Exploration of interactions between prognostic factors of stage I malignant melanoma.

While many studies have sought prognostic factors of malignant melanoma using multivariate survival models, the interaction between predictors has been much less studied. We have studied data from 1,560 patients with stage I melanoma collected at the Cancer Registry of the Canton of Zurich over the period 1980-1990 and explored interactions between predictors by identifying two separate multivariate Cox models for men and women and investigating two-way interactions between predictors in each model. Considerable differences between models for man and women were observed. In particular, in women a pronounced interaction between 'histology' and 'Clark level' was identified. Without this interaction 'histology' and 'Clark level' are not significant but when the interaction term was included both predictors become significant. Thus, omission of an interaction term may preclude the recognition of main effects ('masking'). For female patients with nodular tumours prognosis is essentially independent of Clark level. In contrast, for female patients with non-nodular tumours, prognosis was found to be strongly dependent on Clark level. In the case of Clark level 2 prognosis was extremely good: no patient was observed to die from melanoma. We conclude that it may be worth considering interaction terms. With large enough sample sizes it may be preferable to stratify patients into subgroups and to identify separate models for each stratum instead of having to cope with interactions of higher order.

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

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.