On the use of Fractional Polynomials in Dynamic Cox Models

Despite a sophisticated research on modelling of survival data in the last years, the most popular model used in practice is still the proportional hazards regression model proposed by Cox (1972). This is mainly due to its exceptional simplicity. Nevertheless the fundamental assumption of the Cox model is the proportionality of the hazards, which particularly implies that the covariate effects are constant over time. For many applications this assumption is, however, doubtful. Other, more flexible approaches, which are able to cope with non-proportional hazards usually require non-standard estimation techniques, which are often rather complex and thus not favoured in application. Moreover, the selection of an appropriate test-statistic, to examine the improvement of the fit, is not obvious. In this paper we propose a flexible, yet simple method for modelling dynamic effects in survival data within the Cox framework. The method is based on Fractional Polynomials as introduced by Royston and Altman (1994). This allows for a transformation of the dynamic predictor which leads back to the conventional Cox model and hence fitting is straightforward using standard estimation techniques. In addition, it offers the possibility to easily verify the existence of time-variation. We describe a model selection algorithm which enables to include time-varying effects only when evidence is given in the data, in order to construct a model, which is just as complex as needed. We illustrate the properties of the approach in a simulation study and an application to gastric carcinoma data and compare it with other methods (e.g. the residual score test and smoothed Schoenfeld residuals of Grambsch and Therneau, 1994; natural smoothing splines of Hastie and Tibshirani, 1993)

As in Real Estate, Location Matters: Cellular Expression of Complement Varies Between Macular and Peripheral Regions of the Retina and Supporting Tissues.

The cellular events that dictate the initiation of the complement pathway in ocular degeneration, such as age-related macular degeneration (AMD), is poorly understood. Using gene expression analysis (single cell and bulk), mass spectrometry, and immunohistochemistry, we dissected the role of multiple retinal and choroidal cell types in determining the complement homeostasis. Our scRNA-seq data show that the cellular response to early AMD is more robust in the choroid, particularly in fibroblasts, pericytes and endothelial cells. In late AMD, complement changes were more prominent in the retina especially with the expression of the classical pathway initiators. Notably, we found a spatial preference for these differences. Overall, this study provides insights into the heterogeneity of cellular responses for complement expression and the cooperation of neighboring cells to complete the pathway in healthy and AMD eyes. Further, our findings provide new cellular targets for therapies directed at complement

Preschool children's health and its association with parental education and individual living conditions in East and West Germany

BACKGROUND: Social inequalities in health exist globally and are a major public health concern. This study focus on a systematic investigation into the associations between health indicators, living conditions and parental educational level as indicator of the social status of 6-year-old children living in West and East Germany in the decade after re-unification. Explanations of observed associations between parental education and health indicators were examined. METHODS: All boys and girls entering elementary school and living in predefined areas of East and West Germany were invited to participate in a series of cross-sectional surveys conducted between 1991 and 2000. Data of 28,888 German children with information on parental education were included in the analysis. Information about educational level of the parents, individual living conditions, symptoms and diagnoses of infectious diseases and allergies were taken from questionnaire. At the day of investigation, atopic eczema was diagnosed by dermatologists, blood was taken for the determination of allergen-specific immuno-globulin E, height and weight was measured and lung function tests were done in subgroups. Regression analysis was applied to investigate the associations between the health indicators and parental educational level as well as the child's living conditions. Gender, urban/rural residency and year of survey were used to control for confounding. RESULTS: Average response was 83% in East Germany and 71% in West Germany. Strong associations between health indicators and parental education were observed. Higher educated parents reported more diagnoses and symptoms than less educated. Children of higher educated parents were also more often sensitized against grass pollen or house dust mites, but had higher birth weights, lower airway resistance and were less overweight at the age of six. Furthermore, most of the health indicators were significantly associated with one or more living conditions such as living as a single child, unfavourable indoor air, damp housing condition, maternal smoking during pregnancy or living near a busy road. The total lung capacity and the prevalence of an atopic eczema at the day of investigation were the only health indicators those did not show associations with any of the predictor variables. CONCLUSION: Despite large differences in living conditions and evidence that some poor health outcomes were directly associated with poor living conditions, only few indicators demonstrated poorer health in social disadvantaged children. These were in both parts of Germany increased levels of overweight, higher airway resistance and, in East Germany only, reduced height in children with lower educated parents compared to those of higher education. In both East and West Germany, higher prevalence of airway symptoms was associated with a damp housing condition, and lower birth weight, reduced height and increased airway resistance at the age of six were associated with maternal smoking during pregnancy. The latter explained to a large extent the difference in birth weight and airway resistance between the educational groups