Action profiles of predictors of death and survival time in stage I malignant melanoma

Abstract

BACKGROUND Many studies have been performed to identify prognostic factors of malignant melanoma using multivariate regression models. In these models, it is generally assumed that quantitative predictors such as age or tumor thickness enter linearly into the model, or they are categorized. OBJECTIVE The purpose of the present study is to investigate possible curvature (nonlinearity) of predictors of 'death from MM within 5 years after diagnosis' and 'survival time after diagnosis' avoiding the known shortcomings of categorizing predictors. METHODS Our analyses are based on data of 677 patients with stage I melanoma of the skin collected at the Cancer Registry of the Canton of Zurich. In order to study non-linearity of predictors, we use 'generalized additive models' (GAM): in a GAM the usual prognostic index is replaced in an optimal way by a more flexible form where the individual linear terms are replaced by possibly curved functions of the predictors. Plotting the corresponding curves (the 'action profiles') allows one to visualize easily the shape by which predictors 'act' over the whole range of values. RESULTS Essentially the same results emerged when studying 'death from melanoma' and 'survival time in melanoma': age and tumor thickness have a pronounced nonlinear association with both endpoints taking simultaneously into account effects of sex and tumor site. The action profile for age is J or U shaped. The action profile for thickness has a 'two-phase' pattern. It increases linearly for low thickness values and flattens for higher values. The shape of the action profiles was checked by performing a Monte Carlo simulation ('boot-strapping'). CONCLUSIONS The best prognosis of melanoma was found within a middle age range while younger and older patients showed a poorer prognosis. In our data, the increase in thickness in the range above 2 mm is of much less clinical relevance than in the range below 2 mm. GAMs may be of great value for clinicians in providing a visualization of the shape by which predictors act and to obtain a better understanding of the complex relationships between predictors and survival. Not considering curvature of action profiles may result in excluding relevant predictors.