence, the increases in welfare payments were insufficient to meaningfully improve the affordability of healthy diets in the most vulnerable Australians. In the current cost-of-living crisis, there is an urgent need for more welfare support to help purchase healthy diets. Monitoring of diet cost and affordability is also required.

Data-driven modelling for assessing trophic status in marine ecosystems using machine learning approaches.

Assessing eutrophication in coastal and transitional waters is of utmost importance, yet existing Trophic Status Index (TSI) models face challenges like multicollinearity, data redundancy, inappropriate aggregation methods, and complex classification schemes. To tackle these issues, we developed a novel tool that harnesses machine learning (ML) and artificial intelligence (AI), enhancing the reliability and accuracy of trophic status assessments. Our research introduces an improved data-driven methodology specifically tailored for transitional and coastal (TrC) waters, with a focus on Cork Harbour, Ireland, as a case study. Our innovative approach, named the Assessment Trophic Status Index (ATSI) model, comprises three main components: the selection of pertinent water quality indicators, the computation of ATSI scores, and the implementation of a new classification scheme. To optimize input data and minimize redundancy, we employed ML techniques, including advanced deep learning methods. Specifically, we developed a CHL prediction model utilizing ten algorithms, among which XGBoost demonstrated exceptional performance, showcasing minimal errors during both training (RMSE = 0.0, MSE = 0.0, MAE = 0.01) and testing (RMSE = 0.0, MSE = 0.0, MAE = 0.01) phases. Utilizing a novel linear rescaling interpolation function, we calculated ATSI scores and evaluated the model's sensitivity and efficiency across diverse application domains, employing metrics such as R2, the Nash-Sutcliffe efficiency (NSE), and the model efficiency factor (MEF). The results consistently revealed heightened sensitivity and efficiency across all application domains. Additionally, we introduced a brand new classification scheme for ranking the trophic status of transitional and coastal waters. To assess spatial sensitivity, we applied the ATSI model to four distinct waterbodies in Ireland, comparing trophic assessment outcomes with the Assessment of Trophic Status of Estuaries and Bays in Ireland (ATSEBI) System. Remarkably, significant disparities between the ATSI and ATSEBI System were evident in all domains, except for Mulroy Bay. Overall, our research significantly enhances the accuracy of trophic status assessments in marine ecosystems. The ATSI model, combined with cutting-edge ML techniques and our new classification scheme, represents a promising avenue for evaluating and monitoring trophic conditions in TrC waters. The study also demonstrated the effectiveness of ATSI in assessing trophic status across various waterbodies, including lakes, rivers, and more. These findings make substantial contributions to the field of marine ecosystem management and conservation.

Cluster randomized controlled trial analysis at the cluster level: The clan command.

In this article, we introduce a new command, clan, that conducts a cluster-level analysis of cluster randomized trials. The command simplifies adjusting for individual- and cluster-level covariates and can also account for a stratified design. It can be used to analyze a continuous, binary, or rate outcome.

Assessing the impact of COVID-19 lockdown on surface water quality in Ireland using advanced Irish water quality index (IEWQI) model.

The COVID-19 pandemic has significantly impacted various aspects of life, including environmental conditions. Surface water quality (WQ) is one area affected by lockdowns imposed to control the virus's spread. Numerous recent studies have revealed the considerable impact of COVID-19 lockdowns on surface WQ. In response, this research aimed to assess the impact of COVID-19 lockdowns on surface water quality in Ireland using an advanced WQ model. To achieve this goal, six years of water quality monitoring data from 2017 to 2022 were collected for nine water quality indicators in Cork Harbour, Ireland, before, during, and after the lockdowns. These indicators include pH, water temperature (TEMP), salinity (SAL), biological oxygen demand (BOD5), dissolved oxygen (DOX), transparency (TRAN), and three nutrient enrichment indicators-dissolved inorganic nitrogen (DIN), molybdate reactive phosphorus (MRP), and total oxidized nitrogen (TON). The results showed that the lockdown had a significant impact on various WQ indicators, particularly pH, TEMP, TON, and BOD5. Over the study period, most indicators were within the permissible limit except for MRP, with the exception of during COVID-19. During the pandemic, TON and DIN decreased, while water transparency significantly improved. In contrast, after COVID-19, WQ at 7% of monitoring sites significantly deteriorated. Overall, WQ in Cork Harbour was categorized as "good," "fair," and "marginal" classes over the study period. Compared to temporal variation, WQ improved at 17% of monitoring sites during the lockdown period in Cork Harbour. However, no significant trend in WQ was observed. Furthermore, the study analyzed the advanced model's performance in assessing the impact of COVID-19 on WQ. The results indicate that the advanced WQ model could be an effective tool for monitoring and evaluating lockdowns' impact on surface water quality. The model can provide valuable information for decision-making and planning to protect aquatic ecosystems.

