Prognostic trees to aid prognosis in patients with cutaneous malignant melanomaBMJ 1995; 311 doi: https://doi.org/10.1136/bmj.311.7019.1536 (Published 09 December 1995) Cite this as: BMJ 1995;311:1536
- Tom C Aitchison, senior lecturera,
- Jane M Sirel, research assistanta,
- Douglas C Watt, lecturera,
- Rona M MacKie, professorb for the Scottish Melanoma Group
- aDepartment of Statistics, Glasgow University, Glasgow G12 8QW
- bDepartment of Dermatology, Glasgow University, Glasgow G12 8QQ
- Correspondence to: Professor MacKie.
- Accepted 11 October 1995
Objectives: To design user friendly guides to prognosis for patients who have had invasive primary cutaneous malignant melanomas surgically excised.
Design: Adaptation of the classification tree method was used to derive prognostic trees for four different subgroups of malignant melanoma patients in whom known and possible prognostic variables interacted in different ways.
Subjects: Statistical modelling for prognostic trees was based on 1978 patients whose primary malignant melanoma was first diagnosed in 1979-86 for whom five year follow up and all relevant clinical pathological data were available. The resultant model was validated with 300 patients first diagnosed in 1987 for whom the same information was available.
Main outcome measures: Actual and predicted rate of survival after diagnosis of primary cutaneous malignant melanoma.
Results: The four subgroups of patients were men and women with ulcerated and non-ulcerated cutaneous primary melanomas. Validation of the model showed excellent agreement between actual status of patients in the relevant subgroups and their status as predicted by the model.
Conclusions: The prognostic trees are simple to use and give more accurate prognosis for individual patients than is currently available from tumour thickness alone.
Studies have shown that several factors affect the prognosis and survival of patients with primary invasive cutaneous malignant melanoma.1 2 3 4 Most reports agree that tumour thickness is the most important prognostic factor, but several other factors seem to interact, including sex, presence or absence of ulceration, level of invasion, age at diagnosis, site of tumour, and type of tumour.
We previously reported the results of proportional hazards models developed by the Scottish Melanoma Group to predict survival of patients with primary cutaneous malignant melanoma.5 Four distinct subgroups of patients were identified from this analysis—men and women with ulcerated or non-ulcerated lesions. Within each of these subgroups different sets of prognostic factors were identified, although tumour thickness was always a key factor. For example, among women with ulcerated lesions the site of the primary lesion and the mitotic count were also of prognostic value, whereas tumour thickness was the only relevant prognostic factor for women with non-ulcerated lesions. The details of this analysis are available from us on request in the form of a technical report and would be the preferred basis for predicting prognosis for an individual patient; however, predicting individual patients' survival profiles, and hence likely prognoses, by means of such a proportional hazards model is reasonably complicated, and, as the calculations are computer based, the model is not really suitable for general and widespread use.
We therefore adapted the proportional hazards models to create simplified, user friendly guides to prognosis that could be used for counselling individual patients as well as for identifying different risk groups for inclusion and stratification in clinical trials of any new treatment.
PROPORTIONAL HAZARDS MODEL
The Scottish Melanoma Group carried out a full modelling exercise with proportional hazards models that included the variables sex, level of invasion, age at diagnosis, site of tumour, type of tumour, numbers of mitoses (low or high), pre-existing naevus, regression, and presence or absence of obvious ulceration on histological examination. The analysis was based on all 1978 patients registered with the Scottish Melanoma Group who had a stage 1 primary cutaneous malignant melanoma of Clark level >/=2 during 1979-86, for whom there was full information on all the possible prognostic factors, and who had a minimum of four years follow up. The endpoint in this and all subsequent analyses was death due to malignant melanoma.
SIMPLE PROGNOSTIC TREES
We reanalysed the results for the 1978 patients by means of an adaptation (see below) of classification trees6 for each of the four subgroups identified in the full analysis (that is, based on the proportional hazards models). For each subgroup, the classification tree analysis provided a tree structure, with two branches at each step of the tree and new branches being formed until the data had no further important prognostic information (that is, the data could not be further subdivided by any of the possible prognostic factors to be of any benefit in predicting survival).
These versions of classification trees were based on log rank tests7 at each step in the tree and were therefore appropriate for analysing censored data by a tree based approach. An empirical rule based on a cross validation approach6 was used to determine the pruned trees (figures 1-4), with the extra condition that, whenever possible, at least 50 patients were available at each of the final nodes of the trees. This was achieved in 14 of the 16 nodes among the four trees.
After each node had been arrived at by means of the above approach a Kaplan-Meier8 estimate of the survival function for the particular subgroup was calculated and used to provide the estimates of two year and five year survival.
