27 resultados para Multivariate models

em Helda - Digital Repository of University of Helsinki


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This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

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Väitöskirjassa selvitettiin ikäihmisten laitoshoitoon siirtymisen todennäköisyyttä ja sen taustoja kansainvälisesti ainutlaatuisen rekisteriaineiston avulla. Selvitettäviä asioita olivat eri sairauksien, sosioekonomisten tekijöiden, puolison olemassaolon ja leskeksi jäämisen yhteys laitoshoitoon siirtymiseen yli 65-vuotiailla suomalaisilla. Tutkimuksessa havaittiin, että dementia, Parkinsonin tauti, aivohalvaus, masennusoireet ja muut mielenterveysongelmat, lonkkamurtuma sekä diabetes lisäsivät ikäihmisten todennäköisyyttä siirtyä laitoshoitoon yli 50 prosentilla, kun muut sairaudet ja sosiodemografiset tekijät oli otettu huomioon. Korkeat tulot vähensivät laitoshoidon todennäköisyyttä, kun taas puutteellinen asuminen (ilman peseytymistiloja tai keskus- tai sähkölämmitystä) sekä erittäin puutteellinen asuminen (ilman lämmintä vettä, vesijohtoa, viemäriä tai vesivessaa) lisäsivät todennäkösyyttä, kun muut sosiodemografiset tekijät, sairaudet ja asuinalue oli huomioitu. Kerrostalon hissittömyys ei ollut yhteydessä laitoshoidon todennäköisyyteen. Todennäköisyys siirtyä laitoshoitoon oli jostain syystä korkeampaa niillä ikäihmisillä, jotka asuivat vuokralla ja matalampaa omakotitalossa asuvilla ja niillä, joilla oli auto. Puolison olemassaolo vähensi ja leskeksi jääminen lisäsi laitoshoidon todennäköisyyttä huomattavasti. Todennäköisyys oli erityisen suuri, yli kolminkertainen, kun puolison kuolemasta oli kulunut enintään kuukausi verrattuna niihin, joiden puoliso oli elossa. Todennäköisyys laski, kun puolison kuolemasta kului aikaa. Miesten ja naisten tulokset olivat samansuuntaisia. Korkeat tulot tai koulutus eivät suojanneet riskiltä joutua laitoshoitoon puolison kuoltua. Puolison kuolema näyttää lisäävän hoidon tarvetta, kun kotona ei ole enää puolisoa tukemassa ja huolehtimassa kodin askareista. Laitoshoidon tarve vähenee, jos ja kun lesket ajan kuluessa oppivat elämään yksin. Toisaalta tutkimustulokset saattavat viitata myös siihen, että kaikkein huonokuntoisimmat lesket, jotka eivät pärjää yksin asuessaan, siirtyvät laitoshoitoon hyvin nopeasti puolison kuoltua. Tutkimuksessa oli mukana yhteensä yli 280 000 yli 65-vuotiasta henkilöä, joiden pitkäaikaiseen laitoshoitoon siirtymistä seurattiin tammikuusta 1998 syyskuuhun 2003. Laitoshoidoksi määriteltiin terveyskeskuksissa, sairaaloissa ja vanhainkodeissa tai vastaavissa yksiköissä tapahtuva pitkäaikainen hoito, joka kesti yli 90 vuorokautta tai oli vahvistettu pitkäaikaishoidon päätöksellä. Tutkimuksessa käytetty aineisto koottiin väestörekistereistä, sosiaali- ja terveydenhuollon rekistereistä ja lääkerekistereistä.

