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PubMed2005

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory.

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states-perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of "excess" zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to "excess" zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed-and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros.

Accidents, Traffic↗
PubMed1998

Predicting in-hospital deaths from coronary artery bypass graft surgery. Do different severity measures give different predictions?

OBJECTIVES: Severity-adjusted death rates for coronary artery bypass graft (CABG) surgery by provider are published throughout the country. Whether five severity measures rated severity differently for identical patients was examined in this study. METHODS: Two severity measures rate patients using clinical data taken from the first two hospital days (MedisGroups, physiology scores); three use diagnoses and other information coded on standard, computerized hospital discharge abstracts (Disease Staging, Patient Management Categories, all patient refined diagnosis related groups). The database contained 7,764 coronary artery bypass graft patients from 38 hospitals with 3.2% in-hospital deaths. Logistic regression was performed to predict deaths from age, age squared, sex, and severity scores, and c statistics from these regressions were used to indicate model discrimination. Odds ratios of death predicted by different severity measures were compared. RESULTS: Code-based measures had better c statistics than clinical measures: all patient refined diagnosis related groups, c = 0.83 (95% C.I. 0.81, 0.86) versus MedisGroups, c = 0.73 (95% C.I. 0.70, 0.76). Code-based measures predicted very different odds of dying than clinical measures for more than 30% of patients. Diagnosis codes indicting postoperative, life-threatening conditions may contribute to the superior predictive power of code-based measures. CONCLUSIONS: Clinical and code-based severity measures predicted different odds of dying for many coronary artery bypass graft patients. Although code-based measures had better statistical performance, this may reflect their reliance on diagnosis codes for life-threatening conditions occurring late in the hospitalization, possibly as complications of care. This compromises their utility for drawing inferences about quality of care based on severity-adjusted coronary artery bypass graft death rates.

Coronary Artery Bypass↗
PubMed2004

Statistical estimation of resin composite polymerization sufficiency using microhardness.

With respect to determining sub-surface resin polymerization sufficiency, this study compared a traditional method of applying linear regression to bottom- to top-surface Knoop hardness ratios to an alternative method based on nonlinear regression. Inverse linear regression on ratios was used to estimate the exposure duration required for 80% bottom-surface hardness with respect to the top, in six light-by-material groups. Alternatively, a one-phase, two-parameter, exponential association of the form Y=Y(max)(1-e(-kt)) (where Y(max) is maximum hardness, k is a rate constant, and t is exposure duration), was used to model hardness. Inverse nonlinear regression estimated, for each condition, the exposure duration required for the bottom surface to achieve 80% of corresponding condition (light and material) top-surface Y(max). Mathematically, analysis of ratios was demonstrated to yield potentially less precise and biased estimates. Nonlinear regression yielded better statistical fit and provided easily accessible tests for differences in k across light-system groups. Another recently proposed nonlinear model for polymerization, Y=Y(max)kt(n)/(1+kt(n)), was also considered. While this new model has substantially greater phenomenological and mechanistic justification, we found that the model-fitting process was more sensitive to initial parameter values and sometimes yielded untenable results when applied to our data. However, we believe that these problems would not occur if sample points are well distributed across a wide range of exposure durations, and that the model, Y=Y(max)kt(n)/(1+kt(n)), should be considered for such data sets.

Analysis of Variance↗
PubMed1992

The effects of genetic and phenotypic production potential on response to recombinant bovine somatotropin.