Comparison between the WFD approaches and newly developed water quality model for monitoring transitional and coastal water quality in Northern Ireland.

This study aims to evaluate existing approaches for monitoring and assessing water quality in waterbodies in the North of Ireland using newly developed methodologies. The results reveal significant differences between the new technique and the existing "one-out, all-out" approach in rating water quality. The new approach found the water quality status to be "good," "fair," and "marginal," whereas the existing "one-out, all-out" technique classified water quality as "good," and "moderate," respectively. The new technique outperformed existing approaches in rating the water quality of different waterbody types, with high R2 = 1, NSE = 0.99, and MEF = 0 values. Furthermore, the final assessment of water quality using the new methodologies had the lowest uncertainty (<1 %), whereas the efficiency measures (NSE and MEF) indicate that the new approaches are bias-free to assess water quality at any geographic scale. The results of this study reveal that the newly proposed methodologies are effective in assessing the water quality states of transitional and coastal waterbodies in the North of Ireland. The study also highlighted the limitations of existing approaches and the importance of updating water resource management systems for better protection of these waterbodies. The findings have significant implications for water resource management and planning in the North of Ireland and other similar regions.

Marine waters assessment using improved water quality model incorporating machine learning approaches.

In marine ecosystems, both living and non-living organisms depend on "good" water quality. It depends on a number of factors, and one of the most important is the quality of the water. The water quality index (WQI) model is widely used to assess water quality, but existing models have uncertainty issues. To address this, the authors introduced two new WQI models: the weight based weighted quadratic mean (WQM) and unweighted based root mean squared (RMS) models. These models were used to assess water quality in the Bay of Bengal, using seven water quality indicators including salinity (SAL), temperature (TEMP), pH, transparency (TRAN), dissolved oxygen (DOX), total oxidized nitrogen (TON), and molybdate reactive phosphorus (MRP). Both models ranked water quality between "good" and "fair" categories, with no significant difference between the weighted and unweighted models' results. The models showed considerable variation in the computed WQI scores, ranging from 68 to 88 with an average of 75 for WQM and 70 to 76 with an average of 72 for RMS. The models did not have any issues with sub-index or aggregation functions, and both had a high level of sensitivity (R2 = 1) in terms of the spatio-temporal resolution of waterbodies. The study demonstrated that both WQI approaches effectively assessed marine waters, reducing uncertainty and improving the accuracy of the WQI score.

Healthy Food Prices Increased More Than the Prices of Unhealthy Options during the COVID-19 Pandemic and Concurrent Challenges to the Food System.

Food prices have escalated due to impacts of the COVID-19 pandemic on global food systems, and other regional shocks and stressors including climate change and war. Few studies have applied a health lens to identify the most affected foods. This study aimed to assess costs and affordability of habitual (unhealthy) diets and recommended (healthy, equitable and more sustainable) diets and their components in Greater Brisbane, Queensland, Australia from 2019 to 2022 using the Healthy Diets Australian Standardised Affordability and Pricing protocol. Affordability was determined for reference households at three levels of income: median, minimum wage, and welfare-dependent. The recommended diet cost increased 17.9%; mostly in the last year when the prices of healthy foods, such as fruit, vegetables and legumes, healthy fats/oils, grains, and meats/alternatives, increased by 12.8%. In contrast, the cost of the unhealthy foods and drinks in the habitual diet 'only' increased 9.0% from 2019 to 2022, and 7.0% from 2021 to 2022. An exception was the cost of unhealthy take-away foods which increased by 14.7% over 2019-2022. With government COVID-19-related payments, for the first time recommended diets were affordable for all and food security and diets improved in 2020. However, the special payments were withdrawn in 2021, and recommended diets became 11.5% less affordable. Permanently increasing welfare support and providing an adequate minimum wage, while keeping basic, healthy foods GST-free and increasing GST to 20% on unhealthy foods, would improve food security and diet-related health inequities. Development of a Consumer Price Index specifically for healthy food would help highlight health risks during economic downturns.

