Fixed and random effects in Classical and Bayesian regression

This paper proposes a common and tractable framework for analyzingdifferent definitions of fixed and random effects in a contant-slopevariable-intercept model. It is shown that, regardless of whethereffects (i) are treated as parameters or as an error term, (ii) areestimated in different stages of a hierarchical model, or whether (iii)correlation between effects and regressors is allowed, when the sameinformation on effects is introduced into all estimation methods, theresulting slope estimator is also the same across methods. If differentmethods produce different results, it is ultimately because differentinformation is being used for each methods.

The importance of individual heterogeneity in the decomposition of measures of socioeconomic inequality in health: An approach based on quantile regression

This paper shows how recently developed regression-based methods for thedecomposition of health inequality can be extended to incorporateindividual heterogeneity in the responses of health to the explanatoryvariables. We illustrate our method with an application to the CanadianNPHS of 1994. Our strategy for the estimation of heterogeneous responsesis based on the quantile regression model. The results suggest that thereis an important degree of heterogeneity in the association of health toexplanatory variables which, in turn, accounts for a substantial percentageof inequality in observed health. A particularly interesting finding isthat the marginal response of health to income is zero for healthyindividuals but positive and significant for unhealthy individuals. Theheterogeneity in the income response reduces both overall health inequalityand income related health inequality.

Random measurement error and regression dilution bias.

Summary points: - The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease) - Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null - Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant - Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable

Ignoring information in binary choice with continuous variables: When is less 'more'?

When can a single variable be more accurate in binary choice than multiple sources of information? We derive analytically the probability that a single variable (SV) will correctly predict one of two choices when both criterion and predictor are continuous variables. We further provide analogous derivations for multiple regression (MR) and equal weighting (EW) and specify the conditions under which the models differ in expected predictive ability. Key factors include variability in cue validities, intercorrelation between predictors, and the ratio of predictors to observations in MR. Theory and simulations are used to illustrate the differential effects of these factors. Results directly address why and when one-reason decision making can be more effective than analyses that use more information. We thus provide analytical backing to intriguing empirical results that, to date, have lacked theoretical justification. There are predictable conditions for which one should expect less to be more.

The predictive value of preoperative B-type natriuretic peptide in children undergooing heart surgery.

Introduction: Low cardiac output syndrome is frequent in childrenafter heart surgery for congenital heart disease and may result in pooroutcome and increased morbidity. In the adult population, preoperativebrain natriuretic peptide (BNP) was shown to be predictive of postoperative complications. In children, the value of preoperative BNP onpostoperative outcome is not so clear. The aim of this study was todetermine the predictive value of preoperative BNP on postoperativeoutcome and low cardiac output syndrome in children after heartsurgery for congenital heart disease.Methods: We examined, retrospectively, the postoperative course of97 pediatric patients (mean age 3.7 years, range 0-14 years old) whounderwent heart surgery in a tertiary care pediatric intensive caresetting. NTproBNP was measured preoperatively in all patients(median 412 pg/ml, range 12-35'000 pg/ml). Patients were divided intothree groups according to their NTproBNP levels (group 1: 0-300 pg/ml, group 2: 300-600 pg/ml, group 3: >600 pg/ml) and then,correlations with postoperative outcomes were examined.Results: We found that patients with a high preoperative BNP requiredmore frequently prolonged (>2 days) mechanical ventilation (33%vs 40% vs 61%, p = 0.045) and stayed more frequently longer than6 days in the intensive care unit (42% vs 50% vs 71%, p = 0.03).However, high preoperative BNP was not correlated with occurrenceof low cardiac output syndrome.Conclusion: Preoperative BNP cannot be used, in children, as areliable and sole predictor of postoperative low cardiac outputsyndrome. However it may help identify, before surgery, those patientsat risk of having a difficult postoperative course.

Prediction of functional outcome 18 months after a first psychotic episode: a proton magnetic resonance spectroscopy study.

