Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

The Blinder-Oaxaca decomposition for linear regression models

The counterfactual decomposition technique popularized by Blinder (1973, Journal of Human Resources, 436–455) and Oaxaca (1973, International Economic Review, 693–709) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. This article summarizes the technique and addresses several complications, such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new command called oaxaca is introduced, and examples illustrating its usage are given.

Predictors and overestimation of recalled mobile phone use among children and adolescents

A growing body of literature addresses possible health effects of mobile phone use in children and adolescents by relying on the study participants' retrospective reconstruction of mobile phone use. In this study, we used data from the international case-control study CEFALO to compare self-reported with objectively operator-recorded mobile phone use. The aim of the study was to assess predictors of level of mobile phone use as well as factors that are associated with overestimating own mobile phone use. For cumulative number and duration of calls as well as for time since first subscription we calculated the ratio of self-reported to operator-recorded mobile phone use. We used multiple linear regression models to assess possible predictors of the average number and duration of calls per day and logistic regression models to assess possible predictors of overestimation. The cumulative number and duration of calls as well as the time since first subscription of mobile phones were overestimated on average by the study participants. Likelihood to overestimate number and duration of calls was not significantly different for controls compared to cases (OR=1.1, 95%-CI: 0.5 to 2.5 and OR=1.9, 95%-CI: 0.85 to 4.3, respectively). However, likelihood to overestimate was associated with other health related factors such as age and sex. As a consequence, such factors act as confounders in studies relying solely on self-reported mobile phone use and have to be considered in the analysis.

Sleepless night, the moon is bright: longitudinal study of lunar phase and sleep

Popular belief holds that the lunar cycle affects human physiology, behaviour and health. We examined the influence of moon phase on sleep duration in a secondary analysis of a feasibility study of mobile telephone base stations and sleep quality. We studied 31 volunteers (18 women and 13 men, mean age 50 years) from a suburban area of Switzerland longitudinally over 6 weeks, including two full moons. Subjective sleep duration was calculated from sleep diary data. Data were analysed using multiple linear regression models with random effects. Mean sleep duration was 6 h 49 min. Subjective sleep duration varied with the lunar cycle, from 6 h 41 min at full moon to 7 h 00 min at new moon (P < 0.001). Average sleep duration was shortened by 68 min during the week compared with weekends (P < 0.001). Men slept 17 min longer than women (P < 0.001) and sleep duration decreased with age (P < 0.001). There was also evidence that rating of fatigue in the morning was associated with moon phase, with more tiredness (P = 0.027) at full moon. The study was designed for other purposes and the association between lunar cycle and sleep duration will need to be confirmed in further studies.

Development of a screening tool predicting the transition from acute to chronic low back pain for patients in a GP setting: protocol of a multinational prospective cohort study

BACKGROUND: Low back pain (LBP) is by far the most prevalent and costly musculoskeletal problem in our society today. Following the recommendations of the Multinational Musculoskeletal Inception Cohort Study (MMICS) Statement, our study aims to define outcome assessment tools for patients with acute LBP and the time point at which chronic LBP becomes manifest and to identify patient characteristics which increase the risk of chronicity. METHODS: Patients with acute LBP will be recruited from clinics of general practitioners (GPs) in New Zealand (NZ) and Switzerland (CH). They will be assessed by postal survey at baseline and at 3, 6, 12 weeks and 6 months follow-up. Primary outcome will be disability as measured by the Oswestry Disability Index (ODI); key secondary endpoints will be general health as measured by the acute SF-12 and pain as measured on the Visual Analogue Scale (VAS). A subgroup analysis of different assessment instruments and baseline characteristics will be performed using multiple linear regression models. This study aims to examine: 1. Which biomedical, psychological, social, and occupational outcome assessment tools are identifiers for the transition from acute to chronic LBP and at which time point this transition becomes manifest. 2. Which psychosocial and occupational baseline characteristics like work status and period of work absenteeism influence the course from acute to chronic LBP. 3. Differences in outcome assessment tools and baseline characteristics of patients in NZ compared with CH. DISCUSSION: This study will develop a screening tool for patients with acute LBP to be used in GP clinics to access the risk of developing chronic LBP. In addition, biomedical, psychological, social, and occupational patient characteristics which influence the course from acute to chronic LBP will be identified. Furthermore, an appropriate time point for follow-ups will be given to detect this transition. The generalizability of our findings will be enhanced by the international perspective of this study. TRIAL REGISTRATION: [Clinical Trial Registration Number, ACTRN12608000520336].

