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.^

Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^

Predicting childhood sexual or physical abuse: a logistic regression geo-mapping approach to prevention.

This study investigates the degree to which gender, ethnicity, relationship to perpetrator, and geomapped socio-economic factors significantly predict the incidence of childhood sexual abuse, physical abuse and non- abuse. These variables are then linked to geographic identifiers using geographic information system (GIS) technology to develop a geo-mapping framework for child sexual and physical abuse prevention.

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 with incompletely observed binary

Logistic regression is one of the most important tools in the analysis of epidemiological and clinical data. Such data often contain missing values for one or more variables. Common practice is to eliminate all individuals for whom any information is missing. This deletion approach does not make efficient use of available information and often introduces bias.^ Two methods were developed to estimate logistic regression coefficients for mixed dichotomous and continuous covariates including partially observed binary covariates. The data were assumed missing at random (MAR). One method (PD) used predictive distribution as weight to calculate the average of the logistic regressions performing on all possible values of missing observations, and the second method (RS) used a variant of resampling technique. Additional seven methods were compared with these two approaches in a simulation study. They are: (1) Analysis based on only the complete cases, (2) Substituting the mean of the observed values for the missing value, (3) An imputation technique based on the proportions of observed data, (4) Regressing the partially observed covariates on the remaining continuous covariates, (5) Regressing the partially observed covariates on the remaining continuous covariates conditional on response variable, (6) Regressing the partially observed covariates on the remaining continuous covariates and response variable, and (7) EM algorithm. Both proposed methods showed smaller standard errors (s.e.) for the coefficient involving the partially observed covariate and for the other coefficients as well. However, both methods, especially PD, are computationally demanding; thus for analysis of large data sets with partially observed covariates, further refinement of these approaches is needed. ^

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. ^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Adiposity and the perilipin gene: The role of single locus and multilocus variation, obesity-related quantitative traits, and disease-related phenotypes in the Atherosclerosis Risk in Communities (ARIC) study

Obesity is a complex multifactorial disease and is a public health priority. Perilipin coats the surface of lipid droplets in adipocytes and is believed to stabilize these lipid bodies by protecting triglyceride from early lipolysis. This research project evaluated the association between genetic variation within the human perilipin (PLIN) gene and obesity-related quantitative traits and disease-related phenotypes in Non-Hispanic White (NHW) and African American (AA) participants from the Atherosclerosis Risk in Communities (ARIC) Study. ^ Multivariate linear regression, multivariate logistic regression, and Cox proportional hazards models evaluated the association between single gene variants (rs2304794, rs894160, rs8179071, and rs2304795) and multilocus variation (rs894160 and rs2304795) within the PLIN gene and both obesity-related quantitative traits (body weight, body mass index [BMI], waist girth, waist-to-hip ratio [WHR], estimated percent body fat, and plasma total triglycerides) and disease-related phenotypes (prevalent obesity, metabolic syndrome [MetS], prevalent coronary heart disease [CHD], and incident CHD). Single variant analyses were stratified by race and gender within race while multilocus analyses were stratified by race. ^ Single variant analyses revealed that rs2304794 and rs894160 were significantly related to plasma triglyceride levels in all NHWs and NHW women. Among AA women, variant rs8179071 was associated with triglyceride levels and rs2304794 was associated with risk-raising waist circumference (>0.8 in women). The multilocus effects of variants rs894160 and rs2304795 were significantly associated with body weight, waist girth, WHR, estimated percent body fat, class II obesity (BMI ≥ 35 kg/m2), class III obesity (BMI ≥ 35 kg/m2), and risk-raising WHR (>0.9 in men and >0.8 in women) in AAs. Variant rs2304795 was significantly related to prevalent MetS among AA males and prevalent CHD in NHW women; multilocus effects of the PLIN gene were associated with prevalent CHD among NHWs. Rs2304794 was associated with incident CHD in the absence of the MetS among AAs. These findings support the hypothesis that variation within the PLIN gene influences obesity-related traits and disease-related phenotypes. ^ Understanding these effects of the PLIN genotype on the development of obesity can potentially lead to tailored health promotion interventions that are more effective. ^