Evidence was sought for an interaction between both phenotypic and genetic production potential and response of milk production to administration of bST in three trials of 38, 43, and 35 cows. In each trial, bST was administered in doses of 0, 10.3, 20.6, and, in trial 1 only, 41.2 mg/d for 38 wk from wk 4 of lactation. Data were analyzed for each experiment separately and combined across experiments. Analyses included separate regressions for treated and untreated animals for milk production during the production period on pretreatment production and estimated breeding value for milk production. Breeding value was estimated as the sire's estimated transmitting ability plus one-half of the maternal grandsire's estimated transmitting ability. With the exception of regression on estimated breeding value in trial 1 and in combined data, differences between treated and untreated animals in the regression of milk production on pretreatment milk production or on estimates of breeding value were not statistically significant. However, regressions on pretreatment production were substantially lower for treated than for untreated animals in each of the three trials. Regressions on breeding value estimated from sire and maternal grandsire estimated transmitting abilities were substantially, but not significantly, lower for untreated than for treated animals in all three trials. The results suggest that cows with high production potential for nongenetic reasons may show diminished response to bST, whereas cows with genetically high production potential show enhanced response. However, borderline statistical significance argues for considerable further examination before drawing firm conclusions.

Animals↗
PubMed1984

Stable versus partial response in advanced prostate cancer.

Stable response to therapy in patients with advanced prostate cancer, as experienced in clinical trials of the National Prostatic Cancer Project (NPCP), has been reexamined. Data from ten complete trials totaling over 1,300 patients have been examined for survival patterns within categories of response to therapy. Survival patterns, both for all patients and for those alive at 12 weeks, were significantly poorer for patients categorized as progressors after 12 weeks on treatment than for those categorized as stable or as partial regressions. Furthermore, comparisons of survival patterns for those patients categorized as stable or partial regression revealed no statistically significant differences between them. The similarity of survival for the stable and partial regression categories indicates that the stable category represents more than a segment of the population with slowly progressing disease and can be taken as an indicator of response to therapy.

Adult↗
PubMed1984

Linear regression analysis with repeated measurements.

The statistical aspects of repeated measures linear regression, in which each subject contributes several pairs of measurements to the analysis, are discussed. It is shown that the standard error of a regression coefficient computed from the ordinary least squares analysis can either underestimate or overestimate the true standard error, depending on how values of the independent variable are selected. The application of generalized least squares analysis to repeated measures data is also discussed. Two examples are given.

Adolescent↗
PubMed2006

The predictive value of field versus arrival Glasgow Coma Scale score and TRISS calculations in moderate-to-severe traumatic brain injury.

BACKGROUND: Glasgow Coma Scale (GCS) scores are widely used to quantify level of consciousness in the prehospital environment. The predictive value of field versus arrival GCS is not well defined but has tremendous implications with regard to triage and therapeutic decisions as well as the use of various predictive scoring systems, such as Trauma Score and Injury Severity Score (TRISS). This study explores the predictive value of field GCS (fGCS) and arrival GCS (aGCS) as well as TRISS calculations using field (fTRISS) and arrival (aTRISS) data in patients with moderate-to-severe traumatic brain injury (TBI). METHODS: Major trauma victims with head Abbreviated Injury Scores of 3 or greater were identified from our county trauma registry over a 16-year period. The predictive ability of fGCS with regard to aGCS was explored using univariate statistics and linear regression modeling. The difference between aGCS and fGCS was also modeled against mortality and the composite endpoint using logistic regression, adjusting for fGCS. The predictive value of preadmission GCS (pGCS), defined as either fGCS or aGCS in nonintubated patients without a documented fGCS, with regard to mortality and a composite endpoint representing the need for neurosurgical care (death, craniotomy, invasive intracranial pressure monitoring, or intensive care unit care >48 hours) was determined using receiver-operator curve (ROC) analysis. Finally, fTRISS and aTRISS predicted survival values were compared with each other and to observed survival. RESULTS: A total of 12,882 patients were included. Mean values for fGCS and aGCS were similar (11.4 and 11.5, respectively, p = 0.336), and a strong correlation (r = 0.67, 95% CI 0.66-0.69, p < 0.0001) was observed between them. The difference between fGCS and aGCS was also predictive of outcome after adjusting for fGCS. Good predictive ability was observed for pGCS with regard to both mortality and neurosurgical intervention. Both fTRISS and aTRISS predicted survival values were nearly identical to observed survival. Observed and fTRISS predicted survival were nearly identical in patients undergoing prehospital intubation CONCLUSIONS: Values for fGCS are highly predictive of aGCS, and both are associated with outcome from TBI. A change in GCS from the field to arrival is highly predictive of outcome. The use of field data for TRISS calculations appears to be a valid methodological approach, even in severely injured TBI patients undergoing prehospital intubation.