ESTIMATING PERFORMANCE OF THE PROGNOSTIC TREES
As a first step in assessing the usefulness and accuracy of these trees, they were applied to all 300 patients registered with the Scottish Melanoma Group whose disease was diagnosed in 1987 and who had a minimum of four years of follow up. We applied the appropriate Kaplan-Meier estimate based on the 1979-86 database to each of the 300 test patients and evaluated, for each, the probability of surviving at least one, two, three, and four years. These individual estimates were then summed over all patients in each of the subgroups and compared with the actual number of patients who survived past each of one, two, three, and four years.
THE PROGNOSTIC TREES
Figures 1-4 show the results of the classification tree analyses for the four subgroups. At the end of each final branch is a node (the boxes at the foot of each tree diagram). These nodes contain the number of patients in that particular subdivision of the data and, for illustration, the predicted two year and five year survival for these patients.
For example, if a woman presented with a 4.5 mm thick ulcerated lesion, figure 1indicates that she would have a 66% chance of surviving at least two years and a 43% chance of surviving at least five years (based on a sample of 151 women with ulcerated tumours thicker than 3.9 mm). However, if another woman presented with an ulcerated lesion of only 2 mm then one would take the left hand branch of the tree in figure 1 and ask her age; if she was, say, 50 years old one would carry on through the next step to estimate her prospects of surviving two years as 92% and of surviving five years as 77%.
PERFORMANCE OF THE PROGNOSTIC TREES
Table 1 shows that the general performance of the prognostic trees was very good when the observed survival of the 300 patients diagnosed in 1987 was compared with their predicted survival based on the trees. For example, of the 151 women with non-ulcerated lesions diagnosed in 1987, 129 actually survived at least four years, while the predicted number based on the tree in figure 2 was 127. In general the predicted numbers of surviving patients were close to the corresponding observed numbers; only at the fourth year after diagnosis was there a slight suggestion of conservative underestimation of survival in all four subgroups of patients.
As a further indication of the prognostic accuracy of the trees, table 2 gives the estimated five year rate of disease free survival for potential patients with malignant melanoma and a wide range of prognostic factors that were calculated with the full survival analysis, based on the proportional hazards model, and the prognostic trees in figures 1-4. For example, a man with an ulcerated lesion 3.5 mm thick was predicted to have a 48% probability of surviving at least five years based on the proportional hazards model and a 52% probability based on the prognostic trees—a good agreement. Table2 shows that, in general, the performance of the trees was close to the “correct” result based on the more technically correct proportional hazards model.
These prognostic trees are simple guides to the likelihood of survival from malignant melanoma. They performed well with the test sample of 30 patients both in predicting the number of survivors at up to four years and in their predictive value relative to the full proportional hazards model. They are currently used in our clinic as an aid to counselling patients after diagnosis of melanoma and enable advice to be directed more specifically to individual patients. With greater awareness of melanoma in the community, and thus in some cases earlier presentation these trees will probably need to be revised about every five years, and we plan to do this. In collaboration with colleagues outside Glasgow we are also testing the robustness of the trees in other geographic areas.
The one disadvantage, in a sense, with the trees is the need to split each prognostic factor into two possible groups at each stage of a tree's construction. This is fine for variables such as site that could take only two values (axial or extremity), but produces slightly arbitrary categorisations of continuous variables such as tumour thickness, age, etc. This means that in figure 1 for example, a woman with an ulcerated lesion 4 mm thick (that is, just above the cut off point) gets a substantially different prognosis from a similar patient with a lesion 3.9 mm thick. Clearly this is rather arbitrary for patients near the cut off point, and care should be taken with such patients, with perhaps the more optimistic route being explored first.
However, this is somewhat balanced for by the fact that the trees use such variables more than once and more variables in total than the proportional hazards model to compensate for the rough categorisation of continuous variables such as tumour thickness. For example, in the prognostic prediction for women with non-ulcerated lesions (fig 2)tumour thickness is used twice, while age, level of invasion, and site are also included.
Prognosis for patients with primary invasive cutaneous malignant melanoma can be assessed with considerable accuracy at the time of excision of the primary tumour
We developed four prognostic trees to predict prognosis in four subgroups of patients —men and women with ulcerated or non-ulcerated primary tumours—in whom the possible prognostic variables interacted differently
Prospects for five year disease free survival ranged from 100% for women with non-ulcerated lesions to only 34% for men with ulcerated lesions
Validation of the trees by comparison with results for 300 patients showed excellent agreement between actual status of patients in the relevant subgroups and their predicted status
These prognostic trees are a simple and accurate method of predicting prognosis of patients with malignant melanoma
In spite of these differences with the full and somewhat more complicated approach of the survival analysis, the trees seem to be effective prognostic indicators for the vast majority of patients. These tree diagrams can be used in a clinic as a quick and simple means of assessing an individual patient's prospects of survival after diagnosis of a malignant melanoma.
We thank the secretaries of the Scottish Melanoma Group, Miss E Salt and Mrs J Stewart, for their help.
Funding We thank the Scottish Hospital Endowment Research Trust for financial support and the Cancer Research Campaign for funding the Scottish Melanoma Group.
Conflict of interest None.