Quantitative predictive approaches for Dupuytren disease: a brief review and future perspectives

Georgiana Eftimie; Raluca Eftimie; Georgiana Eftimie; Raluca Eftimie

doi:10.3934/mbe.2022132

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 3: 2876-2895. doi: 10.3934/mbe.2022132

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Quantitative predictive approaches for Dupuytren disease: a brief review and future perspectives

Georgiana Eftimie ¹,
Raluca Eftimie ^{2
,
,}

1.
Clinique de la Miotte, Avenue de la Miotte, Belfort 90000, France
2.
Laboratoire Mathématiques de Besançon, UMR - CNRS 6623 Université de Bourgogne Franche-Comté, Besançon 25000, France

Academic Editor: Yanping Ma

Received: 18 November 2021 Revised: 23 December 2021 Accepted: 03 January 2022 Published: 14 January 2022

In this study we review the current state of the art for Dupuytren's disease (DD), while emphasising the need for a better integration of clinical, experimental and quantitative predictive approaches to understand the evolution of the disease and improve current treatments. We start with a brief review of the biology of this disease and current treatment approaches. Then, since certain aspects in the pathogenesis of this disorder have been compared to various biological aspects of wound healing and malignant processes, next we review some in silico (mathematical modelling and simulations) predictive approaches for complex multi-scale biological interactions occurring in wound healing and cancer. We also review the very few in silico approaches for DD, and emphasise the applicability of these approaches to address more biological questions related to this disease. We conclude by proposing new mathematical modelling and computational approaches for DD, which could be used in the absence of animal models to make qualitative and quantitative predictions about the evolution of this disease that could be further tested in vitro.

Keywords:

Citation: Georgiana Eftimie, Raluca Eftimie. Quantitative predictive approaches for Dupuytren disease: a brief review and future perspectives[J]. Mathematical Biosciences and Engineering, 2022, 19(3): 2876-2895. doi: 10.3934/mbe.2022132

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Abstract

1. Introduction

Reducing air pollution in urban areas is one of the most active debated public policies related to city management, green development and energy saving around the world ^[1,2,3]. Although different tools have been used to control air pollution, a quite confusing feature is that even similar public policies can leads to different outcomes based on different governmental behaviours ^[4,5,6]. For example, the policy of banning vehicles from driving one day per week in Beijing can significantly reduce air pollution ^[7]. However, a similar policy taken by Tianjin, another Chinese super-sized city located 110 km from Beijing, has not been proved to improve air quality. The existing research does not pay much attention to the effects of decentralization on air pollution: it is the changes of incentives of local government caused by decentralization that may cause the heterogeneous effects of air pollution reduction. Also, the impact of authority decentralization on organizing sports events are seldom considered by previous literature. Understanding the effects of local governments' incentives after decentralization on reducing air pollution not only can help to reveal the logic of officials' behaviours, but also is important for making effective environmental policies.

We use Chinese authority decentralization of holding marathon games as a quasi-experiment to identify the causal relationship between local governments' incentives and air pollution reduction. In 2015, the General Administration of Sport of China (GASC) cancelled the approval of marathon games nationwide. From then on, the right to hold marathon games is de facto decentralised from central to local governments. Since then, marathon games thrived in Chinese cities: according to China Marathon Annual Report (2017), ¹ the number of national marathon games reaches 1102 in 2017, while from 2012 to 2016, this number is only 33, 39, 51, 134, and 328, respectively. The decentralization of holding sports games from central to local governments since 2015 may strengthen the incentives of local government to perform better, as they do not need to petition the central government. Therefore, because marathon games held for the first time after 2015 is independently initiated by local government rather than organizing under the order or guidance by central governments, local officials with better understanding of local situation and more private information have stronger motivation perform better during marathon games. In this paper, we discuss an important outcome related to local governments' effort: the reduce of local air pollution.

¹ http://www.athletics.org.cn/

We investigate the effects of authority decentralization of sports game on reducing air pollution for two reasons: first, severe air pollution during marathon games is an important issue in Chinese society. Figure 1 shows the graph of Baidu trend based on the key words of 'air pollution' and 'marathon' searched online. The results show that when marathon games become a hot topic, the problem of air pollution is also closely followed by the public. This trend has been obvious since 2014, especially when air pollution in China has become a serious issue in recent years. According to a World Bank survey including 188 countries, China is the country suffering the second highest concentrations of PM_2.5 in 2013. From 1990 to 2013, the welfare losses due to air pollution have increased by 10.9%, which is the second fastest growth among all countries (in India it is 7.0%) ^[8]. In reaction to public anger about air pollution and social concerns about health problems, the motivation of city officials to cut air pollution during marathon games is strong. Therefore, after the decentralization of sports games, marathon games that are independently held by local governments may have stronger motivation and willingness to reduce air pollution compared to those cities that are authorized before decentralization.

