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.

Development of a Bayesian Joint Logistic Model to Better Study the Association between Haplotypes and Disease

In 2011, there will be an estimated 1,596,670 new cancer cases and 571,950 cancer-related deaths in the US. With the ever-increasing applications of cancer genetics in epidemiology, there is great potential to identify genetic risk factors that would help identify individuals with increased genetic susceptibility to cancer, which could be used to develop interventions or targeted therapies that could hopefully reduce cancer risk and mortality. In this dissertation, I propose to develop a new statistical method to evaluate the role of haplotypes in cancer susceptibility and development. This model will be flexible enough to handle not only haplotypes of any size, but also a variety of covariates. I will then apply this method to three cancer-related data sets (Hodgkin Disease, Glioma, and Lung Cancer). I hypothesize that there is substantial improvement in the estimation of association between haplotypes and disease, with the use of a Bayesian mathematical method to infer haplotypes that uses prior information from known genetics sources. Analysis based on haplotypes using information from publically available genetic sources generally show increased odds ratios and smaller p-values in both the Hodgkin, Glioma, and Lung data sets. For instance, the Bayesian Joint Logistic Model (BJLM) inferred haplotype TC had a substantially higher estimated effect size (OR=12.16, 95% CI = 2.47-90.1 vs. 9.24, 95% CI = 1.81-47.2) and more significant p-value (0.00044 vs. 0.008) for Hodgkin Disease compared to a traditional logistic regression approach. Also, the effect sizes of haplotypes modeled with recessive genetic effects were higher (and had more significant p-values) when analyzed with the BJLM. Full genetic models with haplotype information developed with the BJLM resulted in significantly higher discriminatory power and a significantly higher Net Reclassification Index compared to those developed with haplo.stats for lung cancer. Future analysis for this work could be to incorporate the 1000 Genomes project, which offers a larger selection of SNPs can be incorporated into the information from known genetic sources as well. Other future analysis include testing non-binary outcomes, like the levels of biomarkers that are present in lung cancer (NNK), and extending this analysis to full GWAS studies.

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.^

Relevant drug to drug interactions between itraconazole and non-nucleoside reverse transcriptase inhibitors in HIV-infected patients on maintenance therapy for disseminated histoplasmosis

Objective. Itraconazole is recommended life-long for preventing relapse of disseminated histoplasmosis in HIV-infected patients. I sought to determine if serum itraconazole levels are affected by the type of Highly Active Anti-Retroviral Therapy (NNRTI or PI) being taken concomitantly to treat HIV. ^ Design. Retrospective cohort. ^ Methods. De-identified data were used from an IRB-approved parent study which identified patients on HAART and maintenance itraconazole for confirmed disseminated histoplasmosis between January 2003 and December 2006. Available itraconazole blood levels were abstracted as well as medications taken by each patient at the time of the blood tests. Mean itraconazole levels were compared using the student's t-test. ^ Results. 11 patients met study criteria. Patient characteristics were: median age 36, 91% men, 18% white, 18% black, 55% Hispanic and 9% Asians, median CD4 cell count 120 cells/mm3. 14 blood levels were available for analysis—8 on PI, 4 on NNRTI and 2 on both. 8/8 itraconazole levels obtained while taking concomitant PI were therapeutic (>0.4 μg/mL) in contrast to 0/4 obtained while taking NNRTI. Two patients switched from NNRTI to PI and reached therapeutic levels. Mean levels on NNRTI (0.05 μg/mL, s.d. 0.0) and on PI (2.45 μg/mL, s.d. 0.21) for these two patients were compared via a paired t-test (t = 16.00, d.f. = 1, P = 0.04). Remaining patient levels were compared using an unpaired t-test. Mean itraconazole on concomitant PI (n = 6) was 1.37 μg/mL (s.d. 0.74), while the mean on concomitant NNRTI was 0.05 μg/mL (s.d. 0.0), t = 2.39, d.f. = 6, P = 0.05. ^ Conclusions. Co-administration of NNRTI and itraconazole results in significant decreases in itraconazole blood levels, likely by inducing the CYP3A4 enzyme system. Itraconazole drug levels should be monitored in patients on concomitant NNRTI. PI-based HAART may be preferred over NNRTI-based HAART when using itraconazole to treat HIV-infected patients with disseminated histoplasmosis. ^

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. ^

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.^

Longitudinal and logistic analysis of endocrine hormone profiles, physical maturation, and candidate genes related to pubertal events in children

Children who experience early pubertal development have an increased risk of developing cancer (breast, ovarian, and testicular), osteoporosis, insulin resistance, and obesity as adults. Early pubertal development has been associated with depression, aggressiveness, and increased sexual prowess. Possible explanations for the decline in age of pubertal onset include genetics, exposure to environmental toxins, better nutrition, and a reduction in childhood infections. In this study we (1) evaluated the association between 415 single nucleotide polymorphisms (SNPs) from hormonal pathways and early puberty, defined as menarche prior to age 12 in females and Tanner Stage 2 development prior to age 11 in males, and (2) measured endocrine hormone trajectories (estradiol, testosterone, and DHEAS) in relation to age, race, and Tanner Stage in a cohort of children from Project HeartBeat! At the end of the 4-year study, 193 females had onset of menarche and 121 males had pubertal staging at age 11. African American females had a younger mean age at menarche than Non-Hispanic White females. African American females and males had a lower mean age at each pubertal stage (1-5) than Non-Hispanic White females and males. African American females had higher mean BMI measures at each pubertal stage than Non-Hispanic White females. Of the 415 SNPs evaluated in females, 22 SNPs were associated with early menarche, when adjusted for race ( p<0.05), but none remained significant after adjusting for multiple testing by False Discovery Rate (p<0.00017). In males, 17 SNPs were associated with early pubertal development when adjusted for race (p<0.05), but none remained significant when adjusted for multiple testing (p<0.00017). ^ There were 4955 hormone measurements taken during the 4-year study period from 632 African American and Non-Hispanic White males and females. On average, African American females started and ended the pubertal process at a younger age than Non-Hispanic White females. The mean age of Tanner Stage 2 breast development in African American and Non-Hispanic White females was 9.7 (S.D.=0.8) and 10.2 (S.D.=1.1) years, respectively. There was a significant difference by race in mean age for each pubertal stage, except Tanner Stage 1 for pubic hair development. Both Estradiol and DHEAS levels in females varied significantly with age, but not by race. Estradiol and DHEAS levels increased from Tanner Stage 1 to Tanner Stage 5.^ African American males had a lower mean age at each Tanner Stage of development than Non-Hispanic White males. The mean age of Tanner Stage 2 genital development in African American and Non-Hispanic White males was 10.5 (S.D.=1.1) and 10.8 (S.D.=1.1) years, respectively, but this difference was not significant (p=0.11). Testosterone levels varied significantly with age and race. Non-Hispanic White males had higher levels of testosterone than African American males from Tanner Stage 1-4. Testosterone levels increased for both races from Tanner Stage 1 to Tanner Stage 5. Testosterone levels had the steepest increase from ages 11-15 for both races. DHEAS levels in males varied significantly with age, but not by race. DHEAS levels had the steepest increase from ages 14-17. ^ In conclusion, African American males and females experience pubertal onset at a younger age than Non-Hispanic White males and females, but in this study, we could not find a specific gene that explained the observed variation in age of pubertal onset. Future studies with larger study populations may provide a better understanding of the contribution of genes in early pubertal onset.^

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. ^