Brain Injuries↗
PubMed1992

A comparison of differential white cell counting on the Coulter VCS and the Technicon H1 using simple and multiple regression analysis.

This study uses the statistical methods of simple and multiple regression to compare the differential white blood count on the Coulter VCS and Technicon H1 analysers. The results demonstrate that both are good at distinguishing lymphocytes, neutrophils and eosinophils. Monocyte differential counts show disappointing correlation, both by simple and multiple regression techniques. Basophils, though less frequently a clinical problem, also correlated poorly in this study.

Basophils↗
PubMed1994

An evaluation of three methods for determining colloid osmotic pressure.

Plasma colloid osmotic pressure (COP) is an important determinant in edema formation. Three methods for assessing the COP were evaluated. Direct measurement of COP using the 4420 Wescor Colloid Osmometer was compared to the estimation of COP from both serum total protein and total serum solids (TSS) determinations. Blood samples from twenty adult patients (mean age = 64 years) undergoing cardiopulmonary bypass surgery were collected for COP assessment. Sample collection was performed prior to heparinization/hemodilution, during hypothermic bypass and at the conclusion of bypass following protamine administration. The results obtained from each method were analyzed by a two-way analysis of variance. The Bonferroni technique was used for comparison of sample means when the difference was significant (p less than 0.05). Correlations were reported by linear regression analysis. A statistically significant difference (p less than 0.01) was found between the three methods. A regression equation for the estimation of COP from total serum solids is offered: COP = (3.02 * TSS) + 0.65. Prospective clinical testing between the direct COP measurement and the estimation of COP from TSS using the equation (n = 38) revealed a significant correlation (R2 = .932) and no significant difference between the two (p greater than 0.05).

Albumins↗
PubMed2001

The role of primary school teachers in HIV prevention in South Africa.

South Africa has the fastest growing HIV epidemic in the world. The need for an intensive campaign against its spread cannot be overemphasised. Such efforts may be particularly effective if introduced prior to the onset of risk behaviour. The purpose of this study was to investigate the knowledge of grade 3 and 4 schoolteachers on HIV/AIDS and their opinion on educating their pupils about HIV prevention. A self-administered questionnaire with knowledge, perception and sociodemographic variables was sent to all 120 grade 3 and 4 teachers in the Southern Bushveld district of Northern Province. Descriptive statistics and multiple regression analysis were used to analyse the data. The response rate was 67% (N = 81) and 87.7% were females. The mean age of the respondents was 37.7 (+/- 8.7 SD) years, 55% had a 3-year teacher's training qualification and 27% had a 4-year training qualification. The average teaching experience was 12 years. Most respondents (93.8%) had knowledge of what HIV/AIDS is, but only 85.2% indicated it could be prevented. 14.8% either did not know HIV/AIDS could be prevented or were not sure. Some teachers had an incomplete understanding of the transmission and prevention of HIV/AIDS. Furthermore only 9% mentioned education as a way to prevent HIV/AIDS and 16% abstinence. Of the respondents, 58% indicated teaching HIV prevention to their pupils. Of those who do not teach HIV prevention, 41.2% believed that the pupils were too young, and 20.6% claimed non-availability of guidelines and resources as reasons for not teaching. A significant negative correlation was found between level of qualification and teaching of HIV to pupils (p < 0.05). In conclusion, many primary school teachers were found to be wanting in their HIV/AIDS knowledge. This suggests that the schoolteachers would need to be adequately trained prior to their involvement in HIV/AIDS education to pupils. Grade 3 and 4 teachers may be considered suitable to provide HIV education to their pupils, but there is a need for structured educational programmes they can follow. This study also suggests that teachers were not aware of the Department of Education's HIV policy of providing age-appropriate education to all pupils.

