Diploma d'Estudis Avançats (DEA) - Estadística

URI permanent per a aquesta col·leccióhttps://hdl.handle.net/2445/11505

Estadístiques

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Estudi de l'estat de Salut autopercebut: Modelització de l'índex d'utilitat EQ-5D mitjançant un model tobit
(2008-07-16) Vilagut Saiz, Gemma
Objective: Health status measures usually have an asymmetric distribution and present a high percentage of respondents with the best possible score (ceiling effect), specially when they are assessed in the overall population. Different methods to model this type of variables have been proposed that take into account the ceiling effect: the tobit models, the Censored Least Absolute Deviations (CLAD) models or the two-part models, among others. The objective of this work was to describe the tobit model, and compare it with the Ordinary Least Squares (OLS) model, that ignores the ceiling effect. Methods: Two different data sets have been used in order to compare both models: a) real data comming from the European Study of Mental Disorders (ESEMeD), in order to model the EQ5D index, one of the measures of utilities most commonly used for the evaluation of health status; and b) data obtained from simulation. Cross-validation was used to compare the predicted values of the tobit model and the OLS models. The following estimators were compared: the percentage of absolute error (R1), the percentage of squared error (R2), the Mean Squared Error (MSE) and the Mean Absolute Prediction Error (MAPE). Different datasets were created for different values of the error variance and different percentages of individuals with ceiling effect. The estimations of the coefficients, the percentage of explained variance and the plots of residuals versus predicted values obtained under each model were compared. Results: With regard to the results of the ESEMeD study, the predicted values obtained with the OLS model and those obtained with the tobit models were very similar. The regression coefficients of the linear model were consistently smaller than those from the tobit model. In the simulation study, we observed that when the error variance was small (s=1), the tobit model presented unbiased estimations of the coefficients and accurate predicted values, specially when the percentage of individuals wiht the highest possible score was small. However, when the errror variance was greater (s=10 or s=20), the percentage of explained variance for the tobit model and the predicted values were more similar to those obtained with an OLS model. Conclusions: The proportion of variability accounted for the models and the percentage of individuals with the highest possible score have an important effect in the performance of the tobit model in comparison with the linear model.
Spectral analysis of the luteinizing hormone in the blood samples
(2008-06) Liutsko, Liudmila
Generally, medicine books are concentrated almost exclusively in explaining methodology that analyzes fixed measures, measures done in a certain moment, nevertheless the evolution of the measurement and correct interpretation of the missed values are very important and sometimes can give the key information of the results obtained. Thus, the analysis of the temporary series and spectral analysis or analysis of the time series in the dominion of frequencies can be regarded as an appropriate tool for this kind of studies. In this work the frequency of the pulsating secretion of luteinizing hormone LH (that regulates the fertile life of women) were analyzed in order to determine the existence of the significant frequencies obtained by analysis of Fourier. Detection of the frequencies, with which the pulsating secretion of the LH takes place, is a quite difficult question due to presence of the random errors in measures and samplings, i.e. that pulsating secretions of small amplitude are not detected and disregarded. In physiology it is accepted that cyclical patterns in the secretion of the LH exist and in the results of this research confirm this pattern and determine its frequency presented in the corresponded periodograms to each of studied cycle. The obtained results can be used as key pattern for future sampling frequencies in order to ¿catch¿ the significant picks of the luteinizing hormone and reflect on time for productivity treatment of women.
Anàlisi factorial confirmatòria per a variables categòriques: Aplicació al qüestionari de discapacitat WHODAS-II
(2008-06-20) Vilagut Saiz, Gemma
Objective: To describe the methodology of Confirmatory Factor Analyis for categorical items and to apply this methodology to evaluate the factor structure and invariance of the WHO-Disability Assessment Schedule (WHODAS-II) questionnaire, developed by the World Health Organization. Methods: Data used for the analysis come from the European Study of Mental Disorders (ESEMeD), a cross-sectional interview to a representative sample of the general population of 6 european countries (n=8796). Respondents were administered a modified version of the WHODAS-II, that measures functional disability in the previous 30 days in 6 different dimensions: Understanding and Communicating; Self-Care, Getting Around, Getting Along with Others, Life Activities and Participation. The questionnaire includes two types of items: 22 severity items (5 points likert) and 8 frequency items (continuous). An Exploratory factor analysis (EFA) with promax rotation was conducted on a random 50% of the sample. The remaining half of the sample was used to perform a Confirmatory Factor Analysis (CFA) in order to compare three different models: (a) the model suggested by the results obtained in the EFA; (b) the theoretical model suggested by the WHO with 6 dimensions; (c) a reduced model equivalent to model b where 4 of the frequency items are excluded. Moreover, a second order factor was also evaluated. Finally, a CFA with covariates was estimated in order to evaluate measurement invariance of the items between Mediterranean and non-mediterranean countries. Results: The solution that provided better results in the EFA was that containing 7 factors. Two of the frequency items presented high factor loadings in the same factor, and one of them presented factor loadings smaller than 0.3 with all the factors. With regard to the CFA, the reduced model (model c) presented the best goodness of fit results (CFI=0.992,TLI=0.996, RMSEA=0.024). The second order factor structure presented adequate goodness of fit (CFI=0.987, TLI=0.991, RMSEA=0.036). Measurement non-invariance was detected for one of the items of the questionnaire (FD20 ¿ Embarrassment due to health problems). Conclusions: AFC confirmed the initial hypothesis about the factorial structure of the WHODAS-II in 6 factors. The second order factor supports the existence of a global dimension of disability. The use of 4 of the frequency items is not recommended in the scoring of the corresponding dimensions.
What trees tell us: dendrochronological and statistical analysis of the data
(2008-06) Liutsko, Liudmila
Trees are a great bank of data, named sometimes for this reason as the "silent witnesses" of the past. Due to annual formation of rings, which is normally influenced directly by of climate parameters (generally changes in temperature and moisture or precipitation) and other environmental factors; these changes, occurred in the past, are "written" in the tree "archives" and can be "decoded" in order to interpret what had happened before, mainly applied for the past climate reconstruction. Using dendrochronological methods for obtaining samples of Pinus nigra from the Catalonian PrePirineous region, the cores of 15 trees with total time spine of about 100 - 250 years were analyzed for the tree ring width (TRW) patterns and had quite high correlation between them (0.71 ¿ 0.84), corresponding to a common behaviour for the environmental changes in their annual growth. After different trials with raw TRW data for standardization in order to take out the negative exponential growth curve dependency, the best method of double detrending (power transformation and smoothing line of 32 years) were selected for obtaining the indexes for further analysis. Analyzing the cross-correlations between obtained tree ring width indexes and climate data, significant correlations (p<0.05) were observed in some lags, as for example, annual precipitation in lag -1 (previous year) had negative correlation with TRW growth in the Pallars region. Significant correlation coefficients are between 0.27- 0.51 (with positive or negative signs) for many cases; as for recent (but very short period) climate data of Seu d¿Urgell meteorological station, some significant correlation coefficients were observed, of the order of 0.9. These results confirm the hypothesis of using dendrochronological data as a climate signal for further analysis, such as reconstruction of climate in the past or prediction in the future for the same locality.

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