ESTIMATING TEMPORAL ASSOCIATIONS IN ELECTROCORTICOGRAPHIC (ECoG) TIME SERIES WITH FIRST ORDER PRUNING

Granger causality (GC) is a statistical technique used to estimate temporal associations in multivariate time series. Many applications and extensions of GC have been proposed since its formulation by Granger in 1969. Here we control for potentially mediating or confounding associations between time series in the context of event-related electrocorticographic (ECoG) time series. A pruning approach to remove spurious connections and simultaneously reduce the required number of estimations to fit the effective connectivity graph is proposed. Additionally, we consider the potential of adjusted GC applied to independent components as a method to explore temporal relationships between underlying source signals. Both approaches overcome limitations encountered when estimating many parameters in multivariate time-series data, an increasingly common predicament in today's brain mapping studies.

Seasonal Analyses of Air Pollution and Mortality in 100 U.S. Cities

Time series models relating short-term changes in air pollution levels to daily mortality counts typically assume that the effects of air pollution on the log relative rate of mortality do not vary with time. However, these short-term effects might plausibly vary by season. Changes in the sources of air pollution and meteorology can result in changes in characteristics of the air pollution mixture across seasons. The authors develop Bayesian semi-parametric hierarchical models for estimating time-varying effects of pollution on mortality in multi-site time series studies. The methods are applied to the updated National Morbidity and Mortality Air Pollution Study database for the period 1987--2000, which includes data for 100 U.S. cities. At the national level, a 10 micro-gram/m3 increase in PM(10) at lag 1 is associated with a 0.15 (95% posterior interval: -0.08, 0.39),0.14 (-0.14, 0.42), 0.36 (0.11, 0.61), and 0.14 (-0.06, 0.34) percent increase in mortality for winter, spring, summer, and fall, respectively. An analysis by geographical regions finds a strong seasonal pattern in the northeast (with a peak in summer) and little seasonal variation in the southern regions of the country. These results provide useful information for understanding particle toxicity and guiding future analyses of particle constituent data.

Determinants of CD4 cell count decline after treatment interruption

Patients who had started HAART (Highly Active Anti-Retroviral Treatment) under previous aggressive DHHS guidelines (1997) underwent a life-long continuous HAART that was associated with many short term as well as long term complications. Many interventions attempted to reduce those complications including intermittent treatment also called pulse therapy. Many studies were done to study the determinants of rate of fall in CD4 count after interruption as this data would help guide treatment interruptions. The data set used here was a part of a cohort study taking place at the Johns Hopkins AIDS service since January 1984, in which the data were collected both prospectively and retrospectively. The patients in this data set consisted of 47 patients receiving via pulse therapy with the aim of reducing the long-term complications. ^ The aim of this project was to study the impact of virologic and immunologic factors on the rate of CD4 loss after treatment interruption. The exposure variables under investigation included CD4 cell count and viral load at treatment initiation. The rates of change of CD4 cell count after treatment interruption was estimated from observed data using advanced longitudinal data analysis methods (i.e., linear mixed model). Using random effects accounted for repeated measures of CD4 per person after treatment interruption. The regression coefficient estimates from the model was then used to produce subject specific rates of CD4 change accounting for group trends in change. The exposure variables of interest were age, race, and gender, CD4 cell counts and HIV RNA levels at HAART initiation. ^ The rate of fall of CD4 count did not depend on CD4 cell count or viral load at initiation of treatment. Thus these factors may not be used to determine who can have a chance of successful treatment interruption. CD4 and viral load were again studied by t-tests and ANOVA test after grouping based on medians and quartiles to see any difference in means of rate of CD4 fall after interruption. There was no significant difference between the groups suggesting that there was no association between rate of fall of CD4 after treatment interruption and above mentioned exposure variables. ^

Joint modelling of longitudinal and survival data on breast cancer

Tese de Doutoramento em Ciências (Especialidade em Matemática)

Longitudinal analysis of income-related health inequality

This paper considers the characterisation and measurement of income-related health inequality using longitudinal data. The paper elucidates the nature of the Jones and Lopez Nicholas (2004) index of “health-related income mobility” and explains the negative values of the index that have been reported in all the empirical applications to date. The paper further questions the value of their index to health policymakers and proposes an alternative index of “income-related health mobility” that measures whether the pattern of health changes is biased in favour of those with initially high or low incomes. We illustrate our work by investigating mobility in the General Health Questionnaire measure of psychological well-being over the first nine waves of the British Household Panel Survey from 1991 to 1999.

