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Prediction of toxicity in concurrent chemoradiation for non-small cell lung cancer

Uijterlinde, W.I.

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Citation for published version (APA):Uijterlinde, W. I. (2014). Prediction of toxicity in concurrent chemoradiation for non-small celllung cancer.

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Download date:26 May 2021

Chapter 6

Fractures of thoracic vertebrae in patients with locally advanced non-small cell lung carcinoma

treated with intensity modulated radiotherapy

W.I. UijterlindeC.Chen

J. de BoisJJ. SonkeC. Lange

J.S.A. BelderbosM.M van den Heuvel

Submitted

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Abstract

Purpose: To report on the incidence of vertebral fractures in patients treated

with Intensity Modulated Radiotherapy (IMRT) for locally advanced non-small

cell lung carcinoma (NSCLC) and to analyse the correlation with clinical and

dosimetric parameters.

Patients and methods: Between 2007 and 2012, 524 patients treated with ≥

51 Gy, were retrospectively analysed for the incidence of vertebral fractures

(VF). Clinical and dosimetric parameters were assessed. In addition, a case

control study in 50 patients was performed to study the association between

the radiotherapy dose and fractured vertebrae.

Results: Three hundred and thirty six patients were eligible for analyses.

Twenty-eight patients (8%) suffered from fractures of the thoracic vertebra.

Age was significantly higher in the group with VF (p=0.01). After balancing

age, the percentage of volume that was prescribed with ≥x Gy (Vx) and the

equivalent uniform dose (EUDn), V30 and n=1 respectively,

were significantly associated with fractures of the vertebrae (p < 0.01).

Conclusion: A dose response relation between the dose of IMRT and the

occurrence of thoracic vertebral fractures was established in 8% of the patients

with locally advanced NSCLC.

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6

Introduction

Concurrent chemoradiation (CCRT) is the treatment of choice for locally

advanced non-small cell lung cancer (NSCLC). The increase in survival,

compared to sequential chemoradiation (SCRT) is 6% at 3 years and is mainly

due to the improved local tumor control (1;2). This is, however, at the cost of

increased toxicity such as esophageal and pulmonary toxicity (3;4;5). Radiation-

induced bone damage has not yet been thoroughly studied. This toxicity has

mainly been described for stereotactic body radiotherapy (SBRT) (6;7). Case

reports showed osteoradionecrosis (ORN) in patients treated with radiotherapy

for NSCLC (8). Vertebral fractures (VF) of the thoracic spine were reported in 2

NSCLC patients, treated with 67 Gy on the mediastinum. After respectively 11

and 12 months, a wedge fracture of the 7th thoracic vertebra was observed and

symptoms were pain and immobility. In one patient, necrosis of the vertebra

without tumor progression was observed at autopsy. It has been hypothesized

that, as a result of radiotherapy, the central and peripheral blood flow to the

vertebra is reduced. In head and neck cancer, ORN of the upper cervical spine

has been observerd (9). A biopsy of the cervical vertebrae was performed in 3

patients with suspicion of local recurrence of disease but revealed only chronic

inflammation and necrosis and no recurrent disease. Most demographic

studies on the incidence and prevalence of VF take age and gender into

account because of the relation with osteoporosis. Increased age and a

decreased oestrogen level in post-menopausal women lead to a loss of bone

mineral density (BMD) (10). The prevalence of vertebral fractures in men and

women aged > 50 is 10% and 24% respectively, with an increased prevalence

with growing age (11;12). The biomechanical influences on the spine reflect in

the VF type. The wedge fracture shows a predilection for T6-T8 whereas T12-L1

often shows a compression fracture. Osteoporotic fractures are characterized

by biconcave deformities of the vertebra because of fractured endplates (13).

Beside age and gender, prevalent fractures, smoking, low body weight, chronic

obstructive pulmonary disease (COPD), walking aid use, long-term use of

systemic corticoid steroids and long-term oxygen therapy are prognosticators

for VF (14;15). There is a lack of clinical recognition of VF because of a difficulty

in determining the cause of the symptoms. In most studies lateral X-rays of

the thorax, or spinal radiographs are used for diagnoses (13-17), sometimes

followed by morphometric analysis. Symptoms and quality of life in patients

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suffering from VF are summarized by Ryan et al. Sixty-three percent suffered

from persistent back pain; 47% had difficulty with functional activities and 42%

had difficulty finding suitable clothing (18). With the introduction of Intensity

Modulated Radiotherapy (IMRT), our institute has intensified research on

late-onset toxicity and started collecting data on VF. Because of the clinical

implications and the limited knowledge on RT induced VF, we studied the

incidence of thoracic VF and its relation with the radiotherapy dose, taking into

account the clinical and demographic risk factors.

