Procedure for Detecting Outliers in a Circular Regression Model

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.     

A Note on Maximum Likelihood Ratio Test of No Outliers in Regression Models

A derivation of the maximum likelihood ratio test for testing no outliers in regression models is given using the method of WETHERILL (1981, pp. 106–107) for estimating the regression parameters. This method is essentially similar to the one outlined in BARNETT and LEWIS (1978, p. 263), although by our detailed derivation it is easier to see that the maximum likelihood estimate of θ of model (3) under the hypothesis that the i^th observation in an outlier is the same as that obtained from model (1) when the i^th observation is removed.     

The Cost-Effectiveness Analysis of Teleglaucoma Screening Device

Glaucoma is the leading cause of irreversible vision loss and costs the American economy $2.9 billion. Teleglaucoma remotely detects glaucoma improving access to ophthalmic care in rural areas. It helps manage glaucoma more efficiently to preserve vision and reduce healthcare costs. A cost-effectiveness analysis was conducted using healthcare provider or third-party payer perspective within rural Canada. The study population were patients at-risk of glaucoma which includes those with diabetes and/or hypertension, family history of glaucoma, adults older than 50 years, and concurrent ocular conditions in rural Alberta. Markov modelling was used to model glaucoma health states. Effectiveness was measured in Quality-Adjusted Life Years (QALYs) and costs were used in Canadian dollars. Using TreeAge Pro 2009, incremental cost-effectiveness ratios (ICER) were developed in dollars per QALYs. Deterministic and probabilistic sensitivity analyses were performed to assess the factors affecting cost-effectiveness. Teleglaucoma had a 20% increase in ophthalmologist-referral rate; it reduced patient travel times by 61 hours and physician wait times by 30% in comparison to in-person examination (standard of care). Teleglaucoma costs $872 per patient screened which was 80% less than in-person examination. Teleglaucoma had a greater incremental effectiveness providing an additional 0.12 QALY per patient examination. It was more sensitive (86.5%) and less specific (78.6%) than in-person examination. Teleglaucoma was more cost-effective than in-person examination with an ICER of-$27,460/QALY. This indicated that teleglaucoma will save $27, 460 for each additional QALY gained. Long term benefits showed teleglaucoma prevents 24% cases of glaucoma blindness after 30 years. Teleglaucoma demonstrated improved health outcomes, as well as, cost benefits. It increases access to ophthalmic care and improves healthcare service efficiency, specifically in rural areas. Teleglaucoma is more cost-effective than current in-person examination and can improve the quality of life in glaucoma patients.     

Cox回归模型在肝癌病人生存分析中应用的研究

生存时间是癌症患者和临床医师共同关心的焦点,也是临床癌症诊治工作的重要指标之一．生存分析是研究多种因素与生存时间的关系以及关系程度的大小．Cox回归模型是生存分析中常用的方法之一．本文利用Cox回归模型对786名肝癌患者进行生存分析,确定影响肝癌患者预后的主要因素是癌栓、肝癌部位、治疗方式、肝脏储备功能、端粒酶活性、细胞增殖活性、γ-GT(γ-谷氮酰转肽酶)、术后复发等．为临床研究延长肝癌病人的生存期,提高其生存率提供了有力的依据．     

多重线性回归模型协方差阵扰动的影响分析

讨论多重线性回归模型协方差阵扰动的影响分析,获得了⌒／Ｂ与⌒／Ｂ（Ｇ）的一些关系式,⌒／Ｂ是原模型参数阵Ｂ的最佳莼性无偏估计（ＢＬＵＥ）,⌒／Ｂ（Ｇ）是协方差阵扰动后的模型参数阵Ｂ的ＢＬＵＥ;文章给出了度量影响大小的测度ＤＧ及其多种形式;最后的实例说明了ＤＧ在影响分析时的有效性。     

Routine HIV Screening in Portugal: Clinical Impact and Cost-Effectiveness

Objective

To compare the clinical outcomes and cost-effectiveness of routine HIV screening in Portugal to the current practice of targeted and on-demand screening.

Design

We used Portuguese national clinical and economic data to conduct a model-based assessment.

Methods

We compared current HIV detection practices to strategies of increasingly frequent routine HIV screening in Portuguese adults aged 18-69. We considered several subpopulations and geographic regions with varying levels of undetected HIV prevalence and incidence. Baseline inputs for the national case included undiagnosed HIV prevalence 0.16%, annual incidence 0.03%, mean population age 43 years, mean CD4 count at care initiation 292 cells/μL, 63% HIV test acceptance, 78% linkage to care, and HIV rapid test cost €6 under the proposed routine screening program. Outcomes included quality-adjusted survival, secondary HIV transmission, cost, and incremental cost-effectiveness.