CONTEXT: Recent magnetic resonance imaging studies have attempted to relate volumetric brain measurements in early schizophrenia to clinical and functional outcome some years later. These studies have generally been negative, perhaps because gray and white matter volumes inaccurately assess the underlying dysfunction that might be predictive of outcome. OBJECTIVE: To investigate the predictive value of frontal and temporal spectroscopy measures for outcome in patients with first-episode psychoses. DESIGN: Left prefrontal cortex and left mediotemporal lobe voxels were assessed using proton magnetic resonance spectroscopy to provide the ratio of N-acetylaspartate (NAA) and choline-containing compounds to creatine and phosphocreatine (Cr) (NAA/Cr ratio). These data were used to predict outcome at 18 months after admission, as assessed by a systematic medical record audit. SETTING: Early psychosis clinic. PARTICIPANTS: Forty-six patients with first-episode psychosis. MAIN OUTCOME MEASURES: We used regression models that included age at imaging and duration of untreated psychosis to predict outcome scores on the Global Assessment of Functioning Scale, Clinical Global Impression scales, and Social and Occupational Functional Assessment Scale, as well as the number of admissions during the treatment period. We then further considered the contributions of premorbid function and baseline level of negative symptoms. RESULTS: The only spectroscopic predictor of outcome was the NAA/Cr ratio in the prefrontal cortex. Low scores on this variable were related to poorer outcome on all measures. In addition, the frontal NAA/Cr ratio explained 17% to 30% of the variance in outcome. CONCLUSIONS: Prefrontal neuronal dysfunction is an inconsistent feature of early psychosis; rather, it is an early marker of poor prognosis across the first years of illness. The extent to which this can be used to guide treatment and whether it predicts outcome some years after first presentation are questions for further research.

Test of four colon cancer risk-scores in formalin fixed paraffin embedded microarray gene expression data.

BACKGROUND: Prognosis prediction for resected primary colon cancer is based on the T-stage Node Metastasis (TNM) staging system. We investigated if four well-documented gene expression risk scores can improve patient stratification. METHODS: Microarray-based versions of risk-scores were applied to a large independent cohort of 688 stage II/III tumors from the PETACC-3 trial. Prognostic value for relapse-free survival (RFS), survival after relapse (SAR), and overall survival (OS) was assessed by regression analysis. To assess improvement over a reference, prognostic model was assessed with the area under curve (AUC) of receiver operating characteristic (ROC) curves. All statistical tests were two-sided, except the AUC increase. RESULTS: All four risk scores (RSs) showed a statistically significant association (single-test, P < .0167) with OS or RFS in univariate models, but with HRs below 1.38 per interquartile range. Three scores were predictors of shorter RFS, one of shorter SAR. Each RS could only marginally improve an RFS or OS model with the known factors T-stage, N-stage, and microsatellite instability (MSI) status (AUC gains < 0.025 units). The pairwise interscore discordance was never high (maximal Spearman correlation = 0.563) A combined score showed a trend to higher prognostic value and higher AUC increase for OS (HR = 1.74, 95% confidence interval [CI] = 1.44 to 2.10, P < .001, AUC from 0.6918 to 0.7321) and RFS (HR = 1.56, 95% CI = 1.33 to 1.84, P < .001, AUC from 0.6723 to 0.6945) than any single score. CONCLUSIONS: The four tested gene expression-based risk scores provide prognostic information but contribute only marginally to improving models based on established risk factors. A combination of the risk scores might provide more robust information. Predictors of RFS and SAR might need to be different.

Ruling out coronary heart disease in primary care patients with chest pain: a clinical prediction score.

ABSTRACT: BACKGROUND: Chest pain raises concern for the possibility of coronary heart disease. Scoring methods have been developed to identify coronary heart disease in emergency settings, but not in primary care. METHODS: Data were collected from a multicenter Swiss clinical cohort study including 672 consecutive patients with chest pain, who had visited one of 59 family practitioners' offices. Using delayed diagnosis we derived a prediction rule to rule out coronary heart disease by means of a logistic regression model. Known cardiovascular risk factors, pain characteristics, and physical signs associated with coronary heart disease were explored to develop a clinical score. Patients diagnosed with angina or acute myocardial infarction within the year following their initial visit comprised the coronary heart disease group. RESULTS: The coronary heart disease score was derived from eight variables: age, gender, duration of chest pain from 1 to 60 minutes, substernal chest pain location, pain increases with exertion, absence of tenderness point at palpation, cardiovascular risks factors, and personal history of cardiovascular disease. Area under the receiver operating characteristics curve was of 0.95 with a 95% confidence interval of 0.92; 0.97. From this score, 413 patients were considered as low risk for values of percentile 5 of the coronary heart disease patients. Internal validity was confirmed by bootstrapping. External validation using data from a German cohort (Marburg, n = 774) revealed a receiver operating characteristics curve of 0.75 (95% confidence interval, 0.72; 0.81) with a sensitivity of 85.6% and a specificity of 47.2%. CONCLUSIONS: This score, based only on history and physical examination, is a complementary tool for ruling out coronary heart disease in primary care patients complaining of chest pain.

