Generating Survival Times to Simulate Cox Proportional Hazards Models

This paper discusses techniques to generate survival times for simulation studies regarding Cox proportional hazards models. In linear regression models, the response variable is directly connected with the considered covariates, the regression coefficients and the simulated random errors. Thus, the response variable can be generated from the regression function, once the regression coefficients and the error distribution are specified. However, in the Cox model, which is formulated via the hazard function, the effect of the covariates have to be translated from the hazards to the survival times, because the usual software packages for estimation of Cox models require the individual survival time data. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived. It is shown how the exponential, the Weibull and the Gompertz distribution can be used to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of other distributions than the exponential distribution only is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard

Countrywide and transboundary spatial reconstruction of rainfall using commercial microwave links

Rainfall strongly influences the availability of water on the land surface, and hence, its quantification is utterly relevant for addressing a variety of social, economic, and environmental matters. Quantification via traditional rainfall measuring devices has its limitations and can be supported by opportunistic sensors like commercial microwave links (CMLs), which theoretically enable rainfall estimation on large spatial scales due to their vast global abundance. However, estimation across organizational (e.g., national) boundaries is challenging due to heterogeneous CML data sets with customized rainfall retrieval methods. Moreover, common interpolation techniques have shortcomings in using path-averaged CML observations for spatial rainfall reconstruction. These challenges of CML-based transboundary rainfall estimation have been addressed in this thesis by generating rainfall maps of hourly temporal resolution, which were evaluated using a weather radar reference. Two large CML data sets from Germany and the Czech Republic with distinctly different network characteristics were combined and processed jointly via established and extended algorithms to generate transboundary rainfall maps. Beyond that, the German CML data set was combined with a countrywide network of rain gauges to generate rainfall maps via a stochastic reconstruction approach called Random Mixing (RM). The quality of these maps was analyzed considering an alternative standard Kriging approach and an object-based validation scheme named eSAL, which quantifies errors in structure, amplitude, and location. The computational complexity of RM was examined and reduced. It was found that the German and Czech CML data sets could be processed jointly to generate consistent transboundary rainfall maps once issues of limited data quality were identified and addressed by appropriate universal algorithms. The strong influence of partly hardware-dependent data quality issues could be demonstrated. Furthermore, stochastic reconstruction via RM proved to enable the generation of rainfall maps with accurate pattern representation. Despite a general underestimation and relatively high computational complexity, the method had clear advantages over the Kriging approach as indicated in particular by significantly lower structure errors and by providing probabilistic ensemble solutions. The results yield evidence for the capabilities of generating high-quality CML-based rainfall maps on large spatial scales, even across political borders, and hence, they contribute to better utilize the potential of CMLs as widespread rainfall sensors worldwide

Bias of Maximum-Likelihood estimates in logistic and Cox regression models: A comparative simulation study

Parameter estimates of logistic and Cox regression models are biased for finite samples. In a simulation study we investigated for both models the behaviour of the bias in relation to sample size and further parameters. In the case of a dichotomous explanatory variable x the magnitude of the bias is strongly influenced by the baseline risk defined by the constants of the models and the risk resulting for the high risk group. To conduct a direct comparison of the bias of the two models analyses were based on the same simulated data. Overall, the bias of the two models appear to be similar, however, the Cox model has less bias in situations where the baseline risk is high

Emerging aspects of mobile phone use

The mobile phone is a modern-day invention, which has managed to reach many parts of the world enabling telecommunications across areas where it was not possible before. Although these devices have proved to be life saving in certain circumstances (e.g., after accidents) and helped improve the quality of life in some sectors, concerns continue to be raised about potential adverse health impacts associated with their use. These range from cancer and cognitive deficiencies to subjective effects, such as a feeling of warmth around the ear used, headache and fatigue. We provide an overview of the concerns raised and summarise what is known about them. We conducted a literature search in Pubmed/Medline to identify published papers on health effects of mobile phones, and an intensive search on the Internet to collect data on the global use of mobile phones. In the year 2000, there were an estimated 500 million mobile phone users worldwide. Today, there are about 3.3 billion users. The use of mobile phones among young children and adolescents is also increasing. Health-risk research has mainly focused on adults and on a single outcome, brain tumours. No significant relationship has been established between mobile phone use and the incidence or growth of brain tumours. Other research indicates emerging concerns, including hearing problems and self-reported health symptoms, such as tiredness, stress, headache, anxiety, concentration difficulties and sleep disturbances, but results remain inconclusive. Currently, there is little epidemiological evidence indicating that the use of mobile phones causes adverse health effects

Decreasing sperm quality: a global problem?