Figure 1. Baidu trend of the key words 'air pollution' and 'marathon' from 2013 to 2017.

DownLoad: Full-Size Img PowerPoint

Second, the booming of marathon game gives us an opportunity to identify the causal effects of authority decentralization on controlling air pollution. After 2015, the right of holding new marathon games is decentralized to local government nationwide, which is unexpected by local governments. Therefore, we can estimate the causal effects of authority decentralization on air quality by comparing the changes of air quality during the days of marathon games before or after the enforcement of decentralization policy. The empirical results find that local air pollution during marathon days decrease significantly. More importantly, air pollution during the days of marathon games that are held after decentralization have a larger reduction. To investigate the mechanisms of these results, we further show that political cycles have a close relationship to reducing air pollution under authority decentralization. Furthermore, we point out that the improvement of air quality under decentralization will become larger with the increase of local leaders' career concerns.

This study deepens our understanding of how local officials are incentivised by two different organisational forms—decentralization and centralisation—which is important to environmental protection ^{[9,10,11,12,13]}. Also, this study helps to evaluate the efficiency of environment regulation under strong career concerns by using China as an example ^[14]. Based on the policy shock of authority decentralization related to holding marathon games, this study provides new evidence about the effects of cadre-based incentives on environmental regulation.

This study also echoes the research related to managerial hierarchy (Kräkel, 2021; Liu and Migrow, 2022) ^[15,16]. Our findings resonate with the arguments that the decentralization of public organisations can influence both the economic and non-economic performances of local cities (Huang et al., 2017; Yu and Zhang, 2021) ^[17,18]. In China's administrative hierarchy system, local leaders get promoted based on their performances evaluated by higher level of governments ^[19], and economic growth has been regarded as the major criteria to evaluate the capacity of officials for a long time ^[20]. Compared to existing studies, this paper explores whether decentralization can improve government governances from microlevel. Also, this paper shows that local governments with decentralized rights can improve the total efficiency in the non-economic areas such as organizing sports games, especially if central governments are less competent to allocating local resources.

Furthermore, this study adds new empirical evidence about political career incentives related to environmental regulations. In recent decades, reducing pollution has become an important task related to the promotion of local leaders in China ^[21]. Existing research mainly studies the direct relationship between environmental regulation and political incentives ^[22]. For example, Foulon et al. ^[23] show that public disclosure can strengthen environmental performance. Zheng et al. ^[24] point out that there is a positive relationship between career promotion and pollution reduction. Jia ^[25] finds that the connection between leaders is positively associated with the pay-off of environmental pollution. Chen et al. ^[26] show that target-based evaluation system incentivizes local officials to shift their efforts from GDP growth to environmental performance. Gao et al. ^[27] consider the relationship between political incentives and environmental regulation on industrial land supply. Wu and Cao ^[28] show that county leaders who can reduce air pollution have higher possibility of promotion. Compared to these studies, we focus on the relationship between environmental regulation and political incentives at city level. We also prove that the improvement of air quality only last for a very short period, which implies the possible existence of opportunism among local leaders when making effort to reduce air pollution.

The contribution of this paper is as follows: Firstly, based on a new perspective compared to previous studies, we discuss the impact of authority decentralization, which shows that air quality during the dates of games will increase when cities no longer need to petition the central government in order to hold a marathon. Secondly, we find the positive effects of political career concerns on reducing air pollution by considering the events of organizing sports games, which is less considered by previous studies. Thirdly, the identification strategy based on high-frequency dataset can attenuate the endogenous problem when considering the causal relationship between authority decentralization and environmental regulation.

The rest of this paper is organised as follows: Section 2 discusses the background of Chinese marathon games and data sources, Section 3 contains the empirical result analysis, Section 4 investigates potential mechanisms, and Section 5 concludes.

2. Institutional background and data

2.1. The decentralization of holding marathon games in China

Before 2015, a Chinese city that wants to hold new national or international marathon games needs to be authorised by GASC. Because of the exclusive right of GASC, the number of new approved marathon games is rare. The turning point came in October 2014 when Chinese State Council decided to accelerate the approval of mass and commercial sports events by superior authority. In December 2014, GASC announced the cancellation of the approval of organising national and international sports events. In January 2015, Chinese Athletics Association (CAA), a division of GASC, formally decentralized the right of holding new marathon games.

