Using four case studies, we aim to provide practical guidance and recommendations for the analysis of cluster randomised controlled trials.
Four modelling approaches (Generalized Linear Mixed Models with parameters estimated by maximum likelihood/restricted maximum likelihood; Generalized Linear Models with parameters estimated by Generalized Estimating Equations (1st order or second order) and Quadratic Inference Function, for analysing correlated individual participant level outcomes in cluster randomised controlled trials were identified after we reviewed the literature. We systematically searched the online bibliography databases of MEDLINE, EMBASE, PsycINFO (via OVID), CINAHL (via EBSCO), and SCOPUS. We identified the above-mentioned four statistical analytical approaches and applied them to four case studies of cluster randomised controlled trials with the number of clusters ranging from 10 to 100, and individual participants ranging from 748 to 9,207. Results were obtained for both continuous and binary outcomes using R and SAS statistical packages.
The intracluster correlation coefficient (ICC) estimates for the case studies were less than 0.05 and are consistent with the observed ICC values commonly reported in primary care and community-based cluster randomised controlled trials. In most cases, the four methods produced similar results. However, in a few analyses, quadratic inference function produced different results compared to the generalized linear mixed model, first-order generalized estimating equations, and second-order generalized estimating equations, especially in trials with small to moderate numbers of clusters.
This paper demonstrates the analysis of cluster randomised controlled trials with four modelling approaches. The results obtained were similar in most cases, however, for trials with few clusters we do recommend that the quadratic inference function should be used with caution, and where possible a small sample correction should be used. The generalisability of our results is limited to studies with similar features to our case studies, for example, studies with a similar-sized ICC. It is important to conduct simulation studies to comprehensively evaluate the performance of the four modelling approaches.

Groundwater vulnerability assessment has nowadays evolved into an essential tool towards proper groundwater protection and management, while the DRASTIC method is included among the most widely applied vulnerability assessment methods. However, the high uncertainty of the DRASTIC method mainly associated with the subjectivity in assigning parameters ratings and weights has driven many researchers to apply various methods for improving its efficiency. In this context, in the present study, different techniques were implemented with the aim of modifying the DRASTIC framework and thus enhancing its performance for groundwater vulnerability assessment in the Bouficha aquifer, Tunisia. In a first stage, the land use type (L) was incorporated as an additional parameter in the typical DRASTIC framework, thus taking into consideration the impact of anthropogenic activities on groundwater vulnerability. Subsequently, the rating and weighting systems of the developed DRASTIC-L framework were modified through the application of statistical methods (DRASTIC-L-SA) and genetic algorithms (GA) (DRASTIC-L-GA) in an attempt to investigate and compare both linear and nonlinear modifications. To evaluate the various vulnerability frameworks, correlation between vulnerability values and nitrate concentrations, expressed as Spearman\'s rank correlation coefficient (ρ) and Correlation Index (CI), was examined. The results revealed that the DRASTIC-L-GA framework developed by applying a fully GA-based optimization procedure provided the highest values in terms of the performance metrics used, making it the most suitable for the study area. In addition, the aquifer under study was found to be less vulnerable to pollution when employing the typical DRASTIC framework instead of the modified ones, leading to the conclusion that the former substantially underestimates pollution potential in the study area.

The COVID-19 pandemic in 2020 has caused sudden shocks in transportation systems, specifically the subway ridership patterns in New York City (NYC), U.S. Understanding the temporal pattern of subway ridership through statistical models is crucial during such shocks. However, many existing statistical frameworks may not be a good fit to analyze the ridership data sets during the pandemic, since some of the modeling assumptions might be violated during this time. In this paper, utilizing change point detection procedures, a piecewise stationary time series model is proposed to capture the nonstationary structure of subway ridership. Specifically, the model consists of several independent station based autoregressive integrated moving average (ARIMA) models concatenated together at certain time points. Further, data-driven algorithms are utilized to detect the changes of ridership patterns as well as to estimate the model parameters before and during the COVID-19 pandemic. The data sets of focus are daily ridership of subway stations in NYC for randomly selected stations. Fitting the proposed model to these data sets enhances understanding of ridership changes during external shocks, both in relation to mean (average) changes and the temporal correlations.

With urinary proteomics profiling (UPP) as exemplary omics technology, this review describes a workflow for the analysis of omics data in large study populations. The proposed workflow includes: (i) planning omics studies and sample size considerations; (ii) preparing the data for analysis; (iii) preprocessing the UPP data; (iv) the basic statistical steps required for data curation; (v) the selection of covariables; (vi) relating continuously distributed or categorical outcomes to a series of single markers (e.g., sequenced urinary peptide fragments identifying the parental proteins); (vii) showing the added diagnostic or prognostic value of the UPP markers over and beyond classical risk factors, and (viii) pathway analysis to identify targets for personalized intervention in disease prevention or treatment. Additionally, two short sections respectively address multiomics studies and machine learning. In conclusion, the analysis of adverse health outcomes in relation to omics biomarkers rests on the same statistical principle as any other data collected in large population or patient cohorts. The large number of biomarkers, which have to be considered simultaneously requires planning ahead how the study database will be structured and curated, imported in statistical software packages, analysis results will be triaged for clinical relevance, and presented.

