Prognostic factors in patients with thyroid carcinoma: a competing-risks analysis

Background: Cox proportional-hazards models are widely used to describe survival trends and identify prognostic factors for thyroid carcinoma, but the prognostic model is not accurate enough. This study therefore used a competing-risks model to identify the signicant prognostic factors for different types of thyroid carcinoma. Methods: We identied 38,444 eligible patients in the SEER (Surveillance, Epidemiology, and End Result) database. The potential prognostic factors for thyroid carcinoma were analyzed by Cox regression analysis, cause-specic hazard function (CS) analysis, and subdistribution hazard function (SD). Results: Cox regression analysis, CS analysis and SD analysis found identifying age, being unmarried, no regional lymph nodes examined, AJCC-6 II, III, IV vs I , having follicular, medullary, anaplastic vs Papillary carcinomas, no surgery, no radioiodine, liver metastasis, and lung metastasis as the signicant risk factors for thyroid carcinoma, while being female was protective factor. However, the results from the three multivariate models for being black, tumor size >1 cm, and brain metastasis were inconsistent. Conclusion: In addition to nding that age, pathological type, tumor size, AJCC-6 stage, surgery status, radioiodine status, metastasis as common factors affected the prognosis, we also found that women, being unmarried and had their regional lymph nodes examined can improve the prognosis of thyroid cancer. The discovery of these factors will provide evidences for the prevention and treatment of thyroid cancer.

We collected the following data for each patient: age, race, sex, marital status, insurance status, tumor size, whether regional lymph nodes were removed and examined by the pathologist, AJCC-6 stage, histology, surgery status, radioiodine status, chemotherapy status, bone metastases, brain metastases, liver metastases, lung metastases, survival time (in months), and case outcome. The case outcome was divided into the following three conditions: alive, death due to thyroid carcinoma (endpoint event), and DOC (competing event).
The application of the inclusion and exclusion criteria resulted in the identi cation of 38,444 patients in the SEER database between January 01, 2010 and December 31, 2015.

Statistical analysis
All statistical analyses were performed using SPSS (version 21.0) and SAS 14 (performing competing risks modeling). Mean±standard-deviation values were used to express continuous variables conforming to a normal distribution, and all other variables were expressed as median (25th-75th percentile) values. The cumulative incidence function (CIF) was used in the univariate analysis to analyze each potential prognostic factor, and Gray's test used for the difference test. Cox regression analysis and the competitive risk model (CS analysis and SD analysis) were used for the multivariate analyses, and independent prognostic factors were obtained. Probability values of p<0.05 were considered statistically signi cant.

Patient characteristics
The median age of all patients was 46 years, with an age range from 35 to 57 years. The median age of patients who died due to thyroid cancer was 68 years, with an age range from 57 to 77 years. Most of the patients in both groups (the total patient group and died due to thyroid cancer group) were female, white, and married, had insurance and any medical, a tumor size of £1 cm, PTC, had their regional lymph nodes examined, had received surgery, and had not received chemotherapy. Most of the patients who died due to thyroid cancer were in AJCC-6 stage IV, had not received radioiodine, and had an unknown metastasis status. However, most of the patients in the total patient group were in AJCC-6 stage I, had received radioiodine, and did not have metastasis. The demographics and tumor characteristics of the patients are summarized in Table 1.

Univariate analysis
Gray's test was used to perform a univariate analysis of the following 16 potential prognostic factors: age, sex, race, marital state, insurance status, tumor size, whether regional lymph nodes were examined, AJCC-6 stage, histology, surgery status, radioiodine status, chemotherapy status, bone metastasis, brain metastasis, liver metastasis, and lung metastasis. All 16 factors were found to signi cantly affect the prognosis for death caused by thyroid carcinoma (p<0.05). In addition, the cumulative incidence rates at 50 and 100 months were calculated, as presented in Figure 1 and Table 2.

Multivariate analyses
The application of Cox regression analysis, CS analysis, and SD analysis for the multivariate analyses produced different results. Age, being unmarried, no regional lymph nodes examined, AJCC-6 stages II, III, and IV, having FTC, MTC, and ATC, no surgery, no radioiodine, liver metastasis, and lung metastasis were found to be signi cant risk factors for thyroid carcinoma in all three methods, while being female and not receiving chemotherapy were protective factors. The HR values for these predictive factors differed between the three models.
Cox regression analysis showed that being black (p=0.01, HR=1.25) was a risk factor, while the SD analysis (p=0.6) and CS analysis (p=0.25) did not. Cox regression analysis showed that tumor size >1 cm (p=0.13) was not statistically signi cant, while the SD analysis (p<0.01, HR=2.48) and CS analysis (p=0.01, HR=2.59) showed that this was a signi cant risk factor. Cox regression analysis (p<0.01, HR=1.93) and CS analysis (p=0.01, HR=1.77) indicated that brain metastasis was a risk factor, while the SD analysis (p=0.09) did not (Table 3).

