This revised proposal builds on my current work applying semiparametric statistical methods to model nonlinear exposure-response curves with smooth functions of exposure in occupational cohort studies (R01 CA81345). In the course of adapting penalized splines for survival analysis, we have identified two issues that need further development: criteria for choosing the optimal amount of smoothness and diagnostic statistics to identify influential observations and measure their influence on the fitted values of the curve. These issues will be examined in the presence of right skewed distributions typical of workplace exposures. We propose to compare the goodness of fit and resistance of penalized splines to that of two other common smoothers: restricted cubic splines, and a locally weighted regression smoother called loess. In this revised application, we propose to compare the three smoothing methods by evaluating model fit in a series of simulation studies. Data will be generated under linear, cubic polynomial, and threshold (broken stick) exposure-response models, assuming exposure has a lognormal distribution. We will identify the technique with the best fit to the true data, after calibrating the amount of smoothness across the three methods. We also now propose to develop statistical methods to quantify influence and identify points with high leverage in semiparametric models, with particular attention to values at the high end of the skewed exposure distribution. We will compute Cook's distance for parametric and nonparametric components and develop rules for assessing statistical significance as well as diagnostics for determining the sensitivity of the smoothing parameter to subject deletion. The new diagnostics will be developed for penalized splines and then extended to restricted cubic splines and loess. The models will be applied to the re-analyses of two cancer mortality studies; larynx, lung, prostate and rectal cancer in autoworkers exposed to metalworking fluids (MWF) and lung cancer in workers in California's diatomaceous earth industry exposed to crystalline silica. We plan to focus our methodologic investigations on MWF and silica because we believe that clarifying the shapes of their exposure-response curves can make a substantial contribution to current controversies over their control in the workplace.