As of January 2022, the COVID-19 pandemic was on-going, affecting populations worldwide. The potential risks of the Omicron variant (and future variants) still remain an area of active investigation. Thus, the ultimate human toll of SARS-CoV-2, and, by extension, the variations in that toll among diverse populations, remain unresolved. Nonetheless, an extensive literature on causal factors in the observed patterns of COVID-19 morbidity and cause-specific mortality has emerged-particularly at the aggregate level of analysis. This article explores potential pitfalls in the attribution of COVID outcomes to specific factors in isolation by examining a diverse set of potential factors and their interactions.
We sourced published data to establish a global database of COVID-19 outcomes for 68 countries and augmented these with an array of potential explanatory covariates from a diverse set of sources. We sought population-level aggregate factors from both health- and (traditionally) non-health domains, including: (a) Population biomarkers (b) Demographics and infrastructure (c) Socioeconomics (d) Policy responses at the country-level. We analyzed these data using (OLS) regression and more flexible non-parametric methods such as recursive partitioning, that are useful in examining both potential joint factor contributions to variations in pandemic outcomes, and the identification of possible interactions among covariates across these domains.
Using the national obesity rates of 68 countries as an illustrative predictor covariate of COVID-19 outcomes, we observed marked inconsistencies in apparent outcomes by population. Importantly, we also documented important variations in outcomes, based on interactions of health factors with covariates in other domains that are traditionally not related to biomarkers. Finally, our results suggest that single-factor explanations of population-level COVID-19 outcomes (e.g., obesity vs. cause-specific mortality) appear to be confounded substantially by other factors.
Our methods and findings suggest that a full understanding of the toll of the COVID-19 pandemic, as would be central to preparing for similar future events, requires analysis within and among diverse variable domains, and within and among diverse populations. While this may seem apparent, the bulk of the recent literature on the pandemic has focused on one or a few of these drivers in isolation. Hypothesis generation and testing related to pandemic outcomes will benefit from accommodating the nuance of covariate interactions, in an epidemiologic context. Finally, our results add to the literature on the ecological fallacy: the attempt to infer individual drivers and outcomes from the study of population-level aggregates.

Although oral bisphosphonates (BP) are commonly used, there is conflicting evidence for their safety in the elderly. Safety concerns might trump BP use in older patients with complex health needs. Our study evaluated the safety of BP, focusing on severe acute kidney injury (AKI), gastrointestinal ulcer (GI ulcer), osteonecrosis of the jaw (ONJ), and femur fractures. We used UK primary care data (Clinical Practice Research Datalink [CPRD GOLD]), linked to hospital (Hospital Episode Statistics [HES] inpatient) and ONS mortality data. We included all patients aged >65 with complex health needs and no BP use in the year before study start (January 1, 2010). Complex health needs were defined in three cohorts: an electronic frailty index score ≥3 (frailty cohort), one or more unplanned hospitalization/s (hospitalization cohort); and prescription of ≥10 different medicines in 2009 (polypharmacy cohort). Incidence rates were calculated for all outcomes. Subsequently, all individuals who experienced AKI or GI ulcer anytime during follow-up were included for Self-Controlled Case Series (SCCS) analyses. Incidence rate ratios (IRRs) were estimated separately for AKI and GI ulcer, comparing event rates between BP-exposed and unexposed time windows. No SCCS were conducted for ONJ and femur fractures. We identified 94,364 individuals in the frailty cohort, as well as 78,184 and 95,621 persons in the hospitalization and polypharmacy cohorts. Of those, 3023, 1950, and 2992 individuals experienced AKI and 1403, 1019, and 1453 had GI ulcer/s during follow-up, respectively. Age-adjusted SCCS models found evidence of increased risk of AKI associated with BP use (frailty cohort: IRR 1.65; 95% confidence interval [CI], 1.25-2.19), but no association with GI ulcers (frailty cohort: IRR 1.24; 95% CI, 0.86-1.78). Similar results were obtained for the hospitalization and polypharmacy cohorts. Our study found a 50% to 65% increased risk of AKI associated with BP use in elderly patients with complex health needs. Future studies should further investigate the risk-benefit of BP use in these patients. © 2022 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Conflicting results exist about the relationship between bariatric surgery and fracture risk. Also, prediction of who is at increased risk of fracture after bariatric surgery is not currently available. Hence, we used a combination of a self-controlled case series (SCCS) study to establish the association between bariatric surgery and fracture, and develop a prediction model for postoperative fracture risk estimation using a cohort study. Patients from UK Primary care records from the Clinical Practice Research Datalink GOLD linked to Hospital Episode Statistics undergoing bariatric surgery with body mass index (BMI) ≥30 kg/m2 between 1997 and 2018 were included in the cohort. Those sustaining one or more fractures in the 5 years before or after surgery were included in the SCCS. Fractures were considered in three categories: (i) any except skull and digits (primary outcome); (ii) major (hip, vertebrae, wrist/forearm, and humerus); and (iii) peripheral (forearm and lower leg). Of 5487 participants, 252 (4.6%) experienced 272 fractures (of which 80 were major and 135 peripheral) and were included in the SCCS analyses. Major fracture risk increased after surgery, incidence rate ratios (IRRs) and 95% confidence intervals (CIs): 2.77 (95% CI, 1.34-5.75) and 3.78 (95% CI, 1.42-10.08) at ≤3 years and 3.1 to 5 years postsurgery when compared to 5 years prior to surgery, respectively. Any fracture risk was higher only in the 2.1 to 5 years following surgery (IRR 1.73; 95% CI, 1.08-2.77) when compared to 5 years prior to surgery. No excess risk of peripheral fracture after surgery was identified. A prediction tool for major fracture was developed using 5487 participants included in the cohort study. It was also internally validated (area under the receiver-operating characteristic curve [AUC ROC] 0.70) with use of anxiolytics/sedatives/hypnotics and female as major predictors. Hence, major fractures are nearly threefold more likely after bariatric surgery. A simple prediction tool with five variables identifies high risk patients for major fracture. © 2021 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Schizophrenia Spectrum Disorder (SSD) is characterized by its chronic, episodic nature. The clear definition of such episodes is essential for various clinical and research purposes. Most current definitions of episodes in SSD are based on either hospitalizations or on symptom scales. Both have drawbacks; symptom scales are measured infrequently, while hospitalization rates are often affected by policy. This study presents an approach for defining episodes in healthcare data that does not suffer such drawbacks.
Healthcare use of 13,155 SSD patients in the Northern Netherlands with up to 12 years of follow-up was available. Patient-level structural changes in the trend of healthcare use costs were determined using Exponentially Weighted Moving Average (EWMA) control charts. Control charts restart with updated parameters after a detected structural change. Episodes were defined using these structural changes. The resulting episodes were validated by investigating their association with the Global Assessment of Functioning (GAF) scale.
The mean number of episodes was 0.61 (sd: 0.60) per patient per year. For the sub-group without hospitalizations this was 0.51 (sd: 0.71). Average episode duration of the sub-group (147 days, sd: 309.4) was similar to that of the full sample (150 days, sd: 305.5). A significant inverse association was identified between GAF scores and the episode-state indicator.
The repeated application of EWMA control charts based on healthcare-intensity is a feasible and promising tool for quantifying patient-level healthcare episodes. The validation using GAF scores indicates that our episode indicator is associated with lower levels of global functioning. Results for individuals without hospitalizations indicate that the method is robust with regard to changes in healthcare policy.

