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RESEARCH ARTICLE
Occult metastases and survival of lung cancer
by clinical diagnosis and CT screening: A
simulation study
Xing Chen
1,2
, Ghulam Muhammad Kanhar
2
, Songli Hu
3
, Chaomin Wu
4
, Guanqun Chao
1
*,
Mengqi Jing
1
, Fengjiang Zhang
3
*, Millennia Young
6
, Marek Kimmel
7
, Liying ChenID
1
*,
Olga Y. Gorlova
5
1Department of Medicine, Zhejiang Sir Run Run Shaw Hospital, Zhejiang University, Hangzhou, China,
2Department of Biomedical Engineering, Key Laboratory of Biomedical Engineering of Ministry of Education
of China, Zhejiang University, Hangzhou, Zhejiang, China, 3Department of Anesthesiology, Second
Affiliated Hospital, Zhejiang University, Hangzhou, Zhejiang, China, 4Department of Anesthesiology, The
Fourth Affiliated Hospital, International Institute of Medicine, Zhejiang University School of Medicine, Yiwu,
China, 5Department of Medicine Epidemiology and Population Sciences, Baylor College of Medicine,
Houston, Texas, United States of America, 6Human Health and Performance Directorate / Biomedical
Research & Environmental Sciences Division, NASA Johnson Space Center, Houston, Texas, United States
of America, 7Departments of Statistics and Bioengineering, Rice University, Houston, Texas, United States
of America
*3197020@zju.edu.cn (LC); chaoguanqun@zju.edu.cn (GC); zrzfj@zju.edu.cn (FZ)
Abstract
Objectives
It is significant to know how much early detection and screening could reduce the proportion
of occult metastases and benefit NSCLC patients.
Methods
We used previously designed and validated mathematical models to obtain the characteris-
tics of LC in the population including undetectable metastases at the time of diagnosis. The
survival was simulated using the survival functions from Surveillance, Epidemiology and
End Results (SEER) data stratified by stage.
Results
Based on the simulations, 35.3% of patients diagnosed with stage N0M0 and 56.9% of
those diagnosed with stage N1M0 had nodal or distant metastases that were not discovered
at the time of diagnosis. Among clinically detected Stage I lung cancers with tumor diameter
1–2 cm, 78% were true stage N0M0 (no occult metastases) while it was only 37% for
patients with tumor diameters of 2–3 cm. This size threshold can be translated into a 0.75-
year the “window of opportunity” for the curable disease. In a comparative analysis of two
simulated groups of individuals: (1) clinically diagnosed (2) diagnosed by screening with a
varying screening frequency (quarterly, biannual, annual and biennial), it was estimated
that, once the screening intervals become shorter, substantially more cancers are found,
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OPEN ACCESS
Citation: Chen X, Kanhar GM, Hu S, Wu C, Chao G,
Jing M, et al. (2025) Occult metastases and
survival of lung cancer by clinical diagnosis and CT
screening: A simulation study. PLoS ONE 20(1):
e0313544. https://doi.org/10.1371/journal.
pone.0313544
Editor: Luca Bertolaccini, European Institute of
Oncology: Istituto Europeo di Oncologia, ITALY
Received: September 5, 2024
Accepted: October 27, 2024
Published: January 3, 2025
Copyright: ©2025 Chen et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All relevant data are
within the manuscript and its Supporting
information files.
Funding: This study was funded by the following
grants: National Natural Science Foundation of
China No. 82172064 and 81571769 to X.C.;
’Pioneer’ and ’Leading Goose’ R&D Program of
Zhejiang No. 2022c03188 and 2022C03SA1I1049
to X.C.; CISNET 5 U01 CA097431 to M.K. and O.G.;
FAMRI Young Clinical Scientist Award and Prevent
Cancer Foundation grants to O.G.; NIH grants R01
but at an expense of a higher radiation exposure. The simulation projected that the mortality
reduction in screened patients depending on the frequency, ranged from 15.04% to 18.82%.
Conclusions
The probability of occult metastases significantly increases when the primary tumor exceeds
2 cm in diameter. Effective screening measures that detect smaller tumors will considerably
benefit asymptomatic LC patients.
1. Introduction
Lung cancer remains a disease with a high mortality, even when diagnosed at an early stage,
particularly since asymptomatic metastases are often present at the time of diagnosis [1–4].