Methods and materials

Patient selectionA total of 524 locally advanced NSCLC patients was treated between 2007-

2012 in the Netherlands Cancer Institute (NKI) with ≥ 51 Gy physical dose IMRT

with or without chemotherapy. Medical records and treatment schedules of

these patients were retrospectively reviewed. Vertebral fractures were also

retrospectively screened from the baseline/planning Computer Tomography

Scan (CT) and follow-up CT or Magnetic Resonance Imaging (MRI). Patients

were excluded from the study if no follow-up CT imaging was present, if they

died before the first follow-up imaging, had prior irradiation due to thoracic

or head and neck cancer, had VF prior to radiotherapy (identified from the

planning CT scan), or had VF due to trauma.

TreatmentThe treatments consisted of concurrent chemo radiotherapy: daily cisplatin

(6mg/m²) and 66 Gy (fractions of 2.75 Gy) during 24 sequential working days

(1;2); sequential chemo radiotherapy: 2-4 cycles of chemotherapy doublets

followed by 66Gy in 24 fractions, or RT only: 66y in 24 fractions; 60 Gy in 30

fractions; 51 Gy in 17 fractions.

For radiotherapy planning, a four-dimensional CT scan (4DCT) was acquired

in all patients in order to minimize the respiratory induced systematic errors

and assess the breathing amplitude of the primary tumor. A mid-ventilation

scan (MidV scan) with the tumor closest to its time-averaged mean position

was reconstructed from the 4DCT. This MidV-scan was used to delineate the

gross tumor volume (GTV), involved lymph nodes and organs at risk (OARs). All

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patients had a Fluorodeoxyglucose/Positronemissiontomography (FDG-PET)

scan before the start of treatment.

The GTV was expanded to a planning target volume (PTV) using margins of

12mm plus 1/4 of the primary tumor peak-to-peak amplitude in orthogonal

directions as observed on the 4DCT. For the lymph nodes an isotropic PTV

margin of 12mm was used. Heart, spinal cord, lung and oesophagus were

delineated according to departmental guidelines. Dose distributions were

calculated using inhomogeneity correction (Pinnacle version 9.2). Dose

constraints and objectives were defined in biologically equivalent dose in 2 Gy

per fraction (EQD2). For the esophagus a V

35<65% (α/β=10 Gy) was encouraged

when optimizing the IMRT plan. Dose objectives for other OARs were: mean lung

dose ≤20 Gy (α/β=3 Gy), spinal cord ≤52 Gy (α/β=2 Gy), total mean heart dose

≤40 Gy, 2/3 heart ≤50 Gy, and 1/3 heart ≤66 Gy (α/β=4 Gy). Patients received

repetitive cone-beam CT scans for an off-line setup correction protocol.

Assessment of vertebral fracturesAll patients follow up MRI/CT images using 1 or 5 mm slices and multi-planary

reconstruction were first screened on VF by a chest physician and then forwarded

to the radiologist to discriminate dissemination from injury. Metastatic disease

was determined in case the cortex was taken over by soft tissue (9;17). In case

of a vertebral fracture on the follow up imaging, the planning CT was reviewed

on pre-existent fractures. If a fracture was identified on the planning CT, the

patient was excluded from the study. Otherwise, the location and number of

VF in the RT field were recorded, and the date of the first identified follow-up

imaging was recorded as the onset date. If no VF was identified on any of the

follow-up imaging, the date of the last imaging was recorded as the date of the

last follow-up for VF.

The following clinical parameters were taken into account: age, gender,

chemotherapy, performance status (PS) and Chronic Obstructive Pulmonary

Disease (COPD). GOLD classification was defined based on the forced expiratory

volume (FEV1) before treatment. To determine loss of bone mineral density (BMD),

the baseline RT planning CT was used to calculate the Hounsfield units (HU).

A one-to-one matched case control study was conducted to assess the

relationship between RT dose and VF. The case control study allowed the

analysis to be conducted on a subset of patients with balanced demographic risk

factors. The process of matching case control patients was as follows: 1) For each

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patient with a VF, a matched control patient with longer follow-up was found;

2) A smaller subset of non-VF patients who had the same matching variables

was further selected. The matching criteria included age (+/-5 years), RT dose and

gender; 3) We randomly selected one patient from the qualified subset.

