A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting "rotated" residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series).

The role of stress hormones in the relationship between resting blood pressure and coagulation activity

BACKGROUND: Systemic hypertension confers a hypercoagulable state. We hypothesized that resting mean blood pressure (MBP) interacts with stress hormones in predicting coagulation activity at rest and with acute mental stress. METHODS: We measured plasma clotting factor VII activity (FVII:C), FVIII:C, fibrinogen, D-dimer, epinephrine and norepinephrine, and saliva cortisol in 42 otherwise healthy normotensive and hypertensive medication-free men (mean age 43 +/- 14 years) at rest, immediately after stress, and twice during 60 min of recovery from stress. RESULTS: At rest, the MBP-by-epinephrine interaction predicted FVII:C (beta = -0.33, P < 0.04) and D-dimer (beta = 0.26, P < 0.05), and the MBP-by-cortisol interaction predicted D-dimer (beta = 0.43, P = 0.001), all independent of age and body mass index (BMI). Resting norepinephrine predicted fibrinogen (beta = 0.42, P < 0.01) and D-dimer (beta = 0.37, P < 0.03), both independent of MBP. MBP predicted FVIII:C change from rest to immediately post-stress independent of epinephrine (beta = -0.37, P < 0.03) and norepinephrine (beta = -0.38, P < 0.02). Cortisol change predicted FVIII:C change (beta = -0.30, P < 0.05) independent of age, BMI and MBP. Integrated norepinephrine change from rest to recovery (area under the curve, AUC) predicted D-dimer AUC (beta = 0.34, P = 0.04) independent of MBP. The MBP-by-epinephrine AUC interaction predicted FVII:C AUC (beta = 0.28) and fibrinogen AUC (beta = -0.30), and the MBP-by-norepinephrine AUC interaction predicted FVIII:C AUC (beta = -0.28), all with borderline significance (Ps < 0.09) and independent of age and BMI. CONCLUSIONS: MBP significantly altered the association between stress hormones and coagulation activity at rest and, with borderline significance, across the entire stress and recovery interval. Independent of MBP, catecholamines were associated with procoagulant effects and cortisol reactivity dampened the acute procoagulant stress response.

Sleep disturbance, norepinephrine, and D-dimer are all related in elderly caregivers of people with Alzheimer disease

STUDY OBJECTIVE: Caregiving for a relative with Alzheimer disease has been associated with sympathoadrenal medullary arousal and morbidity and mortality. In this study, we examined if sleep disturbance of elderly caregivers was associated with physiologic markers of cardiovascular risk, including plasma norepinephrine, epinephrine, and the hemostasis marker D-dimer. DESIGN: Cross-sectional. SETTING: Community-based sample of elderly caregivers of spouses with Alzheimer disease assessed within their homes. PARTICIPANTS: A sample of 40 elderly spousal caregivers of patients with Alzheimer disease. MEASUREMENTS AND RESULTS: Participants underwent in-home full-night polysomnography and had plasma assayed for norepinephrine and epinephrine. Using multiple regression analyses and controlling for a number of cardiovascular risk factors (e.g., age, sex, blood pressure, body mass index), increased wake after sleep onset was positively associated with norepinephrine levels (beta = .35; t = 2.45, df = 32, p = .020) and plasma D-dimer (beta = .31; t = 2.18, df = 29, p = .038). Further, plasma norepinephrine was significantly associated with D-dimer (beta = .34; t = 2.11, df = 29, p = .044). Additional analyses indicated that norepinephrine accounted for 28% of the relationship between wake after sleep onset and D-dimer. No association was observed between sleep variables and epinephrine. CONCLUSIONS: These findings provide preliminary evidence that sleep disturbance may contribute to morbidity in caregivers through sympathoadrenal medullary arousal and downstream physiologic effects such as altering the hemostasis environment.

Stress-related reduction in personal mastery is associated with reduced immune cell beta2-adrenergic receptor sensitivity

Background: A growing body of literature suggests that caregiving burden is associated with impaired immune system functioning, which may contribute to elevated morbidity and mortality risk among dementia caregivers. However, potential mechanisms linking these relationships are not well understood. The purpose of this study was to investigate whether stress-related experience of depressive symptoms and reductions in personal mastery were related to alterations in ss2-adrenergic receptor sensitivity.Methods: Spousal Alzheimer's caregivers (N = 106) completed measures assessing the extent to which they felt overloaded by their caregiving responsibilities, experienced depressive symptoms, and believed their life circumstances were under their control. We hypothesized that caregivers reporting elevated stress would report increased depressive symptoms and reduced mastery, which in turn would be associated with reduced ss2- adrenergic receptor sensitivity on peripheral blood mononuclear cells (PBMC), as assessed by in vitro isoproterenol stimulation.Results: Regression analyses indicated that overload was negatively associated with mastery (beta = -0.36, p = 0.001) and receptor sensitivity (beta = -0.24, p = 0.030), whereas mastery was positively associated with receptor sensitivity (beta = 0.29, p = 0.005). Finally, the relationship between overload and receptor sensitivity diminshed upon simultaneous entry of mastery. Sobel's test confirmed that mastery significantly mediated some of the relationship between overload and receptor sensitivity (z = -2.02, p = 0.044).Conclusions: These results suggest that a reduced sense of mastery may help explain the association between caregiving burden and reduced immune cell ss2-receptor sensitivity.

