The most dangerous hospital or the most dangerous equation?

<p>Abstract</p> <p>Background</p> <p>Hospital mortality rates are one of the most frequently selected indicators for measuring the performance of NHS Trusts. A recent article in a national newspaper named the hospital with the highest or lowest mortality in the 2005/6 financial year; a report by the organization Dr Foster Intelligence provided information with regard to the performance of all NHS Trusts in England.</p> <p>Methods</p> <p>Basic statistical theory and computer simulations were used to explore the relationship between the variations in the performance of NHS Trusts and the sizes of the Trusts. Data of hospital standardised mortality ratio (HSMR) of 152 English NHS Trusts for 2005/6 were re-analysed.</p> <p>Results</p> <p>A close examination of the information reveals a pattern which is consistent with a statistical phenomenon, discovered by the French mathematician de Moivre nearly 300 years ago, described in every introductory statistics textbook: namely that variation in performance indicators is expected to be greater in small Trusts and smaller in large Trusts. From a statistical viewpoint, the number of deaths in a hospital is not in proportion to the size of the hospital, but is proportional to the square root of its size. Therefore, it is not surprising to note that small hospitals are more likely to occur at the top and the bottom of league tables, whilst mortality rates are independent of hospital sizes.</p> <p>Conclusion</p> <p>This statistical phenomenon needs to be taken into account in the comparison of hospital Trusts performance, especially with regard to policy decisions.</p

Beyond ‘significance’:Principles and practice of the analysis of credibility

The inferential inadequacies of statistical significance testing are now widely recognized. There is, however, no consensus on how to move research into a ‘post p < 0.05’ era. We present a potential route forward via the Analysis of Credibility, a novel methodology that allows researchers to go beyond the simplistic dichotomy of significance testing and extract more insight from new findings. Using standard summary statistics, AnCred assesses the credibility of significant and non-significant findings on the basis of their evidential weight, and in the context of existing knowledge. The outcome is expressed in quantitative terms of direct relevance to the substantive research question, providing greater protection against misinterpretation. Worked examples are given to illustrate how AnCred extracts additional insight from the outcome of typical research study designs. Its ability to cast light on the use of p-values, the interpretation of non-significant findings and the so-called ‘replication crisis’ is also discussed

Disappeared persons and homicide in El Salvador

During 2012–2013, the homicide rate in El Salvador came down from 69.9 to 42.2 per 100,000 population following a government brokered truce between the leaders of the two major gangs, Mara Salvatrucha and Barrio 18. But despite the apparent successes of the truce, it was speculated that the drop in murders could have been due to the killers simply hid the bodies of their victims. This paper aims at determining whether gangs effectively disappeared their victims to cut down the official counts of murders, or they committed these crimes for other reasons. The results from this study suggest that Salvadoran gangs had been using disappearance as a method to gain sustained social control among residents of already gang-dominated areas, that together with homicide, disappearance is part of a process of territorial spread and strategic strengthening by which these groups are enhancing their capabilities to interfere in the alliances of Mexican drug trafficking organizations with Central American criminal organizations specializing in the trans-shipment of drugs and in providing access to local markets to distribute and sell drugs. Our findings show that the risk for disappearance has been large even before the truce was in place and that actually, it continues as such and going through a process of geographic expansion

Exploring variations in childhood stunting in Nigeria using league table, control chart and spatial analysis

Background: Stunting, linear growth retardation is the best measure of child health inequalities as it captures multiple dimensions of children’s health, development and environment where they live. The developmental priorities and socially acceptable health norms and practices in various regions and states within Nigeria remains disaggregated and with this, comes the challenge of being able to ascertain which of the regions and states identifies with either high or low childhood stunting to further investigate the risk factors and make recommendations for action oriented policy decisions. Methods: We used data from the birth histories included in the 2008 Nigeria Demographic and Health Survey (DHS) to estimate childhood stunting. Stunting was defined as height for age below minus two standard deviations from the median height for age of the standard World Health Organization reference population. We plotted control charts of the proportion of childhood stunting for the 37 states (including federal capital, Abuja) in Nigeria. The Local Indicators of Spatial Association (LISA) were used as a measure of the overall clustering and is assessed by a test of a null hypothesis. Results: Childhood stunting is high in Nigeria with an average of about 39%. The percentage of children with stunting ranged from 11.5% in Anambra state to as high as 60% in Kebbi State. Ranking of states with respect to childhood stunting is as follows: Anambra and Lagos states had the least numbers with 11.5% and 16.8% respectively while Yobe, Zamfara, Katsina, Plateau and Kebbi had the highest (with more than 50% of their underfives having stunted growth). Conclusions: Childhood stunting is high in Nigeria and varied significantly across the states. The northern states have a higher proportion than the southern states. There is an urgent need for studies to explore factors that may be responsible for these special cause variations in childhood stunting in Nigeria

Bias modelling in evidence synthesis

Policy decisions often require synthesis of evidence from multiple sources, and the source studies typically vary in rigour and in relevance to the target question. We present simple methods of allowing for differences in rigour (or lack of internal bias) and relevance (or lack of external bias) in evidence synthesis. The methods are developed in the context of reanalysing a UK National Institute for Clinical Excellence technology appraisal in antenatal care, which includes eight comparative studies. Many were historically controlled, only one was a randomized trial and doses, populations and outcomes varied between studies and differed from the target UK setting. Using elicited opinion, we construct prior distributions to represent the biases in each study and perform a bias‐adjusted meta‐analysis. Adjustment had the effect of shifting the combined estimate away from the null by approximately 10%, and the variance of the combined estimate was almost tripled. Our generic bias modelling approach allows decisions to be based on all available evidence, with less rigorous or less relevant studies downweighted by using computationally simple methods

