923 resultados para Generalised Linear Models


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AIMS To estimate physical activity trajectories for people who quit smoking, and compare them to what would have been expected had smoking continued. DESIGN, SETTING AND PARTICIPANTS A total of 5115 participants in the Coronary Artery Risk Development in Young Adults Study (CARDIA) study, a population-based study of African American and European American people recruited at age 18-30 years in 1985/6 and followed over 25 years. MEASUREMENTS Physical activity was self-reported during clinical examinations at baseline (1985/6) and at years 2, 5, 7, 10, 15, 20 and 25 (2010/11); smoking status was reported each year (at examinations or by telephone, and imputed where missing). We used mixed linear models to estimate trajectories of physical activity under varying smoking conditions, with adjustment for participant characteristics and secular trends. FINDINGS We found significant interactions by race/sex (P = 0.02 for the interaction with cumulative years of smoking), hence we investigated the subgroups separately. Increasing years of smoking were associated with a decline in physical activity in black and white women and black men [e.g. coefficient for 10 years of smoking: -0.14; 95% confidence interval (CI) = -0.20 to -0.07, P < 0.001 for white women]. An increase in physical activity was associated with years since smoking cessation in white men (coefficient 0.06; 95% CI = 0 to 0.13, P = 0.05). The physical activity trajectory for people who quit diverged progressively towards higher physical activity from the expected trajectory had smoking continued. For example, physical activity was 34% higher (95% CI = 18 to 52%; P < 0.001) for white women 10 years after stopping compared with continuing smoking for those 10 years (P = 0.21 for race/sex differences). CONCLUSIONS Smokers who quit have progressively higher levels of physical activity in the years after quitting compared with continuing smokers.

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BACKGROUND Estimating the prevalence of comorbidities and their associated costs in patients with diabetes is fundamental to optimizing health care management. This study assesses the prevalence and health care costs of comorbid conditions among patients with diabetes compared with patients without diabetes. Distinguishing potentially diabetes- and nondiabetes-related comorbidities in patients with diabetes, we also determined the most frequent chronic conditions and estimated their effect on costs across different health care settings in Switzerland. METHODS Using health care claims data from 2011, we calculated the prevalence and average health care costs of comorbidities among patients with and without diabetes in inpatient and outpatient settings. Patients with diabetes and comorbid conditions were identified using pharmacy-based cost groups. Generalized linear models with negative binomial distribution were used to analyze the effect of comorbidities on health care costs. RESULTS A total of 932,612 persons, including 50,751 patients with diabetes, were enrolled. The most frequent potentially diabetes- and nondiabetes-related comorbidities in patients older than 64 years were cardiovascular diseases (91%), rheumatologic conditions (55%), and hyperlipidemia (53%). The mean total health care costs for diabetes patients varied substantially by comorbidity status (US$3,203-$14,223). Patients with diabetes and more than two comorbidities incurred US$10,584 higher total costs than patients without comorbidity. Costs were significantly higher in patients with diabetes and comorbid cardiovascular disease (US$4,788), hyperlipidemia (US$2,163), hyperacidity disorders (US$8,753), and pain (US$8,324) compared with in those without the given disease. CONCLUSION Comorbidities in patients with diabetes are highly prevalent and have substantial consequences for medical expenditures. Interestingly, hyperacidity disorders and pain were the most costly conditions. Our findings highlight the importance of developing strategies that meet the needs of patients with diabetes and comorbidities. Integrated diabetes care such as used in the Chronic Care Model may represent a useful strategy.