A sophisticated model for rating water quality.

Here, we present the Irish Water Quality Index (IEWQI) model for assessing transitional and coastal water quality in an effort to improve the method and develop a tool that can be used by environmental regulators to abate water pollution in Ireland. The developed model has been associated with the adoption of water quality standards formulated for coastal and transitional waterbodies according to the water framework directive legislation by the environmental regulator of Irish water. The model consists of five identical components, including (i) indicator selection technique is to select the crucial water quality indicator; (ii) sub-index (SI) function for rescaling various water quality indicators' information into a uniform scale; (iii) indicators' weight method for estimating the weight values based on the relative significance of real-time information on water quality; (iii) aggregation function for computing the water quality index (WQI) score; and (v) score interpretation scheme for assessing the state of water quality. The IEWQI model was developed based on Cork Harbour, Ireland. The developed IEWQI model was applied to four coastal waterbodies in Ireland, for assessing water quality using 2021 water quality data for the summer and winter seasons in order to evaluate model sensitivity in terms of spatio-temporal resolution of various waterbodies. The model efficiency and uncertainty were also analysed in this research. In terms of different spatio-temporal magnitudes of various domains, the model shows higher sensitivity in four application domains during the summer and winter. In addition, the results of uncertainty reveal that the IEWQI model architecture may be effective for reducing model uncertainty in order to avoid model eclipsing and ambiguity problems. The findings of this study reveal that the IEWQI model could be an efficient and reliable technique for the assessment of transitional and coastal water quality more accurately in any geospatial domain.

Taxonomic review of Saguinus mystax (Spix, 1823) (Primates, Callitrichidae), and description of a new species.

Although the Amazon has the greatest diversity of primates, there are still taxonomic uncertainties for many taxa, such as the species of the Saguinus mystax group. The most geographically broadly distributed and phenotypically diverse species in this group is S. mystax, and its phenotypic diversity has been recognized as three subspecies-S. mystax mystax, S. mystax pileatus and S. mystax pluto-with non-overlapping geographic distributions. In this sense, we carried out an extensive field survey in their distribution areas and used a framework of taxonomic hypothesis testing of genomic data combined with an integrative taxonomic decision-making framework to carry out a taxonomic revision of S. mystax. Our tests supported the existence of three lineages/species. The first species corresponds to Saguinus mystax mystax from the left bank of the Juruá River, which was raised to the species level, and we also discovered and described animals from the Juruá-Tefé interfluve previously attributed to S. mystax mystax as a new species. The subspecies S. m. pileatus and S. m. pluto are recognized as a single species, under a new nomenclatural combination. However, given their phenotypic distinction and allopatric distribution, they potentially are a manifestation of an early stage of speciation, and therefore we maintain their subspecific designations.

A cross-sectional study of Q fever in Camels: Risk factors for infection, the role of small ruminants and public health implications for desert-dwelling pastoral communities.

Q fever represents an important 'neglected zoonosis', with high prevalences recorded across the Middle East region. Among rural desert-dwelling communities in the region, camel milk is largely consumed raw, due to perceptions of dromedaries as a uniquely clean livestock species mentioned in the Qur'an and Islamic hadith, while milk from other livestock species is usually boiled. As a result, camels present a unique public health threat among such communities from milk-borne pathogens, including Coxiella burnetii. In view of this, a cross-sectional study was conducted among dromedary herds in southern Jordan between September 2017 and October 2018, including 404 camels from 121 randomly selected herds. In addition, 510 household members associated with these herds were interviewed regarding potential high-risk practices for zoonotic transmission. Weight adjusted camel population seroprevalence for C. burnetii was 49.6% (95% CI: 44.7-54.5), with evidence of maternally derived immunity in calves ≤6 months old. Adjusted herd-level prevalence was 76.0% (95% CI 72.7-80.2). It was estimated 30.4% (144/477) of individuals consumed raw milk from infected herds monthly or more. Following multivariable logistic regression analysis, seropositive status in camels was found to be associated with increasing age, high herd tick burdens, keeping the herd together throughout the year including when calving, and owning larger (>50) sheep and goat flocks, with goats presenting a higher risk than sheep. Racing camel status was found to be protective. Socioculturally appropriate interventions aimed at raising awareness of potential risks associated with drinking raw camel milk, alongside appropriate livestock management interventions, should be considered.