After selection of the matched control cases, the vertebral corpora of

Th1-Th12 were manually delineated on the planning CT (Figure 1).The

cylindrical shape vertebral corpora is the main portion of a vertebra

anterior to the vertebral canal, as distinct from the arches. To compute dosimetric

parameters, the physical RT dose to each vertebra was first converted to EQD2

voxel-by-voxel using the Linear Quadratic (LQ) model. An α/β ratio of 3 Gy

was used to model late effects. The equivalent uniform dose (EUD) for various

values of the volume parameter n and the percentage of volume prescribed

with ≥x Gy (Vx) for various values of x were then computed from the dose

volume histogram (DVH).

Statistical analysis

Vertebral fractures were analysed in three steps: Firstly, we quantified the

incidence of VF in our patient cohort. Secondly, we analysed the association

between clinical parameters and VF per patient. Finally, the association between

RT dose and VF per vertebra, adjusted for clinical parameters was evaluated.

The incidence of VF was presented by the Kaplan-Meier method, adjusting

for loss to follow-up. A univariate analysis was then conducted to analyse the

association of VF with clinical parameters, using Cox proportional hazards

regression. To analyse the relationship between the RT dose and VF, the

following tests were used to evaluate the matching results in the case control

study: age and follow-up time of the matched case control patients were

tested using Wilcoxon signed rank test. The effect size refers to the Hodges-

Lehmann estimator. Categorical variables like gender (female vs. male), PS (0

vs. ≥1), )were tested using the binomial test (B vs. A). The effect size refers to

the estimated probability of a case-control pair with A in VF group and B in

non-VF group among all the case-control pairs where the case and control do

not belong to the same category. RT dose (66Gy vs. 51Gy) were tested using

the binomial test (B vs. A). The effect size refers to the estimated probability

of a pair (with A in VF group and B in non-VF group) in the unmatched pairs.

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Figure 1. Example of a delineated corpus vertebra in axial view and the delineated vertebra Th01-Th12 in sagittal view.

Assuming that the prior probability of a fracture is identical per vertebra and

the dose-VF relationship is identical per vertebra, our hypothesis was that the

RT dose is associated with vertebral fractures, adjusted for age. Based on the

data structure, we applied a generalized linear mixed model with a nested

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random effect from pair and patient: both Vx

and equivalent uniform dose

(EUDn) were extracted from the dose volume histogram of each vertebra for

the analysis of dose-VF relationship. Vx

represents the percentage of volume

that was planned with EQD2≥x Gy (Appendix). The statistical analysis was

conducted in R (version 2.14.1).

Results

Among the evaluated 524 patients, 166 (32%) had no available follow-up CT/

MRI or died before the first follow-up scan, 14 (3%) had prior thoracic or head

and neck RT, 6 (1%) had a VF prior to radiotherapy, identified from the planning

CT; 2 (<1%) had a fracture due to other causes. As a result, 336 patients were

eligible for this retrospective study (Figure 2). Patient characteristics of the

eligible patient cohort are displayed in Table 1. During the follow up (median

follow up of 34 months) 28 patients (8%) developed a fracture of the thoracic

vertebra. Figure 3 depicts the incidence of VF together with the overall survival.

Of the 28 patients with vertebral fractures, 22 had 1 VF, 5 had 2 VF and 1 patient

had 3 VF. The locations of the in total 35 fractured vertebras were: thoracic 4, 1;

thoracic 5, 8; thoracic 6, 8; thoracic 7, 15 and thoracic 8, 3. The median time to

discovery of the fracture was 7 months (range 2-26). In all fractured vertebrae an

increased signal intensity on the MRI or decreased density on the CT was seen

due to radiation-induced fattening. Univariate analysis showed a significant

difference in age with a higher age in the fractured group (p<0.01, Table 2).

FEV1 values were available in only 222 patients treated with CCRT and were not

significantly associated with VF (COPD GOLD 1-2 versus 3: p=0.62). Concerning

the los off BMD, the average of the mean density for fractured vertebras was

1220 HU (range 1044-1431 HU), while the average of the mean density for non-

fractured vertebras was 1205 HU (range 1144-1269 HU) (p=0.07).

