Multilevel analysis for a longitudinal clinical trial

This study applies the multilevel analysis technique to longitudinal data of a large clinical trial. The technique accounts for the correlation at different levels when modeling repeated blood pressure measurements taken throughout the trial. This modeling allows for closer inspection of the remaining correlation and non-homogeneity of variance in the data. Three methods of modeling the correlation were compared. ^

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

Forecasting cost based on a stochastic utilization plan and a fixed cost function

The application of Markov processes is very useful to health-care problems. The objective of this study is to provide a structured methodology of forecasting cost based upon combining a stochastic model of utilization (Markov Chain) and deterministic cost function. The perspective of the cost in this study is the reimbursement for the services rendered. The data to be used is the OneCare database of claim records of their enrollees over a two-year period of January 1, 1996–December 31, 1997. The model combines a Markov Chain that describes the utilization pattern and its variability where the use of resources by risk groups (age, gender, and diagnosis) will be considered in the process and a cost function determined from a fixed schedule based on real costs or charges for those in the OneCare claims database. The cost function is a secondary application to the model. Goodness-of-fit will be used checked for the model against the traditional method of cost forecasting. ^

Positional candidate cloning of the RP10 form of retinitis pigmentosa

Retinitis pigmentosa (RP) is a genetically heterogeneous group of retinal degenerations that affects over one million people worldwide. To date, 11 autosomal dominant, 13 autosomal recessive, and 5 X-linked forms of retinitis pigmentosa have been identified through linkage analysis, but the disease-causing genes and mutations have been found for only half of these loci. My research uses a positional candidate cloning approach to identify the gene and mutations responsible for one type of autosomal dominant retinitis pigmentosa, RP10. The premise is that identifying the genes and mutations responsible for disease will provide insight into disease mechanisms and provide treatment options. Previous research mapped the RP10 locus to a 5cM region on chromosome 7q31 between markers D7S686 and D7S530. Linkage and fine-point haplotype analysis was used to reduce and refine the RP10 disease interval to a 4cM region located between D7S2471 and a new marker located 45,000bp telomeric of D7S461. In order to identify genes located in the RP10 interval, an extensive EST map was created of this region. Five EST clusters from this map were analyzed to determine if mutations in these genes cause the RP10 form of retinitis pigmentosa. The genomic structure of a known metabotrophic glutamate receptor, GRMS8, was determined first. DNA sequencing of GRM8 in RP10 family members did not identify any disease-causing mutations. Four other EST clusters (A170, A173, A189, and A258) were characterized and determined to be part of the same gene, UBNL1 (ubinuclein-like 1). The full-length mRNA sequence and genomic structure of UBNL1 was determined and then screened in patients. No disease-causing mutations were identified in any of the RP10 family members tested. Recent data made available with the release of the public and Celera genome assemblies indicates that UBNL1 is outside of the RP10 disease region. Despite this complication, characterization of UBNL1 is still important in the understanding of normal visual processes and it is possible that mutations in UBNL1 could cause other forms of retinopathy. The EST map and list of RP10 candidates will continue to aid others in the search for the RP10 gene and mutations. ^

