A comparison of Markov and generalized linear models of hospital mortality

This paper reports a comparison of three modeling strategies for the analysis of hospital mortality in a sample of general medicine inpatients in a Department of Veterans Affairs medical center. Logistic regression, a Markov chain model, and longitudinal logistic regression were evaluated on predictive performance as measured by the c-index and on accuracy of expected numbers of deaths compared to observed. The logistic regression used patient information collected at admission; the Markov model was comprised of two absorbing states for discharge and death and three transient states reflecting increasing severity of illness as measured by laboratory data collected during the hospital stay; longitudinal regression employed Generalized Estimating Equations (GEE) to model covariance structure for the repeated binary outcome. Results showed that the logistic regression predicted hospital mortality as well as the alternative methods but was limited in scope of application. The Markov chain provides insights into how day to day changes of illness severity lead to discharge or death. The longitudinal logistic regression showed that increasing illness trajectory is associated with hospital mortality. The conclusion is reached that for standard applications in modeling hospital mortality, logistic regression is adequate, but for new challenges facing health services research today, alternative methods are equally predictive, practical, and can provide new insights. ^

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

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.^

Using spatial linear models with SAR and CAR structure to examine Texas lung cancer incidence rates

Scholars have found that socioeconomic status was one of the key factors that influenced early-stage lung cancer incidence rates in a variety of regions. This thesis examined the association between median household income and lung cancer incidence rates in Texas counties. A total of 254 individual counties in Texas with corresponding lung cancer incidence rates from 2004 to 2008 and median household incomes in 2006 were collected from the National Cancer Institute Surveillance System. A simple linear model and spatial linear models with two structures, Simultaneous Autoregressive Structure (SAR) and Conditional Autoregressive Structure (CAR), were used to link median household income and lung cancer incidence rates in Texas. The residuals of the spatial linear models were analyzed with Moran's I and Geary's C statistics, and the statistical results were used to detect similar lung cancer incidence rate clusters and disease patterns in Texas.^

Analysis of life expectancy using linear and nonlinear models

Life expectancy has consistently increased over the last 150 years due to improvements in nutrition, medicine, and public health. Several studies found that in many developed countries, life expectancy continued to rise following a nearly linear trend, which was contrary to a common belief that the rate of improvement in life expectancy would decelerate and was fit with an S-shaped curve. Using samples of countries that exhibited a wide range of economic development levels, we explored the change in life expectancy over time by employing both nonlinear and linear models. We then observed if there were any significant differences in estimates between linear models, assuming an auto-correlated error structure. When data did not have a sigmoidal shape, nonlinear growth models sometimes failed to provide meaningful parameter estimates. The existence of an inflection point and asymptotes in the growth models made them inflexible with life expectancy data. In linear models, there was no significant difference in the life expectancy growth rate and future estimates between ordinary least squares (OLS) and generalized least squares (GLS). However, the generalized least squares model was more robust because the data involved time-series variables and residuals were positively correlated. ^

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Changes in the PQRST intervals and heart rate variability associated with rewarming in two newborns undergoing hypothermia therapy.

BACKGROUND: Little is known about the effects of hypothermia therapy and subsequent rewarming on the PQRST intervals and heart rate variability (HRV) in term newborns with hypoxic-ischemic encephalopathy (HIE). OBJECTIVES: This study describes the changes in the PQRST intervals and HRV during rewarming to normal core body temperature of 2 newborns with HIE after hypothermia therapy. METHODS: Within 6 h after birth, 2 newborns with HIE were cooled to a core body temperature of 33.5 degrees C for 72 h using a cooling blanket, followed by gradual rewarming (0.5 degrees C per hour) until the body temperature reached 36.5 degrees C. Custom instrumentation recorded the electrocardiogram from the leads used for clinical monitoring of vital signs. Generalized linear mixed models were calculated to estimate temperature-related changes in PQRST intervals and HRV. Results: For every 1 degrees C increase in body temperature, the heart rate increased by 9.2 bpm (95% CI 6.8-11.6), the QTc interval decreased by 21.6 ms (95% CI 17.3-25.9), and low and high frequency HRV decreased by 0.480 dB (95% CI 0.052-0.907) and 0.938 dB (95% CI 0.460-1.416), respectively. CONCLUSIONS: Hypothermia-induced changes in the electrocardiogram should be monitored carefully in future studies.

