For the analysis of time trends in incidence and mortality rates, the age-period-cohort (apc) model has became a widely accepted method. The considered data are arranged in a two-way table by age group and calendar period, which are mostly subdivided into 5- or 10-year intervals. The disadvantage of this approach is the loss of information by data aggregation and the problems of estimating interactions in the two-way layout without replications. In this article we show how splines can be useful when yearly data, i.e., 1-year age groups and 1-year periods, are given. The estimated spline curves are still smooth and represent yearly changes in the time trends. Further, it is straightforward to include interaction terms by the tensor product of the spline functions. If the data are given in a nonrectangular table, e.g., 5-year age groups and 1-year periods, the period and cohort variables can be parameterized by splines, while the age variable is parameterized as fixed effect levels, which leads to a semiparametric apc model. An important methodological issue in developing the nonparametric and semiparametric models is stability of the estimated spline curve at the boundaries. Here cubic regression splines will be used, which are constrained to be linear in the tails. Another point of importance is the nonidentifiability problem due to the linear dependency of the three time variables. This will be handled by decomposing the basis of each spline by orthogonal projection into constant, linear, and nonlinear terms, as suggested by Holford (1983, Biometrics 39, 311-324) for the traditional apc model. The advantage of using splines for yearly data compared to the traditional approach for aggregated data is the more accurate curve estimation for the nonlinear trend changes and the simple way of modeling interactions between the time variables. The method will be demonstrated with hypothetical data as well as with cancer mortality data.

For an optimized bioreactor design which is adapted to the cultivation of sensitive animal cells different modular bioreactor components for gentle agitation, sufficient aeration and long-term perfusion were developed and investigated with respect to their suitability from laboratory to production scale. Aeration systems have been designed for both shear sensitive cells and cells which tolerate bubbles. The systems are based on either membranes for bubble-free aeration or stainless steel sparger systems. They were characterized by determination of their oxygen transfer capacity and optimized in cultivation processes of different cell lines under process conditions such as batch and perfusion mode. Different impellers for suspension cells and cells grown on carriers were investigated for their suitability to ensure homogeneous gentle mixing. A large pitch blade impeller as well as a novel 3-blade segment impeller are appropriate for homogeneous mixing at low shear rates. Especially with the 3-blade segment impeller fluid mechanical stress can be reduced at a given stirrer speed which is advantageous for the cultivation of cells attached to microcarriers or extremely shear sensitive suspension cells. However, our results indicate that shear sensitivity of animal cells has been generally overestimated. Continuous perfusion of both suspension cell cultures and cells cultivated on microcarriers could be successfully performed over extended periods of time using stainless steel spinfilters with appropriate pore sizes and systems based on microporous hydrophilic membranes. Spinfilters are suitable cell retention systems for technical scale bioreactors allowing continuous perfusion cultures of suspension cells (pore size 10 to 20 microns) as well as anchorage dependent cells grown on microcarriers (pore size 75 microns) over six weeks to 3 months. Applying the developed modules for agitation, aeration and perfusion process adapted bioreactor set-ups can be realized which ensure optimum growth and product formation conditions in order to maximize cell and product yields.

The results of our study lead to the suggestion that smoking, occupation and demographic factors probably play a minor role in the aetiology of renal cell cancer.