Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^

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.

Preclinical modeling of multi-drug cancer therapies

Anticancer drugs typically are administered in the clinic in the form of mixtures, sometimes called combinations. Only in rare cases, however, are mixtures approved as drugs. Rather, research on mixtures tends to occur after single drugs have been approved. The goal of this research project was to develop modeling approaches that would encourage rational preclinical mixture design. To this end, a series of models were developed. First, several QSAR classification models were constructed to predict the cytotoxicity, oral clearance, and acute systemic toxicity of drugs. The QSAR models were applied to a set of over 115,000 natural compounds in order to identify promising ones for testing in mixtures. Second, an improved method was developed to assess synergistic, antagonistic, and additive effects between drugs in a mixture. This method, dubbed the MixLow method, is similar to the Median-Effect method, the de facto standard for assessing drug interactions. The primary difference between the two is that the MixLow method uses a nonlinear mixed-effects model to estimate parameters of concentration-effect curves, rather than an ordinary least squares procedure. Parameter estimators produced by the MixLow method were more precise than those produced by the Median-Effect Method, and coverage of Loewe index confidence intervals was superior. Third, a model was developed to predict drug interactions based on scores obtained from virtual docking experiments. This represents a novel approach for modeling drug mixtures and was more useful for the data modeled here than competing approaches. The model was applied to cytotoxicity data for 45 mixtures, each composed of up to 10 selected drugs. One drug, doxorubicin, was a standard chemotherapy agent and the others were well-known natural compounds including curcumin, EGCG, quercetin, and rhein. Predictions of synergism/antagonism were made for all possible fixed-ratio mixtures, cytotoxicities of the 10 best-scoring mixtures were tested, and drug interactions were assessed. Predicted and observed responses were highly correlated (r2 = 0.83). Results suggested that some mixtures allowed up to an 11-fold reduction of doxorubicin concentrations without sacrificing efficacy. Taken together, the models developed in this project present a general approach to rational design of mixtures during preclinical drug development. ^

Heart rate variability in response to pain stimulus in VLBW infants followed longitudinally during NICU stay.

The objective of this longitudinal study, conducted in a neonatal intensive care unit, was to characterize the response to pain of high-risk very low birth weight infants (<1,500 g) from 23 to 38 weeks post-menstrual age (PMA) by measuring heart rate variability (HRV). Heart period data were recorded before, during, and after a heel lanced or wrist venipunctured blood draw for routine clinical evaluation. Pain response to the blood draw procedure and age-related changes of HRV in low-frequency and high-frequency bands were modeled with linear mixed-effects models. HRV in both bands decreased during pain, followed by a recovery to near-baseline levels. Venipuncture and mechanical ventilation were factors that attenuated the HRV response to pain. HRV at the baseline increased with post-menstrual age but the growth rate of high-frequency power was reduced in mechanically ventilated infants. There was some evidence that low-frequency HRV response to pain improved with advancing PMA.

Assessing homogeneity in workplace exposure under stationary and non-stationary scenarios

In most epidemiological studies, historical monitoring data are scant and must be pooled to identify occupational groups with homogeneous exposures. Homogeneity of exposure is generally assessed in a group of workers who share a common job title or work in a common area. While published results suggest that the degree of homogeneity varies widely across job groups, less is known whether such variation differs across industrial sectors, classes of contaminants, or in the methods used to group workers. Relying upon a compilation of results presented in the literature, patterns of homogeneity among nearly 500 occupational groups of workers were evaluated on the basis of type of industry and agent. Additionally, effects of the characteristics of the sampling strategy on estimated indicators of homogeneity of exposure were assessed. ^ Exposure profiles for occupational groups of workers have typically been assessed under the assumption of stationarity, i.e., the mean exposure level and variance of the distribution that describes the underlying population of exposures are constant over time. Yet, the literature has shown that occupational exposures have declined in the last decades. This renders traditional methods for the description of exposure profiles inadequate. Thus, work was needed to develop appropriate methods to assess homogeneity for groups of workers whose exposures have changed over time. A study was carried out applying mixed effects models with a term for temporal trend to appropriately describe exposure profiles of groups of workers in the nickel-producing industry over a 20-year period. Using a sub-set of groups of nickel-exposed workers, another study was conducted to develop and apply a framework to evaluate the assumption of stationarity of the variances in the presence of systematic changes in exposure levels over time. ^