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OBJECTIVES Pre-antiretroviral therapy (ART) inflammation and coagulation activation predict clinical outcomes in HIV-positive individuals. We assessed whether pre-ART inflammatory marker levels predicted the CD4 count response to ART. METHODS Analyses were based on data from the Strategic Management of Antiretroviral Therapy (SMART) trial, an international trial evaluating continuous vs. interrupted ART, and the Flexible Initial Retrovirus Suppressive Therapies (FIRST) trial, evaluating three first-line ART regimens with at least two drug classes. For this analysis, participants had to be ART-naïve or off ART at randomization and (re)starting ART and have C-reactive protein (CRP), interleukin-6 (IL-6) and D-dimer measured pre-ART. Using random effects linear models, we assessed the association between each of the biomarker levels, categorized as quartiles, and change in CD4 count from ART initiation to 24 months post-ART. Analyses adjusted for CD4 count at ART initiation (baseline), study arm, follow-up time and other known confounders. RESULTS Overall, 1084 individuals [659 from SMART (26% ART naïve) and 425 from FIRST] met the eligibility criteria, providing 8264 CD4 count measurements. Seventy-five per cent of individuals were male with the mean age of 42 years. The median (interquartile range) baseline CD4 counts were 416 (350-530) and 100 (22-300) cells/μL in SMART and FIRST, respectively. All of the biomarkers were inversely associated with baseline CD4 count in FIRST but not in SMART. In adjusted models, there was no clear relationship between changing biomarker levels and mean change in CD4 count post-ART (P for trend: CRP, P = 0.97; IL-6, P = 0.25; and D-dimer, P = 0.29). CONCLUSIONS Pre-ART inflammation and coagulation activation do not predict CD4 count response to ART and appear to influence the risk of clinical outcomes through other mechanisms than blunting long-term CD4 count gain.

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1. The cover of plant species was recorded annually from 1988 to 2000 in nine spatially replicated plots in a species-rich, semi-natural meadow at Negrentino (southern Alps). This period showed large climatic variation and included the centennial maximum and minimum frequency of days with ≥ 10 mm of rain. 2. Changes in species composition were compared between three 4-year intervals characterized by increasingly dry weather (1988–91), a preceding extreme drought (1992–95), and increasingly wet weather (1997–2000). Redundancy analysis and anova with repeated spatial replicates were used to find trends in vegetation data across time. 3. Recruitment capacity, the potential for fast clonal growth and seasonal expansion rate were determined for abundant taxa and tested in general linear models (GLM) as predictors for rates of change in relative cover of species across the climatically defined 4-year intervals. 4. Relative cover of the major growth forms present, graminoids and forbs, changed more in the period following extreme drought than at other times. Recruitment capacity was the only predictor of species’ rates of change. 5. Following perturbation, re-colonization was the primary driver of vegetation dynamics. The dominant grasses, which lacked high recruitment from seed, therefore decreased in relative abundance. This effect persisted until the end of the study and may represent a lasting response to an extreme climatic event.

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Background Nowadays there is extensive evidence available showing the efficacy of cognitive remediation (CR). To date, only limited evidence is available about the impact of the duration of illness on CR effects. The Integrated Neurocognitive Therapy (INT) represents a new developed CR approach. It is a manualized group therapy targeting all 11 NIMH-MATRICS domains. Methods In an international multicenter study, 166 schizophrenia outpatients (DSM-IV-TR) were randomly assigned either to INT or to Treatment-As-Usual (TAU). 60 patients were defined as Early Course group (EC) characterized by less than 5 years of illness, 40 patients were in the Long-Term group (LT) characterized by more than 15 years of illness, and 76 patients were in the Medium-Long-Term group (MLT) characterized by an illness of 5-15 years. Treatment comprised of 15 biweekly sessions. Assessments were conducted before and after treatment and at follow up (1 year). Multivariate General Linear Models (GLM) examined our hypothesis, whether EC, LT, and MLT groups differ under INT and TAU from each other in outcome. Results First of all, the attendance rate of 65% was significantly lower and the drop out rate of 18.5% during therapy was higher in the EC group compared to the other groups. Interaction effects regarding proximal outcome showed that the duration of illness has a strong impact on neurocognitive functioning in speed of processing (F>2.4) and attention (F>2.8). But INT intervention compared to TAU only had a significant effect in more chronically ill patients of MLT and LT, but not in younger patients in EC. In social cognitive domains, only the EC group showed a significant change in attribution (hostility; F>2.5), LT and MLT groups did not. However, no differences between the 3 groups were evident in memory, problem solving, and emotion perception. Regarding more distal outcome, LT patients had more symptoms compared to EC (F>4.4). Finally, EC patients showed higher improvements in psychosocial functioning compared to LT and MLT (F=1.8). Conclusions Against common expectations, long-term, more chronically ill patients showed higher effects in basal cognitive functions compared to younger patients and patients without any active therapy (TAU). On the other hand, early-course patients had a greater potential to change in attribution, symptoms and psychosocial functioning. Consequently, more integrated therapy offers are also recommended for long-term course schizophrenia patients.

