General flation models for count data

The paper discusses very general extensions to existing inflation models for discrete random variables, allowing an arbitrary set of points in the sample space to be either inflated or deflated relative to a baseline distribution. The term flation is introduced to cover either inflation or deflation of counts. Examples include one-inflated count models where the baseline distribution is zero-truncated and count models for data with a few unusual large values. The main result is that inference about the baseline distribution can be based solely on the truncated distribution which arises when the entire set of flation points is truncated. A major application of this result relates to estimating the size of a hidden target population, and examples are provided to illustrate our findings.

Estimating the undetected infections in the Covid-19 outbreak by harnessing capture-recapture methods

OBJECTIVES

A major open question, affecting the decisions of policy makers, is the estimation of the true number of Covid-19 infections. Most of them are undetected, because of a large number of asymptomatic cases. We provide an efficient, easy to compute and robust lower bound estimator for the number of undetected cases.

METHODS

A modified version of the Chao estimator is proposed, based on the cumulative time-series distributions of cases and deaths. Heterogeneity has been addressed by assuming a geometrical distribution underlying the data generation process. An (approximated) analytical variance of the estimator has been derived to compute reliable confidence intervals at 95% level.

RESULTS

A motivating application to the Austrian situation is provided and compared with an independent and representative study on prevalence of Covid-19 infection. Our estimates match well with the results from the independent prevalence study, but the capture-recapture estimate has less uncertainty involved as it is based on a larger sample size. Results from other European countries are mentioned in the discussion. The estimated ratio of the total estimated cases to the observed cases is around the value of 2.3 for all the analyzed countries.

CONCLUSIONS

The proposed method answers to a fundamental open question: "How many undetected cases are going around?". CR methods provide a straightforward solution to shed light on undetected cases, incorporating heterogeneity that may arise in the probability of being detected.

Upper bound estimators of the population size based on ordinal models for capture-recapture experiments

Capture-recapture studies have attracted a lot of attention over the past few decades, especially in applied disciplines where a direct estimate for the size of a population of interest is not available. Epidemiology, ecology, public health, and biodiversity are just a few examples. The estimation of the number of unseen units has been a challenge for theoretical statisticians, and considerable progress has been made in providing lower bound estimators for the population size. In fact, it is well known that consistent estimators for this cannot be provided in the very general case. Considering a case where capture-recapture studies are summarized by a frequency of frequencies distribution, we derive a simple upper bound of the population size based on the cumulative distribution function. We introduce two estimators of this bound, without any specific parametric assumption on the distribution of the observed frequency counts. The behavior of the proposed estimators is investigated using several benchmark datasets and a large-scale simulation experiment based on the scheme discussed by Pledger.

Estimation of the adolescent pregnancy rate in Thailand 2008-2013: an application of capture-recapture method

BACKGROUND

Adolescent pregnancy is an important health and social issue that affects both individual and social well-being. However, deriving a national estimate is challenging in a country with multiple incomplete national databases especially the abortion statistics. The objective of this study was to estimate the adolescent pregnancy rates in Thailand using capture-recapture method.

METHODS

An application of capture-recapture method was conducted using two cross-sectional databases (i.e., the national birth registration and the Ministry of Public Health standard health databases) and one hospital-based data source from medical record reviews. A 3-sources capture-recapture with log-linear model was applied to estimate adolescent pregnancy rates.

RESULTS

A total number of 741,084, 290,922 and 25,478 records were respectively identified from the birth registrations, standard health databases and hospital-based survey data during 2008 to 2013. The estimated adolescent pregnancy rates /1000 adolescent women (95% confidence intervals (CI)) ranged from 56.3 (49.4, 66.9) to 70.3 (60.3, 76.6). The estimated rates were about 12-31% higher than adolescent birth rates reported by the Thailand Public Health Statistics.

CONCLUSIONS

With the capture-recapture method, more accurate adolescent pregnancy rates were estimated. This method should be able to apply to any setting with similar context.

The identity of two meta-analytic likelihoods and the ignorability of double-zero studies

In meta-analysis, the conventional two-stage approach computes an effect estimate for each study in the first stage and proceeds with the analysis of effect estimates in the second stage. For counts of events as outcome, the risk ratio is often the effect measure of choice. However, if the meta-analysis includes many studies with no events the conventional method breaks down. As an alternative one-stage approach, a Poisson regression model and a conditional binomial model can be considered where no event studies do not cause problems. The conditional binomial model excludes double-zero studies, whereas this is seemingly not the case for the Poisson regression approach. However, we show here that both models lead to the same likelihood inference and double-zero studies (in contrast to single-zero studies) do not contribute in either case to the likelihood.