Identfying predictors of St. Louis encephalitis activity in Houston Texas

Generalized linear Poisson and logistic regression models were utilized to examine the relationship between temperature and precipitation and cases of Saint Louis encephalitis virus spread in the Houston metropolitan area. The models were investigated with and without repeated measures, with a first order autoregressive (AR1) correlation structure used for the repeated measures model. The two types of Poisson regression models, with and without correlation structure, showed that a unit increase in temperature measured in degrees Fahrenheit increases the occurrence of the virus 1.7 times and a unit increase in precipitation measured in inches increases the occurrence of the virus 1.5 times. Logistic regression did not show these covariates to be significant as predictors for encephalitis activity in Houston for either correlation structure. This discrepancy for the logistic model could be attributed to the small data set.^ Keywords: Saint Louis Encephalitis; Generalized Linear Model; Poisson; Logistic; First Order Autoregressive; Temperature; Precipitation. ^

A Bayesian approach to estimating the regression coefficients of a multinomial logit model

A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches. ^

Regression with autocorrelated data: A study of time trend of global infant mortality rate

The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

Multiple independent genetic factors at NOS1AP modulate the QT interval in a multi-ethnic population.

Extremes of electrocardiographic QT interval are associated with increased risk for sudden cardiac death (SCD); thus, identification and characterization of genetic variants that modulate QT interval may elucidate the underlying etiology of SCD. Previous studies have revealed an association between a common genetic variant in NOS1AP and QT interval in populations of European ancestry, but this finding has not been extended to other ethnic populations. We sought to characterize the effects of NOS1AP genetic variants on QT interval in the multi-ethnic population-based Dallas Heart Study (DHS, n = 3,072). The SNP most strongly associated with QT interval in previous samples of European ancestry, rs16847548, was the most strongly associated in White (P = 0.005) and Black (P = 3.6 x 10(-5)) participants, with the same direction of effect in Hispanics (P = 0.17), and further showed a significant SNP x sex-interaction (P = 0.03). A second SNP, rs16856785, uncorrelated with rs16847548, was also associated with QT interval in Blacks (P = 0.01), with qualitatively similar results in Whites and Hispanics. In a previously genotyped cohort of 14,107 White individuals drawn from the combined Atherosclerotic Risk in Communities (ARIC) and Cardiovascular Health Study (CHS) cohorts, we validated both the second locus at rs16856785 (P = 7.63 x 10(-8)), as well as the sex-interaction with rs16847548 (P = 8.68 x 10(-6)). These data extend the association of genetic variants in NOS1AP with QT interval to a Black population, with similar trends, though not statistically significant at P<0.05, in Hispanics. In addition, we identify a strong sex-interaction and the presence of a second independent site within NOS1AP associated with the QT interval. These results highlight the consistent and complex role of NOS1AP genetic variants in modulating QT interval.

Correlates of tobacco cessation counseling among Hispanic physicians in the US: a cross-sectional survey study.

BACKGROUND: Physician advice is an important motivator for attempting to stop smoking. However, physicians' lack of intervention with smokers has only modestly improved in the last decade. Although the literature includes extensive research in the area of the smoking intervention practices of clinicians, few studies have focused on Hispanic physicians. The purpose of this study was to explore the correlates of tobacco cessation counseling practices among Hispanic physicians in the US. METHODS: Data were collected through a validated survey instrument among a cross-sectional sample of self-reported Hispanic physicians practicing in New Mexico, and who were members of the New Mexico Hispanic Medical Society in the year 2001. Domains of interest included counseling practices, self-efficacy, attitudes/responsibility, and knowledge/skills. Returned surveys were analyzed to obtain frequencies and descriptive statistics for each survey item. Other analyses included: bivariate Pearson's correlation, factorial ANOVAs, and multiple linear regressions. RESULTS: Respondents (n = 45) reported a low level of compliance with tobacco control guidelines and recommendations. Results indicate that physicians' familiarity with standard cessation protocols has a significant effect on their tobacco-related practices (r = .35, variance shared = 12%). Self-efficacy and gender were both significantly correlated to tobacco related practices (r = .42, variance shared = 17%). A significant correlation was also found between self-efficacy and knowledge/skills (r = .60, variance shared = 36%). Attitudes/responsibility was not significantly correlated with any of the other measures. CONCLUSION: More resources should be dedicated to training Hispanic physicians in tobacco intervention. Training may facilitate practice by increasing knowledge, developing skills and, ultimately, enhancing feelings of self-efficacy.

Impact of medications prescribed for treatment of attention-deficit hyperactivity disorder on physical growth in children and adolescents with HIV.

