Benchmark measures of prognosis relayed to patients throughout the course of their disease are typically estimated from the time of diagnosis. These estimates become less relevant as time from diagnosis increases for a patient, because prognosis usually improves over time. The conditional survival estimate presents a more relevant measure of prognosis for the population of patients who have already survived some number of years beyond their diagnosis.
Conditional survival measures the probability that a cancer patient will survive some additional number of years, given that the patient has already survived for a certain number of years. These estimates have been reported for numerous cancer sites using both the population-based Surveillance, Epidemiology, and End Results (SEER) database and single-institution data.[1-24] As a rule, conditional survival estimates increase as the number of years survived increases, a relationship that is usually even more striking for patients with advanced-stage disease. Accordingly, most authors conclude that conditional survival estimates are an important prognostic measure for both patients and clinicians[2, 3, 7, 8, 11, 13, 17, 20]; however, in practice, the measure is not widely known or commonly disseminated. The purpose of this article was to raise awareness about the importance of using conditional rather than traditional survival estimates for patients who have already survived for ≥ 1 year beyond diagnosis.
Conditional survival estimation does not require additional data or assumptions and is directly calculated from traditional Kaplan-Meier survival estimates. Let S(t) represent the Kaplan-Meier survival estimate at time t. Conditional survival is defined as the probability of surviving an additional number of years (y) given that a patient has already survived for x number of years and is calculated as:
For example, the conditional probability of surviving an additional year for a patient who has already survived 4 years, S(1|4), is simply calculated by dividing the 5-year Kaplan-Meier survival estimate, S(5), by the 4-year Kaplan-Meier survival estimate, S(4): .
Confidence intervals (CIs) can be calculated around conditional survival estimates using a variation of the standard Greenwood formula for the estimation of CIs in unconditional survival, as described by Davis et al.
We used a data example to illustrate these methods and to demonstrate the dynamic nature of prognostic estimates obtained using conditional survival estimation. Data regarding 1774 patients with cutaneous melanoma who presented at Memorial Sloan-Kettering Cancer Center between 2000 and 2010 with stage III disease were selected from a prospectively maintained database. The American Joint Committee on Cancer staging system was used to define stage III disease and its substages. We limited the study sample to patients who presented to Memorial Sloan-Kettering Cancer Center ≤ 120 days after their initial diagnosis, if diagnosed at another institution, resulting in a final sample size for analysis of 944 patients. Institutional Review Board approval was obtained for this retrospective study. Overall survival (OS) was calculated from date of presentation to the date of death from any cause, with surviving patients censored at the date of last follow-up. We computed conditional survival estimates and 95% CIs for patients who had already survived between 1 and 4 years from the time of presentation. Statistical analyses were conducted using R v.2.13.1 statistical software (R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria), including the “survival” package. R functions to help calculate a conditional survival estimate with the 95% CI and to produce plots as seen in Figure 1 are available at http://www.mskcc.org/research/epidemiology-biostatistics/biostatistics/conditional-survival.
The median follow-up among survivors was 1.6 years (interquartile range, 0.1 years-4.2 years). During follow-up, 18% of patients (59 of 337 patients), 38% of patients (128 of 337 patients), and 51% of patients (139 of 270 patients), respectively, with substage IIIA, IIIB, and IIIC disease died of any cause. Figure 1 shows the Kaplan-Meier OS curves as well as conditional survival curves for all patients with stage III disease, and separately by substage IIIA, IIIB, and IIIC disease. Curves within a panel depict increasing amounts of survival from baseline and can be distinguished by their starting points. With each additional year survived, the survival probabilities increase, as noted by the upward shift of the curves over time. Stage-specific survival estimates at the time of presentation and conditional survival estimates for patients who had already survived between 1 and 4 years from the time of presentation are shown in Table 1. The 5-year OS estimates at the time of presentation for patients with substage IIIA, IIIB, and IIIC disease were 72%, 48%, and 29%, respectively. These estimates for OS were slightly lower than, but generally in line with, those of Balch et al, who reported 5-year OS rates of 78%, 59%, and 40%, respectively, for patients with substage IIIA, IIIB, and IIIC melanoma.