Although screening helps find early-stage disease, the debate on the benefits of LC screening
has been continuing for decades. Occult tumors are tumors the presence and location of which
cannot be identified during standard clinical evaluation [5–8]. The presence of occult metasta-
ses in lymph nodes, pleura, or distant sites which are hard to find by standard diagnosis proce-
dures in clinical practice are a likely reason for poor outcomes in early stage non-small cell
lung cancer (NSCLC) [9]. The American College of Surgeons Oncology Group (ACOSOG)
Z0040 trial revealed that 22% of patients with N0 disease had occult nodal metastases associ-
ated with decreased overall and disease-free survival [10,11]. It is increasingly important to
understand how well early LC detection by screening can reduce the proportion of patients
with occult metastases. We compared the probability of occult metastases in clinically detected
and screened populations using a method to predict the true stages by modeling the natural
history and detection of NSCLC.
2. Materials and methods
In this article, we use a microsimulation-based LC natural history and detection model frame-
work [12], which was previously calibrated to Surveillance, Epidemiology and End Results
(SEER), to estimate the presence of occult metastases and survival in a population screened for
LC. We also apply the procedure to gain understanding of the potential of screening to detect
early non-metastatic lung cancers, as a function of primary tumor size at detection. Individuals
aged 55–77 with a smoking history of 30 or more pack-years were considered eligible for
screening, and we applied varying screening intervals in the model framework. We also
applied an updated high-risk group definition as per most recent NCCN guidelines [13],
including individuals aged 50 or older with 20 or more pack-years of smoking.
2.1. Model framework
In this framework, we jointly apply the two-stage clonal expansion (TSCE) carcinogenesis
model, tumor-progression and detection models, and stage- and primary tumor size-specific
survival functions derived from LC patients diagnosed from 2004 to 2008 using data from
SEER as depicted in Fig 1. We construct the individuals timeline from his/her birth to the time
of lung cancer initiation (T
0
, age at tumor onset), progression (T
n
and T
m
, ages at nodal and
distant metastasis), detection (T
dc
, age at detection), and death by combining models of carci-
nogenesis, tumor progression (growth and metastasis), detection, and survival.
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CA149462 to OYG, R03CA1338885 and
R03128025 to O.G., CA55769 to M.R.S.; NIH
U19CA203654 grant; the RR170048 Cancer
Prevention and Research Institute of Texas grant;
and ARC Foundation Project CANC’AIR grant. M.K.
was supported by the National Science Center
(Poland) grant 2021/41/B/NZ2/04134. M.J. was
funded by Medical Health Science and Technology
Project of Zhejiang Provincial Health Commission
(No. 2022KY828). The funders had no role in study
design, data collection and analysis, decision to
publish, or preparation of the manuscript.
Competing interests: No competing interests exist.
Abbreviations: CDF, Cumulative distribution
function; CT, Computed tomography; DMS, Distant
metastases size; LC, Lung Cancer; NCCN, National
comprehensive cancer network; NMS, Nodal
metastases size; NSCLC, Non-small cell lung
cancer; NSCLC, non-small cell lung carcinoma;
PTS, Primary tumor size; SCLC, Small cell lung
carcinoma; SEER, Surveillance, Epidemiology and
End Results; SHG, smoking history generator;
TNM, Tumor node metastases; TSCE, Two-stage
clonal expansion; TVDT, Tumor volume doubling
time.
The smoking based TSCE carcinogenesis model [14] combined with the data on the
patients’ smoking duration and intensity generated by the smoking history generator (SHG,
version 5.2.1) [15–17] is used to predict the occurrence of lung cancer within a person’s life-
time, as well as to calculate the age of the patient at lung cancer initiation. The SHG is a tool
developed by the National Cancer Institute based on historical smoking patterns. It simulates
individual life/smoking histories such as the age at smoking initiation, cessation, and smoking
intensity (cigarettes per day), by gender and birth cohort, initially comprising the period from
1890 to 1984 for the year of birth [17] and subsequently updated to include more contempo-
rary cohorts [18]. The generated smoking histories served as input for the TSCE model that
calculated the age at LC initiation. We used the number of live births in the US from the Cen-
ters for Disease Control and Prevention to determine the exact number of people that needed
to be simulated in each year. The tumor growth and detection models are applied jointly to
predict the age, tumor size, and disease stage at the time of diagnosis for the modeled individ-
ual. We assume that a tumor grows exponentially with a growth rate λ, which obeys Gamma
distribution with parameters of shape Kand scale θ.Fnsð Þ ¼ 1emn
xþ1∗Sxþ1ð Þ, and Fmsð Þ ¼
1emm
xþ1∗Sxþ1ð Þ were the metastases models, where �
Fn,�
Fmare the survival functions for metas-
tasis (nodal or distant), ξis the detachment rate of primary tumor, μ
n
and μ
m
are the transfer
and deposition rates of cancer cells to nodal and distant sites, and Sis the primary tumor vol-
ume. We also assume that the hazard of tumor detection depends linearly on the volume of the
tumor, and denote the efficiency of detection by tumor volume as ηand stage-dependent offset
parameters as W
0
,W
1
and W
2
. The resulting c.d.f. D
p
(s
p
), D
n
(s), and D
m
(s) of detection by
volume of the primary tumor and nodal and distant metastases and the estimates of the model
parameters are given in our previous work [12]. S1 Table in S1 File shows the parameters of
tumor progression and detection models that were used in the simulation framework.
