Asymptotics for Marginal Generalized Linear Models With Sparse Correlations

Marginal generalized linear models can be used for clustered and longitudinal data by fitting a model as if the data were independent and using an empirical estimator of parameter standard errors. We extend this approach to data where the number of observations correlated with a given one grows with sample size and show that parameter estimates are consistent and asymptotically Normal with a slower convergence rate than for independent data, and that an information sandwich variance estimator is consistent. We present two problems that motivated this work, the modelling of patterns of HIV genetic variation and the behavior of clustered data estimators when clusters are large.

Microhardness and marginal adaptation of pre-warmed composites

Objectives: The aim of this study was to examine the effect of pre-warmed composite on the microhardness and marginal adaptation. Methods: Ninety six identical class II cavities were prepared in extracted human molars and filled/cured in three 2 mm increments using a metal matrix. Two composites (Tetric Evo Ceram (IvoclarVivadent) and ELS(Saremco)) were cured with a LED curing unit (Bluephase (IvoclarVivadent)) using curing cycles of 20 and 40 seconds. The composite was used at room temperature or pre-warmed at 54.5ºC (Calset(AdDent)). Twelve teeth were filled for every composite-curing time-composite temperature combination. The teeth were thermocycled (1000 cycles at 5º and 55ºC) and then stored at 37° C for seven days . Dye penetration (basic fuchsine 5% for 8 hours) was measured using a score scale. Knoop microhardness was determined 100, 200, 500, 1000, 1500, 2500, 3500, 4500 and 5500µm from the occlusal surface at a distance of 150 and 1000µm from the metal matrix. The total degree of polymerization of a composite specimen was determined by calculating the area under the hardness curve. Results: Statistical analyses showed no difference in marginal adaptation (p>0.05). Hardness values at 150µm from the matrix were lower than those at 1000µm. There was an increase of the microhardness at the top of each increment and decrease towards the bottom of each increment. Longer curing times resulted in harder composite samples. Multiple linear regression showed that only the curing time (p<0.001) and composite material (p<0.001) had a significant association with the degree of polymerization. The degree of polymerization was not influenced by pre-warming the composite at a temperature of 54.5ºC (p=4.86). Conclusion: Polymerization time can not be reduced by pre-warming the composite on a temperature of 54.5ºC. The marginal adaptation is not compromised by pre-warming the composite.

Marginal Structural Models for Partial Exposure Regimes

Intensive care unit (ICU) patients are ell known to be highly susceptible for nosocomial (i.e. hospital-acquired) infections due to their poor health and many invasive therapeutic treatments. The effects of acquiring such infections in ICU on mortality are however ill understood. Our goal is to quantify these effects using data from the National Surveillance Study of Nosocomial Infections in Intensive Care Units (Belgium). This is a challenging problem because of the presence of time-dependent confounders (such as exposure to mechanical ventilation)which lie on the causal path from infection to mortality. Standard statistical analyses may be severely misleading in such settings and have shown contradicting results. While inverse probability weighting for marginal structural models can be used to accommodate time-dependent confounders, inference for the effect of ?ICU acquired infections on mortality under such models is further complicated (a) by the fact that marginal structural models infer the effect of acquiring infection on a given, fixed day ?in ICU?, which is not well defined when ICU discharge comes prior to that day; (b) by informative censoring of the survival time due to hospital discharge; and (c) by the instability of the inverse weighting estimation procedure. We accommodate these problems by developing inference under a new class of marginal structural models which describe the hazard of death for patients if, possibly contrary to fact, they stayed in the ICU for at least a given number of days s and acquired infection or not on that day. Using these models we estimate that, if patients stayed in the ICU for at least s days, the effect of acquiring infection on day s would be to multiply the subsequent hazard of death by 2.74 (95 per cent conservative CI 1.48; 5.09).