Genetic alterations associated with prostate cancer progression

Prostate cancer is the second most commonly diagnosed cancer among men in the United States. In this study, evidence is presented to support the hypothesis that specific chromosomal aberrations (involving one or more chromosomal regions) are associated with prostate cancer progression from organ-confined to locally advanced tumors and that some aberrations seen in high frequency in metastatic tumors may also be present in a subset of primary tumors. To determine the appropriate approach to address this hypothesis, I have established a modified CGH protocol by microdissection and DOP-PCR for use in detecting chromosomal changes in clinical prostate tumor specimens that is more sensitive and accurate than conventional CGH methods. I have successfully performed the improved CGH protocol to screen for genetic changes of 24 organ confined (pT2) and 21 locally advanced (pT3b) clinical prostate cancer specimens without metastases (N0M0). Comparisons of tumors by stage or Gleason scores following contingency table analysis showed that seven regions of the genome differed significantly between pT2 and pT3b tumors or between low and high Gleason tumors suggesting that these regions may be important in local prostate cancer progression. These included losses on 6p21–25, 6q24–27, 8p, 10q25–26, 15q22–26, and 18cen–q12 as well as gain of 3p13–q13. Multivariate analyses showed that loss of 8p (step1) and loss of 6q25–26 (or 6p21–25 or 10q25–26) (step 2) were predictive of pathologic stage or Gleason groups with 80% accuracy. Additional 5–7 steps in the multivariate model increased the predictive value to 91–95%. Comparison of the CGH data from the primary prostate tumors of this study with those obtained from published literature on metastases and recurrent tumors showed that the clinically more aggressive stage pT3b tumors shared more abnormalities in high frequency with metastases and recurrent tumors than less aggressive stage pT2 tumors. Furthermore, loss of 11cen–q22 was shared only between the primary tumors and metastases while gain of Xcen–q13 and loss of 18cen–q12 were in common between primary and recurrent tumors. These analyses suggest that the multistage model of prostate cancer progression is not linear and that some early primary tumors may be predisposed to metastasize or evolve into recurrent tumors due to the presence of specific genetic alterations. ^

Signal transduction of CEACAM1-L tumor suppressor

CEACAM1-L is an adhesion molecule that suppress the growth of prostate, breast, colon and endometrial tumors. In this study we defined the domain involved in CEACAM1-L tumor suppression activity. DU145 prostate cancer cells were infected with recombinant adenoviruses containing various CEACAM1-L mutant genes, and the effects of the mutant proteins on the growth of DU145 cells were assessed in a nude-mice xenograft model. We found that expression of the CEACAM1-L cytoplasm domain alone led to growth suppression of DU145 cells. These results suggest that the cytoplasmic domain of CEACAM1-L is necessary and sufficient for its growth-suppressive function. ^ The cytoplasmic domain of CEACAM1-L is presumed to be involved in a signaling pathway resulting in the suppression of tumor cell growth. It was not clear whether post-translational modification of CEACAM1-L is required for tumor suppressor function, therefore the importance of phosphorylation in growth-inhibitory signaling pathway was investigated. Full-length CEACAM1-L was found to be phosphorylated in vivo in both tyrosine and serine residues. Mutation of tyrosine 488 to phenylalanine did not abolish the tumor-suppressive activity of CEACAM1-L while mutation of serine 503 to alanine abolished the growth-inhibitory activity. In addition, mutation of serine 503 to aspartic acid produced tumor-suppressive activity similar to that of the wild-type CEACAM1-L. These results suggested that only phosphorylation at serine 503 is essential for CEACAM1-L's growth-inhibitory function in vivo. ^ Phosphorylation of CEACAM1-L may lead to its interaction with molecules in CEACAM1-L's signaling pathway. In the last part of this study we demonstrate that CEACAM1 is able to interact with the adapter protein p66Shc. p66Shc was found to be co-immunoprecipitated with full length CEACAM1-L but not with CEACAM1-L lacking its cytoplasmic tail. Additionally this interaction occurred in the absence of the tyrosine phosphorylation of CEACAM1-L. These results suggest that p66Shc is able to interact with the cytoplasmic domain of CEACAM1-L and this interaction does not require tyrosine phosphorylation. ^ In conclusion, this study suggests that CEACAM1-L signals tumor suppression through its cytoplasmic domain by initially becoming phosphorylated on serine 503. Additionally, the interaction with p66Shc may be involved in CEACAM1-L's signaling pathway. ^

Molecular alterations in nucleotide excision repair genes in malignant glioma and their relevance to malignant progression and drug resistance