Differences across health care systems in outcome and cost-utility of surgical and conservative treatment of chronic low back pain: a study protocol

BACKGROUND: There is little evidence on differences across health care systems in choice and outcome of the treatment of chronic low back pain (CLBP) with spinal surgery and conservative treatment as the main options. At least six randomised controlled trials comparing these two options have been performed; they show conflicting results without clear-cut evidence for superior effectiveness of any of the evaluated interventions and could not address whether treatment effect varied across patient subgroups. Cost-utility analyses display inconsistent results when comparing surgical and conservative treatment of CLBP. Due to its higher feasibility, we chose to conduct a prospective observational cohort study. METHODS: This study aims to examine if1. Differences across health care systems result in different treatment outcomes of surgical and conservative treatment of CLBP2. Patient characteristics (work-related, psychological factors, etc.) and co-interventions (physiotherapy, cognitive behavioural therapy, return-to-work programs, etc.) modify the outcome of treatment for CLBP3. Cost-utility in terms of quality-adjusted life years differs between surgical and conservative treatment of CLBP.This study will recruit 1000 patients from orthopaedic spine units, rehabilitation centres, and pain clinics in Switzerland and New Zealand. Effectiveness will be measured by the Oswestry Disability Index (ODI) at baseline and after six months. The change in ODI will be the primary endpoint of this study.Multiple linear regression models will be used, with the change in ODI from baseline to six months as the dependent variable and the type of health care system, type of treatment, patient characteristics, and co-interventions as independent variables. Interactions will be incorporated between type of treatment and different co-interventions and patient characteristics. Cost-utility will be measured with an index based on EQol-5D in combination with cost data. CONCLUSION: This study will provide evidence if differences across health care systems in the outcome of treatment of CLBP exist. It will classify patients with CLBP into different clinical subgroups and help to identify specific target groups who might benefit from specific surgical or conservative interventions. Furthermore, cost-utility differences will be identified for different groups of patients with CLBP. Main results of this study should be replicated in future studies on CLBP.

The international spine registry SPINE TANGO: status quo and first results

With an official life time of over 5 years, Spine Tango can meanwhile be considered the first international spine registry. In this paper we present an overview of frequency statistics of Spine Tango for demonstrating the genesis of questionnaire development and the constantly increasing activity in the registry. Results from two exemplar studies serve for showing concepts of data analysis applied to a spine registry. Between 2002 and 2006, about 6,000 datasets were submitted by 25 centres. Descriptive analyses were performed for demographic, surgical and follow-up data of three generations of the Spine Tango surgery and follow-up forms. The two exemplar studies used multiple linear regression models to identify potential predictor variables for the occurrence of dura lesions in posterior spinal fusion, and to evaluate which covariates influenced the length of hospital stay. Over the study period there was a rise in median patient age from 52.3 to 58.6 years in the Spine Tango data pool and an increasing percentage of degenerative diseases as main pathology from 59.9 to 71.4%. Posterior decompression was the most frequent surgical measure. About one-third of all patients had documented follow-ups. The complication rate remained below 10%. The exemplar studies identified "centre of intervention" and "number of segments of fusion" as predictors of the occurrence of dura lesions in posterior spinal fusion surgery. Length of hospital stay among patients with posterior fusion was significantly influenced by "centre of intervention", "surgeon credentials", "number of segments of fusion", "age group" and "sex". Data analysis from Spine Tango is possible but complicated by the incompatibility of questionnaire generations 1 and 2 with the more recent generation 3. Although descriptive and also analytic studies at evidence level 2++ can be performed, findings cannot yet be generalised to any specific country or patient population. Current limitations of Spine Tango include the low number and short duration of follow-ups and the lack of sufficiently detailed patient data on subgroup levels. Although the number of participants is steadily growing, no country is yet represented with a sufficient number of hospitals. Nevertheless, the benefits of the project for the whole spine community become increasingly visible.

