Extended table of percentage points of the chi-square distribution /

"NAVWEPS report 7770. NOTS TP 2749."

Exercise sheet 9

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Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.

Implementing aspects of Blueprint 2000: Investigating readiness expectations in selected elementary schools in Broward County, Florida

The purpose of this research study was to investigate if the determination of school readiness as it was evaluated by Broward County kindergarten teachers on the Florida's Expectations of School Readiness checklist can be attributed to the effects of gender, chronological age on school entry, racial or ethnic background, attending public preschool, native language other than English, or socioeconomic status.^ This is a descriptive study in which the number of expectations passed or failed for each of the identifier categories was compared. The Chi-squared distribution was used to evaluate the null hypothesis that "chronological age at entry to school, gender, race or ethnicity, native language other than English, public preschool experience, and socioeconomic status have no effect on the determination of readiness for school". Results were confirmed using t-tests, ANOVA, and linear regression models. The cohort of 1555 Broward County students in the study were evaluated using the Florida's Expectations for School Readiness checklist and were determined not ready for school during the initial data collection year 1996-1997.^ The determination of school readiness was significantly dependent on the gender, and racial or ethnic background of the students in the cohort. The socioeconomic status and native language other than English designations were significant for students only in the areas of preacademic, academic and literacy development. Chronological age on entry to school or attendance in public preschool prior to entry in kindergarten for the cohort was not significant in the determination of readiness for school.^ Given the fact that this study followed only students that were determined not ready for school, it is recommended that a second cohort of both "ready" and "not ready" students be studied. ^

Re-evaluation of pulmonary titanium dioxide nanoparticle distribution using the "relative deposition index": Evidence for clearance through microvasculature

ABSTRACT: BACKGROUND: Translocation of nanoparticles (NP) from the pulmonary airways into other pulmonary compartments or the systemic circulation is controversially discussed in the literature. In a previous study it was shown that titanium dioxide (TiO2) NP were "distributed in four lung compartments (air-filled spaces, epithelium/endothelium, connective tissue, capillary lumen) in correlation with compartment size". It was concluded that particles can move freely between these tissue compartments. To analyze whether the distribution of TiO2 NP in the lungs is really random or shows a preferential targeting we applied a newly developed method for comparing NP distributions. METHODS: Rat lungs exposed to an aerosol containing TiO2 NP were prepared for light and electron microscopy at 1 h and at 24 h after exposure. Numbers of TiO2 NP associated with each compartment were counted using energy filtering transmission electron microscopy. Compartment size was estimated by unbiased stereology from systematically sampled light micrographs. Numbers of particles were related to compartment size using a relative deposition index and chi-squared analysis. RESULTS: Nanoparticle distribution within the four compartments was not random at 1 h or at 24 h after exposure. At 1 h the connective tissue was the preferential target of the particles. At 24 h the NP were preferentially located in the capillary lumen. CONCLUSION: We conclude that TiO2 NP do not move freely between pulmonary tissue compartments, although they can pass from one compartment to another with relative ease. The residence time of NP in each tissue compartment of the respiratory system depends on the compartment and the time after exposure. It is suggested that a small fraction of TiO2 NP are rapidly transported from the airway lumen to the connective tissue and subsequently released into the systemic circulation.

Erectile Dysfunction and Correlated Factors in Brazilian Men Aged 18-40 years

Introduction. Few population-based studies in erectile dysfunction (ED) included subjects less than 40 years old and analyzed the several factors and consequences potentially associated with this condition. Aim. Evaluation of the prevalence of erectile dysfunction (ED) and associated factors in a sample of Brazilian men aged 18 to 40 years old. Methods. Cross-sectional study in which subjects were contacted in public places of 18 major Brazilian cities and interviewed using an anonymous questionnaire. Survey data were submitted to chi-squared, student`s t-test and logistic regression analyses. Main Outcome Measures. The data were collected by means of a self-administered questionnaire with 87 questions about sociodemographic variables, general health, habits and lifestyle-related factors, sexual behavior and sexual difficulties, including ED which was assessed by a single question. Results. Prevalence of ED in 1,947 men was 35.0% (73.7% mild, 26.3% moderate/complete). Greater frequency of ED was seen in subjects that never had information about sex, experienced difficulties in the beginning of sexual life and have never masturbated. ED was associated to lower level of education, but not to race, sexual orientation, employment or marital status. Also, no association was found between ED and smoking, alcoholism, obesity, sedentary life, diabetes, hypertension, cardiovascular disease, hyperlipidemia, depression or anxiety. ED caused negative impact in men`s self-esteem, interpersonal relationships, work and leisure activities, and in sexual life satisfaction. Less than 10% of men with ED had received medical treatment for this problem. Conclusions. Prevalence of ED in this young population was high, mostly of mild severity. Low education and psychosocial problems were associated to ED and, due probably to the sample subjects` young age, no association was found with organic problems. Measures in the fields of education and psychosocial difficulties prevention would have a positive impact in the control of erectile dysfunction in the young population. Martins FG, and Abdo CHN. Erectile dysfunction and correlated factors in Brazilian men aged 18-40 years. J Sex Med 2010;7:2166-2173.

Female asylum seekers with musculoskeletal pain: the importance of diagnosis and treatment of hypovitaminosis D.