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Aim Our aims were to compare the composition of testate amoeba (TA) communities from Santa Cruz Island, Galápagos Archipelago, which are likely in existence only as a result of anthropogenic habitat transformation, with similar naturally occurring communities from northern and southern continental peatlands. Additionally, we aimed at assessing the importance of niche-based and dispersal-based processes in determining community composition and taxonomic and functional diversity. Location The humid highlands of the central island of Santa Cruz, Galápagos Archipelago. Methods We survey the alpha, beta and gamma taxonomic and functional diversities of TA, and the changes in functional traits along a gradient of wet to dry habitats. We compare the TA community composition, abundance and frequency recorded in the insular peatlands with that recorded in continental peatlands of Northern and Southern Hemispheres. We use generalized linear models to determine how environmental conditions influence taxonomic and functional diversity as well as the mean values of functional traits within communities. We finally apply variance partitioning to assess the relative importance of niche- and dispersal-based processes in determining community composition. Results TA communities in Santa Cruz Island were different from their Northern Hemisphere and South American counterparts with most genera considered as characteristic for Northern Hemisphere and South American Sphagnum peatlands missing or very rare in the Galápagos. Functional traits were most correlated with elevation and site topography and alpha functional diversity to the type of material sampled and site topography. Community composition was more strongly correlated with spatial variables than with environmental ones. Main conclusions TA communities of the Sphagnum peatlands of Santa Cruz Island and the mechanisms shaping these communities contrast with Northern Hemisphere and South American peatlands. Soil moisture was not a strong predictor of community composition most likely because rainfall and clouds provide sufficient moisture. Dispersal limitation was more important than environmental filtering because of the isolation of the insular peatlands from continental ones and the young ecological history of these ecosystems.