OBJECTIVE: To examine the relationships between physical growth and medications prescribed for symptoms of attention-deficit hyperactivity disorder in children with HIV. METHODS: Analysis of data from children with perinatally acquired HIV (N = 2251; age 3-19 years), with and without prescriptions for stimulant and nonstimulant medications used to treat attention-deficit hyperactivity disorder, in a long-term observational study. Height and weight measurements were transformed to z scores and compared across medication groups. Changes in z scores during a 2-year interval were compared using multiple linear regression models adjusting for selected covariates. RESULTS: Participants with (n = 215) and without (n = 2036) prescriptions were shorter than expected based on US age and gender norms (p < .001). Children without prescriptions weighed less at baseline than children in the general population (p < .001) but gained height and weight at a faster rate (p < .001). Children prescribed stimulants were similar to population norms in baseline weight; their height and weight growth velocities were comparable with the general population and children without prescriptions (for weight, p = .511 and .100, respectively). Children prescribed nonstimulants had the lowest baseline height but were similar to population norms in baseline weight. Their height and weight growth velocities were comparable with the general population but significantly slower than children without prescriptions (p = .01 and .02, respectively). CONCLUSION: The use of stimulants to treat symptoms of attention-deficit hyperactivity disorder does not significantly exacerbate the potential for growth delay in children with HIV and may afford opportunities for interventions that promote physical growth. Prospective studies are needed to confirm these findings.

Postoperative renal function preservation with nonischemic femoral arterial cannulation for thoracoabdominal aortic repair.

BACKGROUND: Renal failure after thoracoabdominal aortic repair is a significant clinical problem. Distal aortic perfusion for organ and spinal cord protection requires cannulation of the left femoral artery. In 2006, we reported the finding that direct cannulation led to leg ischemia in some patients and was associated with increased renal failure. After this finding, we modified our perfusion technique to eliminate leg ischemia from cannulation. In this article, we present the effects of this change on postoperative renal function. METHODS: Between February 1991 and July 2008, we repaired 1464 thoracoabdominal aortic aneurysms. Distal aortic perfusion was used in 1088, and these were studied. Median patient age was 68 years, and 378 (35%) were women. In September 2006, we began to adopt a sidearm femoral cannulation technique that provides distal aortic perfusion while maintaining downstream flow to the leg. This was used in 167 patients (15%). We measured the joint effects of preoperative glomerular filtration rate (GFR) and cannulation technique on the highest postoperative creatinine level, postoperative renal failure, and death. Analysis was by multiple linear or logistic regression with interaction. RESULTS: The preoperative GFR was the strongest predictor of postoperative renal dysfunction and death. No significant main effects of sidearm cannulation were noted. For peak creatinine level and postoperative renal failure, however, strong interactions between preoperative GFR and sidearm cannulation were present, resulting in reductions of postoperative renal complications of 15% to 20% when GFR was <60 mL>/min/1.73 m(2). For normal GFR, the effect was negated or even reversed at very high levels of GFR. Mortality, although not significantly affected by sidearm cannulation, showed a similar trend to the renal outcomes. CONCLUSION: Use of sidearm cannulation is associated with a clinically important and highly statistically significant reduction in postoperative renal complications in patients with a low GFR. Reduced renal effect of skeletal muscle ischemia is the proposed mechanism. Effects among patients with good preoperative renal function are less clear. A randomized trial is needed.

Body fat distribution and serum lipids in children and adolescents

Previous studies of normal children have linked body fat but not body fat distribution (BFD), to higher blood pressures, lipids, and insulin resistance (Berenson et al., 1988) BFD is a well-established risk factor for cardiovascular disease in adults (Björntorp, 1988). This study investigates the relation of BFD and serum lipids at baseline in children from Project HeartBeat!, a study of the growth and development of cardiovascular risk factors in 678 children in three cohorts measured initially at ages 8, 11, and 14 years. Initially, two of four indices of BFD were significantly related to the lipids: ratio of upper to lower body skinfolds (ln US:LS) and conicity (C Index). A factor analysis reduced the information in the serum lipids to two vectors: (1) total cholesterol + LDL-cholesterol and (2) HDL-cholesterol − triglycerides, which together accounted for 85% of the lipid variation. Using each serum lipid and vector as separate dependent variables, linear and quadratic regression models were constructed to examine the predictive ability of the two BFD variables, controlling for total body fat, gender, ethnicity (Black, non-Black) and maturation. Linear models provided an acceptable fit. Percent body fat (%BF) was a significant predictor in each and every lipid model, independent of age, maturation, or ethnicity (p ≤ 0.05). No BFD variable entered the equation for total or LDL-cholesterol, although there was a significant maturity by BFD interaction for LDL (ln US:LS was a significant predictor in more mature individuals). Both %BF and BFD (by way of Conicity) were significant predictors of HDL-cholesterol and triglycerides (p ≤ 0.01). All models were statistically significant at a high level (p ≤ 0.01), but adjusted R 2's for all models were low (0.05–0.15). Body fat distribution is a significant predictor of lipids in normal children, but secondarily to %BF, and for LDL-cholesterol in particular, the relation is dependent on maturity status. ^