Results

One-time national HIV screening increased HIV-infected survival from 164.09 quality-adjusted life months (QALMs) to 166.83 QALMs compared to current practice and had an incremental cost-effectiveness ratio (ICER) of €28,000 per quality-adjusted life year (QALY). Screening more frequently in higher-risk groups was cost-effective: for example screening annually in men who have sex with men or screening every three years in regions with higher incidence and prevalence produced ICERs of €21,000/QALY and €34,000/QALY, respectively.

Conclusions

One-time HIV screening in the Portuguese national population will increase survival and is cost-effective by international standards. More frequent screening in higher-risk regions and subpopulations is also justified. Given Portugal’s challenging economic priorities, we recommend prioritizing screening in higher-risk populations and geographic settings.     

The Effects of Misspecification of a Regression Model

The consequences of the misspecification of a regression model are considered. For small effects of covariates a proportional consistency theorem is derived. The consistent estimation of the covariance matrix of the estimates is discussed.     

The Analysis of Life Table and Follow-up Data with Covariates Using Poisson Regression Model

The Poisson regression model for the analysis of life table and follow-up data with covariates is presented. An example is presented to show how this technique can be used to construct a parsimonious model which describes a set of survival data. All parameters in the model, the hazard and survival functions are estimated by maximum likelihood.     

Evaluation of the Ethiopian Millennium Rural Initiative: Impact on Mortality and Cost-Effectiveness

Main Objective

Few studies have examined the long-term, impact of large-scale interventions to strengthen primary care services for women and children in rural, low-income settings. We evaluated the impact of the Ethiopian Millennium Rural Initiative (EMRI), an 18-month systems-based intervention to improve the performance of 30 primary health care units in rural areas of Ethiopia.

Methods

We assessed the impact of EMRI on maternal and child survival using The Lives Saved Tool (LiST), Demography (DemProj) and AIDS Impact Model (AIM) tools in Spectrum software, inputting monthly data on 6 indicators 1) antenatal coverage (ANC), 2) skilled birth attendance coverage (SBA), 3) post-natal coverage (PNC), 4) HIV testing during ANC, 5) measles vaccination coverage, and 6) pentavalent 3 vaccination coverages. We calculated a cost-benefit ratio of the EMRI program including lives saved during implementation and lives saved during implementation and 5 year follow-up.

Results

A total of 134 lives (all children) were estimated to have been saved due to the EMRI interventions during the 18-month intervention in 30 health centers and their catchment areas, with an estimated additional 852 lives (820 children and 2 adults) saved during the 5-year post-EMRI period. For the 18-month intervention period, EMRI cost $37,313 per life saved ($42,366 per life if evaluation costs are included). Calculated over the 18-month intervention plus 5 years post-intervention, EMRI cost $5,875 per life saved ($6,671 per life if evaluation costs are included). The cost effectiveness of EMRI improves substantially if the performance achieved during the 18 months of the EMRI intervention is sustained for 5 years. Scaling up EMRI to operate for 5 years across the 4 major regions of Ethiopia could save as many as 34,908 lives.

Significance

A systems-based approach to improving primary care in low-income settings can have transformational impact on lives saved and be cost-effective.     

The Impact and Cost-Effectiveness of a Four-Month Regimen for First-Line Treatment of Active Tuberculosis in South Africa

Background

A 4-month first-line treatment regimen for tuberculosis disease (TB) is expected to have a direct impact on patient outcomes and societal costs, as well as an indirect impact on Mycobacterium tuberculosis transmission. We aimed to estimate this combined impact in a high TB-burden country: South Africa.

Method

An individual based M. tb transmission model was fitted to the TB burden of South Africa using a standard TB natural history framework. We measured the impact on TB burden from 2015–2035 of introduction of a non-inferior 4-month regimen replacing the standard 6-month regimen as first-line therapy. Impact was measured with respect to three separate baselines (Guidelines, Policy and Current), reflecting differences in adherence to TB and HIV treatment guidelines. Further scenario analyses considered the variation in treatment-related parameters and resistance levels. Impact was measured in terms of differences in TB burden and Disability Adjusted Life Years (DALYs) averted. We also examined the highest cost at which the new regimen would be cost-effective for several willingness-to-pay thresholds.

