Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Fluorophotometry is a sensitive method/technique to evaluate epithelial permeability in murine experimental dry eye

Purpose. Fluorophotometry is a well validated method for assessing corneal permeability in human subjects. However, with the growing importance of basic science animal research in ophthalmology, fluorophotometry’s use in animals must be further evaluated. The purpose of this study was to evaluate corneal epithelial permeability following desiccating stress using the modified Fluorotron Master™. ^ Methods. Corneal permeability was evaluated prior to and after subjecting 6-8 week old C57BL/6 mice to experimental dry eye (EDE) for 2 and 5 days (n=9/time point). Untreated mice served as controls. Ten microliters of 0.001% sodium fluorescein (NaF) were instilled topically into each mouse’s left eye to create an eye bath, and left to permeate for 3 minutes. The eye bath was followed by a generous wash with Buffered Saline Solution (BSS) and alignment with the Fluorotron Master™. Seven corneal scans using the Fluorotron Master were performed during 15 minutes (1 st post-wash scans), followed by a second wash using BSS and another set of five corneal scans (2nd post-wash scans) during the next 15 minutes. Corneal permeability was calculated using data calculated with the FM™ Mouse software. ^ Results. When comparing the difference between the Post wash #1 scans within the group and the Post wash #2 scans within the group using a repeated measurement design, there was a statistical difference in the corneal fluorescein permeability of the Post-wash #1 scans after 5 days (1160.21±108.26 vs. 1000.47±75.56 ng/mL, P<0.016 for UT-5 day comparison 8 [0.008]), but not after only 2 days of EDE compared to Untreated mice (1115.64±118.94 vs. 1000.47±75.56 ng/mL, P>0.016 for UT-2 day comparison [0.050]). There was no statistical difference between the 2 day and 5 day Post wash #1 scans (P=.299). The Post-wash #2 scans demonstrated that EDE caused a significant NaF retention at both 2 and 5 days of EDE compared to baseline, untreated controls (1017.92±116.25, 1015.40±120.68 vs. 528.22±127.85 ng/mL, P<0.05 [0.0001 for both]). There was no statistical difference between the 2 day and 5 day Post wash #2 scans (P=.503). The comparison between the Untreated post wash #1 with untreated post wash #2 scans using a Paired T-test showed a significant difference between the two sets of scans (P=0.000). There is also a significant difference between the 2 day comparison and the 5 day comparison (P values = 0.010 and 0.002, respectively). ^ Conclusion. Desiccating stress increases permeability of the corneal epithelium to NaF, and increases NaF retention in the corneal stroma. The Fluorotron Master is a useful and sensitive tool to evaluate corneal permeability in murine dry eye, and will be a useful tool to evaluate the effectiveness of dry eye treatments in animal-model drug trials.^

The information bottleneck method for genome-wide association studies

In population studies, most current methods focus on identifying one outcome-related SNP at a time by testing for differences of genotype frequencies between disease and healthy groups or among different population groups. However, testing a great number of SNPs simultaneously has a problem of multiple testing and will give false-positive results. Although, this problem can be effectively dealt with through several approaches such as Bonferroni correction, permutation testing and false discovery rates, patterns of the joint effects by several genes, each with weak effect, might not be able to be determined. With the availability of high-throughput genotyping technology, searching for multiple scattered SNPs over the whole genome and modeling their joint effect on the target variable has become possible. Exhaustive search of all SNP subsets is computationally infeasible for millions of SNPs in a genome-wide study. Several effective feature selection methods combined with classification functions have been proposed to search for an optimal SNP subset among big data sets where the number of feature SNPs far exceeds the number of observations. ^ In this study, we take two steps to achieve the goal. First we selected 1000 SNPs through an effective filter method and then we performed a feature selection wrapped around a classifier to identify an optimal SNP subset for predicting disease. And also we developed a novel classification method-sequential information bottleneck method wrapped inside different search algorithms to identify an optimal subset of SNPs for classifying the outcome variable. This new method was compared with the classical linear discriminant analysis in terms of classification performance. Finally, we performed chi-square test to look at the relationship between each SNP and disease from another point of view. ^ In general, our results show that filtering features using harmononic mean of sensitivity and specificity(HMSS) through linear discriminant analysis (LDA) is better than using LDA training accuracy or mutual information in our study. Our results also demonstrate that exhaustive search of a small subset with one SNP, two SNPs or 3 SNP subset based on best 100 composite 2-SNPs can find an optimal subset and further inclusion of more SNPs through heuristic algorithm doesn't always increase the performance of SNP subsets. Although sequential forward floating selection can be applied to prevent from the nesting effect of forward selection, it does not always out-perform the latter due to overfitting from observing more complex subset states. ^ Our results also indicate that HMSS as a criterion to evaluate the classification ability of a function can be used in imbalanced data without modifying the original dataset as against classification accuracy. Our four studies suggest that Sequential Information Bottleneck(sIB), a new unsupervised technique, can be adopted to predict the outcome and its ability to detect the target status is superior to the traditional LDA in the study. ^ From our results we can see that the best test probability-HMSS for predicting CVD, stroke,CAD and psoriasis through sIB is 0.59406, 0.641815, 0.645315 and 0.678658, respectively. In terms of group prediction accuracy, the highest test accuracy of sIB for diagnosing a normal status among controls can reach 0.708999, 0.863216, 0.639918 and 0.850275 respectively in the four studies if the test accuracy among cases is required to be not less than 0.4. On the other hand, the highest test accuracy of sIB for diagnosing a disease among cases can reach 0.748644, 0.789916, 0.705701 and 0.749436 respectively in the four studies if the test accuracy among controls is required to be at least 0.4. ^ A further genome-wide association study through Chi square test shows that there are no significant SNPs detected at the cut-off level 9.09451E-08 in the Framingham heart study of CVD. Study results in WTCCC can only detect two significant SNPs that are associated with CAD. In the genome-wide study of psoriasis most of top 20 SNP markers with impressive classification accuracy are also significantly associated with the disease through chi-square test at the cut-off value 1.11E-07. ^ Although our classification methods can achieve high accuracy in the study, complete descriptions of those classification results(95% confidence interval or statistical test of differences) require more cost-effective methods or efficient computing system, both of which can't be accomplished currently in our genome-wide study. We should also note that the purpose of this study is to identify subsets of SNPs with high prediction ability and those SNPs with good discriminant power are not necessary to be causal markers for the disease.^