Conflict diagnostics in directed acyclic graphs, with applications in bayesian evidence synthesis

Complex stochastic models represented by directed acyclic graphs (DAGs) are increasingly employed to synthesise multiple, imperfect and disparate sources of evidence, to estimate quantities that are difficult to measure directly. The various data sources are dependent on shared parameters and hence have the potential to conflict with each other, as well as with the model. In a Bayesian framework, the model consists of three components: the prior distribution, the assumed form of the likelihood and structural assumptions. Any of these components may be incompatible with the observed data. The detection and quantification of such conflict and of data sources that are inconsistent with each other is therefore a crucial component of the model criticism process. We first review Bayesian model criticism, with a focus on conflict detection, before describing a general diagnostic for detecting and quantifying conflict between the evidence in different partitions of a DAG. The diagnostic is a p-value based on splitting the information contributing to inference about a "separator" node or group of nodes into two independent groups and testing whether the two groups result in the same inference about the separator node(s). We illustrate the method with three comprehensive examples: an evidence synthesis to estimate HIV prevalence; an evidence synthesis to estimate influenza case-severity; and a hierarchical growth model for rat weights.This work was supported by the Medical Research Council [Unit Programme Numbers U105260566 and U105260557

Assessing the consistency assumptions underlying network meta-regression using aggregate data

When numerous treatments exist for a disease (treatments 1, 2, 3 etc.), network meta-regression (NMR) examines whether each relative treatment effect (e.g. mean difference for 2 vs. 1, 3 vs. 1, 3 vs. 2 etc.) differs according to a covariate (e.g. disease severity). Two consistency assumptions underlie NMR: consistency of the treatment effects at the covariate value zero and consistency of the regression coefficients for the treatment by covariate interaction. The NMR results may be unreliable when the assumptions do not hold. Furthermore, interactions may exist but are not found because inconsistency of the coefficients is masking them; for example, when the treatment effect increases as the covariate increases using direct evidence but the effect decreases with the increasing covariate using indirect evidence.We outline existing NMR models that incorporate different types of treatment by covariate interaction. We then introduce models that can be used to assess the consistency assumptions underlying NMR for aggregate data. We extend existing node-splitting models, the unrelated mean effects inconsistency model and the design by treatment inconsistency model to incorporate covariate interactions. We propose models for assessing both consistency assumptions simultaneously and models for assessing each of the assumptions in turn to gain a more thorough understanding of consistency.We apply the methods in a Bayesian framework to trial-level data comparing anti-malarial treatments using the covariate average age, and to four fabricated datasets to demonstrate key scenarios.We discuss the pros and cons of the methods and important considerations when applying models to aggregated data

Does Alendronate reduce the risk of fracture in men? A meta-analysis incorporating prior knowledge of anti-fracture efficacy in women

BACKGROUND: Alendronate has been found to reduce the risk of fractures in postmenopausal women as demonstrated in multiple randomized controlled trials enrolling thousands of women. Yet there is a paucity of such randomized controlled trials in osteoporotic men. Our objective was to systematically review the anti-fracture efficacy of alendronate in men with low bone mass or with a history of prevalent fracture(s) and incorporate prior knowledge of alendronate efficacy in women in the analysis. METHODS: We examined randomized controlled trials in men comparing the anti-fracture efficacy of alendronate to placebo or calcium or vitamin D, or any combination of these. Studies of men with secondary causes of osteoporosis other than hypogonadism were excluded. We searched the following electronic databases (without language restrictions) for potentially relevant citations: Medline, Medline in Process (1966-May 24/2004), and Embase (1996–2004). We also contacted the manufacturer of the drug in search of other relevant trials. Two reviewers independently identified two trials (including 375 men), which met all inclusion criteria. Data were abstracted by one reviewer and checked by another. Results of the male trials were pooled using Bayesian random effects models, incorporating prior information of anti-fracture efficacy from meta-analyses of women. RESULTS: The odds ratios of incident fractures in men (with 95% credibility intervals) with alendronate (10 mg daily) were: vertebral fractures, 0.44 (0.23, 0.83) and non-vertebral fractures, 0.60 (0.29, 1.44). CONCLUSION: In conclusion, alendronate decreases the risk of vertebral fractures in men at risk. There is currently insufficient evidence of a statistically significant reduction of non-vertebral fractures, but the paucity of trials in men limit the statistical power to detect such an effect

Risk factors associated with Rift Valley fever epidemics in South Africa in 2008–11

Rift Valley fever (RVF) is a zoonotic and vector-borne disease, mainly present in Africa, which represents a threat to human health, animal health and production. South Africa has experienced three major RVF epidemics (1950–51, 1973–75 and 2008–11). Due to data scarcity, no previous study has quantified risk factors associated with RVF epidemics in animals in South Africa. Using the 2008–11 epidemic datasets, a retrospective longitudinal study was conducted to identify and quantify spatial and temporal environmental factors associated with RVF incidence. Cox regressions with a Besag model to account for the spatial effects were fitted to the data. Coefficients were estimated by Bayesian inference using integrated nested Laplace approximation. An increase in vegetation density was the most important risk factor until 2010. In 2010, increased temperature was the major risk factor. In 2011, after the large 2010 epidemic wave, these associations were reversed, potentially confounded by immunity in animals, probably resulting from earlier infection and vaccination. Both vegetation density and temperature should be considered together in the development of risk management strategies. However, the crucial need for improved access to data on population at risk, animal movements and vaccine use is highlighted to improve model predictions