Renewed: Protocol for a randomised controlled trial of a digital intervention to support quality of life in cancer survivors

INTRODUCTION

Low quality of life is common in cancer survivors. Increasing physical activity, improving diet, supporting psychological well-being and weight loss can improve quality of life in several cancers and may limit relapse. The aim of the randomised controlled trial outlined in this protocol is to examine whether a digital intervention (Renewed), with or without human support, can improve quality of life in cancer survivors. Renewed provides support for increasing physical activity, managing difficult emotions, eating a healthier diet and weight management.

METHODS AND ANALYSIS

A randomised controlled trial is being conducted comparing usual care, access to Renewed or access to Renewed with brief human support. Cancer survivors who have had colorectal, breast or prostate cancer will be identified and invited through general practice searches and mail-outs. Participants are asked to complete baseline measures immediately after screening and will then be randomised to a study group; this is all completed on the Renewed website. The primary outcome is quality of life measured by the European Organization for Research and Treatment of Cancer QLQ-c30. Secondary outcomes include anxiety and depression, fear of cancer recurrence, general well-being, enablement and items relating to costs for a health economics analysis. Process measures include perceptions of human support, intervention usage and satisfaction, and adherence to behavioural changes. Qualitative process evaluations will be conducted with patients and healthcare staff providing support.

ETHICS AND DISSEMINATION

The trial has been approved by the NHS Research Ethics Committee (Reference 18/NW/0013). The results of this trial will be published in peer-reviewed journals and through conference presentations.

TRIAL REGISTRATION NUMBER

ISRCTN96374224; Pre-results.

Virtual chromoendoscopy for the real-time assessment of colorectal polyps in vivo: a systematic review and economic evaluation

BACKGROUND

Current clinical practice is to remove a colorectal polyp detected during colonoscopy and determine whether it is an adenoma or hyperplastic by histopathology. Identifying adenomas is important because they may eventually become cancerous if untreated, whereas hyperplastic polyps do not usually develop into cancer, and a surveillance interval is set based on the number and size of adenomas found. Virtual chromoendoscopy (VCE) (an electronic endoscopic imaging technique) could be used by the endoscopist under strictly controlled conditions for real-time optical diagnosis of diminutive (≤ 5 mm) colorectal polyps to replace histopathological diagnosis.

OBJECTIVE

To assess the clinical effectiveness and cost-effectiveness of the VCE technologies narrow-band imaging (NBI), flexible spectral imaging colour enhancement (FICE) and i-scan for the characterisation and management of diminutive (≤ 5 mm) colorectal polyps using high-definition (HD) systems without magnification.

DESIGN

Systematic review and economic analysis.

PARTICIPANTS

People undergoing colonoscopy for screening or surveillance or to investigate symptoms suggestive of colorectal cancer.

INTERVENTIONS

NBI, FICE and i-scan.

MAIN OUTCOME MEASURES

Diagnostic accuracy, recommended surveillance intervals, health-related quality of life (HRQoL), adverse effects, incidence of colorectal cancer, mortality and cost-effectiveness of VCE compared with histopathology.

DATA SOURCES

Electronic bibliographic databases including MEDLINE, EMBASE, The Cochrane Library and Database of Abstracts of Reviews of Effects were searched for published English-language studies from inception to June 2016. Bibliographies of related papers, systematic reviews and company information were screened and experts were contacted to identify additional evidence.

REVIEW METHODS

Systematic reviews of test accuracy and economic evaluations were undertaken in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement. Meta-analyses were conducted, where possible, to inform the independent economic model. A cost-utility decision-analytic model was developed to estimate the cost-effectiveness of VCE compared with histopathology. The model used a decision tree for patients undergoing endoscopy, combined with estimates of long-term outcomes (e.g. incidence of colorectal cancer and subsequent morbidity and mortality) derived from University of Sheffield School of Health and Related Research's bowel cancer screening model. The model took a NHS perspective, with costs and benefits discounted at 3.5% over a lifetime horizon. There were limitations in the data on the distribution of adenomas across risk categories and recurrence rates post polypectomy.