2.2. Occult metastases
Assuming that tumors smaller than 0.618 mm in diameter, corresponding to the spherical vol-
ume of 0.000124 cm
3
, cannot be detected by CT, we set the detectable size for primary tumor,
Fig 1. The diagram of micro-simulation using the smoking based two-stage clonal expansion model framework.
https://doi.org/10.1371/journal.pone.0313544.g001
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nodal metastases, and distant metastases at 0.000124 cm
3
. We chose this number based on the
fact that the smallest reconstruction slice interval for CT is about 0.3 mm. After assuming that
data at 3 points or slices (with 2 slice interval) could be used to discover the abnormal lung tis-
sue, we arrived at the above-mentioned approximation of the limit of tumor detection [19,20].
Thus, nodal and distant metastases larger than a single malignant cell (volume of 1×10
−9
cm
3
)
and smaller than 0.000124 cm
3
are considered occult metastases.
2.3. Modeling of survival
The survival was simulated using the survival functions derived from SEER data (2004–2008)
stratified by tumor size and stage (IA, IB, IIA, IIB, IIIA, IIIB and IV). The years of survival
after the time of diagnosis were determined using the inverse stage and size-specific survival
function Lung cancer staging is based on the detected primary tumor size (PTS), nodal metas-
tases presence and size (NMS), and distant metastases presence (DMP) (S2 Table in S1 File),
and each simulated person was staged accordingly. For Stage I tumors, Survival was further
stratified by the size of primary tumor using the estimates given in [21].
2.4. Screening unperturbed lung cancer population
We also generated a lung cancer population assuming the symptomatic detection does not
take place and all detection is due to periodic screening. Basic information of the generated
population included age at tumor onset, age at smoking initiation, age at smoking cessation,
smoking intensity, age at nodal and distant metastasis, tumor growth rate, and size of primary
tumor, nodal and distant metastasis at each simulated year. We applied quarterly, biannual,
annual and biennial screening to this population to generate a simulated screen-detected pop-
ulation. The analysis to estimate mortality reduction was performed as a comparison between
unperturbed data (baseline) and the simulated data. The screening specific recorded time-
frame was from 1979 to 1999. Following the previous published definitions [22,23], the differ-
ence in the number of LC deaths between no–screening (baseline) and screening scenarios
(the number of LC death avoided by screening) divided by the deaths in baseline gives the esti-
mates of mortality reduction that could have been achieved by lung cancer screening from
1979 to 1999.
3. Results
Nodal and distant metastases smaller than 0.000124 cm
3
are considered undetectable in the
simulation. Their records were stored to obtain the distributions of occult nodal and distant
metastases. 64.7% of patients diagnosed with the stage N0M0 had no hidden metastasis, while
9.3% and 26.0% of these patients respectively had nodal and distant metastases that were not
discovered at the time of diagnosis (Table 1). Among N0M0 patients with a primary tumor no
larger than 1 cm in diameter, 17.8% and 11.7% had unobservable nodal and distant metastasis
at the time of diagnosis, respectively. There was a considerable proportion (38.7%) of undis-
covered distant metastasis in patients with a primary tumor no larger than 3 cm, while the pro-
portion dropped dramatically to 7.0% in patients with a primary tumor larger than 3 cm. The
fact that the tumors diagnosed at a larger size tended to have a lower metastatic burden implies
that those tumors have lower metastatic potential and therefore are not detected until the pri-
mary tumor reaches the larger size. 56.9% of patients at stage N1M0 had hidden distant metas-
tasis. Among patients with hidden distant metastases, a high proportion (over 80%) had a
primary tumor smaller than 3 cm (Table 1).