Results

It was estimated that a 4-month regimen would avert less than 1% of the predicted 6 million person years with TB disease in South Africa between 2015 and 2035. A similarly small impact was seen on deaths and DALYs averted. Despite this small impact, with the health systems and patient cost savings from regimen shortening, the 4-month regimen could be cost-effective at $436 [NA, 5983] (mean [range]) per month at a willingness-to-pay threshold of one GDP per capita ($6,618).

Conclusion

The introduction of a non-inferior 4-month first-line TB regimen into South Africa would have little impact on the TB burden. However, under several scenarios, it is likely that the averted societal costs would make such a regimen cost-effective in South Africa.     

Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.     

The Cost and Cost-Effectiveness of Scaling up Screening and Treatment of Syphilis in Pregnancy: A Model

Background

Syphilis in pregnancy imposes a significant global health and economic burden. More than half of cases result in serious adverse events, including infant mortality and infection. The annual global burden from mother-to-child transmission (MTCT) of syphilis is estimated at 3.6 million disability-adjusted life years (DALYs) and $309 million in medical costs. Syphilis screening and treatment is simple, effective, and affordable, yet, worldwide, most pregnant women do not receive these services. We assessed cost-effectiveness of scaling-up syphilis screening and treatment in existing antenatal care (ANC) programs in various programmatic, epidemiologic, and economic contexts.

Methods and Findings

We modeled the cost, health impact, and cost-effectiveness of expanded syphilis screening and treatment in ANC, compared to current services, for 1,000,000 pregnancies per year over four years. We defined eight generic country scenarios by systematically varying three factors: current maternal syphilis testing and treatment coverage, syphilis prevalence in pregnant women, and the cost of healthcare. We calculated program and net costs, DALYs averted, and net costs per DALY averted over four years in each scenario. Program costs are estimated at $4,142,287 – $8,235,796 per million pregnant women (2010 USD). Net costs, adjusted for averted medical care and current services, range from net savings of $12,261,250 to net costs of $1,736,807. The program averts an estimated 5,754 – 93,484 DALYs, yielding net savings in four scenarios, and a cost per DALY averted of $24 – $111 in the four scenarios with net costs. Results were robust in sensitivity analyses.

Conclusions

Eliminating MTCT of syphilis through expanded screening and treatment in ANC is likely to be highly cost-effective by WHO-defined thresholds in a wide range of settings. Countries with high prevalence, low current service coverage, and high healthcare cost would benefit most. Future analyses can be tailored to countries using local epidemiologic and programmatic data.     

Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

We propose and analyze an optimal control problem where the control system is a mathematical model for tuberculosis that considers reinfection. The control functions represent the fraction of early latent and persistent latent individuals that are treated. Our aim was to study how these control measures should be implemented, for a certain time period, in order to reduce the number of active infected individuals, while minimizing the interventions implementation costs. The optimal intervention is compared along different epidemiological scenarios, by varying the transmission coefficient. The impact of variation of the risk of reinfection, as a result of acquired immunity to a previous infection for treated individuals on the optimal controls and associated solutions, is analyzed. A cost-effectiveness analysis is done, to compare the application of each one of the control measures, separately or in combination.     

Assessment of the Economic Impact of Belimumab for the Treatment of Systemic Lupus Erythematosus in the Italian Setting: A Cost-Effectiveness Analysis

ObjectiveThe purpose of this analysis is to evaluate the cost-effectiveness of belimumab, a new biological treatment specifically developed for the treatment of Systemic Lupus Erythematosus (SLE), in the Italian setting. SLE is a chronic non-organ specific autoimmune disease characterized by a disregulation of the immune system that involves many organs and systems.MethodsA cost-effectiveness micro-simulation model with a lifetime horizon originally developed for the UK was adapted to the Italian setting. The analysis compared Standard of Care (SoC) alone vs belimumab plus SoC from a National Healthcare Service (NHS) and societal perspective. Health-economic consequences of treatments and organ damage progression were calculated. When available, Italian data were used, otherwise UK costs were converted using Purchasing Power Parities (PPPs). Utility values were based on the EQ-5D™ assessments in the belimumab clinical trials (BLISS 52 and 76). Results were discounted with 3% for costs and effects. A maximum belimumab treatment duration of 6 years was assumed and wastage costs were considered.ResultsCost per life year gained (Incremental Cost-Effectiveness Ratio, ICER) and cost per Quality Adjusted Life Year (QALY) (Incremental Cost-Utility Ratio, ICUR) were €22,990 and €32,859, respectively. These values reduced to €20,119 and €28,754, respectively, when indirect costs were included.ConclusionsIt may be concluded that in the Italian setting and according to the guidelines of the Italian Association of Health Economics (IAHE), belimumab was shown to be cost-effective, in terms of both ICER and ICUR, (€25–40,000/QALY).     