RESULTS

Thirty test accuracy studies were included: 24 for NBI, five for i-scan and three for FICE (two studies assessed two interventions). Polyp assessments made with high confidence were associated with higher sensitivity and endoscopists experienced in VCE achieved better results than those without experience. Two economic evaluations were included. NBI, i-scan and FICE are cost-saving strategies compared with histopathology and the number of quality-adjusted life-years gained was similar for histopathology and VCE. The correct surveillance interval would be given to 95% of patients with NBI, 94% of patients with FICE and 97% of patients with i-scan.

LIMITATIONS

Limited evidence was available for i-scan and FICE and there was heterogeneity among the NBI studies. There is a lack of data on longer-term health outcomes of patients undergoing VCE for assessment of diminutive colorectal polyps.

CONCLUSIONS

VCE technologies, using HD systems without magnification, could potentially be used for the real-time assessment of diminutive colorectal polyps, if endoscopists have adequate experience and training.

FUTURE WORK

Future research priorities include head-to-head randomised controlled trials of all three VCE technologies; more research on the diagnostic accuracy of FICE and i-scan (when used without magnification); further studies evaluating the impact of endoscopist experience and training on outcomes; studies measuring adverse effects, HRQoL and anxiety; and longitudinal data on colorectal cancer incidence, HRQoL and mortality.

STUDY REGISTRATION

This study is registered as PROSPERO CRD42016037767.

FUNDING

The National Institute for Health Research Health Technology Assessment programme.

Delayed antibiotic prescribing for respiratory tract infections: protocol of an individual patient data meta-analysis

INTRODUCTION

Delayed prescribing can be a useful strategy to reduce antibiotic prescribing, but it is not clear for whom delayed prescribing might be effective. This protocol outlines an individual patient data (IPD) meta-analysis of randomised controlled trials (RCTs) and observational cohort studies to explore the overall effect of delayed prescribing and identify key patient characteristics that are associated with efficacy of delayed prescribing.

METHODS AND ANALYSIS

A systematic search of the databases Cochrane Central Register of Controlled Trials, Ovid MEDLINE, Ovid Embase, EBSCO CINAHL Plus and Web of Science was conducted to identify relevant studies from inception to October 2017. Outcomes of interest include duration of illness, severity of illness, complication, reconsultation and patient satisfaction. Study authors of eligible papers will be contacted and invited to contribute raw IPD data. IPD data will be checked against published data, harmonised and aggregated to create one large IPD database. Multilevel regression will be performed to explore interaction effects between treatment allocation and patient characteristics. The economic evaluation will be conducted based on IPD from the combined trial and observational studies to estimate the differences in costs and effectiveness for delayed prescribing compared with normal practice. A decision model will be developed to assess potential savings and cost-effectiveness in terms of reduced antibiotic usage of delayed prescribing and quality-adjusted life years.

ETHICS AND DISSEMINATION

Ethical approval was obtained from the University of Southampton Faculty of Medicine Research Ethics Committee (Reference number: 30068). Findings of this study will be published in peer-reviewed academic journals as well as General Practice trade journals and will be presented at national and international conferences. The results will have important public health implications, shaping the way in which antibiotics are prescribed in the future and to whom delayed prescriptions are issued.

PROSPERO REGISTRATION NUMBER

CRD42018079400.

Nurse staffing levels, missed vital signs and mortality in hospitals: retrospective longitudinal observational study

Background

Low nurse staffing levels are associated with adverse patient outcomes from hospital care, but the causal relationship is unclear. Limited capacity to observe patients has been hypothesised as a causal mechanism.

Objectives

This study determines whether or not adverse outcomes are more likely to occur after patients experience low nurse staffing levels, and whether or not missed vital signs observations mediate any relationship.

Design

Retrospective longitudinal observational study. Multilevel/hierarchical mixed-effects regression models were used to explore the association between registered nurse (RN) and health-care assistant (HCA) staffing levels and outcomes, controlling for ward and patient factors.

Setting and participants

A total of 138,133 admissions to 32 general adult wards of an acute hospital from 2012 to 2015.

Main outcomes

Death in hospital, adverse event (death, cardiac arrest or unplanned intensive care unit admission), length of stay and missed vital signs observations.

Data sources

Patient administration system, cardiac arrest database, eRoster, temporary staff bookings and the Vitalpac system (System C Healthcare Ltd, Maidstone, Kent; formerly The Learning Clinic Limited) for observations.