Recently, it has become apparent that DNA repair mechanisms are involved in the malignant progression and resistance to therapy of gliomas. Many investigators have shown that increased levels of O6-methyl guanine DNA alkyltransferase, a DNA monoalkyl adduct repair enzyme, are correlated with resistance of malignant glioma cell lines to nitrosourea-based chemotherapy. Three important DNA excision repair genes ERCC1 (excision repair cross complementation group 1), ERCC2 (excision repair cross complementation group 2), and ERCC6 (excision repair cross complementation group 6) have been studied in human tumors. Gene copy number variation of ERCC1 and ERCC2 has been observed in primary glioma tissues. A number of reports describing a relationship between ERCC1 gene alterations and resistance to anti-cancer drugs have been also described. The levels of ERCC1 gene expression, however, have not been correlated with drug resistance in gliomas. The expression of ERCC6 gene transcribes has been shown to vary with tissue types and to be highest in the brain. There have been no comprehensive studies so far, however, of ERCC6 gene expression and molecular alterations in malignant glioma. This project examined the ERCC1 expression levels and correlated them with cisplatin resistance in malignant glioma cell lines. We also examined the molecular alterations of ERCC6 gene in primary glioma tissues and cells and analyzed whether these alterations are related to tumor progression and chemotherapy resistance. Our results indicate the presence of mutations and/or deletions in exons II and V of the ERCC6 gene, and these alterations are more frequent in exon II. Furthermore, the mutations and/or deletions in exon II were shown to be associated with increased malignant grade of gliomas. The results on the Levels of ERCC1 gene transcripts showed that expression levels correlate with cisplatin resistance. The increase in ERCC1 mRNA induced by cisplatin could be down-regulated by cyclosporin A and herbimycin A. The results of this study are likely to provide useful information for clinical treatment of human gliomas. ^

Risk Index Score (RISc)

The main objective of this study was to develop and validate a computer-based statistical algorithm based on a multivariable logistic model that can be translated into a simple scoring system in order to ascertain stroke cases using hospital admission medical records data. This algorithm, the Risk Index Score (RISc), was developed using data collected prospectively by the Brain Attack Surveillance in Corpus Christ (BASIC) project. The validity of the RISc was evaluated by estimating the concordance of scoring system stroke ascertainment to stroke ascertainment accomplished by physician review of hospital admission records. The goal of this study was to develop a rapid, simple, efficient, and accurate method to ascertain the incidence of stroke from routine hospital admission hospital admission records for epidemiologic investigations. ^ The main objectives of this study were to develop and validate a computer-based statistical algorithm based on a multivariable logistic model that could be translated into a simple scoring system to ascertain stroke cases using hospital admission medical records data. (Abstract shortened by UMI.)^

Molecular mechanism of PUVA-induced apoptosis in mouse epidermal cells

A combination of psoralens and ultraviolet-A radiation referred to as PUVA, is widely used in the treatment of psoriasis. PUVA therapy is highly effective in killing hyperproliferative cells, but its mechanism of action has not been fully elucidated. Psoralen binds to DNA, and upon photoactivation by UVA, it forms monofunctional adducts and interstrand cross-links. PUVA treatment has been shown to be mutagenic and to produce tumors in animals. In addition, epidemiological studies have reported a 10 to 15 percent increased risk of developing squamous cell carcinoma in individuals treated chronically with PUVA. However, it remains a treatment for skin disorders such as psoriasis because its benefits outweigh its risks. The widespread use of PUVA therapy and its associated cancer risk requires us to understand the molecular mechanisms by which PUVA induces cell death. Immortalized JB6 mouse epidermal cells, p53−/− mice, and Fas Ligand−/− (gld) mice were used to investigate the molecular mechanism by which PUVA kills cells. Treatment of JB6 cells with 10 μg/ml 8-methoxypsoralen followed by irradiation with 20 kJ/m2 UVA resulted in cell death. The cells exhibited morphological and biochemical characteristics of apoptosis such as chromatin condensation, DNA ladder formation, and TUNEL-positivity. PUVA treatment stabilized and phosphorylated p53 leading to its activation, as measured by nuclear localization and induction of p21Waf/Cip1, a transcriptional target of p53. Subsequent in vivo studies revealed that there was statistically significantly less apoptosis in p53 −/− mice than in p53+/+ mice at 72 hours after PUVA. In addition, immunohistochemical analysis revealed more Fas and FasL expression in p53+/+ mice than in p53−/− mice, suggesting that p53 is required to transcriptionally activate Fas, which in turn causes the cells to undergo apoptosis. Studies with gld mice confirmed a role for Fas/FasL interactions in PUVA-induced apoptosis. There was statistically significantly less apoptosis in gld mice compared with wild-type mice 24, 48, and 72 hours after PUVA. These results demonstrate that PUVA-induced apoptosis in mouse epidermal cells requires p53 and Fas/FasL interactions. These findings may be important for designing effective treatments for diseases such as psoriasis without increasing the patient's risk for skin cancer. ^

