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. ^

An examination of the Gonorrhea Cases & Places Study: An analysis of the Theory of Gender and Power, Situational/Environmental Variables Theory, and Sexual Script Theory as it relates to risky sexual behavior in African American adults

Objective. The purpose of the study is to provide a holistic depiction of behavioral & environmental factors contributing to risky sexual behaviors among predominantly high school educated, low-income African Americans residing in urban areas of Houston, TX utilizing the Theory of Gender and Power, Situational/Environmental Variables Theory, and Sexual Script Theory. Methods. A cross-sectional study was conducted via questionnaires among 215 Houston area residents, 149 were women and 66 were male. Measures used to assess behaviors of the population included a history of homelessness, use of crack/cocaine among several other illicit drugs, the type of sexual partner, age of participant, age of most recent sex partner, whether or not participants sought health care in the last 12 months, knowledge of partner's other sexual activities, symptoms of depression, and places where partner's were met. In an effort to determine risk of sexual encounters, a risk index employing the variables used to assess condom use was created categorizing sexual encounters as unsafe or safe. Results. Variables meeting the significance level of p<.15 for the bivariate analysis of each theory were entered into a binary logistic regression analysis. The block for each theory was significant, suggesting that the grouping assignments of each variable by theory were significantly associated with unsafe sexual behaviors. Within the regression analysis, variables such as sex for drugs/money, low income, and crack use demonstrated an effect size of ≥ ± 1, indicating that these variables had a significant effect on unsafe sexual behavioral practices. Conclusions. Variables assessing behavior and environment demonstrated a significant effect when categorized by relation to designated theories.

Transcriptional regulation of the Borrelia burgdorferi antigenically variable VlsE surface protein.

The Lyme disease agent Borrelia burgdorferi can persistently infect humans and other animals despite host active immune responses. This is facilitated, in part, by the vls locus, a complex system consisting of the vlsE expression site and an adjacent set of 11 to 15 silent vls cassettes. Segments of nonexpressed cassettes recombine with the vlsE region during infection of mammalian hosts, resulting in combinatorial antigenic variation of the VlsE outer surface protein. We now demonstrate that synthesis of VlsE is regulated during the natural mammal-tick infectious cycle, being activated in mammals but repressed during tick colonization. Examination of cultured B. burgdorferi cells indicated that the spirochete controls vlsE transcription levels in response to environmental cues. Analysis of PvlsE::gfp fusions in B. burgdorferi indicated that VlsE production is controlled at the level of transcriptional initiation, and regions of 5' DNA involved in the regulation were identified. Electrophoretic mobility shift assays detected qualitative and quantitative changes in patterns of protein-DNA complexes formed between the vlsE promoter and cytoplasmic proteins, suggesting the involvement of DNA-binding proteins in the regulation of vlsE, with at least one protein acting as a transcriptional activator.

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

An examination of the Gonorrhea Cases & Places study: An analysis of the Theory of Gender and Power, Situational/Environmental Variables Theory, and Sexual Script Theory as it relates to risky sexual behavior in African American adults

Objective. The purpose of the study is to provide a holistic depiction of behavioral & environmental factors contributing to risky sexual behaviors among predominantly high school educated, low-income African Americans residing in urban areas of Houston, TX utilizing the Theory of Gender and Power, Situational/Environmental Variables Theory, and Sexual Script Theory. ^ Methods. A cross-sectional study was conducted via questionnaires among 215 Houston area residents, 149 were women and 66 were male. Measures used to assess behaviors of the population included a history of homelessness, use of crack/cocaine among several other illicit drugs, the type of sexual partner, age of participant, age of most recent sex partner, whether or not participants sought health care in the last 12 months, knowledge of partner's other sexual activities, symptoms of depression, and places where partner's were met. In an effort to determine risk of sexual encounters, a risk index employing the variables used to assess condom use was created categorizing sexual encounters as unsafe or safe. ^ Results. Variables meeting the significance level of p<.15 for the bivariate analysis of each theory were entered into a binary logistic regression analysis. The block for each theory was significant, suggesting that the grouping assignments of each variable by theory were significantly associated with unsafe sexual behaviors. Within the regression analysis, variables such as sex for drugs/money, low income, and crack use demonstrated an effect size of ≥±1, indicating that these variables had a significant effect on unsafe sexual behavioral practices. ^ Conclusions. Variables assessing behavior and environment demonstrated a significant effect when categorized by relation to designated theories. ^