Longitudinal analysis of income-related health inequality: welfare foundations and alternative measures

This paper elaborates the approach to the longitudinal analysis of income-related health inequalities first proposed in Allanson, Gerdtham and Petrie (2010). In particular, the paper establishes the normative basis of their mobility indices by embedding their decomposition of the change in the health concentration index within a broader analysis of the change in “health achievement” or wellbeing. The paper further shows that their decomposition procedure can also be used to analyse the change in a range of other commonly-used incomerelated health inequality measures, including the generalised concentration index and the relative inequality index. We illustrate our work by extending their investigation of mobility in the General Health Questionnaire measure of psychological well-being over the first nine waves of the British Household Panel Survey from 1991 to 1999.

Accounting for the dead in the longitudinal analysis of income-related health inequalities

This paper develops an accounting framework to consider the effect of deaths on the longitudinal analysis of income-related health inequalities. Ignoring deaths or using inverse probability weights (IPWs) to re-weight the sample for mortality-related attrition can produce misleading results, since to do so would be to disregard the most extreme of all health outcomes. Incorporating deaths into the longitudinal analysis of income-related health inequalities provides a more complete picture in terms of the evaluation of health changes in respect to socioeconomic status. We illustrate our work by investigating health mobility in Quality Adjusted Life Years (QALYs) as measured by the SF6D from 1999 till 2004 using the British Household Panel Survey (BHPS). We show that for Scottish males explicitly accounting for the dead, rather than using IPWs to account for mortality-related attrition, changes the direction of the relationship between relative health changes and initial income position, while for other population groups it increases the strength of this relationship by up to 14 times. When deaths are explicitly incorporated into the analysis it is found that over this five year period for both Scotland and England & Wales the relative health changes were significantly regressive such that the poor experienced a larger share of the health losses relative to their initial share of health and a large amount of this was related to mortality.

Educational participation post-16: a longitudinal analysis of intentions and outcomes

The issue of levels of participation in post-compulsory education has been emphasised by the current policy initiatives to increase the age to which some form of participation is compulsory. One of the acknowledged weaknesses of research in the field of children's intentions with regard to participation is the lack of longitudinal data. This paper offers a longitudinal analysis using the Youth Survey from the British Household Panel Survey. The results show that most children can express intentions with regard to future participation very early in their secondary school careers and that these intentions are good predictors of actual behaviour five years later. Intentions to stay on are more consistent than intentions to leave and most children who finally leave at 16 have at some point said they want to remain in education post-16. The strongest association with participation levels is attainment at GCSE. However, there are also influences of gender and parental background and these remain, even after attainment is held constant. The results show the value of focusing on intentions for participation at a very early stage of children's school careers and also the importance of current attempts to reform curriculum and assessment for the 14-19 age group.

Anger and posttraumatic stress disorder symptoms in crime victims: A longitudinal analysis

Among trauma-exposed individuals, severity of posttraumatic stress disorder (PTSD) symptoms is strongly correlated with anger. The authors used 2 longitudinal data sets with 282 and 218 crime victims, respectively, to investigate the temporal sequence of anger and PTSD symptoms following the assault. Cross-lagged regression analyses indicated that PTSD symptoms predicted subsequent level of anger, but that anger did not predict subsequent PTSD symptoms. Testing alternative models (common factor model, unmeasured 3rd variable model) that might account for spuriousness of the relation strengthened confidence in the results of the cross-lagged analyses. Further analyses suggested that rumination mediates the effect of PTSD symptoms on anger.