From gene to protein: Investigating the disease etiology of retinitis pigmentosa

Retinitis pigmentosa (RP) is a name given to a group of inherited retinal dystrophies that lead to progressive photoreceptor degeneration, and thus, visual impairment. It is evident at both the clinical and the molecular level that these are heterogeneous disorders, with wide variation in severity, mode of inheritance, and phenotype. The genetics of RP are not simple; the disease can be inherited in dominant, recessive, X-linked, and digenic modes. Autosomal dominant RP (adRP) results from mutations in at least ten mapped loci, but there may be dozens of genetic loci where mutations can cause RP. To date, there are over a hundred genes known to cause retinal degenerative diseases, and less than half of these have been cloned (RetNet). Among the dozens of retinitis pigmentosa loci known to exist, only a few have been identified and the remainders are inferred from linkage studies. Today, the genes for seven of the twelve-adRP loci have been identified, and these are rhodopsin, peripherin/RDS, NRL, ROM1, CRX, RP13 and RP1. My research projects involved a combination of the continued search for genes involved in retinal dystrophies, as well the investigation into the role of peripherin/RDS and RP1 in the disease etiology of autosomal dominant RP. ^ Most of the mutations leading to inherited retinal disorders have been identified in predominately retina expressed genes like rhodopsin, peripherin/RDS, and RP1. Expressed sequence tags (ESTs) that were retina-specific were culled from sequence databases and, together with laboratory analysis, were analyzed as potential candidate genes for retinal dystrophies. Thirteen of the fifty-five identified retina-specific ESTs mapped to within candidate regions for inherited retinopathies. One of these is RP1L1, a homologue of RP1 and a potential cause of adRP. ^ Once a disease-associated gene has been identified, elucidating the role of that gene in the visual process is essential for understanding what happens when the process is defective as it is in adRP. My next projects involved investigating the role of a novel 5′ donor +3 splice site mutation on the mRNA of peripherin/RDS in adRP affected individuals, and comparative sequencing in RP1 to define conserved regions of the protein. Comparative sequencing is a powerful way to delineate critical regions of a sequence because different regions of a gene have different functions, and each region is subject to different levels of functional or structural constraints. Establishing a framework of conserved domains is beneficial not only for structural or functional studies, but can also aid in determining the potential effects of mutations. With the completion of sequencing of human genome, and other organisms such as Saccharomyces cerevisiae, Caenorhabditis elegans , and Drosophila, the facility of comparative sequencing will only increase in the future. Comparative sequencing has already become an established procedure for pinpointing conserved regions of a protein, and is an efficient way to target regions of a protein for experimental and/or evolutionary analysis. ^

The function of math5 and myocilin in mammalian eye development and disease

Complex molecular events underlie vertebrate eye development and disease. The eye is composed of two major tissue types: the anterior and posterior segments. During development, the retinal progenitor cells differentiate into six neuronal and one non-neuronal cell types. These cell types later organize into the distinct laminar structure of the mature retina which occupies the posterior segment. In the developed anterior segment, both the ciliary body and trabecular meshwork regulate intraocular pressure created by the aqueous humor. The disruption in intraocular pressure can lead to a blinding condition called glaucoma. To characterize molecular mechanisms governing retinal development and glaucoma, two separate mouse knockout lines carrying mutations in math5 and myocilin were subjected to a series of in vivo analyses. ^ Math5 is a murine homologue of Drosophila atonal , a bHLH proneural gene essential for the formation of photoreceptor cells. The expression of math5 coincides with the onset of retinal ganglion cell differentiation. The targeted deletion of mouse math5 revealed that a null mutation inhibits the formation of a majority of the retinal ganglion cells. The mutation also interferes with the normal development of other retinal cell types such as amacrine, bipolar and photoreceptor cells. These results suggest that math5 is a proneural gene responsible for differentiation of retinal ganglion cells and may also have a role in normal development of other neuronal cell types within the retina. ^ Myocilin has two unique protein coding regions bearing homology to non-muscle myosin of Dictyostelium discoideum and to olfactomedin, an extracellular matrix molecule first described in the olfactory epithelium of the bullfrog. Recently, autosomal dominant forms of myocilin mutations have been found in individuals with primary open-angle glaucoma. The genetic linkage to glaucoma suggests a role of myocilin in normal intraocular pressure and ocular function. However, the analysis of mice heterozygous and homozygous for a targeted null mutation in myocilin indicates that it is dispensable for normal intraocular pressure or ocular function. Additionally, the lack of a discernable phenotype in both heterozygous and null mice suggests that haploinsufficiency is not a critical mechanism for MYOC-associated glaucoma in humans. Instead, disease-causing mutations likely act by gain of function. ^ In summary, these studies provide novel insights into the embryonic development of the vertebrate retina, and also begin to uncover the molecular mechanisms responsible for the pathogenesis of glaucoma. ^