Discussion
The sample size should be considered carefully when designing a competing-risks analysis. If the proportion of competing events is greater than 10%, a Cox regression analysis can be severely affected by bias [19] that overestimates the event incidence and poorly estimates the HRs. The present study included 1205 DOC patients, representing almost half of the deaths, and so we used a competing-risks model that could avoid this bias to obtain more accurate prognostic factors for thyroid carcinoma. Competing-risks regression approaches focus on two de nitions of hazard: SD and CS. The SD model is useful for predicting an individual's risk or when allocating resources, while the CS model may be better suited for studying the etiology of diseases [20]. Since these two models have their own unique underlying mechanisms, it is necessary to provide the results obtained from SD and CS models simultaneously.
Koller et al. [21] proposed that a SD model tends to estimate the disease risk and prognosis, which is more suitable for establishing a clinical prediction model and risk scores. It is obvious that the HRs obtained in the present SD model were the most valuable, since this model focuses on the direct assessment of actual risks and therefore also the prognosis and medical decision-making.
The Cox regression analysis showed that there was no signi cant difference between tumor sizes of >1 and £1 cm, and that being black was a risk factor in the thyroid carcinoma patients. However, the competing-risks model produced the opposite results. There is a considerable amount of evidence that tumor size is an important prognostic factor for thyroid carcinoma [22]. Meanwhile, the effect of race in predicting thyroid cancer death was inconclusive in our competing-risks model. It could be that the Cox analysis overestimated the HR value for race, resulting in a false-positive result.
All three methods applied in this study indicated that older age, FTC, MTC, and ATC (all vs PTC), AJCC-6 stages II, III, and IV (all vs stage I), liver metastasis, and lung metastasis were detrimental prognostic factors. It is well known that age >45 years, extrathyroidal invasion, distant metastasis, large tumor, vascular invasion, and poor differentiated histology are detrimental prognostic factors [4,23,24].
We found that the female-speci c mortality was lower than the male-speci c mortality in all three methods, even though the incidence rate is higher in females than males [25]. There are con icting reports on the effect of sex on mortality. Ito and Miyauchi [26] and Lin et al. [27] found that a larger proportion of male than female patients died of thyroid cancer, whereas Nguyen et al. [28] found the opposite result. Bray et al. [25] reported that the mortality rates were similar in the sexes, based on global cancer statistics published in 2018. It is possible that any effect of sex on mortality is related to geography and race. More evidence is needed on the effect of sex on thyroid-cancer-speci c death.
All three methods utilized in our study indicated that having the regional lymph nodes removed and examined by the pathologist was a signi cant protective factor for thyroid-cancer-speci c death. There is no report in the literature on whether having regional lymph nodes examined affects the prognosis of thyroid cancer, while there is substantial evidence that local lymph node metastasis is a signi cant risk factor for thyroid-cancer-related death [29][30][31][32][33]. This suggests that in the case of unknown lymph node metastasis, the prognosis of regional lymph nodes removed and examined may be better than that of no regional lymph nodes removed and examined. As described in Shi et al. [34] and Merrill and Johnson[35], we also found that being married has a positive effect on the prognosis of thyroid cancer in all three analysis methods.
The treatment of choice for patients diagnosed with thyroid cancer is surgery, when possible. Usually, surgery is followed by treatment with radioiodine. Chemotherapy is only considered if the patient has any of the following conditions: (1) clinically signi cant disease and evidence of disease progression, (2) a symptomatic tumor burden that cannot be managed with localized treatments or other medical treatment, or (3) the tumor threatens vital structures and cannot be managed with localized treatments [36]. Still, the effects of chemotherapy have not been proven[37-40]. We found that receiving surgery and radioiodine therapy were protective factors, and patients in receiving chemotherapy group had a higher mortality rate than those in not receiving chemotherapy group.
While the above-mentioned factors have been demonstrated to be independent factors for the prognosis of thyroid cancer in three analysis methods, compared to the SD model, Cox regression overrated the prognostic effect of almost all of the variables we investigated, including age, sex, marital state, surgery status, radioiodine status, and metastasis, as also described by .

Conclusion
In addition to nding that age, pathological type, tumor size, AJCC-6 stage, surgery status, radioiodine status, metastasis as common factors affected the prognosis, we also found that women, being unmarried and had their regional lymph nodes examined can improve the prognosis of thyroid cancer. The discovery of these factors will provide evidences for the prevention and treatment of thyroid cancer.

Declarations
Ethics approval and consent to participate This study was approved by the Ethics Committee of Honghui Hospital, Xi'an Jiaotong University, Xi'an Consent for publication All patients came from the SEER database (Surveillance, Epidemiology, and End Result), which is publicly available.

Availability of data and material
The datasets analyzed during current study are available from the corresponding author upon reasonable request.

Competing interests
The authors declare that they have no competing interests.  Regional nodes Examined: whether regional lymph nodes had been removed and examined by the pathologist.