In the case control study, we could not find a matched control for 3 VF patients

with a long follow-up time of 22, 25 and 26 months. In total 25 control patients

were identified for 25 cases (Table 3). The cases and control patients were well

balanced for age and gender. The dosimetric characteristics to the fractured

and non-fractured vertebrae are presented in Table 4. The optimized parameter

values and the maximum log=likelihood in predicting VF are presented in table

5 (appendix).

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524 patients with IMRT ≥

51 Gy physical dose

166 patients with no

follow up CT/MRI

14 patients with prior thoracic or H&N RT

6 patients had VF prior to

RT (1%)

2 patients had VF due to

other causes after RT

336 patients eligible for

analysis (64%)

Table 1. Characteristics of the VF patients (n=28) and the non-VF patients (n=308). COPD status was only available in 222 of the 269 concurrent chemo-radiation (CCRT) patients.

Characteristic VF patients (n=28) Non-VF (n=308)

Median age (y) (range) 70 (42-82) 63 (32-87)

Gender(%)Female 17 (61%) 118 (38%)

Performance status (%)WHO 0WHO 1WHO 2WHO3

7 (25%)18 (64%) 2 (7%) 1 (4%)

96 (31%)193 (63%) 19 (6%) 0 (0%)

TMN stage1A-1B2A-2B3A-3B4

0 (0%) 2 (7%)26 (93%) 0 (0%)

12 (4%) 30 (10%)264 (86%) 2 (1%)

Median GTV volume (cc) (range) 107.0 (25.7-381.1) 107.1 (2.32-1830.0)

Chemotherapy:NoneSequentialConcurrent

5 (18%) 2 (7%)21 (75%)

35 (11%) 25 (8%)248 (81%)

Prescribed RT :2.75Gy × 24fr2Gy × 30fr3Gy × 17Fr

25 (89%) 0 (0%) 3 (11%)

291 (94%) 3 (1%) 14 (5%)

COPDIIIIII

10 (56%)6 (33%)2 (11%)

99 (49%) 89 (44%)16 (8%)

Post=postmenopausal; pre=premenopausal; WHO=world health organisation; TNM=Tumor-Nodule-Metastasis according to the 7th edition of staging; GTV=gross tumor volume; RT=radiotherapy; fr=fractions; COPD= chronic obstructive pulmonary disease; 1,2,3=GOLD Classifi cation

Figure 2. Eligibility criteria

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Figure 3. Kaplan-Meier estimates of the incidence and 95% CI (Greenwood formula) of VF for NSCLC patients (n=336) with a median follow-up of 12 months, together with the overall survival with a median follow-up of 34 months. The number of patients at risk for vertebra fracture (top) and death (bottom) are also given.

Table 2. Univariate analysis of the association between clinical variables and vertebral fractures, using the Cox-proportional hazard model.

Variable Hazard ratio (95% CI) p-value

Age 1.70 per 10 year increase (1.19-2.43) <0.01

Gender: female vs male 1.92 (0.90-4.11) 0.09

Chemotherapy:Chemo+RT vs RT only 0.44 (0.17-1.15) 0.13

Performance status:WHO 1 vs 0WHO 2 vs 0

1.46 (0.61-3.49)4.19 (1.07-16.40)

0.18

COPD1-2 vs 3 0.79 (0.31-2.01) 0.62

WHO=world health organisation; COPD=chronic obstructive pulmonary disease; 1,2,3=Gold Class.

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Table 3. Comparing the clinical variables between the case (n=25) and control (n=25) patients, including the matching variables age, FU-time, gender and the non-matching variables performance status and prescribed RT dose to PTV.

Characteristics Fracture No fracture Effect size* p-value

median age (y) (range)

70(42~82)

68(38~80)

1 0.09

Male 11 (44%) 11 (44%)

median FU-time (mo)(range)

6.4(1.9-24.1)

23.7(6.7-50.4)

-14.2 <0.01

Performance status (%)

WHO=0 7 (28%) 9 (36%) 0.4 0.75

1 15 (60%) 16 (64%)

2 2 (8%) 0 (0%)

3 1 (4%) 0 (0%

Prescribed RT dose to PTV (%) 1 1

24×2.75Gy 25 (100%) 25 (100%)

WHO=world health organization; RT=radiotherapy; PTV=planned target volume*Age, FU-time were tested using Wilcoxon signed rank test. The effect size refers to the Hodges-Lehmann estimator. Categorical variables like menoposal status (pre-post vs. male) or (female vs. male), PS (0 vs. ≥1), RT dose (66Gy vs. 55Gy) were tested using the binomial test (B vs. A). The effect size refers to the estimated probability of a pair (with A in fractured group and B in non-fractured group) in the unmatched pairs.