A novel approach for estimating and predicting uncertainty in water quality index model using machine learning approaches.

With the significant increase in WQI applications worldwide and lack of specific application guidelines, accuracy and reliability of WQI models is a major issue. It has been reported that WQI models produce significant uncertainties during the various stages of their application including: (i) water quality indicator selection, (ii) sub-index (SI) calculation, (iii) water quality indicator weighting and (iv) aggregation of sub-indices to calculate the overall index. This research provides a robust statistically sound methodology for assessment of WQI model uncertainties. Eight WQI models are considered. The Monte Carlo simulation (MCS) technique was applied to estimate model uncertainty, while the Gaussian Process Regression (GPR) algorithm was utilised to predict uncertainties in the WQI models at each sampling site. The sub-index functions were found to contribute to considerable uncertainty and hence affect the model reliability - they contributed 12.86% and 10.27% of uncertainty for summer and winter applications, respectively. Therefore, the selection of sub-index function needs to be made with care. A low uncertainty of less than 1% was produced by the water quality indicator selection and weighting processes. Significant statistical differences were found between various aggregation functions. The weighted quadratic mean (WQM) function was found to provide a plausible assessment of water quality of coastal waters at reduced uncertainty levels. The findings of this study also suggest that the unweighted root means squared (RMS) aggregation function could be potentially also used for assessment of coastal water quality. Findings from this research could inform a range of stakeholders including decision-makers, researchers, and agencies responsible for water quality monitoring, assessment and management.

Robust machine learning algorithms for predicting coastal water quality index.

Coastal water quality assessment is an essential task to keep "good water quality" status for living organisms in coastal ecosystems. The Water quality index (WQI) is a widely used tool to assess water quality but this technique has received much criticism due to the model's reliability and inconsistence. The present study used a recently developed improved WQI model for calculating coastal WQIs in Cork Harbour. The aim of the research is to determine the most reliable and robust machine learning (ML) algorithm(s) to anticipate WQIs at each monitoring point instead of repeatedly employing SI and weight values in order to reduce model uncertainty. In this study, we compared eight commonly used algorithms, including Random Forest (RF), Decision Tree (DT), K-Nearest Neighbors (KNN), Extreme Gradient Boosting (XGB), Extra Tree (ExT), Support Vector Machine (SVM), Linear Regression (LR), and Gaussian Naïve Bayes (GNB). For the purposes of developing the prediction models, the dataset was divided into two groups: training (70%) and testing (30%), whereas the models were validated using the 10-fold cross-validation method. In order to evaluate the models' performance, the RMSE, MSE, MAE, R2, and PREI metrics were used in this study. The tree-based DT (RMSE = 0.0, MSE = 0.0, MAE = 0.0, R2 = 1.0 and PERI = 0.0) and the ExT (RMSE = 0.0, MSE = 0.0, MAE = 0.0, R2 = 1.0 and PERI = 0.0) and ensemble tree-based XGB (RMSE = 0.0, MSE = 0.0, MAE = 0.0, R2 = 1.0 and PERI = +0.16 to -0.17) and RF (RMSE = 2.0, MSE = 3.80, MAE = 1.10, R2 = 0.98, PERI = +3.52 to -25.38) models outperformed other models. The results of model performance and PREI indicate that the DT, ExT, and GXB models could be effective, robust and significantly reduce model uncertainty in predicting WQIs. The findings of this study are also useful for reducing model uncertainty and optimizing the WQM-WQI model architecture for predicting WQI values.

A comprehensive method for improvement of water quality index (WQI) models for coastal water quality assessment.