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Introduction: According to the ecological view, coordination establishes byvirtueof social context. Affordances thought of as situational opportunities to interact are assumed to represent the guiding principles underlying decisions involved in interpersonal coordination. It’s generally agreed that affordances are not an objective part of the (social) environment but that they depend on the constructive perception of involved subjects. Theory and empirical data hold that cognitive operations enabling domain-specific efficacy beliefs are involved in the perception of affordances. The aim of the present study was to test the effects of these cognitive concepts in the subjective construction of local affordances and their influence on decision making in football. Methods: 71 football players (M = 24.3 years, SD = 3.3, 21 % women) from different divisions participated in the study. Participants were presented scenarios of offensive game situations. They were asked to take the perspective of the person on the ball and to indicate where they would pass the ball from within each situation. The participants stated their decisions in two conditions with different game score (1:0 vs. 0:1). The playing fields of all scenarios were then divided into ten zones. For each zone, participants were asked to rate their confidence in being able to pass the ball there (self-efficacy), the likelihood of the group staying in ball possession if the ball were passed into the zone (group-efficacy I), the likelihood of the ball being covered safely by a team member (pass control / group-efficacy II), and whether a pass would establish a better initial position to attack the opponents’ goal (offensive convenience). Answers were reported on visual analog scales ranging from 1 to 10. Data were analyzed specifying general linear models for binomially distributed data (Mplus). Maximum likelihood with non-normality robust standard errors was chosen to estimate parameters. Results: Analyses showed that zone- and domain-specific efficacy beliefs significantly affected passing decisions. Because of collinearity with self-efficacy and group-efficacy I, group-efficacy II was excluded from the models to ease interpretation of the results. Generally, zones with high values in the subjective ratings had a higher probability to be chosen as passing destination (βself-efficacy = 0.133, p < .001, OR = 1.142; βgroup-efficacy I = 0.128, p < .001, OR = 1.137; βoffensive convenience = 0.057, p < .01, OR = 1.059). There were, however, characteristic differences in the two score conditions. While group-efficacy I was the only significant predictor in condition 1 (βgroup-efficacy I = 0.379, p < .001), only self-efficacy and offensive convenience contributed to passing decisions in condition 2 (βself-efficacy = 0.135, p < .01; βoffensive convenience = 0.120, p < .001). Discussion: The results indicate that subjectively distinct attributes projected to playfield zones affect passing decisions. The study proposes a probabilistic alternative to Lewin’s (1951) hodological and deterministic field theory and enables insight into how dimensions of the psychological landscape afford passing behavior. Being part of a team, this psychological landscape is not only constituted by probabilities that refer to the potential and consequences of individual behavior, but also to that of the group system of which individuals are part of. Hence, in regulating action decisions in group settings, informers are extended to aspects referring to the group-level. References: Lewin, K. (1951). In D. Cartwright (Ed.), Field theory in social sciences: Selected theoretical papers by Kurt Lewin. New York: Harper & Brothers.

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Theoretical models predict lognormal species abundance distributions (SADs) in stable and productive environments, with log-series SADs in less stable, dispersal driven communities. We studied patterns of relative species abundances of perennial vascular plants in global dryland communities to: (i) assess the influence of climatic and soil characteristics on the observed SADs, (ii) infer how environmental variability influences relative abundances, and (iii) evaluate how colonisation dynamics and environmental filters shape abundance distributions. We fitted lognormal and log-series SADs to 91 sites containing at least 15 species of perennial vascular plants. The dependence of species relative abundances on soil and climate variables was assessed using general linear models. Irrespective of habitat type and latitude, the majority of the SADs (70.3%) were best described by a lognormal distribution. Lognormal SADs were associated with low annual precipitation, higher aridity, high soil carbon content, and higher variability of climate variables and soil nitrate. Our results do not corroborate models predicting the prevalence of log-series SADs in dryland communities. As lognormal SADs were particularly associated with sites with drier conditions and a higher environmental variability, we reject models linking lognormality to environmental stability and high productivity conditions. Instead our results point to the prevalence of lognormal SADs in heterogeneous environments, allowing for more evenly distributed plant communities, or in stressful ecosystems, which are generally shaped by strong habitat filters and limited colonisation. This suggests that drylands may be resilient to environmental changes because the many species with intermediate relative abundances could take over ecosystem functioning if the environment becomes suboptimal for dominant species.

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Number of days spent in acute hospitals (DAH) at the end of life is regarded as an important care quality indicator for cancer patients. We analysed DAH during 90 days prior to death in patients from four Swiss cantons. Claims data from an insurance provider with about 20% market share and patient record review identified 2086 patients as dying of cancer. We calculated total DAH per patient. Multivariable generalised linear modelling served to evaluate potential explanatory variables. Mean DAH was 26 days. In the multivariable model, using complementary and alternative medicine (DAH = 33.9; +8.8 days compared to non-users) and canton of residence (for patient receiving anti-cancer therapy, Zürich DAH = 22.8 versus Basel DAH = 31.4; for other patients, Valais DAH = 22.7 versus Ticino DAH = 33.7) had the strongest influence. Age at death and days spent in other institutions were additional significant predictors. DAH during the last 90 days of life of cancer patients from four Swiss cantons is high compared to most other countries. Several factors influence DAH. Resulting differences are likely to have financial impact, as DAH is a major cost driver for end-of-life care. Whether they are supply- or demand-driven and whether patients would prefer fewer days in hospital remains to be established.