Temporal variations of dyspnea, fatigue, and lung function in chronic lung disease

Background. Research investigating symptom management in patients with chronic obstructive pulmonary disease (COPD) largely has been undertaken assuming the homeostatic construct, without regard to potential roles of circadian rhythms. Temporal relations among dyspnea, fatigue, peak expiratory flow rate (PEFR) and objective measures of activity/rest have not been reported in COPD. ^ Objectives. The specific aims of this study were to (1) explore the 24-hour patterns of dyspnea, fatigue, and PEFR in subjects with COPD; (2) examine the relations among dyspnea, fatigue, and PEFR in COPD; and (3) examine the relations among objective measures of activity/rest and dyspnea, fatigue, and PEFR in COPD. ^ Methods. The repeated-measures design involved 10 subjects with COPD who self-assessed dyspnea and fatigue by 100 mm visual analog scales, and PEFR by peak flow meter in their home 5 times a day for 8 days. Activity/rest was measured by wrist actigraphy. Single and population mean cosinor analyses and correlations were computed for dyspnea, fatigue, and PEFR; correlations were done among these variables and activity/rest. ^ Results. Circadian rhythms were documented by single cosinor analysis in 40% of the subjects for dyspnea, 60% for fatigue, and 60% for PEFR. The population cosinor analysis of PEFR yielded a significant rhythm (p < .05). The 8-day 24-hour means of dyspnea and fatigue was moderately correlated (r = .48, p < .01). Dyspnea and PEFR, and fatigue and PEFR, were weakly correlated in a negative way (r = −.11, p < .05 and r = −.15, p < .01 respectively). Weak to moderate correlations (r = .12–.34, p < .05) were demonstrated between PEFR and mean activity level measured up to 4 hours before PEFR measurement. ^ Conclusions. The findings suggest that (1) the dyspnea and fatigue experienced by COPD patients are moderately related, (2) there is a weak to modest positive relation between PEFR and activity levels, and (3) temporal variation in lung function may not affect the dyspnea and fatigue experienced by patients with COPD. Further research, examining the relations among dyspnea, fatigue, PEFR, and activity/rest is needed. Replication of this study is suggested with a larger sample size. ^

Descriptive epidemiology of cancer in three regions of Kazakhstan

The current study investigated data quality and estimated cancer incidence and mortality rates using data provided by Pavlodar, Semipalatinsk and Ust-Kamenogorsk Regional Cancer Registries of Kazakhstan during the period of 1996–1998. Assessment of data quality was performed using standard quality indicators including internal database checks, proportion of cases verified from death certificates only, mortality:incidence ratio, data patterns, proportion of cases with unknown primary site, proportion of cases with unknown age. Crude and age-adjusted incidence and mortality rates and 95% confidence intervals were calculated, by gender, for all cancers combined and for 28 specific cancer sites for each year of the study period. The five most frequent cancers were identified and described for every population. The results of the study provide the first simultaneous assessment of data quality and standardized incidence and mortality rates for Kazakh cancer registries. ^

Chemopreventive function of retinoid X receptors in human squamous cell carcinoma of the skin