Does low self-esteem predict depression and anxiety? A meta-analysis of longitudinal studies

Low self-esteem and depression are strongly related, but there is not yet consistent evidence on the nature of the relation. Whereas the vulnerability model states that low self-esteem contributes to depression, the scar model states that depression erodes self-esteem. Furthermore, it is unknown whether the models are specific for depression or whether they are also valid for anxiety. We evaluated the vulnerability and scar models of low self-esteem and depression, and low self-esteem and anxiety, by meta-analyzing the available longitudinal data (covering 77 studies on depression and 18 studies on anxiety). The mean age of the samples ranged from childhood to old age. In the analyses, we used a random-effects model and examined prospective effects between the variables, controlling for prior levels of the predicted variables. For depression, the findings supported the vulnerability model: The effect of self-esteem on depression (β = -.16) was significantly stronger than the effect of depression on self-esteem (β = -.08). In contrast, the effects between low self-esteem and anxiety were relatively balanced: Self-esteem predicted anxiety with β = -.10, and anxiety predicted self-esteem with β = -.08. Moderator analyses were conducted for the effect of low self-esteem on depression; these suggested that the effect is not significantly influenced by gender, age, measures of self-esteem and depression, or time lag between assessments. If future research supports the hypothesized causality of the vulnerability effect of low self-esteem on depression, interventions aimed at increasing self-esteem might be useful in reducing the risk of depression.

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. ^

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Physical activity and strength of the femoral neck during the adolescent growth spurt: A longitudinal analysis

Loading of the femoral neck (FN) is dominated by bending and compressive stresses. We hypothesize that adaptation of the FN to physical activity would be manifested in the cross-sectional area (CSA) and section modulus (Z) of bone, indices of axial and bending strength, respectively. We investigated the influence of physical activity on bone strength during adolescence using 7 years of longitudinal data from 109 boys and 121 girls from the Saskatchewan Paediatric Bone and Mineral Accrual Study (PBMAS). Physical activity data (PAC-Q physical activity inventory) and anthropometric measurements were taken every 6 months and DXA bone scans were measured annually (Hologic QDR2000, array mode). We applied hip structural analysis to derive strength and geometric indices of the femoral neck using DXA scans. To control for maturation, we determined a biological maturity age defined as years from age at peak height velocity (APHV). To account for the repeated measures within individual nature of longitudinal data, multilevel random effects regression analyses were used to analyze the data. When biological maturity age and body size (height and weight) were controlled, in both boys and girls, physical activity was a significant positive independent predictor of CSA and Z of the narrow region of the femoral neck (P < 0.05). There was no independent effect of physical activity on the subperiosteal width of the femoral neck. When leg length and leg lean mass were introduced into the random effects models to control for size and muscle mass of the leg (instead of height and weight), all significant effects of physical activity disappeared. Even among adolescents engaged in normal levels of physical activity, the statistically significant relationship between physical activity and indices of bone strength demonstrate that modifiable lifestyle factors like exercise play an important role in optimizing bone strength during the growing years. Physical activity differences were explained by the interdependence between activity and lean mass considerations. Physical activity is important for optimal development of bone strength. (c) 2005 Elsevier Inc. All rights reserved.

Improving discrimination in data envelopment analysis:some practical suggestions

In some contexts data envelopment analysis (DEA) gives poor discrimination on the performance of units. While this may reflect genuine uniformity of performance between units, it may also reflect lack of sufficient observations or other factors limiting discrimination on performance between units. In this paper, we present an overview of the main approaches that can be used to improve the discrimination of DEA. This includes simple methods such as the aggregation of inputs or outputs, the use of longitudinal data, more advanced methods such as the use of weight restrictions, production trade-offs and unobserved units, and a relatively new method based on the use of selective proportionality between the inputs and outputs. © 2007 Springer Science+Business Media, LLC.

Formulating Mixed Models for Experiments, Including Longitudinal Experiments

Mixed models have become important in analyzing the results of experiments, particularly those that require more complicated models (e.g., those that involve longitudinal data). This article describes a method for deriving the terms in a mixed model. Our approach extends an earlier method by Brien and Bailey to explicitly identify terms for which autocorrelation and smooth trend arising from longitudinal observations need to be incorporated in the model. At the same time we retain the principle that the model used should include, at least, all the terms that are justified by the randomization. This is done by dividing the factors into sets, called tiers, based on the randomization and determining the crossing and nesting relationships between factors. The method is applied to formulate mixed models for a wide range of examples. We also describe the mixed model analysis of data from a three-phase experiment to investigate the effect of time of refinement on Eucalyptus pulp from four different sources. Cubic smoothing splines are used to describe differences in the trend over time and unstructured covariance matrices between times are found to be necessary.