The simulated no-intervention scenario depicted in Table 2 provided an important obser-
vation of the existence of a crucial point in the primary tumor size, which, when exceeded,
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results in a high likelihood of a metastatic stage. While among the tumors with sizes 1–2 cm,
78% are stage N0M0, among the tumors with sizes in the 2–3 cm range, only 37% are N0M0.
At the same time, the proportion of M1 tumors increases from 14% to 41%.
Screening for asymptomatic tumors was simulated in the framework of our model when
not applying the symptomatic detection module, which results in the characteristics of all
tumors (whether they would have produced symptoms or not) being recorded. This does not
occur in reality, but becomes relevant if screening is performed. Table 2 presents the distribu-
tions of nodal and distant metastases in simulated lung cancer patients, who developed disease
but were assumed not to develop any symptoms in their lifetime. In this unperturbed natural
history simulation, there was no secular trend observed. 86% of patients had a stage N0M0
Table 2. Distributions of true nodal and distant metastases in simulated lung cancer patients*without any diagnostic intervention at years 1978, 1988, and 1998,
stratified by tumor size.
Year True stage Total Groups of predicted lung cancer tumor size
TS**0.5 0.5<TS1 1<TS1.5 1.5<TS2 2<TS3 TS >3
1978 (N = 988701) (N = 739313) (N = 59103) (N = 33283) (N = 22865) (N = 31397) (N = 102740)
N0M0, n (%) 857535 (86.7) 739008 (100.0) 57214 (96.8) 28642 (86.0) 15112 (66.1) 11489 (36.6) 6070 (5.9)
N1M0, n (%) 27127 (2.7) 125 (0.0) 755 (1.3) 1824 (5.5) 3007 (13.1) 6895 (22.0) 14521 (14.1)
M1, n (%) 104039 (10.5) 180 (0.0) 1134 (1.9) 2817 (8.5) 4746 (20.8) 13013 (41.4) 82149 (80.0)
1988 (N = 1143627) (N = 849625) (N = 69322) (N = 39152) (N = 27345) (N = 37115) (N = 121068)
N0M0, n (%) 988933 (86.5) 849297 (100.0) 67085 (96.7) 33684 (86.0) 18202 (66.6) 13571 (36.6) 7094 (5.9)
N1M0, n (%) 31285 (2.7) 141 (0.0) 875 (1.3) 2143 (5.5) 3594 (13.1) 7999 (21.6) 16533 (13.7)
M1, n (%) 123409 (10.8) 187 (0.0) 1362 (2.0) 3325 (8.5) 5549 (20.3) 15545 (41.9) 97441 (80.5)
1998 (N = 1209745) (N = 894018) (N = 74101) (N = 41871) (N = 29208) (N = 39941) (N = 130606)
N0M0, n (%) 1042485 (86.2) 893662 (100.0) 71731 (96.8) 36183 (86.4) 19310 (66.1) 14172 (35.5) 7427 (5.7)
N1M0, n (%) 33378 (2.8) 122 (0.0) 962 (1.3) 2186 (5.2) 3833 (13.1) 8661 (21.7) 17614 (13.5)
M1, n (%) 133882 (11.1) 234 (0.0) 1408 (1.9) 3502 (8.4) 6065 (20.8) 17108 (42.8) 105565 (80.8)
*Individuals in whom lung cancer is developing but is not diagnosed and who are alive or have died of other cause; the assumption is that symptoms never develop
regardless of the stage
**TS, Primary tumor size (cm) in diameter
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Table 1. Distributions of occult nodal and distant metastases in the simulated patients symptomatically detected with lung cancer (1988–1999) with stage N0M0,
N1M0 and M1 stratified by tumor size.