The decentralization arouses the enthusiasm of local governments to hold new marathon games. There is much anecdotal evidence of the relationship between marathon games and local leader's increasing efforts. As commented by Wisdom Sports Group, a Chinese listed firm, the decentralization by GASC gives local governments higher motivation to hold marathon games.² Guangming Daily, one of the biggest official newspaper in China, pointed out that organising new marathon games has become a way of showing officials' political achievements.³ Since marathon game has been regarded as a way to exhibit good image of city, local governments have more incentives to improve air quality during marathon days by putting more resources into organising games. For example, during Nanjing International Marathon Games in 2015, high-emission plants are required to be closed to reduce air pollution.⁴

² http://epaper.21jingji.com/html/2016-02/29/content_33078.htm

³ http://theory.people.com.cn/n1/2016/0122/c49157-28075423.html

⁴ http://www.xinhuanet.com/politics/2015-11/06/c_128400872.htm

2.2. Data

Marathon games. Since 2012, the CAA divides the marathon games from low to high into three levels: bronze, silver, and gold based on "The rating standard of Chinese marathon and related sports events" and "CAA marathon and related sporting events grading approach".⁵ The CAA- graded marathon games are the top-level long-distance races in China. We manually collect these marathon games from China Annual Marathon Reports from 2013 to 2017 and supplement it by other online information. Figure 2 depicts the number of CAA-graded marathon games from 2013 to 2017 in 98 major cities in China, which shows that the number of marathon games before 2015 is less than 30. Since 2015, the number reaches more than 50 and continues to increase to over 90 in 2017.

⁵ http://www.runchina.org.cn/mlsf/text/2018013115513152.pdf

Figure 2. Number of CAA-graded marathons from 2013 to 2017.

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The results in Figure 3 further present the number of new marathon games from 1956 to 2017. The number of new marathon games is restricted to fewer than 10 before 2014. From 2015 to 2017, as cities have more freedoms to hold new marathon games, the number increases significantly to 24, 27, and 20, respectively.

Figure 3. Number of new CAA-graded marathon games and associated years.

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Air pollution. The data of air pollution are collected from the Ministry of Ecology and Environment (MEE). Since 2013, the MEE began to use hourly air quality index (AQI), a comprehensive index ranging from 0-500, to measure ambient air quality based on the concentrations of six air pollutants: PM₁₀, PM_2.5, CO, SO₂, NO₂, and O₃. The data are based on environmental monitoring stations (increasing in number in major cities from 76 in 2013 to 368 in 2016). We calculate the average city-level daily AQI and concentrations of each pollutant from 2013 to 2017. Figure 4 exhibits the average AQI and the dates of marathon games based on the forty-day moving average method, which reflects a strong seasonality related to the values of AQI. The results based on daily data in Figure A1 of the appendix are much the same. The vertical red lines represent the dates of marathon games, which reveals that most games are organised in winters when temperatures are low. In Figure A2 of the appendix, we also divide cities into two groups by considering if marathons were first held before or after 2015, and the daily average of AQI in these two groups also shows similar trends.

Figure 4. Average AQI in marathon game cities and marathon game dates. (Note: Time series of average AQI in marathon game cities based on forty-day moving average:

$A Q I_\text{t} = 1 / 41 \sum_{t=-20}^{20} A Q I(t+i)$ , the vertical line is marathon game dates.).

DownLoad: Full-Size Img PowerPoint

Weather. Daily weather data are collected from the National Climatic Data Center under the National Oceanic and Atmospheric Administration (NOAA) of the United States, which contains temperature, wind speed, precipitation, dew point, and station pressure recorded by 499 weather monitoring stations around China on consecutive days. Table 1 displays the descriptive statistics of the key variables related to air pollution and weather. On average, the AQI of marathon cities is 78, and the PM_2.5 and PM₁₀ arrive at 51 and 88 μ/m³, respectively.

Table 1. Summary statistics of key variables.

