Evaluation of sampling strategies for modeling survival of uveal malignant melanoma

To evaluate sampling strategies used to estimate survival after uveal malignant melanoma that exclude some patients who would be censored from the analysis.

Simulation was performed on a population-based data set of 133 patients who had an eye enucleated because of uveal melanoma. One thousand bootstrap samples of 80 patients were drawn, without replacement, according to three sampling strategies: a random draw (conventional strategy), a draw limited to patients who died of the tumor or survived at least 10 years without metastasis ("late-censoring" strategy), and a draw modified so that 40 patients died of melanoma and others survived at least 10 years without metastasis ("fifty-fifty" strategy). The bias in the Kaplan-Meier analysis and Cox proportional hazards regression was quantified.

The late-censoring strategy decreased the proportion of censored patients from 53% to 42%, whereas the fifty-fifty strategy assigned 50% of patients to this group. The former strategy overestimated mortality, the excess being 5.2% and 3.7% at 10 and 20 years, respectively. The latter strategy underestimated mortality, the bias being 1.6% and 4.6% at 10 and 20 years, respectively. The bias differed according to categories of explanatory variables so that the log-rank test statistic was inflated a median of 1.08 times (range, 0.73-1.87) and 1.14 times (range, 0.87-1.84), and the Wald chi(2) statistic of the Cox regression was inflated a median of 1.18 times (range, 0.79-2.13) and 1.16 times (range, 0.71-2.02), respectively, when the late-censoring and fifty-fifty strategies were applied.

Sampling strategies that exclude on purpose a proportion of patients who would be censored produce biased statistics, because they violate assumptions of survival analysis. Only random sampling from an underlying population produces unbiased survival estimates.