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Background and aims: Low stage and curative surgery are established factors for improved survival in gastric cancer. However, not all low-stage patients have a good prognosis. Cyclooxygenase-2 (COX-2) is known to associate with reduced survival in several cancers, and has been shown to play an important role in gastric carcinogenesis. Since new and better prognostic markers are needed for gastric cancer, we studied the prognostic significance of COX-2 and of markers that associate with COX-2 expression. We also studied markers reflecting proliferation and apoptosis, and evaluated their association with COX-2. Our purpose was to construct an accurate prognostic model by combining tissue markers and clinicopathogical factors. Materials and methods: Of 342 consecutive patients who underwent surgery for gastric cancer at Meilahti Hospital, Helsinki University Central Hospital, 337 were included in this study. Low stages I to II were represented by 141 (42%) patients, and high stages III to IV by 196 (58%). Curative surgery was performed on 176 (52%) patients. Survival data were obtained from the national registers. Slides from archive tissue blocks were prepared for immunohistochemistry by use of COX-2, human antigen R (HuR), cyclin A, matrix metalloproteinases 2 and 9 (MMP-2, MMP-9), and Ki-67 antibodies. Immunostainings were scored by microscopy, and scores were entered into a database. Associations of tumor markers with clinicopathological factors were calculated, as well as associations with p53, p21, and results of flow cytometry from earlier studies. Survival analysis was performed by the Kaplan-Meier method, and Cox multivariate models were reconstructed. Cell culture experiments were performed to explore the effect of small interfering (si)RNA of HuR on COX-2 expression in a TMK-1 gastric cancer cell line. Results: Overall 5-year survival was 35.1%. Study I showed that COX-2 was an independent prognostic factor, and that the prognostic impact of COX-2 was more pronounced in low-stage patients. Cytoplasmic HuR expression also associated with reduced survival in gastric cancer patients in a non-independent manner. Cell culture experiments showed that HuR can regulate COX-2 expression in TMK-1 cells in vitro, with an association also between COX-2 and HuR tissue expression in a clinical material. In Study II, cyclin A was an independent prognostic factor and was associated with HuR expression in the gastric cancer material. The results of Study III showed that epithelial MMP-2 associated with survival in univariate, but not in multivariate analysis. However, MMP-9 showed no prognostic value. MMP-2 expression was associated with COX-2 expression. In Study IV, the prognostic power of COX-2 was compared with that of all tested markers associated with survival in Studies I to III, as well as with p21, p53, and flow cytometry results. COX-2 and p53 were independent prognostic factors, and COX-2 expression was associated with that of p53 and Ki-67 and also with aneuploidy. Conclusions: COX-2 is an independent prognostic factor in gastric cancer, and its prognostic power emerges especially in low stage cancer. COX-2 is regulated by HuR, and is associated with factors reflecting invasion, proliferation, and apoptosis. In an extended multivariate model, COX-2 retained its position as an independent prognosticator. COX-2 can be considered a promising new prognostic marker in gastric cancer.