Bayesian joint modeling of longitudinal and survival data

The joint modeling of longitudinal and survival data is a new approach to many applications such as HIV, cancer vaccine trials and quality of life studies. There are recent developments of the methodologies with respect to each of the components of the joint model as well as statistical processes that link them together. Among these, second order polynomial random effect models and linear mixed effects models are the most commonly used for the longitudinal trajectory function. In this study, we first relax the parametric constraints for polynomial random effect models by using Dirichlet process priors, then three longitudinal markers rather than only one marker are considered in one joint model. Second, we use a linear mixed effect model for the longitudinal process in a joint model analyzing the three markers. In this research these methods were applied to the Primary Biliary Cirrhosis sequential data, which were collected from a clinical trial of primary biliary cirrhosis (PBC) of the liver. This trial was conducted between 1974 and 1984 at the Mayo Clinic. The effects of three longitudinal markers (1) Total Serum Bilirubin, (2) Serum Albumin and (3) Serum Glutamic-Oxaloacetic transaminase (SGOT) on patients' survival were investigated. Proportion of treatment effect will also be studied using the proposed joint modeling approaches. ^ Based on the results, we conclude that the proposed modeling approaches yield better fit to the data and give less biased parameter estimates for these trajectory functions than previous methods. Model fit is also improved after considering three longitudinal markers instead of one marker only. The results from analysis of proportion of treatment effects from these joint models indicate same conclusion as that from the final model of Fleming and Harrington (1991), which is Bilirubin and Albumin together has stronger impact in predicting patients' survival and as a surrogate endpoints for treatment. ^

Understanding disparities in emergency department visits for asthma

Asthma is the most common chronic disorder in childhood, affecting an estimated 6.2 million children under 18 years (1). The purpose of this study was to look at individual- and community-level characteristics simultaneously to examine and explain the factors that contribute to the use of emergency department services by children 18 years old or less and to determine if there was an association between air quality and ED visits in the same population, from 2005-2007 in Houston/Harris County. Data were collected from the Houston Safety Net Hospital Emergency Department Use Study and the 2000 US Census. Bivariate and multivariate logistic regression models and mixed effects models were used to analyze data that was collected during the study period.^ There were 704,902 ED visits made by children 18 and younger, who were living in Houston from January 1, 2005 to December 31, 2007. Of those, 19,098 had a primary discharge diagnosis of asthma. Asthma ED visits varied by season, with proportions of ED visits for asthma highest from September-December. African-American children were 2.6 (95% CI, 2.43-2.66) times more likely to have an ED visit for asthma compared to White children. Poverty, single parent headed households, and younger age all a greater likelihood of having gone to the ED for asthma treatment. Compared to Whites living in lightly-monitored pollution areas, African-Americans and Hispanics living in heavily monitored areas were 1.15 (95% CI, 1.04-1.28) times more likely to have an ED visit for asthma.^ Race and poverty seem to account for a large portion of the disparities in ED use found among children. This was true even after accounting for multiple individual- and community-level variables. These results suggest that racial disparities in asthma continue to pose risks for African American children, and they point to the need for additional research into potential explanations and remedies. Programs to reduce inappropriate ED use must be sensitive to an array of complex socioeconomic issues within minority and income populations. ^

The role of cardiorespiratory fitness and weight status on 24-hr ambulatory blood pressure among adolescents