Table 4. The volume and dosimetric characteristics to the fractured (n=29) and the non-fractured (n=512) vertebra in the 50 patients in the case control study.

Characteristics Fracturen=29

No fracturen=512

median Dmax (Gy) (range)

72.1(41.7-82.8)

32.9(0.0-83.3)

median Dmean: (Gy) 52.2 11.0

(range) (17.8-71.4) (0-65.3)

median Volume (cc) 15.2 16.0

(range) (8.3-30.4) (4.6-57.0)

The estimated parameter values for the dose-VF relationship are listed in Table 5 (Appendix). The optimal Vx parameter was V30: the percentage of volume of the vertebra that was planned with ≥30Gy (95% CI V6-V46). For EUD, the optimal n parameter was 1 (95% CI 0.05-inf ) (p=0.01, likelihood ratio test compared with the null model). Note that EUD (n=1) is equivalent to the mean dose of the vertebra.

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Discussion

In this study we report an 8% incidence of thoracic vertebral fractures following

a 7 month median time to discovery in patients with locally advanced NSCLC

treated with IMRT. In a matched control group a significant association was

found of VF with Vx and EUD.

To our knowledge, this is the first analysis of VF with clinical and dosimetric

variables in a large cohort of stage III NSCLC patients. The radiation dose on

the vertebra is associated with the risk for VF; suggesting the direct relation

between radiation dose and the development of osteonecrosis. Interestingly,

low dose cisplatin does not increase the risk for fractures. Besides its clinical

relevance, it helps us to understand the mechanisms of radiotherapy induced

VF and to gain knowledge on associations with clinical and dosimetric

parameters. However, there are still questions to be addressed. Theoretically,

the fracture of a radiated thoracic vertebra is caused by reduced osteosynthesis

(8), but the exact mechanism remains unclear. Although we found a significant

relation between the RT dose and VF, we do not know whether the fracture is

caused directly by RT effects to the osteoblasts or the RT effect on surrounding

arteries and/or peripheral vessels.

Noteworthy is the absence of correlation between COPD and VF. Osteoporosis

in COPD patients has been studied thoroughly (15), but large epidemiological

trials aiming to assess the incidence and prevalence of osteoporosis within

populations of patients with COPD at various stages of disease severity

are lacking (19). Although precise mechanisms involved continue to be

debated, one can assume that inflammatory lung disease, aging and the

use of corticosteroids contribute to reduce skeletal bone tissue. A significant

association between VF and a low FEV1 is described frequently (15;19;20).

However, COPD GOLD class ≥ 2 was almost absent in our cohort and this finding

might explain why this association was not observed in our cohort of patients.

There are some limitations in our study. Due to the retrospective approach, we

were not able to assess health related quality of life questionnaires on a regular

basis. Patient reported outcomes are extremely valuable and would have

contributed to this study. Instead, we used CT/MRI scans to identify VF, which is

so far the most objective method. Secondly, due to the easy cylinder structure,

we chose to delineate the corpus vertebra in the study instead of the entire

vertebra. Furthermore, to assess information on BMD, a Dual Energy X-ray

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Absorption (DXA) scan is the preferable imaging modality. However, because

of the retrospective nature of our study, we were not able to perform this

imaging and instead we used the pre-treatment RT planning CT to calculate

the radiodensity (Hounsfield Units). Post-menopausal women are at risk for

osteoporosis (14;15) but due to the inability to retrieve the exact date of the

climacterium, we used age and gender instead as climacterium is nested in

these 2 variables.

In conclusion, our study suggests a significant association between thoracic

vertebral fractures and the dose of radiotherapy delivered to the corpus

vertebrae. This information might be used for treatment planning constraints.

Outcomes should be validated and additional assessment of health related

quality of life is needed to study the physical, emotional, social and financial

impact of vertebral fractures in NSCLC patients.