Biomass estimation of Triplectides egleri Sattler (Trichoptera, Leptoceridae) in a stream at Ducke Reserve, Central Amazonia

ABSTRACT Biomass is a fundamental measure for understanding the structure and functioning (e.g. fluxes of energy and nutrients in the food chain) of aquatic ecosystems. We aim to provide predictive models to estimate the biomass of Triplectides egleri Sattler, 1963, in a stream in Central Amazonia, based on body and case dimensions. We used body length, head-capsule width, interocular distance and case length and width to derive biomass estimations. Linear, exponential and power regression models were used to assess the relationship between biomass and body or case dimensions. All regression models used in the biomass estimation of T. egleri were significant. The best fit between biomass and body or case dimensions was obtained using the power model, followed by the exponential and linear models. Body length provided the best estimate of biomass. However, the dimensions of sclerotized structures (interocular distance and head-capsule width) also provided good biomass predictions, and may be useful in estimating biomass of preserved and/or damaged material. Case width was the dimension of the case that provided the best estimate of biomass. Despite the low relation, case width may be useful in studies that require low stress on individuals.

Predictive value of the MGMT promoter methylation status in metastatic melanoma patients receiving first-line temozolomide plus bevacizumab in the trial SAKK 50/07.

The O6-methylguanine-DNA-methyltransferase (MGMT) promoter methylation status is a predictive parameter for the response of malignant gliomas to alkylating agents such as temozolomide. First clinical trials with temozolomide plus bevacizumab therapy in metastatic melanoma patients are ongoing, although the predictive value of the MGMT promoter methylation status in this setting remains unclear. We assessed MGMT promoter methylation in formalin-fixed, primary tumor tissue of metastatic melanoma patients treated with first-line temozolomide and bevacizumab from the trial SAKK 50/07 by methylation-specific polymerase chain reaction. In addition, the MGMT expression levels were also analyzed by MGMT immunohistochemistry. Eleven of 42 primary melanomas (26%) revealed a methylated MGMT promoter. Promoter methylation was significantly associated with response rates CR + PR versus SD + PD according to RECIST (response evaluation criteria in solid tumors) (p<0.05) with a trend to prolonged median progression-free survival (8.1 versus 3.4 months, p>0.05). Immunohistochemically different protein expression patterns with heterogeneous and homogeneous nuclear MGMT expression were identified. Negative MGMT expression levels were associated with overall disease stabilization CR+PR+SD versus PD (p=0.05). There was only a poor correlation between MGMT methylation and lack of MGMT expression. A significant proportion of melanomas have a methylated MGMT promoter. The MGMT promoter methylation status may be a promising predictive marker for temozolomide therapy in metastatic melanoma patients. Larger sample sizes may help to validate significant differences in survival type endpoints.

Early multimodal outcome prediction after cardiac arrest in patients treated with hypothermia.

OBJECTIVES: Therapeutic hypothermia and pharmacological sedation may influence outcome prediction after cardiac arrest. The use of a multimodal approach, including clinical examination, electroencephalography, somatosensory-evoked potentials, and serum neuron-specific enolase, is recommended; however, no study examined the comparative performance of these predictors or addressed their optimal combination. DESIGN: Prospective cohort study. SETTING: Adult ICU of an academic hospital. PATIENTS: One hundred thirty-four consecutive adults treated with therapeutic hypothermia after cardiac arrest. MEASUREMENTS AND MAIN RESULTS: Variables related to the cardiac arrest (cardiac rhythm, time to return of spontaneous circulation), clinical examination (brainstem reflexes and myoclonus), electroencephalography reactivity during therapeutic hypothermia, somatosensory-evoked potentials, and serum neuron-specific enolase. Models to predict clinical outcome at 3 months (assessed using the Cerebral Performance Categories: 5 = death; 3-5 = poor recovery) were evaluated using ordinal logistic regressions and receiving operator characteristic curves. Seventy-two patients (54%) had a poor outcome (of whom, 62 died), and 62 had a good outcome. Multivariable ordinal logistic regression identified absence of electroencephalography reactivity (p < 0.001), incomplete recovery of brainstem reflexes in normothermia (p = 0.013), and neuron-specific enolase higher than 33 μg/L (p = 0.029), but not somatosensory-evoked potentials, as independent predictors of poor outcome. The combination of clinical examination, electroencephalography reactivity, and neuron-specific enolase yielded the best predictive performance (receiving operator characteristic areas: 0.89 for mortality and 0.88 for poor outcome), with 100% positive predictive value. Addition of somatosensory-evoked potentials to this model did not improve prognostic accuracy. CONCLUSIONS: Combination of clinical examination, electroencephalography reactivity, and serum neuron-specific enolase offers the best outcome predictive performance for prognostication of early postanoxic coma, whereas somatosensory-evoked potentials do not add any complementary information. Although prognostication of poor outcome seems excellent, future studies are needed to further improve prediction of good prognosis, which still remains inaccurate.