BACKGROUND: Hypovitaminosis D is well known in different populations, but may be under diagnosed in certain populations. We aim to determine the first diagnosis considered, the duration and resolution of symptoms, and the predictors of response to treatment in female asylum seekers suffering from hypovitaminosis D. METHODS: Design: A pre- and post-intervention observational study. Setting: A network comprising an academic primary care centre and nurse practitioners. Participants: Consecutive records of 33 female asylum seekers with complaints compatible with osteomalacia and with hypovitaminosis D (serum 25-(OH) vitamin D < 21 nmol/l). Treatment intervention: The patients received either two doses of 300,000 IU intramuscular cholecalciferol as well as 800 IU of cholecalciferol with 1000 mg of calcium orally, or the oral treatment only. Main outcome measures: We recorded the first diagnosis made by the physicians before the correct diagnosis of hypovitaminosis D, the duration of symptoms before diagnosis, the responders and non-responders to treatment, the duration of symptoms after treatment, and the number of medical visits and analgesic drugs prescribed 6 months before and 6 months after diagnosis. Tests: Two-sample t-tests, chi-squared tests, and logistic regression analyses were performed. Analyses were performed using SPSS 10.0. RESULTS: Prior to the discovery of hypovitaminosis D, diagnoses related to somatisation were evoked in 30 patients (90.9%). The mean duration of symptoms before diagnosis was 2.53 years (SD 3.20). Twenty-two patients (66.7%) responded completely to treatment; the remaining patients were considered to be non-responders. After treatment was initiated, the responders' symptoms disappeared completely after 2.84 months. The mean number of emergency medical visits fell from 0.88 (SD 1.08) six months before diagnosis to 0.39 (SD 0.83) after (P = 0.027). The mean number of analgesic drugs that were prescribed also decreased from 1.67 (SD 1.5) to 0.85 (SD 1) (P = 0.001). CONCLUSION: Hypovitaminosis D in female asylum seekers may remain undiagnosed, with a prolonged duration of chronic symptoms. The potential pitfall is a diagnosis of somatisation. Treatment leads to a rapid resolution of symptoms, a reduction in the use of medical services, and the prescription of analgesic drugs in this vulnerable population.

Proceso INFORNUT: validación de la fase de filtro-FILNUT--y comparación con otros métodos de detección precoz de desnutrición hospitalaria.

INTRODUCTION According to several series, hospital hyponutrition involves 30-50% of hospitalized patients. The high prevalence justifies the need for early detection from admission. There several classical screening tools that show important limitations in their systematic application in daily clinical practice. OBJECTIVES To analyze the relationship between hyponutrition, detected by our screening method, and mortality, hospital stay, or re-admissions. To analyze, as well, the relationship between hyponutrition and prescription of nutritional support. To compare different nutritional screening methods at admission on a random sample of hospitalized patients. Validation of the INFORNUT method for nutritional screening. MATERIAL AND METHODS In a previous phase from the study design, a retrospective analysis with data from the year 2003 was carried out in order to know the situation of hyponutrition in Virgen de la Victoria Hospital, at Malaga, gathering data from the MBDS (Minimal Basic Data Set), laboratory analysis of nutritional risk (FILNUT filter), and prescription of nutritional support. In the experimental phase, a cross-sectional cohort study was done with a random sample of 255 patients, on May of 2004. Anthropometrical study, Subjective Global Assessment (SGA), Mini-Nutritional Assessment (MNA), Nutritional Risk Screening (NRS), Gassull's method, CONUT and INFORNUT were done. The settings of the INFORNUT filter were: albumin < 3.5 g/dL, and/or total proteins <5 g/dL, and/or prealbumin <18 mg/dL, with or without total lymphocyte count < 1.600 cells/mm3 and/or total cholesterol <180 mg/dL. In order to compare the different methods, a gold standard is created based on the recommendations of the SENPE on anthropometrical and laboratory data. The statistical association analysis was done by the chi-squared test (a: 0.05) and agreement by the k index. RESULTS In the study performed in the previous phase, it is observed that the prevalence of hospital hyponutrition is 53.9%. One thousand six hundred and forty four patients received nutritional support, of which 66.9% suffered from hyponutrition. We also observed that hyponutrition is one of the factors favoring the increase in mortality (hyponourished patients 15.19% vs. non-hyponourished 2.58%), hospital stay (hyponourished patients 20.95 days vs. non-hyponourished 8.75 days), and re-admissions (hyponourished patients 14.30% vs. non-hyponourished 6%). The results from the experimental study are as follows: the prevalence of hyponutrition obtained by the gold standard was 61%, INFORNUT 60%. Agreement levels between INFORNUT, CONUT, and GASSULL are good or very good between them (k: 0.67 INFORNUT with CONUT, and k: 0.94 INFORNUT and GASSULL) and wit the gold standard (k: 0.83; k: 0.64 CONUT; k: 0.89 GASSULL). However, structured tests (SGA, MNA, NRS) show low agreement indexes with the gold standard and laboratory or mixed tests (Gassull), although they show a low to intermediate level of agreement when compared one to each other (k: 0.489 NRS with SGA). INFORNUT shows sensitivity of 92.3%, a positive predictive value of 94.1%, and specificity of 91.2%. After the filer phase, a preliminary report is sent, on which anthropometrical and intake data are added and a Nutritional Risk Report is done. CONCLUSIONS Hyponutrition prevalence in our study (60%) is similar to that found by other authors. Hyponutrition is associated to increased mortality, hospital stay, and re-admission rate. There are no tools that have proven to be effective to show early hyponutrition at the hospital setting without important applicability limitations. FILNUT, as the first phase of the filter process of INFORNUT represents a valid tool: it has sensitivity and specificity for nutritional screening at admission. The main advantages of the process would be early detection of patients with risk for hyponutrition, having a teaching and sensitization function to health care staff implicating them in nutritional assessment of their patients, and doing a hyponutrition diagnosis and nutritional support need in the discharge report that would be registered by the Clinical Documentation Department. Therefore, INFORNUT would be a universal screening method with a good cost-effectiveness ratio.

Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.