BACKGROUND: This observational research study investigated the association of cardiorespiratory fitness and weight status with repeated measures of 24-hr ambulatory blood pressure (24-hr ABP). Little is known about these associations and few data exist examining the interaction between cardiorespiratory fitness and weight status and the contributions of each on 24-hr ABP in youth. ^ METHODS: This research study used secondary analysis data from the "Adolescent Blood Pressure and Anger: Ethnic Differences" study. This current study sample included 374 African-American, Anglo-American, and Mexican-American adolescents 11-16 years of age. Mixed-effects models were used for testing the relationship between weight status and cardiorespiratory fitness and repeated measures of ambulatory blood pressure over 24 hours (24-hr ABP). Weight status was categorized into "normal weight" (BMI<85th percentile), "overweight" (85th≤BMI<95th), and "obese" (BMI≥95th). Cardiorespiratory fitness, determined by heart rate recovery (HRR), was defined as the difference between heart rate at peak exercise and heart rate at two minutes post-exercise, as measured by a height-adjusted step test and stratified into two groups: low and high fitness, using a median split. Ambulatory blood pressure (ABP) was monitored for a 24-hr period on a school day using the Spacelabs ambulatory monitor (Model 90207). Blood pressure and heart rate were recorded at 30 minute intervals throughout the day of recording and at 60 minute intervals during sleep. ^ RESULTS: No significant associations were found between weight status and mean 24-hr systolic blood pressure (SBP) or mean arterial pressure (MAP). A significant and inverse association between weight status and mean 24-hr diastolic blood pressure (DBP) was revealed. Cardiorespiratory fitness was significantly and inversely associated with mean 24-hr ABP. High fitness adolescents had significantly lower mean 24-hr SPB, DBP, and MAP measurements than low fitness adolescents. Compared to low fitness adolescents, high fitness adolescents had 1.90 mmHg, 1.16 mmHg, and 1.68 mmHg lower mean 24-hr SBP, DBP, and MAP, respectively. Additionally, high fitness appeared to afford protection from higher mean 24-hr SBP and MAP, irrespective of weight status. Among normal weight adolescents, low fitness resulted in higher mean 24-hr SBP and MAP, compared to their fit counterparts. Among adolescents categorized as high fitness, increasing weight status did not appear to result in higher mean 24-hr SBP or MAP. Cardiorespiratory fitness, rather than weight status, appeared to be a more dominant predictor of mean 24-hr SBP and MAP. ^ CONCLUSIONS: To our knowledge, this research is the first study to investigate the independent and combined contributions of cardiorespiratory fitness and weight status on 24-hr ABP, all objectively measured. The results of this study may potentially guide and inform future research. It appears that early cardiovascular disease (CVD) prevention should focus on improving cardiorespiratory fitness levels among all adolescents, particularly those adolescents least fit, regardless of their weight status, while obesity prevention efforts continue.^

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. ^

Effect of nonnormal random components on level and power in group-randomized trials

The use of group-randomized trials is particularly widespread in the evaluation of health care, educational, and screening strategies. Group-randomized trials represent a subset of a larger class of designs often labeled nested, hierarchical, or multilevel and are characterized by the randomization of intact social units or groups, rather than individuals. The application of random effects models to group-randomized trials requires the specification of fixed and random components of the model. The underlying assumption is usually that these random components are normally distributed. This research is intended to determine if the Type I error rate and power are affected when the assumption of normality for the random component representing the group effect is violated. ^ In this study, simulated data are used to examine the Type I error rate, power, bias and mean squared error of the estimates of the fixed effect and the observed intraclass correlation coefficient (ICC) when the random component representing the group effect possess distributions with non-normal characteristics, such as heavy tails or severe skewness. The simulated data are generated with various characteristics (e.g. number of schools per condition, number of students per school, and several within school ICCs) observed in most small, school-based, group-randomized trials. The analysis is carried out using SAS PROC MIXED, Version 6.12, with random effects specified in a random statement and restricted maximum likelihood (REML) estimation specified. The results from the non-normally distributed data are compared to the results obtained from the analysis of data with similar design characteristics but normally distributed random effects. ^ The results suggest that the violation of the normality assumption for the group component by a skewed or heavy-tailed distribution does not appear to influence the estimation of the fixed effect, Type I error, and power. Negative biases were detected when estimating the sample ICC and dramatically increased in magnitude as the true ICC increased. These biases were not as pronounced when the true ICC was within the range observed in most group-randomized trials (i.e. 0.00 to 0.05). The normally distributed group effect also resulted in bias ICC estimates when the true ICC was greater than 0.05. However, this may be a result of higher correlation within the data. ^

Statistical issues on studies of mixed longitudinal design

Mixed longitudinal designs are important study designs for many areas of medical research. Mixed longitudinal studies have several advantages over cross-sectional or pure longitudinal studies, including shorter study completion time and ability to separate time and age effects, thus are an attractive choice. Statistical methodology used in general longitudinal studies has been rapidly developing within the last few decades. Common approaches for statistical modeling in studies with mixed longitudinal designs have been the linear mixed-effects model incorporating an age or time effect. The general linear mixed-effects model is considered an appropriate choice to analyze repeated measurements data in longitudinal studies. However, common use of linear mixed-effects model on mixed longitudinal studies often incorporates age as the only random-effect but fails to take into consideration the cohort effect in conducting statistical inferences on age-related trajectories of outcome measurements. We believe special attention should be paid to cohort effects when analyzing data in mixed longitudinal designs with multiple overlapping cohorts. Thus, this has become an important statistical issue to address. ^ This research aims to address statistical issues related to mixed longitudinal studies. The proposed study examined the existing statistical analysis methods for the mixed longitudinal designs and developed an alternative analytic method to incorporate effects from multiple overlapping cohorts as well as from different aged subjects. The proposed study used simulation to evaluate the performance of the proposed analytic method by comparing it with the commonly-used model. Finally, the study applied the proposed analytic method to the data collected by an existing study Project HeartBeat!, which had been evaluated using traditional analytic techniques. Project HeartBeat! is a longitudinal study of cardiovascular disease (CVD) risk factors in childhood and adolescence using a mixed longitudinal design. The proposed model was used to evaluate four blood lipids adjusting for age, gender, race/ethnicity, and endocrine hormones. The result of this dissertation suggest the proposed analytic model could be a more flexible and reliable choice than the traditional model in terms of fitting data to provide more accurate estimates in mixed longitudinal studies. Conceptually, the proposed model described in this study has useful features, including consideration of effects from multiple overlapping cohorts, and is an attractive approach for analyzing data in mixed longitudinal design studies.^