Observed stage True stage Total Groups of predicted lung cancer tumor size
TS*0.5 0.5<TS1 1<TS1.5 1.5<TS2 2<TS3 TS >3
N0M0 (N = 380017) (N = 3040) (N = 18301) (N = 47534) (N = 59685) (N = 100031) (N = 151426)
N0M0, n (%) 245871 (64.7) 2860 (94.1) 12151 (66.4) 20749 (43.7) 21735 (36.4) 53346 (53.3) 135030 (89.1)
N1M0, n (%) 35342 (9.3) 122 (4.0) 3704 (20.2) 12000 (25.2) 9583 (16.1) 4084 (4.1) 5849 (3.9)
M1, n (%) 98804 (26.0) 58 (1.9) 2446 (13.4) 14785 (31.1) 28367 (47.5) 42601 (42.6) 10547 (7.0)
N1M0** (N = 321221) (N = 813) (N = 5500) (N = 16827) (N = 24513) (N = 62866) (N = 210702)
N1M0, n (%) 138412 (43.1) 150 (18.5) 506 (9.2) 3512 (20.9) 4769 (19.2) 12084 (19.2) 117391 (55.7)
N1M1, n (%) 182809 (56.9) 663 (81.5) 4994 (90.8) 13315 (79.1) 19744 (80.8) 50782 (80.8) 93311 (44.3)
M1 (N = 732786) (N = 2058) (N = 13450) (N = 33883) (N = 54203) (N = 138575) (N = 490617)
M1, n (%) 732786 (100) 2058 (100) 13450 (100) 33883 (100) 54203 (100) 138575 (100) 490617 (100)
*TS, Primary tumor size (cm) in diameter
**In SEER data, 7208 were N0M1, which is 9.7% of 74109 that had Nand Mstaged. This stage is not modeled.
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disease, of which about 86% had a primary tumor smaller than 0.5 cm in diameter and 80% of
the tumors would have been undetectable by imaging because of screening detection limits.
Most of the patients with nodal and distant metastases (N1M0 or M1) had a detectable primary
tumor (tumor size 1cm in diameter). Moreover, tumor size by stage distribution did not
show variation by age. In Fig 2, we present the timeline estimated using our model, whereby
two scenarios are considered. The first one (“unperturbed”) implies no intervention in the
course of the disease. The second concerns disease detected by usual clinical practice (through
symptoms). The “window of opportunity” for the curable disease has a 0.75-year width, if it is
assumed that the smallest detectable tumors have 5 mm size.
Detection at an early stage is vital to reducing the unacceptably high rate of lung cancer
fatality. However, to estimate the right frequency of screening it is important to take into
account cost and exposure to radiation. In this study we applied varying screening frequency
(quarterly, biannual, annual and biennial) to high-risk individuals as defined by NCCN rec-
ommendations. We simulated two groups of high-risk individuals. Group 1 consist of high
risk individuals aged 55 to 77 years having smoking history of 30 or more pack-years who are
either current smokers or quit smoking in the past 15 years. Group 2 consists of high-risk indi-
viduals aged 50 to 74 years with smoking history of 20 or more pack-years, either current
smokers or those who quit smoking in the past 15 years. Furthermore, following the recent
NCCN recommendation [13], we increased the smoking cessation duration from 10 to 15
years. It appeared that the screening interval for a given duration of cessation and pack-year
scenario had no significant effect on age at diagnosis, number of CT screens and overall sur-
vival years of lung cancer patients of Group 1 and Group 2 as shown in Table 3. While consid-
ering the screening interval in each group there is a significant difference in age at diagnosis,
number of CT scans and survival years of lung cancer patients. In comparison to baseline, the
model-simulated screening leads to an earlier age at diagnosis, longer survival, and mortality
reduction.
Survival Function: We validated the fitted model by comparing the stage-specific survival
in SEER and simulated data, which were comparable as shown in Fig 3. Furthermore, we per-
formed the comparative analysis between SEER and stage simulated data without tumor size
information. The staging information without tumor size is shown in S1-S6 Figs in S1 File.
However, to further validate the model we used another methodology from published paper
not based on SEER to estimate the survival function specific to stage 1 only [21]. We used the
calculated estimates in the simulation model and extracted the data for the analysis. When
comparing an overall distribution of survival of the SEER, baseline and screening simulated
data distribution by selecting screening parameters of group 1 with screening frequency once a
year and smoking cessation time fifteen years as shown in Table 3, we observed a major
Fig 2. (a) NSCLC progression timeline (in years from the first malignant cell) where the median lengths of the
following time intervals are presented: Progression from 0 to 2 mm, 2 to 5 mm, 5 mm to cure threshold, and cure
threshold to detection. Two versions of the timeline refer to the unperturbed disease (top) and detected disease
(bottom), respectively. (b) Median and the first and third quartile of the tumor volume doubling time (TVDT) in the
unperturbed versus detected NSCLC.
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difference in survival plots as shown in Fig 4, owing to a difference in the stage distribution
between the screened and unscreened populations.