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.^

A novel method for evaluating an interaction effect of correlated continuous covariates in a linear model

Interaction effect is an important scientific interest for many areas of research. Common approach for investigating the interaction effect of two continuous covariates on a response variable is through a cross-product term in multiple linear regression. In epidemiological studies, the two-way analysis of variance (ANOVA) type of method has also been utilized to examine the interaction effect by replacing the continuous covariates with their discretized levels. However, the implications of model assumptions of either approach have not been examined and the statistical validation has only focused on the general method, not specifically for the interaction effect.^ In this dissertation, we investigated the validity of both approaches based on the mathematical assumptions for non-skewed data. We showed that linear regression may not be an appropriate model when the interaction effect exists because it implies a highly skewed distribution for the response variable. We also showed that the normality and constant variance assumptions required by ANOVA are not satisfied in the model where the continuous covariates are replaced with their discretized levels. Therefore, naïve application of ANOVA method may lead to an incorrect conclusion. ^ Given the problems identified above, we proposed a novel method modifying from the traditional ANOVA approach to rigorously evaluate the interaction effect. The analytical expression of the interaction effect was derived based on the conditional distribution of the response variable given the discretized continuous covariates. A testing procedure that combines the p-values from each level of the discretized covariates was developed to test the overall significance of the interaction effect. According to the simulation study, the proposed method is more powerful then the least squares regression and the ANOVA method in detecting the interaction effect when data comes from a trivariate normal distribution. The proposed method was applied to a dataset from the National Institute of Neurological Disorders and Stroke (NINDS) tissue plasminogen activator (t-PA) stroke trial, and baseline age-by-weight interaction effect was found significant in predicting the change from baseline in NIHSS at Month-3 among patients received t-PA therapy.^

Statistical Methods for Differential Expressions of Genes Detected in Multiple-Condition Experiment of Microarray

Most studies of differential gene-expressions have been conducted between two given conditions. The two-condition experimental (TCE) approach is simple in that all genes detected display a common differential expression pattern responsive to a common two-condition difference. Therefore, the genes that are differentially expressed under the other conditions other than the given two conditions are undetectable with the TCE approach. In order to address the problem, we propose a new approach called multiple-condition experiment (MCE) without replication and develop corresponding statistical methods including inference of pairs of conditions for genes, new t-statistics, and a generalized multiple-testing method for any multiple-testing procedure via a control parameter C. We applied these statistical methods to analyze our real MCE data from breast cancer cell lines and found that 85 percent of gene-expression variations were caused by genotypic effects and genotype-ANAX1 overexpression interactions, which agrees well with our expected results. We also applied our methods to the adenoma dataset of Notterman et al. and identified 93 differentially expressed genes that could not be found in TCE. The MCE approach is a conceptual breakthrough in many aspects: (a) many conditions of interests can be conducted simultaneously; (b) study of association between differential expressions of genes and conditions becomes easy; (c) it can provide more precise information for molecular classification and diagnosis of tumors; (d) it can save lot of experimental resources and time for investigators.^