Predicting Adverse Events in Children with Fever and Chemotherapy-Induced Neutropenia. Results of the Prospective Multicenter SPOG 2003 FN Study

PURPOSE To develop a score predicting the risk of adverse events (AEs) in pediatric patients with cancer who experience fever and neutropenia (FN) and to evaluate its performance. PATIENTS AND METHODS Pediatric patients with cancer presenting with FN induced by nonmyeloablative chemotherapy were observed in a prospective multicenter study. A score predicting the risk of future AEs (ie, serious medical complication, microbiologically defined infection, radiologically confirmed pneumonia) was developed from a multivariate mixed logistic regression model. Its cross-validated predictive performance was compared with that of published risk prediction rules. Results An AE was reported in 122 (29%) of 423 FN episodes. In 57 episodes (13%), the first AE was known only after reassessment after 8 to 24 hours of inpatient management. Predicting AE at reassessment was better than prediction at presentation with FN. A differential leukocyte count did not increase the predictive performance. The score predicting future AE in 358 episodes without known AE at reassessment used the following four variables: preceding chemotherapy more intensive than acute lymphoblastic leukemia maintenance (weight = 4), hemoglobin > or = 90 g/L (weight = 5), leukocyte count less than 0.3 G/L (weight = 3), and platelet count less than 50 G/L (weight = 3). A score (sum of weights) > or = 9 predicted future AEs. The cross-validated performance of this score exceeded the performance of published risk prediction rules. At an overall sensitivity of 92%, 35% of the episodes were classified as low risk, with a specificity of 45% and a negative predictive value of 93%. CONCLUSION This score, based on four routinely accessible characteristics, accurately identifies pediatric patients with cancer with FN at risk for AEs after reassessment.

New reference tables and user-friendly Internet application for predicted heart weights.

BACKGROUND: Knowledge of normal heart weight ranges is important information for pathologists. Comparing the measured heart weight to reference values is one of the key elements used to determine if the heart is pathological, as heart weight increases in many cardiac pathologies. The current reference tables are old and in need of an update. AIMS: The purposes of this study are to establish new reference tables for normal heart weights in the local population and to determine the best predictive factor for normal heart weight. We also aim to provide technical support to calculate the predictive normal heart weight. METHODS: The reference values are based on retrospective analysis of adult Caucasian autopsy cases without any obvious pathology that were collected at the University Centre of Legal Medicine in Lausanne from 2007 to 2011. We selected 288 cases. The mean age was 39.2 years. There were 118 men and 170 women. Regression analyses were performed to assess the relationship of heart weight to body weight, body height, body mass index (BMI) and body surface area (BSA). RESULTS: The heart weight increased along with an increase in all the parameters studied. The mean heart weight was greater in men than in women at a similar body weight. BSA was determined to be the best predictor for normal heart weight. New reference tables for predicted heart weights are presented as a web application that enable the comparison of heart weights observed at autopsy with the reference values. CONCLUSIONS: The reference tables for heart weight and other organs should be systematically updated and adapted for the local population. Web access and smartphone applications for the predicted heart weight represent important investigational tools.

Poststroke fatigue following minor infarcts: a prospective study.

OBJECTIVE: To explore the potential relationship between fatigue following strokes and poststroke mood, cognitive dysfunction, disability, and infarct site and to determine the predictive factors in the development of poststroke fatigue (PSF) following minor infarcts. METHODS: Ninety-nine functionally active patients aged less than 70 years with a first, nondisabling stroke (NIH Stroke Scale score ≤6 in acute phase and ≤3 after 6 months, modified Rankin Scale score ≤1 at 6 months) were assessed during the acute phase and then at 6 (T1) and 12 months (T2) after their stroke. Scores in the Fatigue Assessment Inventory were described and correlated to age, gender, neurologic and functional impairment, lesion site, mood scores, neuropsychological data, laboratory data, and quality of life at T1 and T2 using a multivariate logistic regression analysis in order to determine which variables recorded at T1 best predicted fatigue at T2. RESULT: As many as 30.5% of the patients at T1 and 34.7% at T2 (11.6% new cases between T1 and T2) reported fatigue. At both 6 and 12 months, there was a significant association between fatigue and a reduction in professional activity. Attentional-executive impairment, depression, and anxiety levels remained associated with PSF throughout this time period, underlining the critical role of these variables in the genesis of PSF. There was no significant association between the lesion site and PSF. CONCLUSION: This study suggests that attentional and executive impairment, as well as depression and anxiety, may play a critical role in the development of PSF.