A cross-sectional analysis of the association between polycyclic aromatic hydrocarbons and diesel particulate matter exposures and hypertension among individuals of Mexican origin residing in Houston, TX

Background. Research has shown that elevations of only 10 mmHg diastolic blood pressure (BP) and 5 mmHg systolic BP are associated with substantial (as large as 50%) increases in risks for cardiovascular disease, a leading cause of death, worldwide. Epidemiological studies have found that particulate matter (PM) increases blood pressure (BP) and many biological mechanisms which may suggest that the organic matter of PM contributes to the increase in BP. To understand components of PM which may contribute to the increase in BP, this study focuses on diesel particulate matter (DPM) and polycyclic aromatic hydrocarbons (PAHs). To our knowledge, there have been only four epidemiological studies on BP and DPM, and no epidemiological studies on BP and PAHs. ^ Objective. Our objective was to evaluate the association between prevalent hypertension and two ambient exposures: DPM and PAHs amongst the Mano a Mano cohort. ^ Methods. The Mano a Mano cohort which was established by the M.D. Anderson Cancer Center in 2001, is comprised of individuals of Mexican origin residing in Houston, TX. Using geographical information systems, we linked modeled annual estimates of PAHs and DPM at the census track level from the U.S. Environmental Protection Agency's National-Scale Air Toxics Assessment to residential addresses of cohort members. Mixed-effects logistic regression models were applied to determine associations between DPM and PAHs and hypertension while adjusting for confounders. ^ Results. Ambient levels of DPM, categorized into quartiles, were not statistically associated with hypertension and did not indicate a dose response relationship. Ambient levels of PAHs, categorized into quartiles, were not associated with hypertension, but did indicate a dose response relationship in multiple models (for example: Q2: OR = 0.98; 95% CI, 0.73–1.31, Q3: OR = 1.08; 95% CI, 0.82–1.41, Q4: OR = 1.26; 95% CI, 0.94–1.70). ^ Conclusion. This is the first assessment to analyze the relationship between ambient levels of PAHs and hypertension and it is amongst a few studies investigating the association between ambient levels of DPM and hypertension. Future analyses are warranted to explore the effects DPM and PAHs using different categorizations in order to clarify their relationships with hypertension.^

Data quality in trauma transfusion studies and the impact of missing data on predicting massive transfusion

Maximizing data quality may be especially difficult in trauma-related clinical research. Strategies are needed to improve data quality and assess the impact of data quality on clinical predictive models. This study had two objectives. The first was to compare missing data between two multi-center trauma transfusion studies: a retrospective study (RS) using medical chart data with minimal data quality review and the PRospective Observational Multi-center Major Trauma Transfusion (PROMMTT) study with standardized quality assurance. The second objective was to assess the impact of missing data on clinical prediction algorithms by evaluating blood transfusion prediction models using PROMMTT data. RS (2005-06) and PROMMTT (2009-10) investigated trauma patients receiving ≥ 1 unit of red blood cells (RBC) from ten Level I trauma centers. Missing data were compared for 33 variables collected in both studies using mixed effects logistic regression (including random intercepts for study site). Massive transfusion (MT) patients received ≥ 10 RBC units within 24h of admission. Correct classification percentages for three MT prediction models were evaluated using complete case analysis and multiple imputation based on the multivariate normal distribution. A sensitivity analysis for missing data was conducted to estimate the upper and lower bounds of correct classification using assumptions about missing data under best and worst case scenarios. Most variables (17/33=52%) had <1% missing data in RS and PROMMTT. Of the remaining variables, 50% demonstrated less missingness in PROMMTT, 25% had less missingness in RS, and 25% were similar between studies. Missing percentages for MT prediction variables in PROMMTT ranged from 2.2% (heart rate) to 45% (respiratory rate). For variables missing >1%, study site was associated with missingness (all p≤0.021). Survival time predicted missingness for 50% of RS and 60% of PROMMTT variables. MT models complete case proportions ranged from 41% to 88%. Complete case analysis and multiple imputation demonstrated similar correct classification results. Sensitivity analysis upper-lower bound ranges for the three MT models were 59-63%, 36-46%, and 46-58%. Prospective collection of ten-fold more variables with data quality assurance reduced overall missing data. Study site and patient survival were associated with missingness, suggesting that data were not missing completely at random, and complete case analysis may lead to biased results. Evaluating clinical prediction model accuracy may be misleading in the presence of missing data, especially with many predictor variables. The proposed sensitivity analysis estimating correct classification under upper (best case scenario)/lower (worst case scenario) bounds may be more informative than multiple imputation, which provided results similar to complete case analysis.^

