Logistic regression analysis of potential prognostic factors for pulmonary thromboembolism

Objective: To identify potential prognostic factors for pulmonary thromboembolism (PTE), establishing a mathematical model to predict the risk for fatal PTE and nonfatal PTE.Method: the reports on 4,813 consecutive autopsies performed from 1979 to 1998 in a Brazilian tertiary referral medical school were reviewed for a retrospective study. From the medical records and autopsy reports of the 512 patients found with macroscopically and/or microscopically,documented PTE, data on demographics, underlying diseases, and probable PTE site of origin were gathered and studied by multiple logistic regression. Thereafter, the jackknife method, a statistical cross-validation technique that uses the original study patients to validate a clinical prediction rule, was performed.Results: the autopsy rate was 50.2%, and PTE prevalence was 10.6%. In 212 cases, PTE was the main cause of death (fatal PTE). The independent variables selected by the regression significance criteria that were more likely to be associated with fatal PTE were age (odds ratio [OR], 1.02; 95% confidence interval [CI], 1.00 to 1.03), trauma (OR, 8.5; 95% CI, 2.20 to 32.81), right-sided cardiac thrombi (OR, 1.96; 95% CI, 1.02 to 3.77), pelvic vein thrombi (OR, 3.46; 95% CI, 1.19 to 10.05); those most likely to be associated with nonfatal PTE were systemic arterial hypertension (OR, 0.51; 95% CI, 0.33 to 0.80), pneumonia (OR, 0.46; 95% CI, 0.30 to 0.71), and sepsis (OR, 0.16; 95% CI, 0.06 to 0.40). The results obtained from the application of the equation in the 512 cases studied using logistic regression analysis suggest the range in which logit p > 0.336 favors the occurrence of fatal PTE, logit p < - 1.142 favors nonfatal PTE, and logit P with intermediate values is not conclusive. The cross-validation prediction misclassification rate was 25.6%, meaning that the prediction equation correctly classified the majority of the cases (74.4%).Conclusions: Although the usefulness of this method in everyday medical practice needs to be confirmed by a prospective study, for the time being our results suggest that concerning prevention, diagnosis, and treatment of PTE, strict attention should be given to those patients presenting the variables that are significant in the logistic regression model.

POLYCHOTOMOUS LOGISTIC REGRESSION ANALYSIS (HYPERTENSION, CORONARY HEART DISEASE)

The history of the logistic function since its introduction in 1838 is reviewed, and the logistic model for a polychotomous response variable is presented with a discussion of the assumptions involved in its derivation and use. Following this, the maximum likelihood estimators for the model parameters are derived along with a Newton-Raphson iterative procedure for evaluation. A rigorous mathematical derivation of the limiting distribution of the maximum likelihood estimators is then presented using a characteristic function approach. An appendix with theorems on the asymptotic normality of sample sums when the observations are not identically distributed, with proofs, supports the presentation on asymptotic properties of the maximum likelihood estimators. Finally, two applications of the model are presented using data from the Hypertension Detection and Follow-up Program, a prospective, population-based, randomized trial of treatment for hypertension. The first application compares the risk of five-year mortality from cardiovascular causes with that from noncardiovascular causes; the second application compares risk factors for fatal or nonfatal coronary heart disease with those for fatal or nonfatal stroke. ^

Distribution of ABCB1 polymorphisms among Brazilians: impact of population admixture

Introduction: Interethnic admixture is a source of cryptic population structure that may lead to spurious genotype-phenotype associations in pharmacogenomic studies. We studied the impact of population stratification on the distribution of ABCB1 polymorphisms (1236C > T, 2677G > T/A and 3435C > T) among Brazilians, a highly admixed population with Amerindian, European and African ancestral roots. Methods: Individual DNA from 320 healthy adults was genotyped with a panel of ancestry informative markers, and the proportions of African component of ancestry (ACA) were estimated. ABCB1 genotypes were determined by the single base extension/termination method. We describe the association between ABCB1 polymorphisms and ACA by fitting a linear proportional odds logistic regression model to the data. Results: The distribution of the ABCB1 2677G > T/A and 3435C > T, but not the 1236C > T, SNPs displayed a significant trend for decreasing frequency of the T alleles and TT genotypes from White to Intermediate to Black individuals. The same trend was observed in the frequency of the T/nonG/T haplotype at the 1236, 2677 and 3435 loci. When the population sample was proportioned in quartiles, according to the individual ACA estimates, the frequency of the T allele and TT genotype at each locus declined progressively from the lowest (< 0.25 ACA) to the highest (> 0.75 ACA) quartile. Linear proportional odds logistic regression analysis confirmed that the odds of having the T allele at each locus decreases in a continuous manner with the increase of the ACA, throughout the ACA range (0.13-0.94) observed in the overall population sample. A significant association was also detected between the individual ACA estimates and the presence of the T/nonG/T haplotype in the overall population. Conclusion: Self-identification according to the racial/color categories proposed by the Brazilian Census is insufficient to properly control for population stratification in pharmacogenomic studies of ABCB1.