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Influence of beveling and ultrasound application on marginal adaptation of box-only Class II (slot) resin composite restorations

A laboratory study was performed to assess the influence of beveling the margins of cavities and the effects on marginal adaptation of the application of ultrasound during setting and initial light curing. After minimal access cavities had been prepared with an 80 microm diamond bur, 80 box-only Class II cavities were prepared mesially and distally in 40 extracted human molars using four different oscillating diamond coated instruments: (A) a U-shaped PCS insert as the non-beveled control (EMS), (B) Bevelshape (Intensiv), (C) SonicSys (KaVo) and (D) SuperPrep (KaVo). In groups B-D, the time taken for additional bevel finishing was measured. The cavities were filled with a hybrid composite material in three increments. Ultrasound was also applied to one cavity per tooth before and during initial light curing (10 seconds). The specimens were subjected to thermomechanical stress in a computer-controlled masticator device. Marginal quality was assessed by scanning electron microscopy and the results were compared statistically. The additional time required for finishing was B > D > C (p < or = 0.05). In all groups, thermomechanical loading resulted in a decrease in marginal quality. Beveling resulted in higher values for "continuous" margins compared with that of the unbeveled controls. The latter showed better marginal quality at the axial walls when ultrasound was used. Beveling seems essential for good marginal adaptation but requires more preparation time. The use of ultrasonic vibrations may improve the marginal quality of unbeveled fillings and warrants further investigation.

Retention of canopy trees as biological legacies for balancing woody biomass production and biodiversity in managed aspen forests of the Great Lakes Region

Green-tree retention under the conceptual framework of ecological forestry has the potential to provide both biomass feedstock for industry and maintain quality wildlife habitat. I examined the effects of retained canopy trees as biological legacies (“legacy trees”) in aspen (Populus spp.) forests on above-ground live woody biomass, understory plant floristic quality, and bird diversity. Additionally, I evaluated habitat quality for a high conservation priority species, the Golden-winged Warbler (Vermivora chrysoptera). I selected 27 aspen-dominated forest stands in northern Wisconsin with nine stands in each of three legacy tree retention treatments (conifer retention, hardwood retention, and clearcuts or no retention) across a chronosequence (4-36 years post-harvest). Conifer retention stands had greater legacy tree and all tree species biomass but lower regenerating tree biomass than clearcuts. Coniferous but not hardwood legacy trees appeared to suppress regenerating tree biomass. I evaluated the floristic quality of the understory plant assemblage by estimating the mean coefficient of conservatism (C). Mean C was lower in young stands than in middle-age or old stands; there was a marginally significant (p=0.058) interaction effect between legacy tree retention treatment and stand age. Late-seral plant species were positively associated with stand age and legacy tree diameter or age revealing an important relationship between legacy tree retention and stand development. Bird species richness was greatest in stands with hardwood retention particularly early in stand development. Six conservation priority bird species were indicators of legacy tree retention or clearcuts. Retention of legacy trees in aspen stands provided higher quality nest habitat for the Golden-winged Warbler than clearcuts based on high pairing success and nesting activity. Retention of hardwoods, particularly northern red oak (Quercus rubra), yielded the most consistent positive effects in this study with the highest bird species richness and the highest quality habitat for the Golden-winged Warbler. This treatment maintained stand biomass comparable to clearcuts and did not suppress regenerating tree biomass. In conclusion, legacy tree retention can enhance even-aged management techniques to produce a win-win scenario for the conservation of declining bird species and late-seral understory plants and for production of woody biomass feedstock from naturally regenerating aspen forests.

Public preferences of the Great Lakes Environment : a Lake Michigan pilot study

The Great Lakes watershed is home to over 40 million people, and the health of the Great Lakes ecosystem is vital to the overall economic, societal, and environmental health of the U.S. and Canada. However, environmental issues related to them are sometimes overlooked. Policymakers and the public face the challenges of balancing economic benefits with the need to conserve and/or replenish regional natural resources to ensure long term prosperity. From the literature review, nine critical stressors of ecological services were delineated, which include pollution and contamination, agricultural erosion, non-native species, degraded recreational resources, loss of wetlands habitat, climate change, risk of clean water shortage, vanishing sand dunes, and population overcrowding; this list was validated through a series of stakeholder discussions and focus groups in Grand Rapids. Focus groups were conducted in Grand Rapids to examine the awareness of, concern with, and willingness to expend resources on these stressors. Stressors that the respondents have direct contact with tend to be the most important. The focus group results show that concern related to pollution and contamination is much higher than for any of the other stressors. Low responses to climate change result in recommendations for outreach programs.

