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. ^

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.^

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. ^

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. ^

The impact of a child's unexpected hospitalization upon Taiwanese parents' situational anxiety

Background. The parents of a sick child likely experience situational anxiety due to their young child being unexpectedly hospitalized. The emotional upheaval may be great enough that their anxiety inhibits them in providing positive support to their hospitalized child. Because anxiety affects psychological distress as well as behavioral distress, identifying parental distress helps parents improving their coping mechanisms. ^ Purpose. The study compared situational anxiety levels between Taiwanese fathers and mothers and focused on differences between parental anxiety levels at the beginning of the child's unplanned hospitalization and at time of discharge. The study also identified factors related to the parents' distress and use of coping mechanisms. ^ Methods. A descriptive, comparative research design was used to determine the difference between the anxiety levels of 62 Taiwanese father-mother dyads during the situational crisis of their child's unexpected hospitalization. The Mandarin version (M) of Visual Analog Scale (VAS-M), State-Trait Anxiety Inventory (STAI-M), and the Index of Parent Participation/Hospitalized Child (IPP/HC-M) were used to differentiate maternal and paternal anxiety levels and identify factors related to the parents' distress. Questionnaires were completed by parents within 24-36 hours of the child's hospital admission and within 24 hours prior to discharge. A paired t-test, two sample t-test, and linear mixed regression model were used to test and support the study hypothesis. ^ Results. The findings reveal that the mothers' anxiety levels did not significantly differ from the fathers' anxiety level when their child had a sudden admission to the hospital. In particular, parental state anxiety levels did not decrease during the child's hospital stay and subsequent discharge. Moreover, anxiety levels did not differ between parents regardless of whether the child's disease was acute or chronic. The most effective factor related to parental situational anxiety was parental perception of the severity of the child's illness. ^ Conclusions. Parental anxiety was found to be significantly related to changes in their perception of the severity of their child's illness. However, the study was not able to illustrate how parental involvement in the child's hospital care was related to parental perception of the severity of their child's illness. Future studies, using a qualitative approach to gamer more information as to what variables influence parental anxiety during a situational crisis, may provide a richer database from which to modify key variables as well as the instruments used to improve the quality of the data obtained. ^

Motivational interviewing and feedback for college drinkers: Handling missing values with complete case analysis and multiple imputation

Objective: In this secondary data analysis, three statistical methodologies were implemented to handle cases with missing data in a motivational interviewing and feedback study. The aim was to evaluate the impact that these methodologies have on the data analysis. ^ Methods: We first evaluated whether the assumption of missing completely at random held for this study. We then proceeded to conduct a secondary data analysis using a mixed linear model to handle missing data with three methodologies (a) complete case analysis, (b) multiple imputation with explicit model containing outcome variables, time, and the interaction of time and treatment, and (c) multiple imputation with explicit model containing outcome variables, time, the interaction of time and treatment, and additional covariates (e.g., age, gender, smoke, years in school, marital status, housing, race/ethnicity, and if participants play on athletic team). Several comparisons were conducted including the following ones: 1) the motivation interviewing with feedback group (MIF) vs. the assessment only group (AO), the motivation interviewing group (MIO) vs. AO, and the intervention of the feedback only group (FBO) vs. AO, 2) MIF vs. FBO, and 3) MIF vs. MIO.^ Results: We first evaluated the patterns of missingness in this study, which indicated that about 13% of participants showed monotone missing patterns, and about 3.5% showed non-monotone missing patterns. Then we evaluated the assumption of missing completely at random by Little's missing completely at random (MCAR) test, in which the Chi-Square test statistic was 167.8 with 125 degrees of freedom, and its associated p-value was p=0.006, which indicated that the data could not be assumed to be missing completely at random. After that, we compared if the three different strategies reached the same results. For the comparison between MIF and AO as well as the comparison between MIF and FBO, only the multiple imputation with additional covariates by uncongenial and congenial models reached different results. For the comparison between MIF and MIO, all the methodologies for handling missing values obtained different results. ^ Discussions: The study indicated that, first, missingness was crucial in this study. Second, to understand the assumptions of the model was important since we could not identify if the data were missing at random or missing not at random. Therefore, future researches should focus on exploring more sensitivity analyses under missing not at random assumption.^

Characterization of the ebp(fm) pilus-encoding operon of Enterococcus faecium and its role in biofilm formation and virulence in a murine model of urinary tract infection.

