International migration data in Europe are collected by individual countries with separate collection systems and designs. As a result, reported data are inconsistent in availability, definition and quality. In this paper, we propose a Bayesian

Background Predicting hospital length of stay (LoS) for patients with COVID-19 infection is essential to ensure that adequate bed capacity can be provided without unnecessarily restricting care for patients with other conditions. Here, we demonstrate the utility of three complementary methods for predicting LoS using UK national- and hospital-level data. Method On a national scale, relevant patients were identified from the COVID-19 Hospitalisation in England Surveillance System (CHESS) reports. An Accelerated Failure Time (AFT) survival model and a truncation corrected method (TC), both with underlying Weibull distributions, were fitted to the data to estimate LoS from hospital admission date to an outcome (death or discharge) and from hospital admission date to Intensive Care Unit (ICU) admission date. In a second approach we fit a multi-state (MS) survival model to data directly from the Manchester University NHS Foundation Trust (MFT). We develop a planning tool that uses LoS estimates from these models to predict bed occupancy. Results All methods produced similar overall estimates of LoS for overall hospital stay, given a patient is not admitted to ICU (8.4, 9.1 and 8.0 days for AFT, TC and MS, respectively). Estimates differ more significantly between the local and national level when considering ICU. National estimates for ICU LoS from AFT and TC were 12.4 and 13.4 days, whereas in local data the MS method produced estimates of 18.9 days. Conclusions Given the complexity and partiality of different data sources and the rapidly evolving nature of the COVID-19 pandemic, it is most appropriate to use multiple analysis methods on multiple datasets. The AFT method accounts for censored cases, but does not allow for simultaneous consideration of different outcomes. The TC method does not include censored cases, instead correcting for truncation in the data, but does consider these different outcomes. The MS method can model complex pathways to different outcomes whilst accounting for censoring, but cannot handle non-random case missingness. Overall, we conclude that data-driven modelling approaches of LoS using these methods is useful in epidemic planning and management, and should be considered for widespread adoption throughout healthcare systems internationally where similar data resources exist.

The aim of the paper is to present Bayesian forecasts of immigration for seven European countries to 2025, based on quantitative data and qualitative knowledge elicited from country-specific migration experts in a two-round Delphi survey. In line with earlier results, most of the immigration processes under study were found to be barely predictable in the long run, exhibiting non-stationary features. This outcome was obtained largely irrespectively of the expert knowledge input, which nevertheless was found useful in describing the predictive uncertainty, especially in the short term. It is argued that, under the non-stationarity of migration processes, too long forecasts horizons are inadequate, which is a serious challenge for population forecasts in general. Copyright (c) 2010 Royal Statistical Society.

In this article, we develop a fully integrated and dynamic Bayesian approach to forecast populations by age and sex. The approach embeds the Lee-Carter type models for forecasting the age patterns, with associated measures of uncertainty, of fertility, mortality, immigration, and emigration within a cohort projection model. The methodology may be adapted to handle different data types and sources of information. To illustrate, we analyze time series data for the United Kingdom and forecast the components of population change to the year 2024. We also compare the results obtained from different forecast models for age-specific fertility, mortality, and migration. In doing so, we demonstrate the flexibility and advantages of adopting the Bayesian approach for population forecasting and highlight areas where this work could be extended.

Migration is one of the most unpredictable demographic processes. The aim of this article is to provide a blueprint for assessing various possible forecasting approaches in order to help safeguard producers and users of official migration statistics against misguided forecasts. To achieve that, we first evaluate the various existing approaches to modelling and forecasting of international migration flows. Subsequently, we present an empirical comparison of ex post performance of various forecasting methods, applied to international migration to and from the United Kingdom. The overarching goal is to assess the uncertainty of forecasts produced by using different forecasting methods, both in terms of their errors (biases) and calibration of uncertainty. The empirical assessment, comparing the results of various forecasting models against past migration estimates, confirms the intuition about weak predictability of migration, but also highlights varying levels of forecast errors for different migration streams. There is no single forecasting approach that would be well suited for different flows. We therefore recommend adopting a tailored approach to forecasts, and applying a risk management framework to their results, taking into account the levels of uncertainty of the individual flows, as well as the differences in their potential societal impact.

In this article, we first discuss the need to augment reported flows of international migration in Europe with additional knowledge gained from experts on measurement, quality and coverage. Second, we present our method for eliciting this information. Third, we describe how this information is converted into prior distributions for subsequent use in a Bayesian model for estimating migration flows amongst countries in the European Union (EU) and European Free Trade Association (EFTA). The article concludes with an assessment of the importance of expert information and a discussion of lessons learned from the elicitation process.

Survey data collection costs have risen to a point where many survey researchers and polling companies are abandoning large, expensive probability-based samples in favor of less expensive nonprobability samples. The empirical literature suggests this strategy may be suboptimal for multiple reasons, among them that probability samples tend to outperform nonprobability samples on accuracy when assessed against population benchmarks. However, nonprobability samples are often preferred due to convenience and costs. Instead of forgoing probability sampling entirely, we propose a method of combining both probability and nonprobability samples in a way that exploits their strengths to overcome their weaknesses within a Bayesian inferential framework. By using simulated data, we evaluate supplementing inferences based on small probability samples with prior distributions derived from nonprobability data. We demonstrate that informative priors based on nonprobability data can lead to reductions in variances and mean squared errors for linear model coefficients. The method is also illustrated with actual probability and nonprobability survey data. A discussion of these findings, their implications for survey practice, and possible research extensions are provided in conclusion.

Background: Predicting hospital length of stay (LoS) for patients with COVID-19 infection is essential to ensure that adequate bed capacity can be provided without unnecessarily restricting care for patients with other conditions. Here, we demonstrate the utility of three complementary methods for predicting LoS using UK national- and hospital-level data. Method: On a national scale, relevant patients were identified from the COVID-19 Hospitalisation in England Surveillance System (CHESS) reports. An Accelerated Failure Time (AFT) survival model and a truncation corrected method (TC), both with underlying Weibull distributions, were fitted to the data to estimate LoS from hospital admission date to an outcome (death or discharge) and from hospital admission date to Intensive Care Unit (ICU) admission date. In a second approach we fit a multi-state (MS) survival model to data directly from the Manchester University NHS Foundation Trust (MFT). We develop a planning tool that uses LoS estimates from these models to predict bed occupancy. Results: All methods produced similar overall estimates of LoS for overall hospital stay, given a patient is not admitted to ICU (8.4, 9.1 and 9.3 days for AFT, TC and MS, respectively). Estimates differ more significantly between the local and national level when considering ICU. National estimates for ICU LoS from AFT and TC were 12.4 and 13.4 days, whereas in local data the MS method produced estimates of 22.8 days. Conclusions: Given the complexity and partiality of different data sources and the rapidly evolving nature of the COVID-19 pandemic, it is most appropriate to use multiple analysis methods on multiple datasets. The AFT method accounts for censored cases, but does not allow for simultaneous consideration of different outcomes. The TC method does not include censored cases but does consider these different outcomes. The MS method can model complex pathways to different outcomes whilst accounting for censoring, but cannot handle non-random case missingness. Overall, we conclude that data-driven modelling approaches of LoS using these methods is useful in epidemic planning and management, and should be considered for widespread adoption throughout healthcare systems internationally where similar data resources exist.