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.

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Logistic regression models for ordinal response: A study of self-efficacy in colorectal cancer screening

The ordinal logistic regression models are used to analyze the dependant variable with multiple outcomes that can be ranked, but have been underutilized. In this study, we describe four logistic regression models for analyzing the ordinal response variable. ^ In this methodological study, the four regression models are proposed. The first model uses the multinomial logistic model. The second is adjacent-category logit model. The third is the proportional odds model and the fourth model is the continuation-ratio model. We illustrate and compare the fit of these models using data from the survey designed by the University of Texas, School of Public Health research project PCCaSO (Promoting Colon Cancer Screening in people 50 and Over), to study the patient’s confidence in the completion colorectal cancer screening (CRCS). ^ The purpose of this study is two fold: first, to provide a synthesized review of models for analyzing data with ordinal response, and second, to evaluate their usefulness in epidemiological research, with particular emphasis on model formulation, interpretation of model coefficients, and their implications. Four ordinal logistic models that are used in this study include (1) Multinomial logistic model, (2) Adjacent-category logistic model [9], (3) Continuation-ratio logistic model [10], (4) Proportional logistic model [11]. We recommend that the analyst performs (1) goodness-of-fit tests, (2) sensitivity analysis by fitting and comparing different models.^

Application of logistic regression for fault analysis in an industrial printing process

A statistical technique for fault analysis in industrial printing is reported. The method specifically deals with binary data, for which the results of the production process fall into two categories, rejected or accepted. The method is referred to as logistic regression, and is capable of predicting future fault occurrences by the analysis of current measurements from machine parts sensors. Individual analysis of each type of fault can determine which parts of the plant have a significant influence on the occurrence of such faults; it is also possible to infer which measurable process parameters have no significant influence on the generation of these faults. Information derived from the analysis can be helpful in the operator's interpretation of the current state of the plant. Appropriate actions may then be taken to prevent potential faults from occurring. The algorithm is being implemented as part of an applied self-learning expert system.

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

Logistic Regression in Modelling Data for CVC - Related Infection

2000 Mathematics Subject Classification: 62J12, 62P10.

A hybrid approach to combining CART and logistic regression for stock ranking

The benefits of applying tree-based methods to the purpose of modelling financial assets as opposed to linear factor analysis are increasingly being understood by market practitioners. Tree-based models such as CART (classification and regression trees) are particularly well suited to analysing stock market data which is noisy and often contains non-linear relationships and high-order interactions. CART was originally developed in the 1980s by medical researchers disheartened by the stringent assumptions applied by traditional regression analysis (Brieman et al. [1984]). In the intervening years, CART has been successfully applied to many areas of finance such as the classification of financial distress of firms (see Frydman, Altman and Kao [1985]), asset allocation (see Sorensen, Mezrich and Miller [1996]), equity style timing (see Kao and Shumaker [1999]) and stock selection (see Sorensen, Miller and Ooi [2000])...

Aspirin therapy in patients with acute respiratory distress syndrome (ARDS) is associated with reduced intensive care unit mortality: a prospective analysis

INTRODUCTION: Acute respiratory distress syndrome (ARDS) is a common clinical syndrome with high mortality and long-term morbidity. To date there is no effective pharmacological therapy. Aspirin therapy has recently been shown to reduce the risk of developing ARDS, but the effect of aspirin on established ARDS is unknown.

METHODS: In a single large regional medical and surgical ICU between December 2010 and July 2012, all patients with ARDS were prospectively identified and demographic, clinical, and laboratory variables were recorded retrospectively. Aspirin usage, both pre-hospital and during intensive care unit (ICU) stay, was included. The primary outcome was ICU mortality. We used univariate and multivariate logistic regression analyses to assess the impact of these variables on ICU mortality.

RESULTS: In total, 202 patients with ARDS were included; 56 (28%) of these received aspirin either pre-hospital, in the ICU, or both. Using multivariate logistic regression analysis, aspirin therapy, given either before or during hospital stay, was associated with a reduction in ICU mortality (odds ratio (OR) 0.38 (0.15 to 0.96) P = 0.04). Additional factors that predicted ICU mortality for patients with ARDS were vasopressor use (OR 2.09 (1.05 to 4.18) P = 0.04) and APACHE II score (OR 1.07 (1.02 to 1.13) P = 0.01). There was no effect upon ICU length of stay or hospital mortality.