Acquired Immunodeficiency Syndrome↗
PubMed1981

Regional mobility in Greece: a statistical analysis of the phenomenon.

The author uses regression models and census data to examine social and economic factors influencing the migration of the rural population in Greece. "The basic conclusion...is that the mobility of the rural population is mainly affected by the trend of individuals to work in non-agricultural sectors where work becomes more productive. Equally important is the influence of the more general trend of the population to migrate and the special characteristics of the population in some regions near the frontiers." (SUMMARY IN FRE)

Demography↗
PubMed2005

Secure analysis of distributed chemical databases without data integration.

We present a method for performing statistically valid linear regressions on the union of distributed chemical databases that preserves confidentiality of those databases. The method employs secure multi-party computation to share local sufficient statistics necessary to compute least squares estimators of regression coefficients, error variances and other quantities of interest. We illustrate our method with an example containing four companies' rather different databases.

Algorithms↗
PubMed1987

A correlation and path coefficient analysis of components of calciuria in normal subjects and idiopathic stone formers.

The composition of 24 h urine samples collected by 50 normal controls and 76 stone formers (30 hypercalciurics, 13 hyperuricosurics and 33 patients without metabolic abnormalities) were studied. Statistically significant multiple regression equations were obtained between calciuria and the urinary excretions of sulfate, citrate, sodium and creatinine. The three former ions were selected as variables because they were assumed to affect the tubular fluid concentration of ionized calcium and interfere with the reabsorption of calcium. Urinary creatinine was included because it increased the statistical significance of the multiple regression equations; it is assumed to be a function of body size. The regression equations differed between both groups of subjects because stone formers excreted significantly more sulfate and less citrate than controls. The four factors considered (sulfate, citrate, sodium and creatinine) account for 28.3, 6.8, 7.3 and 26.4% of the total variation of calciuria of normal controls and 45.0, 2.6, 8.6 and 14.7%, respectively, for stone formers.

Adult↗
PubMed1994

Antipsychotic medication and suicide risk among schizophrenic and paranoid inpatients. A controlled retrospective study.

A retrospective analysis of the psychotrophic medication, illness history and recent mental symptoms of 28 schizophrenic or paranoid inpatients who had committed suicide and the same number of matched control subjects was carried out. The groups were first compared separately for every variable, and 6 statistically most significant variables in the paired comparisons were then entered into a stepwise linear logistic regression model. Four statistically significant differences between the groups were found with the paired comparisons. The suicide group had more often previous suicide attempts, lower neuroleptic doses, more depressive symptoms and less positive schizophrenic symptoms compared to their controls. The results of the regression analysis suggested that the lower neuroleptic doses in the suicide group were more probably a consequence of the differences in the symptom profile than in a direct causal relationship to the suicides per se.

Adult↗
PubMed1999

Statistics of sexual size dimorphism.

In comparative studies of sexual size dimorphism (SSD), the methods used to quantify dimorphism are controversial. SSD is commonly expressed as a ratio between species mean values of males and females, such as M/F or (M-F)/([M+F]/2), but a number of investigators have suggested that ratios should not be used, mainly because their distributions usually violate the assumptions of parametric statistical tests, or because they lead to spurious relationships that invalidate the interpretation and statistical significance of regressions and correlations. As an alternative to ratios, the comparative study of SSD can be conducted by a combination of regression with sex-specific data and residuals from this regression. Twenty-five data sets were selected from the literature and used to duplicate a variety of statistical procedures commonly employed in studies of SSD. All analyses were repeated with five different ratios and with methods that avoid the calculation of any ratios. These data and a review of the statistical properties of ratios and residuals indicate that: (1) most of the ratios used in the SSD literature are unnecessary, and several commonly used ratios are statistically inferior to others. Only two ratios are needed, one on a logarithmic scale and one on a linear scale; (2) there is no problem with spurious correlation or non-normality when ratios are used in several types of statistical procedures commonly employed in studies of SSD; (3) residuals cannot replace ratios for the evaluation of many questions regarding the pattern of SSD among species; and (4) residuals usually are used incorrectly, leading to misspecified regression equations. Most of the questions for which residuals are used should be addressed by multiple regression. These results apply to studies using comparative methods with or without adjustments for phylogenetic effects.