The role of ATM in the cell cycle control of V(D)J recombination

Lymphocyte development requires the assembly of diversified antigen receptor complexes generated by the genetically programmed V(D)J recombination event. Because germline DNA is cut, introducing potentially dangerous double-stranded breaks (DSBs) and rearranged prior to repair, its activity is limited to the non-cycling stages of the cell cycle, G0/G1. The potential involvement of a key mediator, Ataxia Telangiectasia Mutated or ATM, in the DNA damage response (DDR) and cell cycle checkpoints has been implicated in recombination, but its role is not fully understood. Thymic lymphomas from ATM deficient mice contain clonal chromosomal translocations involving the T-cell antigen receptor (TCR). A previous report found ATM and its downstream target p53 associated with V(D)J intermediates, suggesting the DDR senses recombination. In this study, we sought to understand the role of ATM in V(D)J recombination. Developing thymocytes from ATM deficient mice were analyzed according to the cell cycle to detect V(D)J intermediates. Examination of all TCR loci in the non-cycling (G0/G1) and cycling (S/G2/M) fractions revealed the persistence of intermediates in ATM deficient thymocytes, contrary to the wild-type in which intermediates are found only during G0/G1. Further analysis found no defect in end-joining of intermediates, nor were they detected in developed T-cells. Based upon the presence of persisting intermediates, the recombination initiating nuclease Rag-2 was examined; strict regulation limits it to G 0/G1. Rag-2 regulation was not affected by an ATM deficiency as Rag-2 expression remained contained within G0/G 1, indicating recombination is not continuous. To determine if an ATM deficiency affects recognition of V(D)J breaks, sites of recombination identified by a TCR locus or Rag expression were analyzed according to co-localization with a DDR factor phosphorylated immediately after DNA damage, phosphorylated H2AX (γH2AX). No differences in co-localization were found between the wild-type and ATM deficiency, demonstrating ATM deficient lymphocytes retain the ability to recognize DSBs. Together, these results suggest ATM is necessary in the cell cycle regulation of recombination but not essential for the identification of V(D)J breaks. ATM ensures the containment of intermediates within G0/G1 and maintains genomic stability of developing lymphocytes, emphasizing its fundamental role in preventing tumorigenesis.^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

SYSTEMIC TOXICITY IN RODENTS FOLLOWING ACUTE AND SUBCHRONIC INHALATION OF FORMALDEHYDE (FLOW CYTOMETRY, CELL CYCLE KINETICS, ALKALINE ELUTION)

Systemic toxicity was evaluated in Sprague-Dawley (SD) rats and A-strain mice exposed to HCHO inhalation at 0, 0.5, 3, or 15 ppm for six hours/day, five days/week for up to 24 weeks. Toxicity was measured by flow cytometry to detect changes in cell cycle RNA and DNA content and by alkaline elution to detect DNA protein cross-link (DPC) formation.^ A G(,2)M block was detected in SD rat marrow following one week of exposure to 0.5, 3, or 15 ppm HCHO, but this block did not persist. No effect was noticed in mouse marrow. Only a minimal increase in RNA content was detected in rat or mouse marrow while exfoliated lung cells showed a significant increase in RNA activity after one week of exposure.^ Acute exposure in SD rats for four hours/day for one or three days at 150 ppm showed an increase in RNA activity in exfoliated lung cells but not in the marrow after one day. On the third day, dead cells were detected in exfoliated lung cells.^ In alkaline elution studies, no DPC were detected in marrow of SD rats after 24 weeks exposure up to 15 ppm. During acute exposures, a dose response relationship was detected in SD rat exfoliated lung cells which yielded cross-linking factors of 0.954, 1.237, and 1.417 following a four hour exposure to 15, 50, or 150 ppm, respectively. No DPC were detected in the marrow at 150 ppm. In vitro exposures to HCHO of CHO and SHE cells and rat marrow cells revealed the production of DPC and DNA-DNA cross-links.^ Cytoxan treatment of SD rats was used to provide positive controls for flow cytometry and alkaline elution. A drastic reduction in RNA content and cycling cells occurred one day following treatment. After four days, RNA content was greatly increased; and on day eleven the marrow had regenerated. DPCs were detected in both the marrow and the exfoliated lung cells.^ The lack of significant responses in SD rats and A-strain mice below 15 ppm HCHO is explainable by host defense mechanisms. Apparently, the mucociliary apparatus and enzymatic detoxification are sufficient to reduce systemic toxicity to low level concentrations of formaldehyde. ^

Detecting genetic and nutritional lung cancer risk factors related to folate metabolism using Bayesian generalized linear models

Complex diseases, such as cancer, are caused by various genetic and environmental factors, and their interactions. Joint analysis of these factors and their interactions would increase the power to detect risk factors but is statistically. Bayesian generalized linear models using student-t prior distributions on coefficients, is a novel method to simultaneously analyze genetic factors, environmental factors, and interactions. I performed simulation studies using three different disease models and demonstrated that the variable selection performance of Bayesian generalized linear models is comparable to that of Bayesian stochastic search variable selection, an improved method for variable selection when compared to standard methods. I further evaluated the variable selection performance of Bayesian generalized linear models using different numbers of candidate covariates and different sample sizes, and provided a guideline for required sample size to achieve a high power of variable selection using Bayesian generalize linear models, considering different scales of number of candidate covariates. ^ Polymorphisms in folate metabolism genes and nutritional factors have been previously associated with lung cancer risk. In this study, I simultaneously analyzed 115 tag SNPs in folate metabolism genes, 14 nutritional factors, and all possible genetic-nutritional interactions from 1239 lung cancer cases and 1692 controls using Bayesian generalized linear models stratified by never, former, and current smoking status. SNPs in MTRR were significantly associated with lung cancer risk across never, former, and current smokers. In never smokers, three SNPs in TYMS and three gene-nutrient interactions, including an interaction between SHMT1 and vitamin B12, an interaction between MTRR and total fat intake, and an interaction between MTR and alcohol use, were also identified as associated with lung cancer risk. These lung cancer risk factors are worthy of further investigation.^