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Uveal melanoma (UM) is the second most common primary intraocular cancer worldwide. It is a relatively rare cancer, but still the second most common type of primary malignant melanoma in humans. UM is a slowly growing tumor, and gives rise to distant metastasis mainly to the liver via the bloodstream. About 40% of patients with UM die of metastatic disease within 10 years of diagnosis, irrespective of the type of treatment. During the last decade, two main lines of research have aimed to achieve enhanced understanding of the metastasis process and accurate prognosis of patients with UM. One emphasizes the characteristics of tumor cells, particularly their nucleoli, and markers of proliferation, and the other the characteristics of tumor blood vessels. Of several morphometric measurements, the mean diameter of the ten largest nucleoli (MLN) has become the most widely applied. A large MLN has consistently been associated with high likelihood of dying from UM. Blood vessels are of paramount importance in metastasis of UM. Different extravascular matrix patterns can be seen in UM, like loops and networks. This presence is associated with death from metastatic melanoma. However, the density of microvessels is also of prognostic importance. This study was undertaken to help understanding some histopathological factors which might contribute to developing metastasis in UM patients. Factors which could be related to tumor progression to metastasis disease, namely nucleolar size, MLN, microvascular density (MVD), cell proliferation, and The Insulin-like Growth Factor 1 Receptor(IGF-1R), were investigated. The primary aim of this thesis was to study the relationship between prognostic factors such as tumor cell nucleolar size, proliferation, extravascular matrix patterns, and dissemination of UM, and to assess to what extent there is a relationship to metastasis. The secondary goal was to develop a multivariate model which includes MLN and cell proliferation in addition to MVD, and which would fit better with population-based, melanoma-related survival data than previous models. I studied 167 patients with UM, who developed metastasis even after a very long time following removal of the eye, metastatic disease was the main cause of death, as documented in the Finnish Cancer Registry and on death certificates. Using an independent population-based data set, it was confirmed that MLN and extravascular matrix loops and networks were unrelated, independent predictors of survival in UM. Also, it has been found that multivariate models including MVD in addition to MLN fitted significantly better with survival data than models which excluded MVD. This supports the idea that both the characteristics of the blood vessels and the cells are important, and the future direction would be to look for the gene expression profile, whether it is associated more with MVD or MLN. The former relates to the host response to the tumor and may not be as tightly associated with the gene expression profile, yet most likely involved in the process of hematogenous metastasis. Because fresh tumor material is needed for reliable genetic analysis, such analysis could not be performed Although noninvasive detection of certain extravascular matrix patterns is now technically possible,in managing patients with UM, this study and tumor genetics suggest that such noninvasive methods will not fully capture the process of clinical metastasis. Progress in resection and biopsy techniques is likely in the near future to result in fresh material for the ophthalmic pathologist to correlate angiographic data, histopathological characteristics such as MLN, and genetic data. This study supported the theory that tumors containing epithelioid cells grow faster and have poorer prognosis when studied by cell proliferation in UM based on Ki-67 immunoreactivity. Cell proliferation index fitted best with the survival data when combined with MVD, MLN, and presence of epithelioid cells. Analogous with the finding that high MVD in primary UM is associated with shorter time to metastasis than low MVD, high MVD in hepatic metastasis tends to be associated with shorter survival after diagnosis of metastasis. Because the liver is the main organ for metastasis from UM, growth factors largely produced in the liver hepatocyte growth factor, epidermal growth factor and insulin-like growth factor-1 (IGF-1) together with their receptors may have a role in the homing and survival of metastatic cells. Therefore the association between immunoreactivity for IGF-1R in primary UM and metastatic death was studied. It was found that immunoreactivity for IGF-IR did not independently predict metastasis from primary UM in my series.

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Many active pharmaceutical ingredients (APIs) have both anhydrate and hydrate forms. Due to the different physicochemical properties of solid forms, the changes in solid-state may result in therapeutic, pharmaceutical, legal and commercial problems. In order to obtain good solid dosage form quality and performance, there is a constant need to understand and control these phase transitions during manufacturing and storage. Thus it is important to detect and also quantify the possible transitions between the different forms. In recent years, vibrational spectroscopy has become an increasingly popular tool to characterise the solid-state forms and their phase transitions. It offers several advantages over other characterisation techniques including an ability to obtain molecular level information, minimal sample preparation, and the possibility of monitoring changes non-destructively in-line. Dehydration is the phase transition of hydrates which is frequently encountered during the dosage form production and storage. The aim of the present thesis was to investigate the dehydration behaviour of diverse pharmaceutical hydrates by near infrared (NIR), Raman and terahertz pulsed spectroscopic (TPS) monitoring together with multivariate data analysis. The goal was to reveal new perspectives for investigation of the dehydration at the molecular level. Solid-state transformations were monitored during dehydration of diverse hydrates on hot-stage. The results obtained from qualitative experiments were used to develop a method and perform the quantification of the solid-state forms during process induced dehydration in a fluidised bed dryer. Both in situ and in-line process monitoring and quantification was performed. This thesis demonstrated the utility of vibrational spectroscopy techniques and multivariate modelling to monitor and investigate dehydration behaviour in situ and during fluidised bed drying. All three spectroscopic methods proved complementary in the study of dehydration. NIR spectroscopy models could quantify the solid-state forms in the binary system, but were unable to quantify all the forms in the quaternary system. Raman spectroscopy models on the other hand could quantify all four solid-state forms that appeared upon isothermal dehydration. The speed of spectroscopic methods makes them applicable for monitoring dehydration and the quantification of multiple forms was performed during phase transition. Thus the solid-state structure information at the molecular level was directly obtained. TPS detected the intermolecular phonon modes and Raman spectroscopy detected mostly the changes in intramolecular vibrations. Both techniques revealed information about the crystal structure changes. NIR spectroscopy, on the other hand was more sensitive to water content and hydrogen bonding environment of water molecules. This study provides a basis for real time process monitoring using vibrational spectroscopy during pharmaceutical manufacturing.