基于Median函数的分段回归模型及其在生物学上的应用

在生物学科研工作中,经常会遇到因变量和自变量之间存在着多种不同的趋势,分段回归模型可以很好的拟合变量间这种非线性趋势.本文介绍了基于Median函数的分段回归模型,可以同时对各项回归参数和转折点进行估计,最后,本文结合生物学上的实例运用SAS统计软件进行了分段回归模型的拟合.     

Cost-Effectiveness Analysis of Three Leprosy Case Detection Methods in Northern Nigeria

Background

Despite several leprosy control measures in Nigeria, child proportion and disability grade 2 cases remain high while new cases have not significantly reduced, suggesting continuous spread of the disease. Hence, there is the need to review detection methods to enhance identification of early cases for effective control and prevention of permanent disability. This study evaluated the cost-effectiveness of three leprosy case detection methods in Northern Nigeria to identify the most cost-effective approach for detection of leprosy.

Methods

A cross-sectional study was carried out to evaluate the additional benefits of using several case detection methods in addition to routine practice in two north-eastern states of Nigeria. Primary and secondary data were collected from routine practice records and the Nigerian Tuberculosis and Leprosy Control Programme of 2009. The methods evaluated were Rapid Village Survey (RVS), Household Contact Examination (HCE) and Traditional Healers incentive method (TH). Effectiveness was measured as number of new leprosy cases detected and cost-effectiveness was expressed as cost per case detected. Costs were measured from both providers'' and patients'' perspectives. Additional costs and effects of each method were estimated by comparing each method against routine practise and expressed as incremental cost-effectiveness ratio (ICER). All costs were converted to the U.S. dollar at the 2010 exchange rate. Univariate sensitivity analysis was used to evaluate uncertainties around the ICER.

Results

The ICER for HCE was $142 per additional case detected at all contact levels and it was the most cost-effective method. At ICER of $194 per additional case detected, THs method detected more cases at a lower cost than the RVS, which was not cost-effective at $313 per additional case detected. Sensitivity analysis showed that varying the proportion of shared costs and subsistent wage for valuing unpaid time did not significantly change the results.

Conclusion

Complementing routine practice with household contact examination is the most cost-effective approach to identify new leprosy cases and we recommend that, depending on acceptability and feasibility, this intervention is introduced for improved case detection in Northern Nigeria.     

Determinants of Serum PCBs in Adolescents and Adults: Regression Tree Analysis and Linear Regression Analysis

Regression tree analysis, a non-parametric method, was undertaken to identify predictors of the serum concentration of polychlorinated biphenyls (sum of marker PCB ¹ ABBREVIATIONS: BMI: body-mass index, CV: cross validation, ln: natural logarithm, ns: not significant, PCAHs: polychlorinated aromatic hydrocarbons, PCBs: polychlorinated biphenyls, R² _a: adjusted coefficient of determination, VIF: variance inflation factor. View all notes 138, 153, and 180) in humans. This method was applied on biomonitoring data of the Flemish Environment and Health study (2002–2006) and included 1679 adolescents and 1583 adults. Potential predictor variables were collected via a self-administered questionnaire, assessing information on lifestyle, food intake, use of tobacco and alcohol, residence history, health, education, hobbies, and occupation. Relevant predictors of human PCB exposure were identified with regression tree analysis using ln-transformed sum of PCBs, separately in adolescents and adults. The obtained results were compared with those from a standard linear regression approach. The results of the non-parametric analysis confirm the selection of the covariates in the multiple regression models. In both analyses, blood fat, gender, age, body-mass index (BMI) or change in bodyweight, former breast-feeding, and a number of nutritional factors were identified as statistically significant predictors in the serum PCB concentration, either in adolescents, in adults or in both. Regression trees can be used as an explorative analysis in combination with multiple linear regression models, where relationships between the determinants and the biomarkers can be quantified.     

A Note on Comparing Stochastically Restricted Linear Estimators in a Regression Model

In his recent paper Liski (1989) derived conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix when the parameter vector of a regression model is subject to competing stochastic restrictions. The aim of this note is to provide another necessary and sufficient condition which admits an easier interpretation of superiority related to the covariance matrix criterion.     

Comparing Stochastically Restricted Estimators in a Linear Regression Model

The minimum dispersion linear unbiased estimators of the vector of parameters in a linear regression model are compared when the parameters of the model are subject to stochastic linear restrictions with different dispersion matrices of the disturbances involved in them.