Here, we present an improved water quality index (WQI) model for assessment of coastal water quality using Cork Harbour, Ireland, as the case study. The model involves the usual four WQI components - selection of water quality indicators for inclusion, sub-indexing of indicator values, sub-index weighting and sub-index aggregation - with improvements to make the approach more objective and data-driven and less susceptible to eclipsing and ambiguity errors. The model uses the machine learning algorithm, XGBoost, to rank and select water quality indicators for inclusion based on relative importance to overall water quality status. Of the ten indicators for which data were available, transparency, dissolved inorganic nitrogen, ammoniacal nitrogen, BOD5, chlorophyll, temperature and orthophosphate were selected for summer, while total organic nitrogen, dissolved inorganic nitrogen, pH, transparency and dissolved oxygen were selected for winter. Linear interpolation functions developed using national recommended guideline values for coastal water quality are used for sub-indexing of water quality indicators and the XGBoost rankings are used in combination with the rank order centroid weighting method to determine sub-index weight values. Eight sub-index aggregation functions were tested - five from existing WQI models and three proposed by the authors. The computed indices were compared with those obtained using a multiple linear regression (MLR) approach and R2 and RMSE used as indicators of aggregation function performance. The weighted quadratic mean function (R2 = 0.91, RMSE = 4.4 for summer; R2 = 0.97, RMSE = 3.1 for winter) and the unweighted arithmetic mean function (R2 = 0.92, RMSE = 3.2 for summer; R2 = 0.97, RMSE = 3.2 for winter) proposed by the authors were identified as the best functions and showed reduced eclipsing and ambiguity problems compared to the others.

Ancient DNA of the pygmy marmoset type specimen Cebuella pygmaea (Spix, 1823) resolves a taxonomic conundrum.

The pygmy marmoset, the smallest of the anthropoid primates, has a broad distribution in Western Amazonia. Recent studies using molecular and morphological data have identified two distinct species separated by the Napo and Solimões-Amazonas rivers. However, reconciling this new biological evidence with current taxonomy, i.e., two subspecies, Cebuella pygmaea pygmaea (Spix, 1823) and Cebuella pygmaea niveiventris (Lönnberg, 1940), was problematic given the uncertainty as to whether Spix's pygmy marmoset ( Cebuella pygmaea pygmaea) was collected north or south of the Napo and Solimões-Amazonas rivers, making it unclear to which of the two newly revealed species the name pygmaea would apply. Here, we present the first molecular data from Spix's type specimen of Cebuella pygmaea, as well as novel mitochondrial genomes from modern pygmy marmosets sampled near the type locality (Tabatinga) on both sides of the river. With these data, we can confirm the correct names of the two species identified, i.e., C. pygmaea for animals north of the Napo and Solimões-Amazonas rivers and C. niveiventris for animals south of these two rivers. Phylogenetic analyses of the novel genetic data placed into the context of cytochrome b gene sequences from across the range of pygmy marmosets further led us to re-evaluate the geographical distribution for the two Cebuella species. We dated the split of these two species to 2.54 million years ago. We discuss additional, more recent, subdivisions within each lineage, as well as potential contact zones between the two species in the headwaters of these rivers.

Risk Factors for Middle East Respiratory Syndrome Coronavirus Infection among Camel Populations, Southern Jordan, 2014-2018.

After the first detection of Middle East respiratory syndrome coronavirus (MERS-CoV) in camels in Jordan in 2013, we conducted 2 consecutive surveys in 2014-2015 and 2017-2018 investigating risk factors for MERS-CoV infection among camel populations in southern Jordan. Multivariate analysis to control for confounding demonstrated that borrowing of camels, particularly males, for breeding purposes was associated with increased MERS-CoV seroprevalence among receiving herds, suggesting a potential route of viral transmission between herds. Increasing age, herd size, and use of water troughs within herds were also associated with increased seroprevalence. Closed herd management practices were found to be protective. Future vaccination strategies among camel populations in Jordan could potentially prioritize breeding males, which are likely to be shared between herds. In addition, targeted management interventions with the potential to reduce transmission between herds should be considered; voluntary closed herd schemes offer a possible route to achieving disease-free herds.

An integrative analysis uncovers a new, pseudo-cryptic species of Amazonian marmoset (Primates: Callitrichidae: Mico) from the arc of deforestation.

Amazonia has the richest primate fauna in the world. Nonetheless, the diversity and distribution of Amazonian primates remain little known and the scarcity of baseline data challenges their conservation. These challenges are especially acute in the Amazonian arc of deforestation, the 2500 km long southern edge of the Amazonian biome that is rapidly being deforested and converted to agricultural and pastoral landscapes. Amazonian marmosets of the genus Mico are little known endemics of this region and therefore a priority for research and conservation efforts. However, even nascent conservation efforts are hampered by taxonomic uncertainties in this group, such as the existence of a potentially new species from the Juruena-Teles Pires interfluve hidden within the M. emiliae epithet. Here we test if these marmosets belong to a distinct species using new morphological, phylogenomic, and geographic distribution data analysed within an integrative taxonomic framework. We discovered a new, pseudo-cryptic Mico species hidden within the epithet M. emiliae, here described and named after Horacio Schneider, the pioneer of molecular phylogenetics of Neotropical primates. We also clarify the distribution, evolutionary and morphological relationships of four other Mico species, bridging Linnean, Wallacean, and Darwinian shortfalls in the conservation of primates in the Amazonian arc of deforestation.