Health outcomes, quality improvement and cost-effectiveness of the Community Diabetes Education (CoDE) program: Results of a randomized controlled trial

The objectives of this dissertation were to evaluate health outcomes, quality improvement measures, and the long-term cost-effectiveness and impact on diabetes-related microvascular and macrovascular complications of a community health worker-led culturally tailored diabetes education and management intervention provided to uninsured Mexican Americans in an urban faith-based clinic. A prospective, randomized controlled repeated measures design was employed to compare the intervention effects between: (1) an intervention group (n=90) that participated in the Community Diabetes Education (CoDE) program along with usual medical care; and (2) a wait-listed comparison group (n=90) that received only usual medical care. Changes in hemoglobin A1c (HbA1c) and secondary outcomes (lipid status, blood pressure and body mass index) were assessed using linear mixed-models and an intention-to-treat approach. The CoDE group experienced greater reduction in HbA1c (-1.6%, p<.001) than the control group (-.9%, p<.001) over the 12 month study period. After adjusting for group-by-time interaction, antidiabetic medication use at baseline, changes made to the antidiabetic regime over the study period, duration of diabetes and baseline HbA1c, a statistically significant intervention effect on HbA1c (-.7%, p=.02) was observed for CoDE participants. Process and outcome quality measures were evaluated using multiple mixed-effects logistic regression models. Assessment of quality indicators revealed that the CoDE intervention group was significantly more likely to have received a dilated retinal examination than the control group, and 53% achieved a HbA1c below 7% compared with 38% of control group subjects. Long-term cost-effectiveness and impact on diabetes-related health outcomes were estimated through simulation modeling using the rigorously validated Archimedes Model. Over a 20 year time horizon, CoDE participants were forecasted to have less proliferative diabetic retinopathy, fewer foot ulcers, and reduced numbers of foot amputations than control group subjects who received usual medical care. An incremental cost-effectiveness ratio of $355 per quality-adjusted life-year gained was estimated for CoDE intervention participants over the same time period. The results from the three areas of program evaluation: impact on short-term health outcomes, quantification of improvement in quality of diabetes care, and projection of long-term cost-effectiveness and impact on diabetes-related health outcomes provide evidence that a community health worker can be a valuable resource to reduce diabetes disparities for uninsured Mexican Americans. This evidence supports formal integration of community health workers as members of the diabetes care team.^

A biophysical model of synaptic plasticity and metaplasticity can account for the dynamics of the backward shift of hippocampal place fields.

Hippocampal place cells in the rat undergo experience-dependent changes when the rat runs stereotyped routes. One such change, the backward shift of the place field center of mass, has been linked by previous modeling efforts to spike-timing-dependent plasticity (STDP). However, these models did not account for the termination of the place field shift and they were based on an abstract implementation of STDP that ignores many of the features found in cortical plasticity. Here, instead of the abstract STDP model, we use a calcium-dependent plasticity (CaDP) learning rule that can account for many of the observed properties of cortical plasticity. We use the CaDP learning rule in combination with a model of metaplasticity to simulate place field dynamics. Without any major changes to the parameters of the original model, the present simulations account both for the initial rapid place field shift and for the subsequent slowing down of this shift. These results suggest that the CaDP model captures the essence of a general cortical mechanism of synaptic plasticity, which may underlie numerous forms of synaptic plasticity observed both in vivo and in vitro.