<p>Abstract</p> <p>Background</p> <p>Carlsen and coworkers (1992) reviewed 61 heterogeneous observational studies on semen quality published between 1938 and 1990. This review indicates that mean sperm density decreased significantly between 1940 and 1990. An extended meta-analysis with 101 studies confirmed a decline in sperm density for the period from 1934 to 1996 (2000). The key message of the meta-analyses is that sperm counts have decreased globally by about 50% over the past decades. This assessment has been questioned.</p> <p>Discussion</p> <p>A major methodological problem of the meta-analysis is the use of data collected in different countries, at different times, on different populations and with different methods of semen analysis. Furthermore, the results of studies concerning semen analysis are frequently biased e.g. by selection criteria of volunteers. In most studies on human semen characteristics the populations under study are insufficiently defined and the study participants are not a representative population sample. The incidence of testicular cancer has increased in Caucasian men worldwide. The investigation of common risk factors for male reproductive disorders requires well designed epidemiological studies and the collection of individual data.</p> <p>Summary</p> <p>Former meta-analyses of sperm count data show a global downward trend. This conclusion should be interpreted with caution. The included studies are of great heterogeneity due to geographical and/or ethnical variation, different study designs and different methodological standards. Population-based prospective studies are needed to investigate secular trends in male reproductive disorders.</p

Public-Private-Partnerships

The continuing trend of increasing frequency and severity of losses from natural and man-made-catastrophes during the last decades has drawn attention to catastrophe risk management. Considering the loss potential of catastrophic events, the private insurance markets' capacity does not seem to be suffi-cient. Problems concerning the supply of adequate catastrophe insurance coverage – resulting mainly from insurability constraints – are aggravated by difficulties of lacking insurance demand. This paper addresses aspects of efficient solutions to increase the supply of and demand for insurance coverage against catastrophic threats. In this context, the government`s role as a risk bearer becomes an increasingly important issue. In particular, we will demonstrate that "pure private" and "pure public" strategies are dominated by "mixed" strategies involving a cooperation of the private and the public sec-tor. Based on an adequate design of a Public-Private Partnership, advantages of the private insurance market can be combined with the state’s capacity reserves and power to set a general (legal) framework for improving a society’s risk sharing and risk management. Strategies with public involvement are more or less severe interventions in the market system which re-quires them to be well-motivated and makes them applicable under certain conditions only. Supplying public capacity for losses from catastrophe events may be favoured from an economic point of view to expand the limits of insurability, but only by using risk-adequate pricing strategies and not for permanent subsidisation of certain business sectors. The state’s role consists not only in supplying coverage capac-ity, but also in setting an adequate general framework (building regulations, land use planning, etc.) to assure necessary claim prevention. On the other hand, in order to increase the demand for catastrophe insurance, establishing mandatory insurance for fundamental risks can be considered as a useful tool for internalizing externalities caused by lacking insurance demand. Besides the introduction of a compulsory insurance system, general conditions must be set by the state in order to assure the acceptance of manda-tory insurance (tax-privileged provisions, public capacity support for "uninsurable" individual risks, etc.).Katastrophenrisiken; Versicherungspflicht; Public-Private-Partnership

The Generalized Estimating Equations in the Past Ten Years: An Overview and A Biomedical Application

The Generalized Estimating Equations (GEE) proposed by Liang and Zeger (1986) have found considerable attention in the last years and several extensions have been proposed. This paper will give a more intuitive description how GEE have been developed during the last years. Additionally we will describe the advantages and disadvantages of the different parametrisations that have been proposed in the literature. We will also give a brief review of the literature available on this topic. [ Published in: Biometrical Journal 40 (2), 115-139

Familial Associations of Lipid Profiles: A Generalised Estimating Equations Approach

Elevated plasma levels of apolipoproteins A1 (apoA1) and B (apoB) are important protective factors and risk factors, respectively, for atherosclerosis and coronary heart disease. It is well known that both apoA1 and apoB reveal strong familial aggregation. Our goal was to investigate whether exogenous variables influence these associations. We used marginal regression models for the mean and association structure (Generalised Estimating Equations 2; GEE2) to analyse data from 1435 family members within 469 families of different sizes included in the Donolo-Tel Aviv Three-Generation Offspring Study. The usual robust variance matrix was approximated by extensions of jackknife estimators of variance to GEE2 models. Upon use of this approach estimation of standard errors in models with quite complex correlation structures was possible. All analyses were easily carried out using a menu-driven stand-alone software tool for marginal regression modelling. We demonstrate that a variety of hypotheses can be tested using Wald statistics by modelling regression matrices for the association structure. We show that correlation for apoB between parent-offspring pairs increased with decreasing age difference and that pairs with individuals of the same gender had more similar apoA1 levels than individuals of different gender. Associations between different relative pairs did not all agree with those expected from differences in kinship coefficients. The analysis using GEE2 models revealed structures that would not have been detected by other models and should therefore be used in addition to traditional approaches of analysing family data. GEE2 should be considered a standard method for the investigation of familial aggregation. [ Published in: Statistics in Medicine 19, Issue 24, 3345-3357

Combining commercial microwave link and rain gauge observations to estimate countrywide precipitation: a stochastic reconstruction and pattern analysis approach

Accurate spatiotemporal precipitation quantification is a crucial prerequisite for hydrological analyses. The optimal reconstruction of the spatial distribution, that is, the rainfall patterns, is particularly challenging. In this study, we reconstructed spatial rainfall on a countrywide scale for Germany by combining commercial microwave link and rain gauge observations for a better representation of the variability and spatial structure of rainfall. We further developed and applied the Random-Mixing-Whittaker-Shannon method, enabling the stochastic reconstruction of ensembles of spatial fields via linear combinations of unconditional random fields. The pattern of rainfall objects is evaluated by three performance characteristics, that is, ensemble Structure-, Amplitude-, and Location-error. Precipitation estimates obtained are in good agreement with the gauge-adjusted weather radar product RADOLAN-RW of the German Weather Service (DWD) which was used as a reference. Compared to reconstructions by Ordinary Kriging, Random Mixing showed clear advantages in the pattern representation via a five times smaller median structure error