Multivariate Cox proportional hazard models were applied to verify prognostic factors selected in the univariate log-rank test and calculate the hazard ratios of each prognostic factor.
Development and Validation of the Nomograms
To minimize the influence of information loss, we used a backward stepwise method to further sort out prognostic factors verified in the multivariate analysis. The Akaike information criterion (AIC) is widely used as an objective tool for selecting between different competing models, and lower AIC values suggest relative superiority [36, 38]. The backward stepwise method initially included all independent prognostic factors identified in the multivariate analysis to calculate the AIC. Each prognostic factor then was excluded successively to calculate the AIC to see whether a smaller AIC was achieved. Finally, the smallest AIC was achieved and therefore prognostic factors to be incorporated in the nomograms were determined. Nomograms incorporating sorted prognostic factors were developed to predict 3- and 5-year overall survival and cancer-specific survival.
Bootstrapped validation, which used a resample with 500 iterations, was applied to validate the nomograms internally and externally. Harrell’s concordance index (C-index) was applied to evaluate predictive ability of the nomograms. The value of the C-index ranges from 0.5 to 1.0, whereas 0.5 indicates total chance and 1.0 indicates perfect matching . Calibration plots also were used to validate the nomograms by comparing nomogram predictions with actual outcomes.
Univariate analysis and multivariate Cox regression were conducted using SPSS Version 22.0 (IBM Corporation, Armonk, NY, USA). Development and validation of the nomograms were performed using R version 3.3.1 (http://www.r-project.org/) with rms  and cmprsk  packages. All p values were two-sided and a probability less than 0.05 was considered statistically significant.
Independent Prognostic Factors for Patients With Chondrosarcoma
After controlling for potentially confounding variables such as race, sex, and primary site, we found that age at diagnosis, histologic subtype, grade, surgery, tumor size, and distant metastasis proved to be associated with overall survival (Table 3). Similarly, these six variables still proved to be independently associated with cancer-specific survival after controlling for confounding variables (Table 4).
Nomograms for 3- and 5-Year Survival
The six independent prognostic factors for overall survival and for cancer-specific survival were identified and incorporated to construct nomograms for 3- and 5-year overall and cancer-specific survival, respectively (Fig. 2). These nomograms can easily be used by providers in the office to estimate a patient’s prognosis; the only clinical details a provider needs to use these nomograms effectively are age, histologic subtype, tumor grade, whether surgery was performed, tumor size, and the presence or absence of metastases. Independent prognostic factors in the multivariate analysis were further sorted by a backward stepwise method with the AIC to minimize information loss and arrive at the nomograms.
To use the nomograms, one can add the points of each predictor (Table 5) based on personalized information and correlate the total points with the event probability that we want to predict. For example, a 55-year-old man was diagnosed with grade III conventional chondrosarcoma with a primary tumor of 6.0 cm; he then underwent surgery and had no signs of metastasis. By adding the points, he ended up with 11.1 and 12.6 points in overall survival and cancer-specific survival nomograms, respectively. Eventually, his estimated 5-year overall survival and cancer-specific survival rates were 67% and 70%, respectively, according to the nomograms.
The nomograms were validated internally and externally. In the training cohort for internal validation, the concordance indices (C-index) for overall survival and cancer-specific survival prediction were 0.803 (95% CI, 0.773-0.833) and 0.829 (95% CI, 0.796-0.862), respectively. In the validation cohort for external validation, the C-indices for overall survival and cancer-specific survival prediction were 0.753 (95% CI, 0.714-0.792) and 0.759 (95% CI, 0.720-0.798), respectively. Internal and external calibration plots for 3- and 5-year overall survival and cancer-specific survival showed excellent agreement between nomogram prediction and observed outcomes (Fig. 3).
Chondrosarcoma is the second-most-common malignancy of the skeleton, and although numerous factors—including patient age, tumor size, tumor grade, and metastasis—have been individually identified as having prognostic value by prior studies [7, 12, 21, 25, 28, 32], using those factors in combination in a practical way is impossible without a nomogram. A well-validated nomogram can help the clinician anticipate a patient’s prognosis, as has been shown for osteosarcoma, prostate cancer, gastric cancer, lung cancer, and breast cancer [3, 9, 18, 19, 22, 26, 29, 33, 34]. However, to our knowledge, there is no prognostic nomogram for chondrosarcoma. Based on the SEER database , which consists of 18 cancer registries covering approximately 30% of the total US population, we therefore constructed comprehensive and novel nomograms for predicting 3- and 5-year overall survival and cancer-specific survival of patients with chondrosarcoma (Fig. 2), which can be used in the clinical setting using patient-specific information likely to be available to the orthopaedic oncologist.