Variable	Obs.	Mean	Std. Dev.	Min.	Max.
AQI	83, 711	78.19	46.12	0	497.90
PM_2.5 (μ/m3)	83, 711	50.74	39.13	0	878.82
PM₁₀ (μ/m3)	83, 711	87.85	60.06	0	1586.01
Average temperature (°F)	83, 711	62.11	16.31	-14.95	97.03
Dew Point (°F)	83, 711	50.74	19.36	-24.30	83.40
Wind speed (km/h)	83, 711	5.12	2.45	0	37.35
Air pressure (pa)	83, 711	676.10	388.62	0	1037.03
Precipitation (mm)	83, 711	1.66	10.60	0	99.90
Holiday	83, 711	0.05	0.22	0	1.00
Note: Data are collected and calculated by authors.

| Show Table

DownLoad: CSV

Local government leaders. We manually collect the characteristics of municipal secretaries and mayors such as education, age and tenure from the internet. Table 2 is the summary statistics of local leaders from 2013 to 2017.

Table 2. Summary statistics of local leaders' characteristics.

Variable	Obs.	Mean	Std. Dev.
Panel A: Municipal secretary
Age (year)	78, 199	53.67	3.50
Tenure (year)	78, 199	2.09	1.62
Second term indicator (tenure > 5)	78, 199	0.05	0.22
Panel A: Municipal secretary
Education indicator (PhD = 1, lower than PhD = 0)	78, 199	0.35	0.48
Turnover (Within 6 months before and after the marathon games = 1, others = 0)	78, 199	0.36	0.48
Promotion (Promoted to higher level next term = 1, others = 0)	51, 051	0.48	0.50
Panel B: Mayor
Age (year)	78, 657	52.48	3.89
Tenure (year)	78, 657	2.08	1.58
Second term indicator (tenure > 5)	78, 657	0.04	0.20
Education indicator (PhD = 1, lower = 0)	78, 657	0.23	0.42
Turnover (Within 6 months before and after the marathon dates = 1, others = 0)	78, 657	0.35	0.48
Promotion (Promoted to higher level next tenure = 1, others = 0)	54, 851	0.67	0.47
Note: Data are collected and calculated by authors.

| Show Table

DownLoad: CSV

3. Empirical result analysis

3.1. Methodology

Firstly, we estimate the impact of air pollution within an 11-day window based on Eq (1):

$\log \left(P_{i t}\right) = \alpha_{i \text{t}}+\sum\limits_{t = -5}^{+5} \beta_{i t} D_i^t \times { decentralize }+f\left(t_i\right)+\Gamma_t+W_{i t}+\varepsilon_{i t}$

(1)

where decentralize measures the effect of decentralization on air pollution, and it equals 1 if the year of new marathon games that are first held is after 2015, otherwise 0. $D_{i t}$ denotes variables related to air pollution such as AQI, PM_2.5 and PM₁₀ in city i at the $t$ th day before or after marathon games. $\alpha_{i t}$ represents city-year fixed effects, which can capture time-varying factors within city-level. $D_{i}^{-t}$ and $D_{i}^{+t}$ equal 1 for city i in the $t$ th day before or after marathon games, separately. $D_i^0$ , which is the variable we are most interested in, equals 1 for city i in the day of marathon games, otherwise 0. $\beta_{i t}$ depicts the dynamic effects before, during or after the games within an 11-day window; $f\left(t_{i}\right)$ includes a series of city-specific polynomial time trends from the first to third orders, which controls the non-linear time-varying confounding variables across cities such as nonlinear dynamic factors or unexpected time shocks ^{[29,30,31,32]}; $\Gamma_{t}$ contains holiday, year-city, week and day of week fixed effects. To control other un-observed variations across cities during marathon days, we include a marathon date dummy which equals 1 at the date when any one of the cities have marathon games. $W_{it}$ is a vector of weather control variables as mentioned in the previous section. $\varepsilon_{i t}$ is an error term.

3.2. The level of air pollution during marathon games

As a preliminary test, in Figure 5, we first visualize the dynamic effects of marathon on PM_2.5 and PM₁₀ based on Eq (1). In Figure 5(A), the graph implies that the levels of PM_2.5 and PM₁₀ decrease significantly on the day of marathon. In Figure 5(B), we include co-pollutants of CO, NO₂, SO₂, and O₃, and the graph presents similar results. These findings suggest that air pollution decreases during marathon games, which also is consistent with the initiation that air quality during marathon days will improve because of less traffic flow. In Table A1 of the appendix, we also report the effects of marathon games on local AQI within an 11-day window from 2013 to 2017 based on different control variables, and the results are much the same.

