The NRF model had moderately favourable prognostic performance in the MPT group as well as in the BM group. This finding was supported by two points. First, the survival analysis of the BM and MPT groups showed clear differences between the three groups of the NRF model classification. Second, the results of the discrimination performance evaluation by two methods (C-index and time-dependent AUROC) were acceptable. Considering that the NRF model is simple and easy to use and requires no detailed imaging or blood tests, it is highly useful in daily practice.

This present study appears to have analyse patients with a better prognosis compared to past studies involving patients with various diseases. The NRF model, developed by Chow et al. for patients receiving PRT for miscellaneous tumours [4, 18] included a patient group where 70% had BM, 69% had visceral metastases, 18% were referred to the clinic for brain metastases, and others were referred for symptomatic relief of bleeding, shortness of breath, and tumour mass [18]. The MSTs reported by Chow et al. for groups I, II, and III were 60 weeks (8.6 months), 26 weeks (3.7 months), and 9 weeks (1.3 months), respectively [4]. In a validation study of the NRF model involving patients with miscellaneous tumours, where 32.5% received PRT for brain metastases, 50.1% for bone metastases, and 17.4% for other sites, the MSTs for groups I, II, and III were 15.0, 6.5, and 2.3 months, respectively [6]. Another validation study of the NRF model in an outpatient palliative care clinic, regardless of PRT, showed MSTs for groups I, II, and III were 9.0, 4.6, and 2.1 months, respectively [10]. Our MSTs, which appear longer than those in these studies, suggest that the NRF model may be useful in stratifying the prognosis of patients with a better overall prognosis.

In the evaluation of discrimination performance by time-independent methods, Chow et al. [4]. evaluated the model performance of the NRF model, mainly using the C-index [4]. They reported a model C-index of 0.65 for the training set, 0.66 for the temporal validation set, and 0.63 for the external validation set [4], and our C-index was similar to those values (0.685 for the BM group and 0.625 for the MPT group). Other studies of patients who received irradiation or re-irradiation for spinal metastases reported C-indexes of 0.76 and 0.6, respectively [8, 9]. The external validation set of the RTOG 9714 trial for patients with breast or prostate cancer with BMs reported a C-index of 0.94, indicating very high model performance [5]. On the other hand, in the evaluation of discrimination performance by time-dependent methods, Yap et al. [7]. evaluated the discrimination performance of the NRF model using the Uno C statistic [7]. The Uno C statistic, as well as Harrel’s C-index, when significantly greater than 0.5, indicates favourable model discrimination, demonstrating the model’s ability to predict survival with higher precision as values approach 1 in a 0 to 1 range [19]. The Uno C statistic for the NRF model was 0.58 for 3 months, 0.58 for 6 months, and 0.59 for 12 months [7]. As also shown in the present results of the time-dependent AUROC, the discrimination performance of the NRF model was approximately equally as favourable in the short term (a few months) and in the long term (12–24 months). This finding contrasts with the high short-term discriminative performance of another widely used prognostic model in the palliative care setting, the Palliative Prognostic Index, which showed poorer long-term discriminative ability [20].

Stereotactic body radiation therapy (SBRT) for painful BM increases treatment costs and delays the start of radiation. However, its high complete pain response rate [21, 22] and potential for long-term pain control [23] might make it suitable for patients with a good long-term prognosis. This study supports such decision-making, suggesting that the NRF model may be a useful tool in determining the suitability of SBRT.

As a study limitation, we performed explorative sub-analyses of a single-centre retrospective study (the BM group) and a three-centre prospective observational study (the MPT group). Our results should be tested prospectively, preferably in multicentre settings.