Great Lakes tributary phosphorus bioavailability

Information on phosphorus bioavailability can provide water quality managers with the support required to target point source and watershed loads contributing most significantly to water quality conditions. This study presents results from a limited sampling program focusing on the five largest sources of total phosphorus to the U.S. waters of the Great Lakes. The work provides validation of the utility of a bioavailability-based approach, confirming that the method is robust and repeatable. Chemical surrogates for bioavailability were shown to hold promise, however further research is needed to address site-to-site and seasonal variability before a universal relationship can be accepted. Recent changes in the relative contribution of P constituents to the total phosphorus analyte and differences in their bioavailability suggest that loading estimates of bioavailable P will need to address all three components (SRP, DOP and PP). A bioavailability approach, taking advantage of chemical surrogate methodologies is recommended as a means of guiding P management in the Great Lakes.

Critical evaluation of diameter increment modelling in the Great Lakes region

Simulations of forest stand dynamics in a modelling framework including Forest Vegetation Simulator (FVS) are diameter driven, thus the diameter or basal area increment model needs a special attention. This dissertation critically evaluates diameter or basal area increment models and modelling approaches in the context of the Great Lakes region of the United States and Canada. A set of related studies are presented that critically evaluate the sub-model for change in individual tree basal diameter used in the Forest Vegetation Simulator (FVS), a dominant forestry model in the Great Lakes region. Various historical implementations of the STEMS (Stand and Tree Evaluation and Modeling System) family of diameter increment models, including the current public release of the Lake States variant of FVS (LS-FVS), were tested for the 30 most common tree species using data from the Michigan Forest Inventory and Analysis (FIA) program. The results showed that current public release of the LS-FVS diameter increment model over-predicts 10-year diameter increment by 17% on average. Also the study affirms that a simple adjustment factor as a function of a single predictor, dbh (diameter at breast height) used in the past versions, provides an inadequate correction of model prediction bias. In order to re-engineer the basal diameter increment model, the historical, conceptual and philosophical differences among the individual tree increment model families and their modelling approaches were analyzed and discussed. Two underlying conceptual approaches toward diameter or basal area increment modelling have been often used: the potential-modifier (POTMOD) and composite (COMP) approaches, which are exemplified by the STEMS/TWIGS and Prognosis models, respectively. It is argued that both approaches essentially use a similar base function and neither is conceptually different from a biological perspective, even though they look different in their model forms. No matter what modelling approach is used, the base function is the foundation of an increment model. Two base functions – gamma and Box-Lucas – were identified as candidate base functions for forestry applications. The results of a comparative analysis of empirical fits showed that quality of fit is essentially similar, and both are sufficiently detailed and flexible for forestry applications. The choice of either base function in order to model diameter or basal area increment is dependent upon personal preference; however, the gamma base function may be preferred over the Box-Lucas, as it fits the periodic increment data in both a linear and nonlinear composite model form. Finally, the utility of site index as a predictor variable has been criticized, as it has been widely used in models for complex, mixed species forest stands though not well suited for this purpose. An alternative to site index in an increment model was explored, using site index and a combination of climate variables and Forest Ecosystem Classification (FEC) ecosites and data from the Province of Ontario, Canada. The results showed that a combination of climate and FEC ecosites variables can replace site index in the diameter increment model.