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2. Schaake-Koning C, van den Bogaert W, Dalesio O, et al. Effects of concomitant cisplatin and radiotherapy on inoperable non-small-cell lung cancer. N Engl J Med, 326: 524-530, 1992

3. O’Rourke N,.Roqué I Figuls M, Farré Bernadó N, Macbeth F. Cochrane Database Concurrent chemoradiotherapy in non-small cell lung cancer.Syst Rev, 16: 2010

4. Uijterlinde W, Chen C, Kwint M, de Bois J, Vincent A, Sonke JJ, Belderbos J, van den Heuvel M.; Prognostic parameters for acute esophagus toxicity in intensity modulated radiotherapy and concurrent chemotherapy for locally advanced non-small cell lung cancer Radiother Oncol, 107: 392-7, 2013

5. Chen C, Uijterlinde W, Sonke JJ, de Bois J, van den Heuvel M, Belderbos J. Severe late esophagus toxicity in NSCLC patients treated with IMRT and concurrent chemotherapy. Radiother Oncol, 108: 337-41, 2013

6. Rodríguez-Ruiz ME1, San Miguel I, Gil-Bazo I, Perez-Gracia JL, Arbea L, Moreno-Jimenez M, Aristu J.. Pathological vertebral fracture after stereotactic body radiation therapy for lung metastases. Case report and literature review. Radiat Oncol, 7:50, 2012

7. Boehling NS, Grosshans DR, Allen PK, McAleer MF, Burton AW, Azeem S, Rhines LD, Chang EL.Vertebral compression fracture risk after stereotactic body radiotherapy for spinal metastases. J Neurosurg Spine, 16:379-86, 2012

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14. van der Klift M, de Laet CE, McCloskey EV, et al: Risk factors for incident vertebral fractures in men and women: the Rotterdam Study. J Bone Miner Res, 19: 1172-1180, 2004

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21. Clayton D,Hills M. Chapters 3 and 13. In: Statistical models in epidemiology New York: Oxford Uni-versity Press; 1993

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Appendix

EUDn calculationBoth V

x and equivalent uniform dose (EUD

n) were extracted from the dose

volume histogram of each vertebra for the analysis of dose-VF relationship. Vx

represents the percentage of volume that was planned with EQD2≥x Gy. EUDn

was calculated as below:

1/2

1

1nN

nn i i

iEUD EQD V

V =

= ∑ (1),

where Vi represents the volume receiving EQD

2i in the ith bin, V the total volume,

n the volume effect (21). When n0, EUDn becomes the maximum dose to the

vertebra; when n=1, EUDn is identical to the mean dose.

Generalized linear mixed modelThe data of the case control study has a nested structure: The vertebras are

nested within the patients and the patients are nested within the pairs. Thus

there exhibits a restricted randomization in this study. In the analysis, the

nested variation from pairs and patients are not interesting for the dose-VF

relationship. Therefore, we decided to use a generalized linear mixed model

(GLMM) and treat pairs/patients as random effects.

Suppose 1ijkY = indicates the presence of fracture of the kth (k=1, …,12) vertebra

in the jth (j=1,2) patient of the ith (i=1,…,25) pair, ijkY then follows a Bernoulli

distribution B(1, )ijkp . Let ijkx be the dose variable for the corresponding

vertebra, ijkp is the expected probability of fracture at dose value ijkx .The

model can be described as the following formula:

2

2

Bernoulli(1, )

( )

var( ) (1 )

logit( )

(0, )

(0, )

ijk ijk

ijk ijk

ijk ijk ijk

ijk ijk i ij

i pair

ij patients

Y pE Y p

Y p pp x a b

a N

b N

a b

s

s

=

= × −

= + ⋅ + +

:

:

:

(2),

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Fractures of thoracic vertebrae and IMRT

139

6

where ia and ijb refer to the random variation from the pair i and patient ij,

respectively. Both variations follow a normal distribution. Optimal values of

these parameters were then estimated through maximum likelihood estimation

(MLE) and 95% CIs were computed using profile likelihood method (22).

Table 5. Optimized parameter values with the 95% CIs (profile likelihood) and the maximum log-likelihood (MaxLLH) in predicting vertebral fractures (VF) for NSCLC patients (n=541). The MaxLLH for the null model with only intercept is -113.066 (df=3).

Model Estimated parameter value (95% CI) MaxLLH (df) p-value

Vx

α x β

-5.22 (-16.80 - -4.05)

30 (6-46) 0.04 (0.03-0.09)

-91.71 (df=5) <0.01

EUD α n β

-5.51( -7.31 - -4.31)

1.00 (0.05-inf ) 0.07 (0.05-0.10)

-90.12 (df=5) <0.01

Vx = The percentage of volume that was prescribed with ≥x GyEUD = Equivalent uniform dose

.

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