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. ^

Ethnic differences in adolescents' mental distress

Objectives. The aims of this cross-sectional study were to (1) examine differences among four ethnic groups of middle school students (Anglos, African Americans [AAs], Hispanics, and Asians) on (a) three indicators of mental distress (depression, somatic symptoms, suicidal ideation) (b) social stress (general social stress, process-oriented stress, discrimination) and resources (family relationships, coping, self-esteem) and (2) identify significant risk factors and resources for each ethnic group by examining the moderating effects of ethnicity. ^ Methods. Respondents included 316 students from three schools (144 Anglos, 66 AAs, 77 Hispanics, 29 Asians/Others) who completed self-administered questionnaires. Social stress and somatic symptoms were measured by using the SAFE-C and Somatic Symptom Scale, respectively. The DSD was used to assess depression and suicidal ideation. Resources were measured by using the FES, age-appropriate adaptations of two existing coping scales, and Rosenberg's Self-Esteem Scale. For specific aims, descriptive statistics, ANOVA, ANCOVA, and logistic regression analysis were used. ^ Findings. No statistically significant ethnic group or gender differences were observed in depression and somatic symptoms, but the odds of experiencing depression symptoms were about 9.7 times greater for Hispanic females than for the referent group, Anglo males. Hispanics were also 2.04 times more likely to have suicidal ideation than Anglos ( P < 0.05). AAs and Hispanics reported significantly higher levels of stress than Anglos (OR: 2.2–4.3, 0.00 ≤ P ≤ 0.03). These findings imply that adolescents in these ethnic groups may be exposed to considerable amounts of stress even if they do not exhibit significant symptoms of mental distress yet. Negative moderating effects for ethnicity were found by the significant interaction between ethnicity and social stress in somatic symptoms among AAs and Hispanics. This finding indicates that AA and Hispanic adolescents may require higher levels of social stress to exhibit the same amount of somatic symptoms as Anglo adolescents. Observed ethnic differences in social stress and interaction between social stress and ethnicity in relation to somatic symptoms demonstrated a need for subsequent longitudinal studies, and provided a rationale for incorporating social stress as a critical component not only in research but also in culturally sensitive prevention programs. ^

Breast cancer risk and heterocyclic amines and effect modification by NAT gene polymorphisms

Breast cancer is the most common cancer in women in the United States and is a leading cause of cancer-related deaths (1). Recently, dietary heterocyclic amines (HCAs) have been proposed to be a risk factor for breast cancer (2). This study uses the data collected for a case-control study conducted at the M.D. Anderson Cancer Center to assess the association between breast cancer risk and HCAs {2-amino-1-methyl-6-phenylimidazole [4,5-b] pyridine (PhIP), 2-amino-3,8-dimethylimidazo [4,5-f] quinoxaline (MeIQx), 2-amino-3,4,8-trimethylimidazo [4,5-f] quinoxaline (DiMeIQx) and mutagenicity of HCAs} and to examine if this association is modified by genetic polymorphisms of N-acetyl transferases (NAT1/NAT2). The NAT1/2 genotype was determined using Taqman technology. HCAs were estimated by using a meat preparation questionnaire on meat type, cooking method, and doneness, combined with a quantitative HCA database. Three hundred and fifty patients with breast cancer attending the Diagnostic Radiology Clinic at M. D. Anderson Cancer Center and fulfilling the eligibility criteria were compared to three hundred and fifty patients attending the same clinic for benign breast lesions to answer these questions. Logistic regression models were used to control for known risk factors and showed no statistically significant association between breast cancer versus benign breast cancer lesions and dietary intake of heterocyclic amines. There was no clear difference in their effect after subgroup analyses in different acetylator strata of NAT1/2 and no statistical interactions were found between NAT1/2 genotypes and HCAs, suggesting no effect modification by NAT1/2 acetylator status. These results suggest the need for further research to analyze if these null associations were because of the benign breast lesions sharing the risk factors with breast cancer or any other factors which haven't been explored yet.^

Lab animal allergy surveillance at a private medical school in three dissimilar animal research facilities

Very few studies have described MUP-1 concentrations and measured prevalence of Laboratory Animal Allergy (LAA) at such a diverse institution as the private medical school (MS) that is the focus of this study. Air sampling was performed in three dissimilar animal research facilities at MS and quantitated using a commercially available ELISA. Descriptive data was obtained from an anonymous laboratory animal allergy survey given to both animal facility employees and the researchers who utilize these facilities alike. Logistic regression analysis was then implemented to investigate specific factors that may be predictive of developing LAA as well as factors influencing the reporting of LAA symptoms to the occupational health program. Concentrations of MUP-1 detected ranged from below detectable levels (BDL) to a peak of 22.64 ng/m3 . Overall, 68 employees with symptoms claimed they improved while away from work and only 25 employees reported their symptoms to occupational health. Being Vietnamese, a smoker, not wearing a mask, and working in any facility longer than one year were all significant predictors of having LAA symptoms. This study suggests a LAA monitoring system that relies on self-reporting can be inadequate in estimating LAA problems. In addition, efforts need to be made to target training and educational materials for non-native English speaking employees to overcome language and cultural barriers and address their specific needs. ^

Determining appropriate measurement methods for etiological research of computing-related musculoskeletal symptoms and disorders