We recently identified 15 genes encoding putative surface proteins with features of MSCRAMMs and/or pili in the Enterococcus faecium TX0016 (DO) genome, including four predicted pilus-encoding gene clusters; we also demonstrated that one of these, ebpABC(fm), is transcribed as an operon, that its putative major pilus subunit, EbpC(fm) (also called pilB), is polymerized into high molecular weight complexes, and that it is enriched among clinical E. faecium isolates. Here, we created a deletion of the ebpABC(fm) operon in an endocarditis-derived E. faecium strain (TX82) and showed, by a combination of whole-cell ELISA, flow cytometry, immunoblot and immunogold electron microscopy, that this deletion abolished EbpC(fm) expression and eliminated EbpC(fm)-containing pili from the cell surface. However, transcription of the downstream sortase, bps(fm), was not affected. Importantly, the ebpABC(fm) deletion resulted in significantly reduced biofilm formation (p < 0.0001) and initial adherence (p < 0.0001) versus the wild-type; both were restored by complementing ebpABC(fm) in trans, which also restored cell surface expression of EbpC(fm) and pilus production. Furthermore, the deletion mutant was significantly attenuated in two independent mixed infection mouse urinary tract experiments, i.e., outnumbered by the wild-type in kidneys (p = 0.0003 and < 0.0001, respectively) and urinary bladders (p = 0.0003 and = 0.002). In conclusion, we have shown that the ebpABC(fm) locus encodes pili on the E. faecium TX82 cell surface and provide the first evidence that pili of this emerging pathogen are important for its ability to form biofilm and to cause infection in an ascending UTI model.

Traditional linkage analysis in admixed families

Currently there is no general method to study the impact of population admixture within families on the assumptions of random mating and consequently, Hardy-Weinberg equilibrium (HWE) and linkage equilibrium (LE) and on the inference obtained from traditional linkage analysis. ^ First, through simulation, the effect of admixture of two populations on the log of the odds (LOD) score was assessed, using Prostate Cancer as the typical disease model. Comparisons between simulated mixed and homogeneous families were performed. LOD scores under both models of admixture (within families and within a data set of homogeneous families) were closest to the homogeneous family scores of the population having the highest mixing proportion. Random sampling of families or ascertainment of families with disease affection status did not affect this observation, nor did the mode of inheritance (dominant/recessive) or sample size. ^ Second, after establishing the effect of admixture on the LOD score and inference for linkage, the presence of induced disequilibria by population admixture within families was studied and an adjustment procedure was developed. The adjustment did not force all disequilibria to disappear but because the families were adjusted for the population admixture, those replicates where the disequilibria exist are no longer affected by the disequilibria in terms of maximization for linkage. Furthermore, the adjustment was able to exclude uninformative families or families that had such a high departure from HWE and/or LE that their LOD scores were not reliable. ^ Together these observations imply that the presence of families of mixed population ancestry impacts linkage analysis in terms of the LOD score and the estimate of the recombination fraction. ^

Design of mixed-longitudinal studies

Cross-sectional designs, longitudinal designs in which a single cohort is followed over time, and mixed-longitudinal designs in which several cohorts are followed for a shorter period are compared by their precision, potential for bias due to age, time and cohort effects, and feasibility. Mixed longitudinal studies have two advantages over longitudinal studies: isolation of time and age effects and shorter completion time. Though the advantages of mixed-longitudinal studies are clear, choosing an optimal design is difficult, especially given the number of possible combinations of the number of cohorts and number of overlapping intervals between cohorts. The purpose of this paper is to determine the optimal design for detecting differences in group growth rates.^ The type of mixed-longitudinal study appropriate for modeling both individual and group growth rates is called a "multiple-longitudinal" design. A multiple-longitudinal study typically requires uniform or simultaneous entry of subjects, who are each observed till the end of the study.^ While recommendations for designing pure-longitudinal studies have been made by Schlesselman (1973b), Lefant (1990) and Helms (1991), design recommendations for multiple-longitudinal studies have never been published. It is shown that by using power analyses to determine the minimum number of occasions per cohort and minimum number of overlapping occasions between cohorts, in conjunction with a cost model, an optimal multiple-longitudinal design can be determined. An example of systolic blood pressure values for cohorts of males and cohorts of females, ages 8 to 18 years, is given. ^

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. ^