Results

Over the first 5 days of stay, each additional hour of RN care was associated with a 3% reduction in the hazard of death [hazard ratio (HR) 0.97, 95% confidence interval (CI) 0.94 to 1.0]. Days on which the HCA staffing level fell below the mean were associated with an increased hazard of death (HR 1.04, 95% CI 1.02 to 1.07), but the hazard of death increased as cumulative staffing exposures varied from the mean in either direction. Higher levels of temporary staffing were associated with increased mortality. Adverse events and length of stay were reduced with higher RN staffing. Overall, 16% of observations were missed. Higher RN staffing was associated with fewer missed observations in high-acuity patients (incidence rate ratio 0.98, 95% CI 0.97 to 0.99), whereas the overall rate of missed observations was related to overall care hours (RN + HCA) but not to skill mix. The relationship between low RN staffing and mortality was mediated by missed observations, but other relationships between staffing and mortality were not. Changing average skill mix and staffing levels to the levels planned by the Trust, involving an increase of 0.32 RN hours per patient day (HPPD) and a similar decrease in HCA HPPD, would be associated with reduced mortality, an increase in staffing costs of £28 per patient and a saving of £0.52 per patient per hospital stay, after accounting for the value of reduced stays.

Limitations

This was an observational study in a single site. Evidence of cause is not definitive. Variation in staffing could be influenced by variation in the assessed need for staff. Our economic analysis did not consider quality or length of life.

Conclusions

Higher RN staffing levels are associated with lower mortality, and this study provides evidence of a causal mechanism. There may be several causal pathways and the absolute rate of missed observations cannot be used to guide staffing decisions. Increases in nursing skill mix may be cost-effective for improving patient safety.

Future work

More evidence is required to validate approaches to setting staffing levels. Other aspects of missed nursing care should be explored using objective data. The implications of findings about both costs and temporary staffing need further exploration.

Trial registration

This study is registered as ISRCTN17930973.

Funding

This project was funded by the National Institute for Health Research (NIHR) Health Services and Delivery Research programme and will be published in full in Health Services and Delivery Research; Vol. 6, No. 38. See the NIHR Journals Library website for further project information.

A correction to the age-adjustment of the GH-2000 score used in the detection of growth hormone misuse

OBJECTIVE

The GH-2000 biomarker test has been introduced by the World Anti-Doping Agency as a method of detecting growth hormone misuse in professional sport. The test involves the measurement insulin-like growth factor-I and the amino-terminal pro-peptide of type III collagen (P-III-NP) which increase in a dose-dependent manner in response to GH. These measurements are combined in sex specific formulae that include an age adjustment. The original age adjustment overcorrects the effect of age in male athletes and could potentially place older men at a disadvantage. The purpose of this note is to investigate the performance of a previously suggested correction term in two new and larger data sets.

RESULTS

The GH-2000 score was calculated for 7307 samples obtained from 15 accredited WADA laboratories in 2017 and 3916 samples measured at Drug Control Centre, King's College London, UK between 2013 and 2017. The GH-2000 scores were investigated for positive age effects using standard regression modelling. As previously, all analyses confirmed a positive age effect. Applying the earlier suggested correction term of 0.032 × age showed a significant over-correction leading to a negative association of the GH-2000 score with age. We now suggest a smaller age correction of 0.020 × age, which corresponds to the smallest effect found in the earlier studies.

Non-invasive tests for the detection of oesophageal varices in compensated cirrhosis: systematic review and meta-analysis

INTRODUCTION

Conclusive data on the accuracy and clinical applicability of non-invasive screening tests for oesophageal varices (OV) in patients with compensated cirrhosis remain lacking. We conducted this study to identify currently available tests, estimate their diagnostic performance and then exemplify how these could be utilized in clinical practice.

MATERIALS AND METHODS

A systematic literature search was performed to identify all primary studies that reported accuracy using oesophagogastroduodenoscopy (OGD) as the gold standard. Sources searched included Ovid MEDLINE, Ovid EMBASE and The Cochrane Library databases.

RESULTS

Twenty-one studies with a total of 2471 patients were identified. Several tests were evaluated in more than three studies. Platelet count/spleen diameter ratio (PSR) had the highest summary area under the curve for detection of any size OV of 0.85 (95% confidence interval 0.78-0.92). At a cut-off of 909 (n = 4 studies) and prevalence rates of 10, 20, 30, 40 and 50% for OV, PSR screening correctly avoided the need for OGD in 70, 62, 55, 47 and 39% of patients, respectively.