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In this dissertation, I present an overall methodological framework for studying linguistic alternations, focusing specifically on lexical variation in denoting a single meaning, that is, synonymy. As the practical example, I employ the synonymous set of the four most common Finnish verbs denoting THINK, namely ajatella, miettiä, pohtia and harkita ‘think, reflect, ponder, consider’. As a continuation to previous work, I describe in considerable detail the extension of statistical methods from dichotomous linguistic settings (e.g., Gries 2003; Bresnan et al. 2007) to polytomous ones, that is, concerning more than two possible alternative outcomes. The applied statistical methods are arranged into a succession of stages with increasing complexity, proceeding from univariate via bivariate to multivariate techniques in the end. As the central multivariate method, I argue for the use of polytomous logistic regression and demonstrate its practical implementation to the studied phenomenon, thus extending the work by Bresnan et al. (2007), who applied simple (binary) logistic regression to a dichotomous structural alternation in English. The results of the various statistical analyses confirm that a wide range of contextual features across different categories are indeed associated with the use and selection of the selected think lexemes; however, a substantial part of these features are not exemplified in current Finnish lexicographical descriptions. The multivariate analysis results indicate that the semantic classifications of syntactic argument types are on the average the most distinctive feature category, followed by overall semantic characterizations of the verb chains, and then syntactic argument types alone, with morphological features pertaining to the verb chain and extra-linguistic features relegated to the last position. In terms of overall performance of the multivariate analysis and modeling, the prediction accuracy seems to reach a ceiling at a Recall rate of roughly two-thirds of the sentences in the research corpus. The analysis of these results suggests a limit to what can be explained and determined within the immediate sentential context and applying the conventional descriptive and analytical apparatus based on currently available linguistic theories and models. The results also support Bresnan’s (2007) and others’ (e.g., Bod et al. 2003) probabilistic view of the relationship between linguistic usage and the underlying linguistic system, in which only a minority of linguistic choices are categorical, given the known context – represented as a feature cluster – that can be analytically grasped and identified. Instead, most contexts exhibit degrees of variation as to their outcomes, resulting in proportionate choices over longer stretches of usage in texts or speech.

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This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

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This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

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Hypertension, obesity, dyslipidemia and dysglycemia constitute metabolic syndrome, a major public health concern, which is associated with cardiovascular mortality. High dietary salt (NaCl) is the most important dietary risk factor for elevated blood pressure. The kidney has a major role in salt-sensitive hypertension and is vulnerable to harmful effects of increased blood pressure. Elevated serum urate is a common finding in these disorders. While dysregulation of urate excretion is associated with cardiovascular diseases, present studies aimed to clarify the role of xanthine oxidoreductase (XOR), i.e. xanthine dehydrogenase (XDH) and its post-translational isoform xanthine oxidase (XO), in cardiovascular diseases. XOR yields urate from hypoxanthine and xanthine. Low oxygen levels upregulate XOR in addition to other factors. In present studies higher renal XOR activity was found in hypertension-prone rats than in the controls. Furthermore, NaCl intake increased renal XOR dose-dependently. To clarify whether XOR has any causal role in hypertension, rats were kept on NaCl diets for different periods of time, with or without a XOR inhibitor, allopurinol. While allopurinol did not alleviate hypertension, it prevented left ventricular and renal hypertrophy. Nitric oxide synthases (NOS) produce nitric oxide (NO), which mediates vasodilatation. A paucity of NO, produced by NOS inhibition, aggravated hypertension and induced renal XOR, whereas NO generating drug, alleviated salt-induced hypertension without changes in renal XOR. Zucker fa/fa rat is an animal model of metabolic syndrome. These rats developed substantial obesity and modest hypertension and showed increased hepatic and renal XOR activities. XOR was modified by diet and antihypertensive treatment. Cyclosporine (CsA) is a fungal peptide and one of the first-line immunosuppressive drugs used in the management of organ transplantation. Nephrotoxicity ensue high doses resulting in hypertension and limit CsA use. CsA increased renal XO substantially in salt-sensitive rats on a high NaCl diet, indicating a possible role for this reactive oxygen species generating isoform in CsA nephrotoxicity. Renal hypoxia, common to these rodent models of hypertension and obesity, is one of the plausible XOR inducing factors. Although XOR inhibition did not prevent hypertension, present experimental data indicate that XOR plays a role in the pathology of salt-induced cardiac and renal hypertrophy.