|No. of Years From Presentation||Probability of Surviving to Certain No. of Years From Presentation (95% CI)|
|Stage III (n = 944)|
|0a||0.89 (0.87–0.91)||0.74 (0.71–0.78)||0.64 (0.60–0.68)||0.54 (0.50–0.58)||0.49 (0.45–0.54)|
|1||—||0.84 (0.81–0.87)||0.71 (0.68–0.75)||0.61 (0.56–0.65)||0.55 (0.51–0.60)|
|2||—||—||0.85 (0.82–0.89)||0.72 (0.68–0.77)||0.66 (0.61–0.71)|
|3||—||—||—||0.85 (0.81–0.89)||0.78 (0.73–0.83)|
|Substage IIIA (n = 337)|
|0a||0.96 (0.93–0.98)||0.88 (0.84–0.92)||0.81 (0.76–0.87)||0.76 (0.69–0.82)||0.72 (0.65–0.79)|
|1||—||0.92 (0.88–0.96)||0.85 (0.80–0.90)||0.79 (0.73–0.85)||0.75 (0.68–0.82)|
|2||—||—||0.93 (0.88–0.97)||0.86 (0.80–0.92)||0.82 (0.75–0.89)|
|3||—||—||—||0.93 (0.88–0.98)||0.89 (0.83–0.95)|
|Substage IIIB (n = 337)|
|0a||0.90 (0.87–0.94)||0.76 (0.71–0.81)||0.63 (0.57–0.7)||0.53 (0.47–0.60)||0.48 (0.41–0.55)|
|1||—||0.84 (0.79–0.89)||0.70 (0.64–0.77)||0.59 (0.52–0.66)||0.53 (0.45–0.60)|
|2||—||—||0.84 (0.78–0.90)||0.70 (0.62–0.78)||0.63 (0.54–0.71)|
|3||—||—||—||0.84 (0.77–0.91)||0.75 (0.66–0.83)|
|Substage IIIC (n = 270)|
|0a||0.80 (0.75–0.86)||0.59 (0.53–0.66)||0.46 (0.39–0.53)||0.33 (0.27–0.41)||0.29 (0.22–0.37)|
|1||—||0.73 (0.66–0.80)||0.57 (0.49–0.65)||0.41 (0.33–0.50)||0.35 (0.27–0.44)|
|2||—||—||0.77 (0.69–0.86)||0.56 (0.46–0.66)||0.48 (0.38–0.59)|
|3||—||—||—||0.73 (0.62–0.83)||0.63 (0.50–0.75)|
However, as demonstrated in Figure 1, survival estimates at the time of diagnosis of stage III disease underestimate long-term survival as the patient is followed over time. Conditional survival estimates account for survival time and give the patient an updated, and more hopeful, estimate of survival. This is important because many patients are followed closely for years after surgery and want to know how their chances of long-term survival improve. Although the gains are generally slight for patients with substage IIIA disease, the probability of surviving to year 5 did increase from 72% at the time of presentation to 95% for patients surviving 4 years. This difference was even greater for patients with higher-substage disease. Among patients with substage IIIB disease, the probability of surviving to year 5 increased from 48% at the time of presentation to 90% for patients surviving 4 years. Notable gains were observed in survival probabilities among patients with substage IIIC disease, in whom the probability of surviving to year 5 increased from 29% at the time of presentation to 86% for patients surviving 4 years (Table 1). These findings confirm those of Xing et al, who examined patients with melanoma from the SEER registry and found that 5-year conditional survival improved dramatically for surviving patients with stage III and IV disease.
It is clear that estimates obtained at baseline do a poor job of predicting survival by “leaving information on the table.” Conditional survival estimates provide dynamic prognostication using the information that a given patient has survived some time after baseline, and are obtained through the baseline Kaplan-Meier estimates without requiring any additional data, unjustified assumptions, or specialized methods. The use of stage III melanoma data in the current study is purely exemplary; conditional survival estimates are relevant for all cancer sites. It is well known by clinicians that the longer a patient lives, the longer he is expected to live, and we urge that these estimates should be formally calculated and shared with the patient. Considering the major role played by survival estimates during follow-up in patient counseling and the development of survivorship programs, we strongly recommend the routine use of conditional survival estimates.