CONCLUSIONS

PSR appears to be the most accurate and validated non-invasive screening test for OV in patients with compensated cirrhosis. At a cut-off of 909, PSR could be clinically useful to avoid OGDs in a significant proportion of patients.

Why do endocrine profiles in elite athletes differ between sports?

BACKGROUND

Endocrine profiles have been measured on blood samples obtained immediately post-competition from 693 elite athletes from 15 Olympic Sports competing at National or International level; four were subsequently excluded leaving 689 for the current analysis.

METHODS

Body composition was measured by bioimpedance in a sub-set of 234 (146 men and 88 women) and from these data a regression model was constructed that enabled 'estimated' lean body mass and fat mass to be calculated on all athletes. One way ANOVA was used to assess the differences in body composition and endocrine profiles between the sports and binary logistical regression to ascertain the characteristic of a given sport compared to the others.

RESULTS

The results confirmed many suppositions such as basketball players being tall, weightlifters short and cross-country skiers light. The hormone profiles were more surprising with remarkably low testosterone and free T3 (tri-iodothyronine) in male powerlifters and high oestradiol, SHBG (sex hormone binding globulin) and prolactin in male track and field athletes. Low testosterone concentrations were seen 25.4% of male elite competitors in 12 of the 15 sports and high testosterone concentrations in 4.8% of female elite athletes in 3 of the 8 sports tested. Interpretation of the results is more difficult; some of the differences between sports are at least partially due to differences in age of the athletes but the apparent differences between sports remain significant after adjusting for age. The prevalence of 'hyperandrogenism' (as defined by the IAAF (International Association of Athletics Federations) and IOC (International Olympic Committee)) amongst this cohort of 231 elite female athletes was the highest so far recorded and the very high prevalence of 'hypoandrogenism' in elite male athletes a new finding.

CONCLUSIONS

It is unclear whether the differences in hormone profiles between sports is a reason why they become elite athletes in that sport or is a consequence of the arduous processes involved. For components of body composition we know that most have a major genetic component and this may well be true for endocrine profiles.

Meta-Analysis

Objectives: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here.

Methods: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here.

Results: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. [1] concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand.

Conclusions: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. [1]. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

Erratum to: “Youden’s Index and the Likelihood Ratio Positive in Diagnostic Testing”

Unfortunately, the letter “Youden’s Index and the Likelihood Ratio Positive in Diagnostic Testing“ by D. Böhning contained an error. It contained the wrong Figure 4. The correct Figure is now supplied here.

D. Böhning sent us this statement: “I am grateful to Professor Hughes for pointing this out. There was no intention with my own letter to be critical on the letter by Professor Hughes or dispute its results but rather to add some thoughts of my own to the subject of interest.“

Log-likelihood positive as a function of a cut-off value c for two normal distributions with equal unit variance and mean difference of 2

Youden’s Index and the Likelihood Ratio Positive in Diagnostic Testing

We refer to a recent letter to the editor by Hughes [1] and show that, despite existing similarities between Youden’s index and the log-likelihood ratio positive, important differences between these two measures remain to exist which can play an important difference in clinical practice.

Exact statistical calculation of the uncertainty term in the decision limits of the GH-2000 score for growth hormone misuse (doping) detection

The GH-2000 score has been developed as a powerful and unique technique for the detection of growth hormone misuse by sportsmen and women. The score depends upon the measurement of two growth hormone sensitive markers, insulin-like growth factor-I and the amino-terminal pro-peptide of type III collagen. It also includes a term to adjust for the age of the athlete. Decision limits for the GH-2000 score have been developed and are incorporated into the guidelines of the World Anti-Doping Agency. These decision limits are derived by setting a 1 in 10,000 false-positive rate rule. As these decision limits are estimated from samples of GH-2000 scores, they carry uncertainty. In previous work, this uncertainty has been addressed by establishing an upper 95% confidence interval for the true decision limits based on a normal approximation which has been shown to be appropriate if sample sizes are large (such as 1000 and above). Here, we show that these approximations, whether reasonable or not, can be entirely avoided by developing an upper 95% confidence interval for the true decision limits using an approach based upon the t-distribution. While there are considerable differences for smaller sample sizes, these become negligible when the sample size is large such as 1000 and above.