Retinoid therapy has been successful for the treatment of skin squamous cell carcinoma (SCC). A suppression of the predominant retinoid X receptor expressed in skin, retinoid X receptor α (RXRα), has been reported in skin SCC. These observations have led to the hypothesis that retinoid receptor loss contributes to the tumorigenic phenotype of epithelial cancers. To test this hypothesis, the RXRα gene was mapped in order to generate a targeting construct. Additionally the transcriptional regulation of the human RXRα a gene in keratinocytes was characterized after identifying the transcription initiation sites, the promoter, and enhancer regions of this gene. The structure is highly conserved between human and mouse. A nontumorigenic human skin-derived cell line called near diploid immortalized keratinocytes (NIKS) has the advantage of growing as organotypic raft cultures, under physiological conditions closely resembling in-vivo squamous stratification. We have exploited the raft culture technique to develop an in-vitro model for skin SCC progression that includes the NIKS cells, HaCaT cells, a premalignant cell line, and SRB 12-p9 cells, a tumorigenic SCC skin cell line. The differentiation, proliferation and nuclear receptor ligand response characteristics of this system were studied and significant and novel results were obtained. RXRs are obligate heterodimerization partners with many of the nuclear hormone receptors, including retinoic acid receptors (RARs), vitamin D3 receptors (VDR), thyroid hormone receptors (T3 R) and peroxisome proliferator activate receptors (PPARs), which are all known to be active in skin. Treatment of the three cell lines in raft culture with the RXR specific ligand BMS649, BMS961 (RARγ-specific), vitamin D3 (VDR ligand), thryoid hormone (T3R ligand) and clofibrate (PPARa ligand), and the combination of BMS649 with each of the 4 receptor partner ligands, resulted in distinct effects on differentiation, proliferation and apoptosis. The effects of activation of RXRs in each of the four-receptor pathways; in the context of skin SCC progression, with an emphasis on the VDR/RXR pathway, are discussed. These studies will lead to a better understanding of RXRα action in human skin and will help determine its role in SCC tumorigenesis, as well as its potential as a target for the prevention, treatment, and control of skin cancer. ^

Evaluation of Mycobacterium avium complex lung disease in women

Mycobacterium avium complex (MAC) is a ubiquitous organism responsible for most pulmonary and disseminated disease caused by non-tuberculosis (NTM) mycobacteria. Though MAC lung disease without predisposing factors is uncommon, in recent years it has been increasingly described in middle-aged and elderly women. Recognition and correct diagnosis, is often delayed due to the indolent nature of the disease. It is unclear if these women have significant clinical disease as or if their airways are simply colonized by the bacterium. This study describes the clinical presentation, identifies risk factors, and describes the clinical significance of MAC lung disease in HIV-negative women aged 50 or greater. ^ A hybrid study design utilizing both cross-sectional and case-control methodologies was used. A comparison population was selected from previously identified tuberculosis suspects found throughout Harris County. The study population had at least one acid fast bacillus pulmonary culture performed between 1/1/1998 and 12/31/2000 from a pulmonary source. Clinical presentation and symptoms were analyzed using a cross-sectional design. Past medical history and other risk factors were evaluated using a traditional case-control study design. Differences in categorical variables were estimated with the Chi Square or Fisher's Exact test as appropriate. Odds ratios and 95% confidence intervals were utilized to evaluate associations. Multivariate logistic regression was used to identify predictive factors for MAC. All statistical tests were two-sided and P-values <0.05 were considered statistically significant. ^ Culture confirmed MAC pulmonary cases were more likely to be white, have bronchiectasis, scoliosis, evidence of cavitation and pleural changes on chest radiography and granulomas on histopathologic examination than women whose pulmonary cultures were AFB negative. After controlling for selected risk factors, white race continued to be significantly associated with MAC lung disease (OR = 4.6, 95% CI = 2.3, 9.2). In addition, asthma history, smoking history and alcohol use were less likely to be evident among MAC cases in a multivariate analysis. Right upper and right middle lobe disease was further noted among clinically significant cases. Based on population data, MAC lung disease appears to represent a significant clinical syndrome in HIV-negative women thus supporting the theory of the Lady Windermere Syndrome. ^