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Previous studies of normal children have linked body fat but not body fat distribution (BFD), to higher blood pressures, lipids, and insulin resistance (Berenson et al., 1988) BFD is a well-established risk factor for cardiovascular disease in adults (Björntorp, 1988). This study investigates the relation of BFD and serum lipids at baseline in children from Project HeartBeat!, a study of the growth and development of cardiovascular risk factors in 678 children in three cohorts measured initially at ages 8, 11, and 14 years. Initially, two of four indices of BFD were significantly related to the lipids: ratio of upper to lower body skinfolds (ln US:LS) and conicity (C Index). A factor analysis reduced the information in the serum lipids to two vectors: (1) total cholesterol + LDL-cholesterol and (2) HDL-cholesterol − triglycerides, which together accounted for 85% of the lipid variation. Using each serum lipid and vector as separate dependent variables, linear and quadratic regression models were constructed to examine the predictive ability of the two BFD variables, controlling for total body fat, gender, ethnicity (Black, non-Black) and maturation. Linear models provided an acceptable fit. Percent body fat (%BF) was a significant predictor in each and every lipid model, independent of age, maturation, or ethnicity (p ≤ 0.05). No BFD variable entered the equation for total or LDL-cholesterol, although there was a significant maturity by BFD interaction for LDL (ln US:LS was a significant predictor in more mature individuals). Both %BF and BFD (by way of Conicity) were significant predictors of HDL-cholesterol and triglycerides (p ≤ 0.01). All models were statistically significant at a high level (p ≤ 0.01), but adjusted R 2's for all models were low (0.05–0.15). Body fat distribution is a significant predictor of lipids in normal children, but secondarily to %BF, and for LDL-cholesterol in particular, the relation is dependent on maturity status. ^

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Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

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Study 1: Schools provide a range of opportunities for youth to be active, however, over the past decade, these opportunities have been declining. Sports teams are a promising venue to promote physical activity yet limited research has examined the gender an ethnic differences in sport participation. The purpose of this study is to examine trends in sport participation from 1991-2009 among US high school students. Secondly, we examined the association between gender and ethnicity with sports over time. This serial cross-sectional study used surveillance data from the Youth Risk Behavior Survey, a probability based sample weighted to represent gender and race/ethnic subpopulations of US high school students. The findings of this paper reveal persistent gender and ethnic disparities for sports participation among US youth. Since sports teams may provide a substantial source of physical activity, greater efforts should be undertaken to increase the participation of girls, especially minorities, in sports teams. ^ Study 2: Sports team participation is congruent with teaching and supporting healthy eating, yet limited research has examined the association between sports participation and dietary behaviors. This study aims to determine the association between youth sports participation and dietary behaviors among elementary-aged children. Significant dose-response associations were observed between number of sports teams and consumption of most fruits and vegetables. The likelihood of eating fruit for boys increased with the number of sports teams (1 team: OR=1.89; 3 teams: OR=3.44, p<0.001) and the likelihood of consuming green vegetables for girls was higher with the number of sports teams (1 team: OR=1.50; 3 teams: OR=2.39; p<0.001). For boys, the odds of consuming fruit-flavored drinks was higher ( p=0.019) and the odds of drinking soda was lower (p=0.018) with participation in increasing number of sports teams whereas for girls, sports participation was positively associated with diet soda consumption (p=0.006). ^ Study 3: Parents and peers have been shown to have a strong influence over the physical activity, dietary, and sedentary behaviors of youth. Youth sports teams have the potential to offer physical activity, displace sedentary behaviors, and promote a healthy diet. The purpose of this study is to assess how peer and parental support for physical activity and healthy eating, coupled with sport participation, is associated obesity related risk factors including diet and sedentary behaviors. A secondary analysis of data from the School Physical Activity and Nutrition study, a state-representative survey, was conducted. Eighth (n=3,931) and 11th (n=2,785) grade students were categorized into four groups based upon the level of peer and parental support derived from a three item scale and their participation in sports (sports/high support, sports/low support, no sports/high support, no sports/low support). Linear models were conducted to determine the difference in means between these groups for the following outcome variables: previous day fruit and vegetable intake, scores for an unhealthy and healthy food index, and hours spent watching television, playing video games, and working on a computer. Eighth graders had significantly greater levels of parental support for healthy eating and physical activity compared to 11th grade. Both 8 th and 11th graders in the sport/high support for healthy eating from peers and parents scored significantly higher on the healthy food index than other groups. Eighth and 11th graders in the sport/high support for physical activity from peers participated in fewer hours of sedentary behaviors than any other group (p ≤ 0.032). Although it is thought that sport participation may offer opportunities to support a healthy diet and displace sedentary time by offering providing physical activity, our study found that parental and peer support for activity and healthy eating may further attenuate this association. Parents and peer support should be an important target when developing strategies to improve healthy diets and reduce sedentary time among youth, especially in the context of youth sports. (Abstract shortened by UMI.)^