Completeness of reporting and risks of overstating impact in cluster randomised trials: a systematic review.

Overstating the impact of interventions through incomplete or inaccurate reporting can lead to inappropriate scale-up of interventions with low impact. Accurate reporting of the impact of interventions is of great importance in global health research to protect scarce resources. In global health, the cluster randomised trial design is commonly used to evaluate complex, multicomponent interventions, and outcomes are often binary. Complete reporting of impact for binary outcomes means reporting both relative and absolute measures. We did a systematic review to assess reporting practices and potential to overstate impact in contemporary cluster randomised trials with binary primary outcome. We included all reports registered in the Cochrane Central Register of Controlled Trials of two-arm parallel cluster randomised trials with at least one binary primary outcome that were published in 2017. Of 73 cluster randomised trials, most (60 [82%]) showed incomplete reporting. Of 64 cluster randomised trials for which it was possible to evaluate, most (40 [63%]) reported results in such a way that impact could be overstated. Care is needed to report complete evidence of impact for the many interventions evaluated using the cluster randomised trial design worldwide.

Exploring Perceived Barriers and Facilitators of PrEP Uptake among Young People in Uganda, Zimbabwe, and South Africa.

Pre-exposure prophylaxis (PrEP) is an effective HIV prevention strategy. Few studies have explored adolescents and young people's perspectives toward PrEP. We conducted 24 group discussions and 60 in-depth interviews with males and females aged 13-24 years in Uganda, Zimbabwe, and South Africa between September 2018 and February 2019. We used the framework approach to generate themes and key concepts for analysis following the social ecological model. Young people expressed a willingness to use PrEP and identified potential barriers and facilitators of PrEP uptake. Barriers included factors at individual (fear of HIV, fear of side effects, and PrEP characteristics), interpersonal (parental influence, absence of a sexual partner), community (peer influence, social stigma), institutional (long waiting times at clinics, attitudes of health workers), and structural (cost of PrEP and mode of administration, accessibility concerns) levels. Facilitators included factors at individual (high HIV risk perception and preventing HIV/desire to remain HIV negative), interpersonal (peer influence, social support and care for PrEP uptake), community (adequate PrEP information and sensitization, evidence of PrEP efficacy and safety), institutional (convenient and responsive services, provision of appropriate and sufficiently resourced services), and structural (access and availability of PrEP, cost of PrEP) levels. The findings indicated that PrEP is an acceptable HIV prevention method. PrEP uptake is linked to personal and environmental factors that need to be considered for successful PrEP roll-out. Multi-level interventions needed to promote PrEP uptake should consider the social and structural drivers and focus on ways that can inspire PrEP uptake and limit the barriers.

Power and sample-size calculations for trials that compare slopes over time: Introducing the slopepower command.

Trials of interventions that aim to slow disease progression may analyze a continuous outcome by comparing its change over time-its slope-between the treated and the untreated group using a linear mixed model. To perform a sample-size calculation for such a trial, one must have estimates of the parameters that govern the between- and within-subject variability in the outcome, which are often unknown. The algebra needed for the sample-size calculation can also be complex for such trial designs. We have written a new user-friendly command, slopepower, that performs sample-size or power calculations for trials that compare slope outcomes. The package is based on linear mixed-model methodology, described for this setting by Frost, Kenward, and Fox (2008, Statistics in Medicine 27: 3717-3731). In the first stage of this approach, slopepower obtains estimates of mean slopes together with variances and covariances from a linear mixed model fit to previously collected user-supplied data. In the second stage, these estimates are combined with user input about the target effectiveness of the treatment and design of the future trial to give an estimate of either a sample size or a statistical power. In this article, we present the slopepower command, briefly explain the methodology behind it, and demonstrate how it can be used to help plan a trial and compare the sample sizes needed for different trial designs.