Two studies among college students were conducted to evaluate appropriate measurement methods for etiological research on computing-related upper extremity musculoskeletal disorders (UEMSDs). ^ A cross-sectional study among 100 graduate students evaluated the utility of symptoms surveys (a VAS scale and 5-point Likert scale) compared with two UEMSD clinical classification systems (Gerr and Moore protocols). The two symptom measures were highly concordant (Lin's rho = 0.54; Spearman's r = 0.72); the two clinical protocols were moderately concordant (Cohen's kappa = 0.50). Sensitivity and specificity, endorsed by Youden's J statistic, did not reveal much agreement between the symptoms surveys and clinical examinations. It cannot be concluded self-report symptoms surveys can be used as surrogate for clinical examinations. ^ A pilot repeated measures study conducted among 30 undergraduate students evaluated computing exposure measurement methods. Key findings are: temporal variations in symptoms, the odds of experiencing symptoms increased with every hour of computer use (adjOR = 1.1, p < .10) and every stretch break taken (adjOR = 1.3, p < .10). When measuring posture using the Computer Use Checklist, a positive association with symptoms was observed (adjOR = 1.3, p < 0.10), while measuring posture using a modified Rapid Upper Limb Assessment produced unexpected and inconsistent associations. The findings were inconclusive in identifying an appropriate posture assessment or superior conceptualization of computer use exposure. ^ A cross-sectional study of 166 graduate students evaluated the comparability of graduate students to College Computing & Health surveys administered to undergraduate students. Fifty-five percent reported computing-related pain and functional limitations. Years of computer use in graduate school and number of years in school where weekly computer use was ≥ 10 hours were associated with pain within an hour of computing in logistic regression analyses. The findings are consistent with current literature on both undergraduate and graduate students. ^

Household risk factors and the health and nutritional status of children in rural Honduras

During this cross-sectional study, both quantitative and qualitative research methods were used to elucidate the role that household environment and sanitation play in the nutritional status of children in a rural Honduran community. Anthropometric measurements were taken as measures of nutritional status among children under five years of age, while interviews regarding the household environment were conducted with their primary caregivers. Community participatory activities were conducted with primary caregivers, and results from water quality testing were analyzed for E. coli contamination. Anthropometric results were compared using the 1977 NCHS Growth Charts and the 2006 WHO Child Growth Standard to examine the implications of using the new WHO standard. The references showed generally good or excellent agreement between z-score categories, except among height-for-age classifications for males 24-35.9 months and weight-for-age classifications for males older than 24 months. Comparing the proportion of stunted, underweight, and wasted children, using the WHO standard generally resulted in higher proportions of stunting, lower underweight proportions, and higher overweight proportions. Logistic regression was used to determine which household and sanitation factors most influenced the growth of children. Results suggest only having water from a spring, stream, or other type of surface water as the primary source of drinking water is a significant risk factor for stunting. A protective association was seen between the household wealth index and stunting. Through participatory activities, the community provided insight on health issues important for improving child health. These activities yielded findings to be harnessed as a powerful resource to unify efforts for change. The qualitative findings were triangulated with the quantitative interview and water testing results to provide intervention recommendations for the community and its primary health care clinic. Recommendations include educating the community on best water consumption practices and encouraging the completion of at least some primary education for primary caregivers to improve child health. It is recommended that a community health worker program be developed to support and implement community interventions to improve water use and household sanitation behaviors and to encourage the involvement of the community in targeting and guiding successful interventions. ^

Sleep quality and quantity and associated factors among high school students from south Texas

Background. Insufficient and poor quality sleep among adolescents affects not only the cognitive functioning, but overall health of the individual. Existing research suggests that adolescents from varying ethnic groups exhibit differing sleep patterns. However, little research focuses on sleep patterns and associated factors (i.e. tobacco use, mental health indicators) among Hispanic youth. ^ Methods. The study population (n=2,536) included students in grades 9-12 who attended one of the three public high schools along the Texas-Mexico border in 2003. This was a cross sectional study using secondary data collected via a web-based, confidential, self-administered survey. Separate logistic regression models were estimated to identify factors associated with reduced (<9 hours/night) and poor quality sleep on average during weeknights. ^ Results. Of participants, 49.5% reported reduced sleep while 12.8% reported poor quality sleep. Factors significantly (p<0.05) associated with poor quality sleep were: often feeling stressed or anxious (OR=5.49), being born in Mexico (OR=0.65), using a computer/playing video games 15+ hours per week (OR=2.29), working (OR=1.37), being a current smoker (OR=2.16), and being a current alcohol user (OR=1.64). Factors significantly associated with reduced quantity of sleep were: often feeling stressed or anxious (OR=2.74), often having headaches/stomachaches (OR=1.77), being a current marijuana user (OR=1.70), being a current methamphetamine user (OR=4.92), and being a current alcohol user (OR=1.27). ^ Discussion. Previous research suggests that there are several factors that can influence sleep quality and quantity in adolescents. This paper discusses these factors (i.e. work, smoking, alcohol, etc.) found to be associated with poor sleep quality and reduced sleep quantity in the Hispanic adolescent population. A reduced quantity of sleep (81.20% of the participants) and a poor quality of sleep (12.80% of the participants) were also found in high school students from South Texas. ^