Survival and mortality reduction: The analysis of simulated data estimated that screening
strategies resulted a significant decrease in LC mortality with significant survival years. The
simulated data estimated the mortality reduction following screening interval group 1: quar-
terly 15.18% (95% CI 10.87%±19.50%), biannual 15.49% (95% CI 11.15%±19.84%), annual
15.43% (95% CI 10.77%±20.11%), biennial 15.04% (95% CI 10.73%±19.36%) and group 2:
quarterly 18.71% (95% CI 13.44%±23.98%), biannual 18.43% (95% CI 13.24%±23.69%),
Table 3. Comparative analysis of SEER overall, baseline, and two simulated groups that differ by smoking history and are screened at different intervals; Stage 1
only.
Smoking
History
Screening start
& end age
Quit
year
Screening
Frequency*
Age at diagnosis Survival year Age at Death CT Screen
LC**
Mean ±SD Median ±IQR Mean ±SD Median ±IQR Mean ±SD Median ±IQR
SEER 68.23±9.77 69(62~75) 5.33±4.66 4.16(1.41~8.00) 73.56±9.50 74.50
(67.66~80.33)
Baseline 66.02
±14.19
67(57~76) 5.68±6.26 3.29(1.24~7.86) 71.70
±14.60
73.00
(63.01~81.77)
0
Group
1
30 55–77 10 0.5 66.03
±10.01
66(59~73) 13.33
±10.87
9.51
(4.38~22.00)
79.36
±12.76
79.00
(71.00~88.00)
88
30 55–77 10 1 65.47±9.83 66(59~72) 13.63
±10.95
10.00
(4.77~22.08)
79.10
±12.75
78.77
(70.75~87.78)
175
30 55–77 10 2 65.16±9.78 65(59~71) 13.72
±10.91
10.00
(4.85~22.18)
78.88
±12.77
78.50
(70.31~87.50)
330
30 55–77 10 4 64.95±9.73 65(59~71) 13.75
±10.93
10.00
(4.80~22.25)
78.73
±12.72
78.25
(70.25~87.25)
643
30 55–77 15 0.5 65.83
±10.00
66(60~72) 13.36
±10.95
9.47
(4.31~22.00)
79.20
±12.82
79.00
(70.82~88.00)
100
30 55–77 15 1 65.85±9.84 66(59~72) 13.61
±10.91
10.00
(4.86~22.03)
79.31
±12.75
79.00
(71.00~88.00)
186
30 55–77 15 2 65.33±9.75 65(59~72) 13.75
±10.95
10.00
(4.86~22.33)
79.08
±12.71
78.54
(70.51~87.50)
352
30 55–77 15 4 65.19±9.74 65(59~72) 13.79
±10.92
10.00
(4.87~22.49)
78.98
±12.79
78.50
(70.39~87.50)
687
Group
2
20 50–74 10 0.5 64.59
±10.38
65(58~71) 13.91
±11.17
10.00
(4.68~23.00)
78.50
±13.03
78.00
(70.00~87.00)
134
20 50–74 10 1 64.51
±10.28
65(57~72) 14.12
±11.12
10.01
(5.00~23.00)
78.63
±13.02
78.04
(70.00~87.00)
240
20 50–74 10 2 64.21
±10.25
64(57~71) 14.20
±11.12
10.50
(5.00~23.10)
78.41
±13.02
78.03
(69.86~87.00)
457
20 50–74 10 4 63.75
±10.17
64(57~72) 14.33
±11.18
10.60
(5.00~23.29)
78.08
±13.01
77.78
(69.38~86.75)
930
20 50–74 15 0.5 64.79
±10.37
65(58~72) 13.85±6.26 10.00
(4.67~23.00)
78.65
±13.02
78.27
(70.00~87.14)
141
20 50–74 15 1 64.60
±10.22
65(58~71) 14.06
±11.13
10.01
(5.00~23.00)
78.66
±12.95
78.24
(70.00~87.08)
264
20 50–74 15 2 64.19
±10.27
65(57~71) 14.16
±11.12
10.50
(5.00~23.00)
78.35
±13.06
78.00
(69.64~87.00)
496
20 50–74 15 4 63.98
±10.23
64(57~71) 14.30
±11.15
10.50
(5.00~23.29)
78.29
±13.02
78.00
(69.61~87.00)
985
*screening interval: 0.5 denotes 1 CT scan in two years (biennial), 1 denotes 1 CT scan in 1 year (annual), 2 denotes 2 CT scans in one year (biannual), and 4 denotes 4
CT scans in one year. The data used in table is the representation of stage 1.