Researchers and clinicians in neuropsychology often compare individual patients against healthy control samples, to quantify evidence for cognitive-behavioural deficits and dissociations. Statistical methods for these comparisons have been developed that control Type I (false positive) errors effectively. However, remarkably little attention has been given to the power of these tests. In this practical primer, we describe, in minimally technical terms, the origins and limits of power for case-control comparisons. We argue that power calculations can play useful roles in single-case study design and interpretation, and we make suggestions for optimising power in practice. As well as providing figures, tables and tools for estimating the power of case-control comparisons, we hope to assist researchers in setting realistic expectations for what such tests can achieve in general.

UNASSIGNED: Stability of risk estimates from prediction models may be highly dependent on the sample size of the dataset available for model derivation. In this paper, we evaluate the stability of cardiovascular disease risk scores for individual patients when using different sample sizes for model derivation; such sample sizes include those similar to models recommended in the national guidelines, and those based on recently published sample size formula for prediction models.
UNASSIGNED: We mimicked the process of sampling N patients from a population to develop a risk prediction model by sampling patients from the Clinical Practice Research Datalink. A cardiovascular disease risk prediction model was developed on this sample and used to generate risk scores for an independent cohort of patients. This process was repeated 1000 times, giving a distribution of risks for each patient. N = 100,000, 50,000, 10,000, N min (derived from sample size formula) and N epv10 (meets 10 events per predictor rule) were considered. The 5-95th percentile range of risks across these models was used to evaluate instability. Patients were grouped by a risk derived from a model developed on the entire population (population-derived risk) to summarise results.
UNASSIGNED: For a sample size of 100,000, the median 5-95th percentile range of risks for patients across the 1000 models was 0.77%, 1.60%, 2.42% and 3.22% for patients with population-derived risks of 4-5%, 9-10%, 14-15% and 19-20% respectively; for N = 10,000, it was 2.49%, 5.23%, 7.92% and 10.59%, and for N using the formula-derived sample size, it was 6.79%, 14.41%, 21.89% and 29.21%. Restricting this analysis to models with high discrimination, good calibration or small mean absolute prediction error reduced the percentile range, but high levels of instability remained.
UNASSIGNED: Widely used cardiovascular disease risk prediction models suffer from high levels of instability induced by sampling variation. Many models will also suffer from overfitting (a closely linked concept), but at acceptable levels of overfitting, there may still be high levels of instability in individual risk. Stability of risk estimates should be a criterion when determining the minimum sample size to develop models.