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.

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

Financial impact of the Medicare prospective payment system on long term acute care hospitals

Objective. Long Term Acute Care Hospitals (LTACs) are subject to Medicare rules because they accept Medicare and Medicaid patients. In October 2002, Medicare changed the LTAC reimbursement formulas, from a cost basis system to a Prospective Payment System (PPS). This study examines whether the PPS has negatively affected the financial performance of the LTAC hospitals in the period following the reimbursement change (2003-2006), as compared to the period prior to the change (1999-2003), and if so, to what extent. This study will also examine whether the PPS has resulted in a decreased average patient length of stay (LOS) in the LTAC hospitals for the period of 2003-2006 as compared to the prior period of 1999-2003, and if so, to what extent. ^ Methods. The study group consists of two large LTAC hospital systems, Kindred Healthcare Inc. and Select Specialty Hospitals of Select Medical Corporation. Financial data and operational indicators were reviewed, tabulated and dichotomized into two groups, covering the two periods: 1999-2002 and 2003-2006. The financial data included net annual revenues, net income, revenue per patient per day and profit margins. It was hypothesized that the profit margins for the LTAC hospitals were reduced because of the new PPS. Operational indicators, such as annual admissions, annual patient days, and average LOS were analyzed. It was hypothesized that LOS for the LTAC hospitals would have decreased. Case mix index, defined as the weighted average of patients’ DRGs for each hospital system, was not available to cast more light on the direction of LOS. ^ Results. This assessment found that the negative financial impacts did not materialize; instead, financial performance improved during the PPS period (2003-2006). The income margin percentage under the PPS increased for Kindred by 24%, and for Select by 77%. Thus, the study’s working hypothesis of reduced income margins for the LTACs under the PPS was contradicted. As to the average patient length of stay, LOS decreased from 34.7 days to 29.4 days for Kindred, and from 30.5 days to 25.3 days for Select. Thus, on the issue of LTAC shorter length of stay, the study’s working hypothesis was confirmed. ^ Conclusion. Overall, there was no negative financial effect on the LTAC hospitals during the period of 2003-2006 following Medicare implementation of the PPS in October 2002. On the contrary, the income margins improved significantly. ^ During the same period, LOS decreased following the implementation of the PPS. This was consistent with the LTAC hospitals’ pursuit of financial incentives.^

Financial impact of the Medicare prospective payment system on long term acute care hospitals

Objective. Long Term Acute Care Hospitals (LTACs) are subject to Medicare rules because they accept Medicare and Medicaid patients. In October 2002, Medicare changed the LTAC reimbursement formulas, from a cost basis system to a Prospective Payment System (PPS). This study examines whether the PPS has negatively affected the financial performance of the LTAC hospitals in the period following the reimbursement change (2003–2006), as compared to the period prior to the change (1999–2003), and if so, to what extent. This study will also examine whether the PPS has resulted in a decreased average patient length of stay (LOS) in the LTAC hospitals for the period of 2003–2006 as compared to the prior period of 1999-2003, and if so, to what extent. ^ Methods. The study group consists of two large LTAC hospital systems, Kindred Healthcare Inc. and Select Specialty Hospitals of Select Medical Corporation. Financial data and operational indicators were reviewed, tabulated and dichotomized into two groups, covering the two periods: 1999–2002 and 2003–2006. The financial data included net annual revenues, net income, revenue per patient per day and profit margins. It was hypothesized that the profit margins for the LTAC hospitals were reduced because of the new PPS. Operational indicators, such as annual admissions, annual patient days, and average LOS were analyzed. It was hypothesized that LOS for the LTAC hospitals would have decreased. Case mix index, defined as the weighted average of patients’ DRGs for each hospital system, was not available to cast more light on the direction of LOS. ^ Results. This assessment found that the negative financial impacts did not materialize; instead, financial performance improved during the PPS period (2003–2006). The income margin percentage under the PPS increased for Kindred by 24%, and for Select by 77%. Thus, the study’s working hypothesis of reduced income margins for the LTACs under the PPS was contradicted. As to the average patient length of stay, LOS decreased from 34.7 days to 29.4 days for Kindred, and from 30.5 days to 25.3 days for Select. Thus, on the issue of LTAC shorter length of stay, the study’s working hypothesis was confirmed. ^ Conclusion. Overall, there was no negative financial effect on the LTAC hospitals during the period of 2003–2006 following Medicare implementation of the PPS in October 2002. On the contrary, the income margins improved significantly. ^ During the same period, LOS decreased following the implementation of the PPS. This was consistent with the LTAC hospitals’ pursuit of financial incentives. ^