Dementia severity of the care receiver predicts procoagulant response in Alzheimer caregivers

BACKGROUND: The procoagulant factor D-dimer has been shown to be associated with thrombus formation and degradation as seen with conditions such as myocardial infarction and unstable angina. Research has demonstrated that spousal dementia caregivers have elevated levels of D-dimer relative to their non-caregiving peers. OBJECTIVE: The objective of this study was to determine the relationship of basal level and laboratory stressor-induced concentration of D-dimer to severity of dementia in spousal care recipients. METHODS: Seventy-one elderly caregivers were compared with a comparison group of 37 non-caregivers (average age: 71 years). Clinical Dementia Rating (CDR), a global measure of dementia, was used to assess severity of spousal dementia. Plasma D-dimer was measured at baseline and in response to an acute speech stressor. RESULTS: Regression analysis revealed a significant positive association between severity of spousal dementia and caregiver D-dimer, both at baseline and in response to acute stress, while controlling for age. The model examined an exponential relationship, with D-dimer increasing progressively across the span of dementia stages. DISCUSSION: Dementia severity of the care recipient was associated with increasing hypercoagulability among elderly caregivers. Effect size estimates suggest that such D-dimer increases may have clinical implications, particularly among late-stage caregivers.

Avoidant coping partially mediates the relationship between patient problem behaviors and depressive symptoms in spousal Alzheimer caregivers

OBJECTIVE: Caring for a loved one with Alzheimer disease is a highly stressful experience that is associated with significant depressive symptoms. Previous studies indicate a positive association between problem behaviors in patients with Alzheimer disease (e.g., repeating questions, restlessness, and agitation) and depressive symptoms in their caregivers. Moreover, the extant literature indicates a robust negative relationship between escape-avoidance coping (i.e., avoiding people, wishing the situation would go away) and psychiatric well-being. The purpose of this study was to test a mediational model of the associations between patient problem behaviors, escape-avoidance coping, and depressive symptoms in Alzheimer caregivers. METHODS: Ninety-five spousal caregivers (mean age: 72 years) completed measures assessing their loved ones' frequency of problem behaviors, escape-avoidance coping, and depressive symptoms. A mediational model was tested to determine if escape-avoidant coping partially mediated the relationship between patient problem behaviors and caregiver depressive symptoms. RESULTS: Patient problem behaviors were positively associated with escape-avoidance coping (beta = 0.38, p < 0.01) and depressive symptoms (beta = 0.26, p < 0.05). Escape-avoidance coping was positively associated with depressive symptoms (beta = 0.33, p < 0.01). In a final regression analysis, the impact of problem behaviors on depressive symptoms was less after controlling for escape-avoidance coping. Sobel's test confirmed that escape-avoidance coping significantly mediated the relationship between problem behaviors and depressive symptoms (z = 2.07, p < 0.05). CONCLUSION: Escape-avoidance coping partially mediates the association between patient problem behaviors and depressive symptoms among elderly caregivers of spouses with dementia. This finding provides a specific target for psychosocial interventions for caregivers.

Personal mastery attenuates the effect of caregiving stress on psychiatric morbidity

This study examined the protective effects of personal mastery on the relations between both objective and subjective stress and psychiatric morbidity in 79 spousal Alzheimer caregivers. Results indicated that with low mastery, the relations between patient problem behaviors and caregiver psychiatric symptoms was significant (t[71] = 2.03; p = 0.046). However, with high mastery, no significant association was found (t[71] = -0.76; p = 0.452). Similarly, the relations between role overload and psychiatric morbidity was significant when mastery was low (t[71] = 2.22; p = 0.029), but not high (t[71] = -1.49; p = 0.140). These results suggest that caregivers with a greater sense of personal mastery may be protected from the negative effects of caregiver stress.

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

A Diagnostic Test for the Mixing Distribution in a Generalised Linear Mixed Model

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women.

Semiparametric Latent Variable Regression Models for Spatio-temporal Modeling of Mobile Source Particles in the Greater Boston Area

Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modeling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies conducted at specific household locations as well as 15 ambient monitoring sites in the city. The models allow for both flexible, nonlinear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic particles, with some recording only outdoor concentrations of black or elemental carbon, some recording indoor concentrations of black carbon, and others recording both indoor and outdoor concentrations of black carbon. A joint model for outdoor and indoor exposure that specifies a spatially varying latent variable provides greater spatial coverage in the area of interest. We propose a penalised spline formation of the model that relates to generalised kringing of the latent traffic pollution variable and leads to a natural Bayesian Markov Chain Monte Carlo algorithm for model fitting. We propose methods that allow us to control the degress of freedom of the smoother in a Bayesian framework. Finally, we present results from an analysis that applies the model to data from summer and winter separately