** The number of screen to find lung cancer and the estimated cost of single CT screening is $3074 [24].
https://doi.org/10.1371/journal.pone.0313544.t003
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annual 18.82% (95% CI 13.25%±24.39%), biennial 18.39% (95% CI 13.02%±23.77%). We
assessed the mortality reduction from 1980 to 1999. The simulated data screening intervals
projected annual mortality reduction for group 1 which peaked in 1980 at 33.58% and
decreased to 2.06% by 1999 and group 2 in 1980 at 41.07% and decreased to 3.69% by 1999 are
shown in S7-S9 Figs in S1 File. Our study estimates a decrease in mortality and demonstrates
the potential of lung cancer screening to reduce LC mortality. Observing difference between
group 1 and group 2 screening intervals based on data and description presented in Table 3 we
think group 1 screening interval is considerably better option in terms of time, cost, and reduc-
ing exposure to radiation.
4. Discussion
A validated mathematical model for simulating the progression and detection of LC at the
individual level was used to obtain the characteristics of LC in a population at the time of
Fig 3. The comparative analysis of five-year survival between SEER and tumor size-based stages simulated
screening data.
https://doi.org/10.1371/journal.pone.0313544.g003
Fig 4. The comparative analysis of an overall five-year survival between SEER, baseline and screening simulated
data.
https://doi.org/10.1371/journal.pone.0313544.g004
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diagnosis. Detection threshold of CT scan was assumed to determine undetectable metastases.
The survival was simulated using the survival function from Surveillance, Epidemiology and
End Results (SEER) data stratified by stage, and for Stage I tumors, further stratified by size
[21].
Screening detection was applied to the unperturbed LC population (without any diagnostic
interventions). The tumor size- and stage-specific survival was similar in the screened and
unscreened populations as shown in Fig 3, but the tumor size and stage distributions in these
two populations were very different. The primary tumor size and stage have been changing
rapidly with the passage of time and new research approaches [25]. Keeping in mind the cur-
rent and proposed stage groups as per TNM subsets [26], our model is accurate, the variation
difference between SEER tumor size based stage simulated data especially for the survival is
acceptable as seen in Fig 3. In the presence of screening tumors are detected earlier than in its
absence. As we can see in Table 3, the screening starts earlier than actual median age at lung
cancer onset, T
0
, of the baseline and SEER, and this difference case would remain the same for
T
n
, T
m
and T
dc
in the model. The survival is consistent with that of screen-detected LC as it
was in previously published LC screening study [27]. While screening does not improve the
survival time if a case is detected with a metastasized tumor the cases screened at an early cur-
able stage are more likely to go through surgeries and have a vital chance to be treated success-
fully and get additional years of life. The screening strategies help get additional years of life
and considerably reduces LC mortality in comparison to other current strategies [28–30]. To
check the effectiveness of our screening model we performed a comparative analysis of five-
year and fifteen-year survival difference between SEER, baseline and tumor size based simu-
lated screening data. (The details are in S6 Fig in S1 File). The lung cancer spontaneous detec-
tion in presence of nodal or distant metastases is much more likely than when only the
primary tumor is present (W1,W2 >> W0), but finding small metastases is more complicated
than the detection of primary tumor only, in clinical practice. Our model predicts mean dura-
tion from tumor onset to detection consistent with a previous progression study [31]. Among
the tumors detected, the mean size of the nodal or distant metastases was less than 1 cm in
diameter, which is significantly smaller than suggested by other projections based on screening
data for different cancers [32,33].
Comparison with other Studies: Recently, Lin and Plevritis [34] published the estimates of
the disease progression timeline for non-small cell lung cancer (NSCLC; their Fig 4c), based
on a computational model with parameter estimates obtained using simulation-based likeli-
hood maximization. The model hypotheses differ somewhat from ours but it is interesting to
compare the predictions and to discuss the differences. The most interesting comparison is
that the “window of opportunity” for the curable disease has 0.6-year width in Lin and Plevritis
(2012) versus 0.75-year width in our study (Fig 2), if it is assumed that the smallest detectable
tumors have 5 mm size. If it is assumed that the smallest detectable size is 2mm, then the win-
dow of opportunity becomes 2.1 year in Lin and Plevritis (2012) versus 1.38 in our paper.
Numbers do not seem radically different; however, they represent opposite directions if the
smallest detectable size is varied. These differences can be traced back to differences in volume
doubling times. Lin and Plevritis estimate the median volume doubling time as 134 days,
whereas the corresponding number in our paper is 79 days. It seems that this latter difference
is due to the fact that Lin and Plevritis assume the starting tumor volume to be 1 mm
3
, whereas
ours is that of a single cell. Another likely reason is a difference in assumed metastatic rates.