CONCLUSION: Aspirin therapy was associated with a reduced risk of ICU mortality. These data are the first to demonstrate a potential protective role for aspirin in patients with ARDS. Clinical trials to evaluate the role of aspirin as a pharmacological intervention for ARDS are needed.

Impact of job insecurity on sexual desire: an exploratory analysis.

To explore, for the first time, the impact of job insecurity on sexual desire. Cross-sectional analysis of a nationally representative sample of 7247 individuals aged 20-64 years working as full or part-time employees in Switzerland. The logistic regression analysis showed that workers aged 20-49 years perceiving high levels of job insecurity are exposed to a significantly higher risk of decrease of sexual desire compared to the reference group. The risk is 53% higher among men (OR 1.53; 95% CI 1.16-2.01) and 47% for woman (OR 1.47; 1.13-1.91). No increased risk was found for employees aged 50-64 years old. An increasing fear of job loss is associated with a deterioration in sexual desire. These first preliminary findings should promote further epidemiological and clinical prospective studies on the impact of job insecurity on intimate relationships and sexual dysfunction.

Ambulance call triage outcomes for patients reporting pain : a retrospective cross-sectional analysis of pain score versus traige level

Objective: To identify any association between the response priority code generated during calls to the ambulance communication centre and patient reports of pain severity.

Methods: A retrospective analysis of patient care records was undertaken for all patients transported by paramedics over a 7-day period. The primary research interest was the association between the response code allocated at the time of telephone triage and the initial pain severity score recorded using a numeric rating scale (NRS). Univariate and multivariate logistic regression methods were used to analyse the association between the response priority variable and explanatory variables.

Results: There were 1246 cases in which both an initial pain score using the NRS and a response code were recorded. Of these cases, 716/1246 (57.5%) were associated with a code 1 ("time-critical") response. After adjusting for gender, age, cause of pain and duration of pain, a multivariate logistic regression analysis found no significant change in the odds of a patient in pain receiving a time-critical response compared with patients who had no pain, regardless of their initial pain score (NRS 1–3, odds ratio (OR) 1.11, 95% CI 0.7 to 1.8; NRS 4–7, OR 1.12, 95% CI 0.7 to 1.8; NRS 8–10, OR 0.84, 95% CI 0.5 to 1.4).

Conclusion: The severity of pain experienced by the patient appeared to have no influence on the priority (urgency) of the dispatch response. Triage systems used to prioritise ambulance calls and decide the urgency of response or type of referral options should consider pain severity to facilitate timely and humane care.

Role of dietary pattern analysis in determining cognitive status in elderly Australian adults

Principal Component Analysis (PCA) was used to determine the association between dietary patterns and cognitive function and to examine how classification systems based on food groups and food items affect levels of association between diet and cognitive function. The present study focuses on the older segment of the Australian Diabetes, Obesity and Lifestyle Study (AusDiab) sample (age 60+) that completed the food frequency questionnaire at Wave 1 (1999/2000) and the mini-mental state examination and tests of memory, verbal ability and processing speed at Wave 3 (2012). Three methods were used in order to classify these foods before applying PCA. In the first instance, the 101 individual food items asked about in the questionnaire were used (no categorisation). In the second and third instances, foods were combined and reduced to 32 and 20 food groups, respectively, based on nutrient content and culinary usage—a method employed in several other published studies for PCA. Logistic regression analysis and generalized linear modelling was used to analyse the relationship between PCA-derived dietary patterns and cognitive outcome. Broader food group classifications resulted in a greater proportion of food use variance in the sample being explained (use of 101 individual foods explained 23.22% of total food use, while use of 32 and 20 food groups explained 29.74% and 30.74% of total variance in food use in the sample, respectively). Three dietary patterns were found to be associated with decreased odds of cognitive impairment (CI). Dietary patterns derived from 101 individual food items showed that for every one unit increase in ((Fruit and Vegetable Pattern: p = 0.030, OR 1.061, confidence interval: 1.006–1.118); (Fish, Legumes and Vegetable Pattern: p = 0.040, OR 1.032, confidence interval: 1.001–1.064); (Dairy, Cereal and Eggs Pattern: p = 0.003, OR 1.020, confidence interval: 1.007–1.033)), the odds of cognitive impairment decreased. Different results were observed when the effect of dietary patterns on memory, processing speed and vocabulary were examined. Complex patterns of associations between dietary factors and cognition were evident, with the most consistent finding being the protective effects of high vegetable and plant-based food item consumption and negative effects of ‘Western’ patterns on cognition. Further long-term studies and investigation of the best methods for dietary measurement are needed to better understand diet-disease relationships in this age group.

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.