Assessing vegetation cover and biomass in restored erosion areas in Iceland using SPOT satellite data

Due to highly erodible volcanic soils and a harsh climate, livestock grazing in Iceland has led to serious soil erosion on about 40% of the country's surface. Over the last 100 years, various revegetation and restoration measures were taken on large areas distributed all over Iceland in an attempt to counteract this problem. The present research aimed to develop models for estimating percent vegetation cover (VC) and aboveground biomass (AGB) based on satellite data, as this would make it possible to assess and monitor the effectiveness of restoration measures over large areas at a fairly low cost. Models were developed based on 203 vegetation cover samples and 114 aboveground biomass samples distributed over five SPOT satellite datasets. All satellite datasets were atmospherically corrected, and digital numbers were converted into ground reflectance. Then a selection of vegetation indices (VIs) was calculated, followed by simple and multiple linear regression analysis of the relations between the field data and the calculated VIs. Best results were achieved using multiple linear regression models for both %VC and AGB. The model calibration and validation results showed that R2 and RMSE values for most VIs do not vary very much. For percent VC, R2 values range between 0.789 and 0.822, leading to RMSEs ranging between 15.89% and 16.72%. For AGB, R2 values for low-biomass areas (AGB < 800 g/m2) range between 0.607 and 0.650, leading to RMSEs ranging between 126.08 g/m2 and 136.38 g/m2. The AGB model developed for all areas, including those with high biomass coverage (AGB > 800 g/m2), achieved R2 values between 0.487 and 0.510, resulting in RMSEs ranging from 234 g/m2 to 259.20 g/m2. The models predicting percent VC generally overestimate observed low percent VC and slightly underestimate observed high percent VC. The estimation models for AGB behave in a similar way, but over- and underestimation are much more pronounced. These results show that it is possible to estimate percent VC with high accuracy based on various VIs derived from SPOT satellite data. AGB of restoration areas with low-biomass values of up to 800 g/m2 can likewise be estimated with high accuracy based on various VIs derived from SPOT satellite data, whereas in the case of high biomass coverage, estimation accuracy decreases with increasing biomass values. Accordingly, percent VC can be estimated with high accuracy anywhere in Iceland, whereas AGB is much more difficult to estimate, particularly for areas with high-AGB variability.

Domains of importance to the quality of life of older people from two Swiss regions

BACKGROUND Quality of life (QoL) is a subjective perception whose components may vary in importance between individuals. Little is known about which domains of QoL older people deem most important. OBJECTIVE This study investigated in community-dwelling older people the relationships between the importance given to domains defining their QoL and socioeconomic, demographic and health status. METHODS Data were compiled from older people enrolled in the Lc65+ cohort study and two additional, population-based, stratified random samples (n = 5,300). Principal components analysis (PCA) was used to determine the underlying domains among 28 items that participants defined as important to their QoL. The components extracted were used as dependent variables in multiple linear regression models to explore their associations with socioeconomic, demographic and health status. RESULTS PCA identified seven domains that older persons considered important to their QoL. In order of importance (highest to lowest): feeling of safety, health and mobility, autonomy, close entourage, material resources, esteem and recognition, and social and cultural life. A total of six and five domains of importance were significantly associated with education and depressive symptoms, respectively. The importance of material resources was significantly associated with a good financial situation (β = 0.16, P = 0.011), as was close entourage with living with others (β = 0.20, P = 0.007) and as was health and mobility with age (β = -0.16, P = 0.014). CONCLUSION The importance older people give to domains of their QoL appears strongly related to their actual resources and experienced losses. These findings may help clinicians, researchers and policy makers better adapt strategies to individuals' needs.

Influence of previous surgery on patient-rated outcome after surgery for degenerative disorders of the lumbar spine.

PURPOSE Few studies have used multivariate models to quantify the effect of multiple previous spine surgeries on patient-oriented outcome after spine surgery. This study sought to quantify the effect of prior spine surgery on 12-month postoperative outcomes in patients undergoing surgery for different degenerative disorders of the lumbar spine. METHODS The study included 4940 patients with lumbar degenerative disease documented in the Spine Tango Registry of EUROSPINE, the Spine Society of Europe, from 2004 to 2015. Preoperatively and 12 months postoperatively, patients completed the multidimensional Core Outcome Measures Index (COMI; 0-10 scale). Patients' medical history and surgical details were recorded using the Spine Tango Surgery 2006 and 2011 forms. Multiple linear regression models were used to investigate the relationship between the number of previous surgeries and the 12-month postoperative COMI score, controlling for the baseline COMI score and other potential confounders. RESULTS In the adjusted model including all cases, the 12-month COMI score showed a 0.37-point worse value [95 % confidence intervals (95 % CI) 0.29-0.45; p < 0.001] for each additional prior spine surgery. In the subgroup of patients with lumbar disc herniation, the corresponding effect was 0.52 points (95 % CI 0.27-0.77; p < 0.001) and in lumbar degenerative spondylolisthesis, 0.40 points (95 % CI 0.17-0.64; p = 0.001). CONCLUSIONS We were able to demonstrate a clear "dose-response" effect for previous surgery: the greater the number of prior spine surgeries, the systematically worse the outcome at 12 months' follow-up. The results of this study can be used when considering or consenting a patient for further surgery, to better inform the patient of the likely outcome and to set realistic expectations.