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Nephrin is a transmembrane protein belonging to the immunoglobulin superfamily and is expressed primarily in the podocytes, which are highly differentiated epithelial cells needed for primary urine formation in the kidney. Mutations leading to nephrin loss abrogate podocyte morphology, and result in massive protein loss into urine and consequent early death in humans carrying specific mutations in this gene. The disease phenotype is closely replicated in respective mouse models. The purpose of this thesis was to generate novel inducible mouse-lines, which allow targeted gene deletion in a time and tissue-specific manner. A proof of principle model for succesful gene therapy for this disease was generated, which allowed podocyte specific transgene replacement to rescue gene deficient mice from perinatal lethality. Furthermore, the phenotypic consequences of nephrin restoration in the kidney and nephrin deficiency in the testis, brain and pancreas in rescued mice were investigated. A novel podocyte-specific construct was achieved by using standard cloning techniques to provide an inducible tool for in vitro and in vivo gene targeting. Using modified constructs and microinjection procedures two novel transgenic mouse-lines were generated. First, a mouse-line with doxycycline inducible expression of Cre recombinase that allows podocyte-specific gene deletion was generated. Second, a mouse-line with doxycycline inducible expression of rat nephrin, which allows podocyte-specific nephrin over-expression was made. Furthermore, it was possible to rescue nephrin deficient mice from perinatal lethality by cross-breeding them with a mouse-line with inducible rat nephrin expression that restored the missing endogenous nephrin only in the kidney after doxycycline treatment. The rescued mice were smaller, infertile, showed genital malformations and developed distinct histological abnormalities in the kidney with an altered molecular composition of the podocytes. Histological changes were also found in the testis, cerebellum and pancreas. The expression of another molecule with limited tissue expression, densin, was localized to the plasma membranes of Sertoli cells in the testis by immunofluorescence staining. Densin may be an essential adherens junction protein between Sertoli cells and developing germ cells and these junctions share similar protein assembly with kidney podocytes. This single, binary conditional construct serves as a cost- and time-efficient tool to increase the understanding of podocyte-specific key proteins in health and disease. The results verified a tightly controlled inducible podocyte-specific transgene expression in vitro and in vivo as expected. These novel mouse-lines with doxycycline inducible Cre recombinase and with rat nephrin expression will be useful for conditional gene targeting of essential podocyte proteins and to study in detail their functions in the adult mice. This is important for future diagnostic and pharmacologic development platforms.

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This dissertation examines the short- and long-run impacts of timber prices and other factors affecting NIPF owners' timber harvesting and timber stocking decisions. The utility-based Faustmann model provides testable hypotheses of the exogenous variables retained in the timber supply analysis. The timber stock function, derived from a two-period biomass harvesting model, is estimated using a two-step GMM estimator based on balanced panel data from 1983 to 1991. Timber supply functions are estimated using a Tobit model adjusted for heteroscedasticity and nonnormality of errors based on panel data from 1994 to 1998. Results show that if specification analysis of the Tobit model is ignored, inconsistency and biasedness can have a marked effect on parameter estimates. The empirical results show that owner's age is the single most important factor determining timber stock; timber price is the single most important factor in harvesting decision. The results of the timber supply estimations can be interpreted using utility-based Faustmann model of a forest owner who values a growing timber in situ.