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The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

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La predicción de la fenología del haba es un paso crítico para optimizar el manejo de los cultivos, así como para el desarrollo de modelos de cultivos. Este artículo examina la respuesta fenológica del cultivo de haba (Vicia faba L.) a diversos regímenes térmicos y fotoperíodicos evaluada mediante modelos lineales. Se realizaron diecisiete fechas de siembra durante tres años en Lugo, España (43°04’ N; 7°30’ W; altitud 480 m) en las que se hicieron observaciones fenológicas. El tiempo desde emergencia a floración se describe satisfactoriamente mediante un modelo fototérmico. Las tasas de desarrollo de siembra a emergencia, floración hasta la primera vaina y primera vaina hasta madurez fisiológica fueron modeladas en forma satisfactoria, utilizando solamente la temperatura como variable independiente. Los valores de temperaturas basales variaron entre 2,09 y 4,47°C, dependiendo del subperíodo fenológico. El fotoperíodo base resultó de 6,9 h mientras el fotoperíodo crítico fue de 16,2 h.

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Secchi depth is a measure of water transparency. In the Baltic Sea region, Secchi depth maps are used to assess eutrophication and as input for habitat models. Due to their spatial and temporal coverage, satellite data would be the most suitable data source for such maps. But the Baltic Sea's optical properties are so different from the open ocean that globally calibrated standard models suffer from large errors. Regional predictive models that take the Baltic Sea's special optical properties into account are thus needed. This paper tests how accurately generalized linear models (GLMs) and generalized additive models (GAMs) with MODIS/Aqua and auxiliary data as inputs can predict Secchi depth at a regional scale. It uses cross-validation to test the prediction accuracy of hundreds of GAMs and GLMs with up to 5 input variables. A GAM with 3 input variables (chlorophyll a, remote sensing reflectance at 678 nm, and long-term mean salinity) made the most accurate predictions. Tested against field observations not used for model selection and calibration, the best model's mean absolute error (MAE) for daily predictions was 1.07 m (22%), more than 50% lower than for other publicly available Baltic Sea Secchi depth maps. The MAE for predicting monthly averages was 0.86 m (15%). Thus, the proposed model selection process was able to find a regional model with good prediction accuracy. It could be useful to find predictive models for environmental variables other than Secchi depth, using data from other satellite sensors, and for other regions where non-standard remote sensing models are needed for prediction and mapping. Annual and monthly mean Secchi depth maps for 2003-2012 come with this paper as Supplementary materials.