Animals↗
PubMed2002

Private schools and "Latino flight" from black schoolchildren.

Several recent studies provided evidence that white students' choice between private and public schools is influenced by the racial composition of the local student population. None of these studies, however, examined whether Latinos are also fleeing to private schools in response to black schoolchildren. I explore the "Latino-flight" hypothesis using data from the National Educational Longitudinal Study and a recently released confidential data set from the National Center for Educational Statistics. In probit regressions for the probability of Latinos attending private schools, I found a large, positive, and statistically significant coefficient on the black share of the school-age population. The coefficient estimates imply that a 10-percentage point increase in the black share increases the probability of private school attendance by 25.7% to 33.2% among Latino 8th graders and 35.2% to 52.2% among Latino 10th graders. I interpret these results as providing evidence of "Latino flight" from public schools into private schools. I did not find evidence that Latinos respond differently to black schoolchildren than do whites.

Adolescent↗
PubMedDate not supplied

Correlation between objective and subjective assessments of nasal patency.

The correlation between the subjective sensation of nasal patency and nasal resistance (NR) to airflow was examined in a large population. The subjective estimation was assessed by a visual analogue scale and the NR by active anterior rhinomanometry in 158 subjects. Evaluation and statistical analysis--including correlation and regression analysis--were computerized. A statistically significant correlation was found between the subjective and objective values (r = -0.301, p < 0.001). There was no correlation between the parameters if the groups with or without nasal obstruction were evaluated apart. In 84% of the cases, the narrower side of the nose was identified with both the objective and the subjective methods. Statistically significant correlations were exhibited between the subjective and the objective measures if unilateral NR and the ipsilateral subjective values were related to each other (n = 316, r = -0.476, p < 0.001), in both cases, on the side of the higher and the lower NR. The best correlation was found on the side of the higher NR, that is when nasal breathing is more impeded. Subjective estimation seems to be sufficient only to indicate the more obstructed side of the nose independently from the dimensions of the NR values.

Adult↗
PubMed2002

The relationship between self-reported and clinical measures and the number of days to return to sport following acute lateral ankle sprains.

STUDY DESIGN: This is a prospective observational study. OBJECTIVE: To determine the relationship of self-reported and clinical measures to the number of days to return to sport following acute lateral ankle sprains. BACKGROUND: In order to direct rehabilitation, injury classification schemes should include self-reported and clinical measures that help prognosticate the number of days to return to sport (DAYS). METHODS AND MEASURES: Twenty Division II college athletes (7 men, 13 women; mean age = 19.2 +/- 1.1 years) were assessed following an acute lateral ankle sprain and upon return to sport. Athletes were assessed by three self-reported measures: global function question, Short Form-36 Physical Function scale (SF36PF), visual analog pain scale, and four clinical measures: ankle active range of motion (AROM), ankle dorsiflexion strength, ankle plantar flexion strength, ambulation status. Simple regression, multiple regression, and effect sizes (ES) were used to analyze these data. RESULTS: The simple regression revealed a statistically significant relationship between DAYS and the global function question (r2 = .22), the SF36PF (r2 = .28), and the patient's ambulation status (r2 = .27). A multiple regression using these three variables in combination was also statistically significant (P = .015) and explained approximately one-third of the variance in DAYS, (r2 = .37). All dependent variables revealed large or moderate ES. CONCLUSION: Self-reported functional measures in conjunction with the athlete's ambulation status are important factors in predicting the number of days to return to sport following acute lateral ankle sprains. Further research using large sample sizes and other clinical and functional measures is necessary.

Acute Disease↗