Figure 5. Dynamic effects of the marathon games on PM_2.5 and PM₁₀. (Note: Figure 5(A) is the dynamic effects of marathon games on PM2.5 and PM10 without co-pollutants. Figure 5(B) is the dynamic effects of marathon games on PM2.5 and PM10 with co-pollutants of CO, NO2, SO2 and O3.).

DownLoad: Full-Size Img PowerPoint

3.3. The impact of decentralization on air pollution

In this section, we first estimate the effects of authority decentralization on air pollution by considering subsamples of marathon games that were first held before or after decentralization since 2015, separately. The dynamic results in Figure 6(A) imply that the level of AQI during the days of marathons that are first organised before decentralisation does not change significantly. The results based on PM_2.5 and PM₁₀ in Figure 6(B) are much the same. On the contrary, the results in Figure 6(C), (D) illustrate that air quality during the days of marathon games that are first held after decentralisation improves significantly. The preliminary results in Figure 6 show that authority decentralization has significant negative effects on reducing air pollution.

Figure 6. Dynamic effects on air pollution with cities first held marathon around 2015. (Note: Figure 6(A) is the dynamic effects of marathon games on AQI in cities with new marathon games before 2015. Figure 6(B) is the dynamic effects of marathon games on PM2.5 and PM10 in cities with new marathon before 2015. Figure 6(C) is the dynamic effects of marathon games on AQI in cities with new marathon games after 2015. Figure 6(D) is the dynamic effects of marathon games on PM2.5 and PM10 in cities with new marathon after 2015.).

DownLoad: Full-Size Img PowerPoint

Next, we formally consider the relationship between marathon decentralization and local air quality based on Eq (1). To attenuate the endogenous problem such that the improvement of air quality may be affected by leaders' deliberate choices of marathon days, we construct an instrument variable (IV) based on marathon temperature. Specifically, a city that wants to hold marathon games should choose the date that meets the requirements of suitable temperatures. According to the "Grading approach of Marathon and related sporting events" released by the CAA, the suitable temperature for marathon runners is around 15 ℃. The results in Figure A3 of the appendix show that the average temperatures on the days of marathon games are around 15 ℃. We therefore construct IV based on suitable temperature: if temperature is between 5 and 25 ℃, the value of IV is one, otherwise 0. We also choose the temperature interval of 5–15 ℃ as a robustness check. The results based on 2SLS model are reported in Table 3, which reveal a negative impact of decentralization on air pollution. Specifically, the authority decentralization of marathon games leads to the decrease of air pollution during the days of marathon games (D⁰ × decentralize). Overall, our basic results in Table 3 prove that the air pollution during marathon games held after decentralization will significantly decrease by around 10–20%.

Table 3. The effects of decentralization on Log (AQI).

	(1)	(2)
	Temp5-25 IV	Temp5-15 IV
D–5 × decentralize	-0.07	-0.03
	(-1.63)	(-0.41)
D–4 × decentralize	-0.04	0.04
	(-0.73)	(0.47)
D–3 × decentralize	-0.09**	0.01
	(-2.02)	(0.16)
D–2 × decentralize	-0.09*	-0.06
	(-1.95)	(-0.57)
D–1 × decentralize	-0.05	-0.10
	(-1.20)	(-1.19)
D0 × decentralize	-0.11***	-0.20**
	(-2.72)	(-2.33)
D+1 × decentralize	-0.10**	-0.15*
	(-2.31)	(-1.71)
D+2 × decentralize	-0.05	0.09
	(-1.09)	(1.03)
D+3 × decentralize	-0.06	0.07
	(-1.33)	(0.81)
D+4 × decentralize	-0.03	0.04
	(-0.61)	(0.39)
D+5 × decentralize	-0.04	0.02
	(-0.80)	(0.17)
Weather	YES	YES
City-year FE	YES	YES
Week FE	YES	YES
Day of week FE	YES	YES
Obs.	83, 578	83, 578
R2	0.48	0.48
First stage results
Temp × decentralize	0.57***	0.58***
	(9.45)	(10.37)
F-Stat.	23.79	7.64
Note: Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

| Show Table

DownLoad: CSV

3.4. Placebo checks

One concern about the robustness of the results in Section 3.3 is that the negative effects of decentralization on air pollution during the days of marathon might be found by chance. In this section, we try to attenuate such concerns by replacing the true marathon dates with randomly selected ones for 1000 times within the same cities and years as a placebo test. The distribution of the coefficients of the interactive terms in Eq (1) based on fake marathon dates is depicted in Figure 7(A), which turns out that the true coefficient is at the left end tail. Figure 7(B) further shows that only 50 out of 1000 cases of estimated terms have p-values at less than the 5% significant level, which further confirms the robustness of our results.