Several limitations should be considered in our study. First, 327 patients with chondrosarcoma, which represented nearly ⅓ of the cohort, were excluded from the study because of missing data. Although age, histologic subtype, grade, surgery, and distant metastasis still proved to be independently associated with survival after including patients with missing data on tumor size (see Tables, Supplemental Digital Content 1 and Supplemental Digital Content 2), potential bias still existed because the scores of each predictor in the nomograms might change if we included patients with missing data. Second, we did not include some known prognostic factors such as margin status  and pathologic fracture , which might improve predictive ability if incorporated. The reason was that the SEER database did not collect information regarding these variables. Third, since the SEER database does not collect information for local recurrence, we were not able to develop the nomogram predicting local recurrence for patients with chondrosarcoma. Fourth, we developed and validated the nomograms from the same retrospective dataset. To really know the predictive ability of the nomograms, prospective validation is needed, or at least, validation with another database. Fifth, results of a backward selection process might be sample-specific as selection depends on statistical criteria that may vary from sample to sample. This may result in some bias; for example, the C-index is likely lower if the nomograms are applied to non-SEER registry data. Moreover, owing to the insufficient sample of patients with chondrosarcoma of short bones, we combined patients with chondrosarcoma of long bones and short bones in the extremity subgroup, which may result in bias. Finally, although we used multivariate analysis to control for the influence of confounding variables on a single variable, it was still difficult to eliminate such influence between variables; for example, metastasis is associated with tumor grade and such correlation could not be eradicated in the study.
After controlling for confounding variables, we identified six independent prognostic factors for overall survival (Table 3) and cancer-specific survival (Table 4). Regarding cancer-specific survival, it is noteworthy that a small overestimation of mortality is expected owing to the existence of competing risks . The cumulative incidence function is a robust method for analyzing cause-specific incidence when competing events exist. However, in consideration of better comparability with previous studies [14, 34, 39], we still used the Cox model rather than the competing risk model for multivariate analysis of cancer-specific survival. Verification of age, grade, tumor size, surgery, and distant metastasis as independent prognostic factors for overall survival and cancer-specific survival is in line with previous studies [12, 17, 25, 28, 32, 35]. We are not aware of any studies that used multivariate analysis to identify histologic type as an independent prognostic factor, although Giuffrida et al.  calculated survival rates based on different histologic types. According to our research, histologic type showed a substantial effect on prognosis and patients with conventional chondrosarcoma were found to have relatively better survival than those with dedifferentiated chondrosarcoma. Regarding primary tumor site, Andreou et al.  reported that patients with chondrosarcoma of the axial skeleton and pelvic girdle had poorer prognoses than patients with chondrosarcoma of the extremities. Another study showed that appendicular chondrosarcoma was associated with better survival than axial chondrosarcoma only in patients with grade III disease . Based on an analysis of 2890 patients with chondrosarcoma, Giuffrida et al.  concluded that patients with appendicular chondrosarcoma had better overall survival than patients with axial chondrosarcoma in univariate analysis, but the multivariate analysis showed that site was not a significant prognostic factor for overall survival. However, in our study, primary tumor site was not identified as a prognostic factor for either overall survival or cancer-specific survival in the univariate analysis. Giuffrida et al.  first reported that female sex was correlated with better survival in univariate analysis but not in multivariate analysis, meaning that attributing improved survival to sex is likely to instead be a function of confounding variables; in our study, we did not find sex to be associated with survival in patients with grade II and grade III chondrosarcoma.
We also created a nomogram, based on the independent predictors of overall and cancer-specific survival that we identified; this nomogram can be easily used in practice to estimate a patient’s prognosis (Fig. 2). To our knowledge, no other nomogram of this sort exists for patients with chondrosarcoma. An effective nomogram can increase the surgeon’s ability to provide patients with precise estimates of the likelihood of survival at particular time intervals, and to help the surgeon identify patients at higher risk of early death. To use the nomograms, one adds the points of each predictor (Table 5) and correlates the total points with the event probability that we seek to predict. For example, a 65-year-old woman was diagnosed with grade II conventional chondrosarcoma with a primary tumor of 8.0 cm; she then underwent surgery and had signs of metastasis. Totaling the points for this patient, we see that she had 18.8 and 18.9 points in the overall-survival and cancer-specific survival nomograms, respectively. This results in estimated 3-year overall survival and cancer-specific survival rates of 43% and 49%, respectively, according to the nomograms. Because development and validation of the nomograms are based on the SEER database , future studies should investigate whether the nomograms apply well to patients from other registries and evaluate the accuracy of the predictions one can make using the nomograms we have developed.
We developed and preliminarily validated nomograms predicting 3- and 5-year overall survival and cancer-specific survival of patients with chondrosarcoma based on the SEER database . The nomograms seemed accurate when tested in validation cohorts, and they require only basic information, which should be available to all providers in the office setting. If our findings can be validated by others using other databases or in prospective studies, this may prove to be a useful tool for clinicians and patients. Another potential use of our nomogram would be to identify patients at high risk of death so they could be invited to participate in studies evaluating novel treatments for patients with an extremely poor prognosis. Currently, no such strategies are in standard use, but we hope that such treatments might be forthcoming.
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