A STUDY OF INFLUENZA AND OF STATISTICAL METHODS USED TO REPORT INFLUENZA

This paper defines and compares several models for describing excess influenza pneumonia mortality in Houston. First, the methodology used by the Center for Disease Control is examined and several variations of this methodology are studied. All of the models examined emphasize the difficulty of omitting epidemic weeks.^ In an attempt to find a better method of describing expected and epidemic mortality, time series methods are examined. Grouping in four-week periods, truncating the data series to adjust epidemic periods, and seasonally-adjusting the series y(,t), by:^ (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)^ is the best method examined. This new series w(,t) is stationary and a moving average model MA(1) gives a good fit for forecasting influenza and pneumonia mortality in Houston.^ Influenza morbidity, other causes of death, sex, race, age, climate variables, environmental factors, and school absenteeism are all examined in terms of their relationship to influenza and pneumonia mortality. Both influenza morbidity and ischemic heart disease mortality show a very high relationship that remains when seasonal trends are removed from the data. However, when jointly modeling the three series it is obvious that the simple time series MA(1) model of truncated, seasonally-adjusted four-week data gives a better forecast.^

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.^

Comparison of two statistical methods for rare variant association analysis

Studies have shown that rare genetic variants have stronger effects in predisposing common diseases, and several statistical methods have been developed for association studies involving rare variants. In order to better understand how these statistical methods perform, we seek to compare two recently developed rare variant statistical methods (VT and C-alpha) on 10,000 simulated re-sequencing data sets with disease status and the corresponding 10,000 simulated null data sets. The SLC1A1 gene has been suggested to be associated with diastolic blood pressure (DBP) in previous studies. In the current study, we applied VT and C-alpha methods to the empirical re-sequencing data for the SLC1A1 gene from 300 whites and 200 blacks. We found that VT method obtains higher power and performs better than C-alpha method with the simulated data we used. The type I errors were well-controlled for both methods. In addition, both VT and C-alpha methods suggested no statistical evidence for the association between the SLC1A1 gene and DBP. Overall, our findings provided an important comparison of the two statistical methods for future reference and provided preliminary and pioneer findings on the association between the SLC1A1 gene and blood pressure.^

A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^

Instrumental variable method for the causal relationship between soluble receptor for advanced glycation end-products (sRAGE) and risk of pancreatic cancer

This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^

Estimates of hospital and physician costs of epilepsy in the United States for 1995 comparing the provider -based survey method and a patient -based medical charts and billing method

This investigation compares two different methodologies for calculating the national cost of epilepsy: provider-based survey method (PBSM) and the patient-based medical charts and billing method (PBMC&BM). The PBSM uses the National Hospital Discharge Survey (NHDS), the National Hospital Ambulatory Medical Care Survey (NHAMCS) and the National Ambulatory Medical Care Survey (NAMCS) as the sources of utilization. The PBMC&BM uses patient data, charts and billings, to determine utilization rates for specific components of hospital, physician and drug prescriptions. ^ The 1995 hospital and physician cost of epilepsy is estimated to be $722 million using the PBSM and $1,058 million using the PBMC&BM. The difference of $336 million results from $136 million difference in utilization and $200 million difference in unit cost. ^ Utilization. The utilization difference of $136 million is composed of an inpatient variation of $129 million, $100 million hospital and $29 million physician, and an ambulatory variation of $7 million. The $100 million hospital variance is attributed to inclusion of febrile seizures in the PBSM, $−79 million, and the exclusion of admissions attributed to epilepsy, $179 million. The former suggests that the diagnostic codes used in the NHDS may not properly match the current definition of epilepsy as used in the PBMC&BM. The latter suggests NHDS errors in the attribution of an admission to the principal diagnosis. ^ The $29 million variance in inpatient physician utilization is the result of different per-day-of-care physician visit rates, 1.3 for the PBMC&BM versus 1.0 for the PBSM. The absence of visit frequency measures in the NHDS affects the internal validity of the PBSM estimate and requires the investigator to make conservative assumptions. ^ The remaining ambulatory resource utilization variance is $7 million. Of this amount, $22 million is the result of an underestimate of ancillaries in the NHAMCS and NAMCS extrapolations using the patient visit weight. ^ Unit cost. The resource cost variation is $200 million, inpatient is $22 million and ambulatory is $178 million. The inpatient variation of $22 million is composed of $19 million in hospital per day rates, due to a higher cost per day in the PBMC&BM, and $3 million in physician visit rates, due to a higher cost per visit in the PBMC&BM. ^ The ambulatory cost variance is $178 million, composed of higher per-physician-visit costs of $97 million and higher per-ancillary costs of $81 million. Both are attributed to the PBMC&BM's precise identification of resource utilization that permits accurate valuation. ^ Conclusion. Both methods have specific limitations. The PBSM strengths are its sample designs that lead to nationally representative estimates and permit statistical point and confidence interval estimation for the nation for certain variables under investigation. However, the findings of this investigation suggest the internal validity of the estimates derived is questionable and important additional information required to precisely estimate the cost of an illness is absent. ^ The PBMC&BM is a superior method in identifying resources utilized in the physician encounter with the patient permitting more accurate valuation. However, the PBMC&BM does not have the statistical reliability of the PBSM; it relies on synthesized national prevalence estimates to extrapolate a national cost estimate. While precision is important, the ability to generalize to the nation may be limited due to the small number of patients that are followed. ^