However, there are no estimates presented in Lin and Plevritis (2012).
Screening Intervals: LC detection at an early stage has been an elusive goal for decades.
While screening is a really hectic and costly process, setting an optimal screening interval
could reduce the cost without compromising the survival of LC patients. To address the
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benefits and harms of screening we compared two simulated data groups of high risk individu-
als with different recommended screening intervals [35–40]. Previously, de Koning et al. [41]
estimated further harms and benefits of LC screening by using 5 models calibrated to NLST
and PLCO and presented best case scenario of annual screening age 55 to 80 years. The previ-
ous studies [42–47] proposed annual screening strategies and evaluated the harms and benefit
of lung cancer screening based on risk factors with start age and end age at screening from 50
or 55 to 74 or 77 or 80 years.
In this study the comparative analysis of two simulated data groups (Table 3) explains that
the group 1, biennial screening starting at age at 55 years and ending at age 77 years with
smoking history of least 30 pack per years and quit year minimum 10 years and maximum 15
years is more advantageous than group 2 in terms of benefits and harms in comparison to
quarterly, biannual and annual screening strategies.
Group 1 biennial screening has a considerable reduction in number of CT scans, while,
annual screening interval results in more detected patients with lower age at diagnosis than
biennial screening interval but at the expense of double the number of CT scans. In group 2
screening start at age 50 years and end at age 74 years with smoking history of least 20 pack-
years and quit year minimum 10 years and maximum 15 years. The comparative analysis
between group 1 and group 2 showed that there is no significant difference on overall age at
diagnosis and survival years of lung cancer patients but there are large differences in the num-
ber of patients screened and estimated number of CT scans as shown in Table 3. However, as
the duration of screening intervals decreases, the number of CT scan will increase, which leads
to additional cost and over diagnosis ratio, as well as increased radiation dose exposure. The
screening is applied to high-risk individuals, not all of whom would develop lung cancer, and a
more frequent screening will avert more deaths in those destined to develop LC but will cause
more harm to those who are not. Frequent exposure to the radiation might cause other types
of cancers. The analysis of simulated data shows that lung cancer screening strategies signifi-
cantly reduced mortality and increased survival. Previous studies utilized similar strategies
with different cohort effects to estimate mortality reduction [22,48]. Observing the differences
Group 1 offers a more efficient screening strategy in terms of time, cost, and radiation
exposure.
Limitations: It seems that for Stage I at least, the more frequent screening finds cancer ear-
lier. However, survival for screen-detected tumors is available for grouped sizes such as from 5
to 10 mm. For this reason, current study cannot model the differential survival benefit of find-
ing a tumor of 6 mm versus 9 mm in size. The same limitation exists for all the size groups.
This limits the resolution with which we can differentiate survivals. This leads to an apparently
paradoxical effect that more frequent screening the patients may die (slightly) earlier, which is
an artifact of the size groupings.
5. Conclusion
We used a previously developed and validated model of the natural progression and spontane-
ous detection of lung cancer, based on biologically and clinically sound assumptions: This
model framework provided a platform to assess the outcome of secondary prevention strate-
gies for clinical application, such as a periodic screening. Furthermore, we applied screening
strategy with respect to smoking history to address the benefits and harms of frequent screen-
ing of high-risk individuals. This model suggests the optimal screening interval which could
reduce cost and reduce radiation exposure without compromising survival of LC patients.
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Supporting information
S1 File. This file (supplementary documents) includes S1 and S2 Tables and S1-S9 Figs,
which provide additional data and analyses to support statements in manuscript.
(DOCX)
Author Contributions
Conceptualization: Xing Chen.
Data curation: Xing Chen, Ghulam Muhammad Kanhar.
Formal analysis: Xing Chen, Ghulam Muhammad Kanhar.
Funding acquisition: Xing Chen, Mengqi Jing, Marek Kimmel, Olga Y. Gorlova.
Investigation: Ghulam Muhammad Kanhar, Guanqun Chao, Mengqi Jing.
Methodology: Xing Chen, Ghulam Muhammad Kanhar.
Project administration: Songli Hu, Fengjiang Zhang, Liying Chen.
Supervision: Songli Hu.
Writing – original draft: Ghulam Muhammad Kanhar.
Writing – review & editing: Xing Chen, Chaomin Wu, Fengjiang Zhang, Millennia Young,
Marek Kimmel, Liying Chen, Olga Y. Gorlova.
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