Anemia is associated with abdominal aortic aneurysm (AAA) size and decreased long-term survival after endovascular AAA repair

OBJECTIVE: Anemia is a common comorbid condition in various inflammatory states and an established predictor of mortality in patients with chronic heart failure, ischemic heart disease, and end-stage renal disease. The present study of patients with abdominal aortic aneurysm (AAA) undergoing endovascular repair (EVAR) assessed the relationships between baseline hemoglobin concentration and AAA size, as well as anemia and long-term survival. METHODS: Between March 1994 and November 2006, 711 patients (65 women, mean age 75.8 +/- 7.8 years) underwent elective EVAR. Anemia was defined as a hemoglobin level <13 g/dL in men and <12 g/dL in women. Post-EVAR mean follow-up was 48.3 +/- 32.0 months. Association of hemoglobin level with AAA size was assessed with multiple linear regression. Mortality was determined with use of the internet-based Social Security Death Index and the electronic hospital record. Kaplan-Meier survival curves of anemic and nonanemic patient groups were compared by the log-rank method. Multivariable logistic regression models were used to determine the influence of anemia on vital status after EVAR. RESULTS: A total of 218/711 (30.7%) of AAA patients undergoing EVAR had anemia at baseline. After adjustment for various risk factors, hemoglobin level was inversely related to maximum AAA diameter (beta: - .144, 95%-CI: -1.482 - .322, P = .002). Post-EVAR survival was 65.5% at 5 years and 44.4% at 10 years. In long-term follow-up, survival was significantly lower in patients with anemia as compared to patients without anemia (P < .0001 by log-rank). Baseline hemoglobin levels were independently related to long-term mortality in multivariable Cox regression analysis adjusted for various risk factors (adjusted HR: 0.866, 95% CI: .783 to .958, P = .005). Within this model, statin use (adjusted HR: .517, 95% CI: .308 to .868, P = .013) was independently related to long-term survival, whereas baseline AAA diameter (adjusted HR: 1.022, 95% CI: 1.009 to 1.036, P = .001) was an independently associated with increased mortality. CONCLUSIONS: Baseline hemoglobin concentration is independently associated with AAA size and reduced long-term survival following EVAR. Thus, the presence or absence of anemia offers a potential refinement of existing risk stratification instruments.

Quantitative assessment of soil parameters in Western Tajikistan using a soil spectral library approach

Soil degradation is a major problem in the agriculturally dominated country of Tajikistan, which makes it necessary to determine and monitor the state of soils. For this purpose a soil spectral library was established as it enables the determination of soil properties with relatively low costs and effort. A total of 1465 soil samples were collected from three 10x10 km test sites in western Tajikistan. The diffuse reflectance of the samples was measured with a FieldSpec PRO FR from ASD in the spectral range from 380 to 2500 nm in laboratory. 166 samples were finally selected based on their spectral information and analysed on total C and N, organic C, pH, CaCO₃, extractable P, exchangeable Ca, Mg and K, and the fractions clay, silt and sand. Multiple linear regression was used to set up the models. Two third of the chemically analysed samples were used to calibrate the models, one third was used for hold-out validation. Very good prediction accuracy was obtained for total C (R² = 0.76, RMSEP = 4.36 g kg⁻¹), total N (R² = 0.83, RMSEP = 0.30 g kg⁻¹) and organic C (R² = 0.81, RMSEP = 3.30 g kg⁻¹), good accuracy for pH (R² = 0.61, RMSEP = 0.157) and CaCO3(R² = 0.72, RMSEP = 4.63 %). No models could be developed for extractable P, exchangeable Ca, Mg and K, and the fractions clay, silt and sand. It can be concluded that the spectral library approach has a high potential to substitute standard laboratory methods where rapid and inexpensive analysis is required.

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.