Applications of LiDAR remote sensing of forest structure in the Upper Great Lakes region, USA

We used active remote sensing technology to characterize forest structure in a northern temperate forest on a landscape- and local-level in the Upper Peninsula of Michigan. Specifically, we used a form of active remote sensing called light detection and ranging (e.g., LiDAR) to aid in the depiction of current forest structural stages and total canopy gap area estimation. On a landscape-level, LiDAR data are shown not only to be a useful tool in characterizing forest structure, in both coniferous and deciduous forest cover types, but also as an effective basis for data-driven surrogates for classification of forest structure. On a local-level, LiDAR data are shown to be a benchmark reference point to evaluate field-based canopy gap area estimations, due to the highly accurate nature of such remotely sensed data. The application of LiDAR remote sensed data can help facilitate current and future sustainable forest management.

INTEGRATED ASSESSMENT OF ANTHROPOGENIC, CLIMATE, AND POLICY INDUCED CHANGES OF PHOSPHORUS EXPORT IN THE UNITED STATES LAURENTIAN GREAT LAKES WATERSHEDS

Anthropogenic activities have increased phosphorus (P) loading in tributaries to the Laurentian Great Lakes resulting in eutrophication in small bays to most notably, Lake Erie. Changes to surface water quality from P loading have resulted in billions of dollars in damage and threaten the health of the world’s largest freshwater resource. To understand the factors affecting P delivery with projected increasing urban lands and biofuels expansion, two spatially explicit models were coupled. The coupled models predict that the majority of the basin will experience a significant increase in urban area P sources while the agriculture intensity and forest sources of P will decrease. Changes in P loading across the basin will be highly variable spatially. Additionally, the impacts of climate change on high precipitation events across the Great Lakes were examined. Using historical regression relationships on phosphorus concentrations, key Great Lakes tributaries were found to have future changes including decreasing total loads and increases to high-flow loading events. The urbanized Cuyahoga watersheds exhibits the most vulnerability to these climate-induced changes with increases in total loading and storm loading , while the forested Au Sable watershed exhibits greater resilience. Finally, the monitoring network currently in place for sampling the amount of phosphorus entering the U.S. Great Lakes was examined with a focus on the challenges to monitoring. Based on these interviews, the research identified three issues that policy makers interested in maintaining an effective phosphorus monitoring network in the Great Lakes should consider: first, that the policy objectives driving different monitoring programs vary, which results in different patterns of sampling design and frequency; second, that these differences complicate efforts to encourage collaboration; and third, that methods of funding sampling programs vary from agency to agency, further complicating efforts to generate sufficient long-term data to improve our understanding of phosphorus into the Great Lakes. The dissertation combines these three areas of research to present the potential future impacts of P loading in the Great Lakes as anthropogenic activities, climate and monitoring changes. These manuscripts report new experimental data for future sources, loading and climate impacts on phosphorus.

Carbon in the Peatlands in the Great Lakes Region

Peatlands cover only ~3% of the global land area, but store ~30% of the worlds' soil carbon. There are many different peat types that store different amounts of carbon. Most inventories of carbon storage in northern peatlands have been conducted in the expansive Sphagnum dominated peatlands. Although, northern white cedar peatlands (NW cedar, Thuja occidentalis L.) are also one of the most common peatland types in the Great Lakes Region, occupying more than 2 million hectares. NW cedar swamps are understudied, due in part to the difficulties in collection methods. General lack of rapid and consistent sampling methods has also contributed in a lack of carbon stock quantification for many peatlands. The main objective of this thesis is to quantify: 1) to evaluate peat sampling methods 2) the amount of C-stored and the rates of long-term carbon accumulation in NW cedar peatlands. We sampled 38 peatlands separated into four categories (black ash, NW cedar swamp, sedge, and Sphagnum) during the summers of 2011/2012 across northern MN and the Upper Peninsula of MI. Basal dates of peat indicate that cedar peatlands were between 1970-7790 years old. Cedar peatlands are generally shallower than Sphagnum peat, but due to their higher bulk density, hold similar amounts of carbon with our sites averaging ~800 MgC ha-1. We estimate that NW cedar peatlands store over 1.7 Gt of carbon in the Great Lakes Region. Each of the six methods evaluated had a different level of accuracy and requires varying levels of effort and resources. The depth only method and intermittent sampling method were the most accurate methods of peatland sampling.