Figure 7. The effects on air pollution results from falsely assigned dates of marathon. (Notes: Figure 7(A) shows the distribution of coefficients

$D^0 \times { decentralize }$ by using OLS method based on randomly selected marathon game dates within each city and each year 1000 times. Figure 7(B) shows the distribution of associated p values. The true position of coefficients and associated p values are shown with vertical dash line in the graphs.).

DownLoad: Full-Size Img PowerPoint

4. Potential mechanisms

We argue that the negative relationship between authority decentralization and air pollution might be caused by cadre incentives and political cycles of local leaders. In this section, we empirically explore some potential mechanisms based on these ideas.

4.1. Promotion incentives

Local leaders with higher possibility of promotion might be more willing to take actions to improve air quality during the days of marathon games after decentralization. Specifically, local leaders with stronger career concerns will make greater effort to reduce air pollution to show their capabilities. We consider if it is the promotion of local leaders associated with authority decentralization that leads to the improvement of air quality by introducing Eq (2):

$\log \left(P_{i t}\right) = \alpha_{i \text{t}}+\sum\limits_{t = -5}^{+5} \beta_{i t} D_i^t \times { decentralize }_{i t} \times { promote }_{i t}+ { age }+ { edu }+ { tenure }+f\left(t_i\right)+\Gamma_t+W_{i t}+\varepsilon_{i t}$

(2)

where ${ promote }$ is 1 if leader of city i is promoted in the next term, otherwise 0. ^{6, 7}We control several characteristics of leaders such as ${ age }$ (in years), ${ temire }$ (working years) and ${ education }$ (1 if PhD, 0 otherwise).

⁶ In China, a dual political system of communist party and government organs exists among each level of the political hierarchy. At a city-level, the top position is a municipal party secretary, followed immediately by a mayor.

⁷ Follow the definition of Li and Zhou (2005), for a municipal secretary, we consider the following position changes as promotions: (1) Member of Standing Committee of Provincial Committee (MSCPC); (2) Provincial (vice-) Governor or Provincial (vice-) Secretary; (3) Any other positions that are equal to, or above, the MSCPC. As for a mayor, besides these three positions, we also consider becoming municipal secretary as a promotion in his political rank. As Chinese political officials have few options available outside the political system, we define other situations of local leaders as non-promotional, which includes moving to a same-level position, retirement, or demotion.

The results in Columns (1) and (2) of Table 4 proves that when the promotion probability of city leader is high, the air pollution during marathon date will significantly decrease after marathon decentralization. Such results imply that promotion incentive is an important factor related to the reduction of air pollution after authority decentralization. In Table A2 of the appendix, the estimations based on 2SLS model are also similar.

Table 4. Effects of decentralization based on promotion incentives.

	Municipal secretary	Mayor
	(1)	(2)
	Log (AQI)
D⁰ × promote × decentralize	-0.18***	-0.14***
	(-3.12)	(-2.74)
Obs.	50, 883	54, 673
R²	0.47	0.48
	Log (PM_2.5)
D⁰ × promote × decentralize	-0.26***	-0.18**
	(-3.36)	(-2.58)
Obs.	50, 883	54, 673
R²	0.46	0.47
	Log (PM₁₀)
D⁰ × promote × decentralize	-0.20***	-0.15***
	(-2.76)	(-2.61)
Obs.	50, 883	54, 673
R²	0.50	0.52
Weather	YES	YES
City-year FE	YES	YES
Week FE	YES	YES
Day of week FE	YES	YES
Note: For simplicity, the table only shows the coefficients of interactions during marathon games. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

| Show Table

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4.2. Political cycles

Political cycles are essential for local economic development. The motivations of the incumbent and newcomers are not the same because of the huge variation in promotion incentives, thus might also affect the changes of air quality during marathon games after authority decentralization. To test such argument, we set a dummy as turnover: if the transition of local leaders happened within six months before or after the dates of a marathon game, its value is 1, otherwise 0. The coefficients in Columns (1) and (2) reveal that if cities are undergoing local leader turnovers, the effects of authority decentralization will become larger. Specifically, the level of air pollution during marathon significantly decreases by about 18% and 14%, respectively, when secretaries or mayors are about to change. In Table A3 of the appendix, the results based on 2SLS model are much the same. Such results confirm that the reduction of air pollution during marathon days has a close relationship with political cycles.

Table 5. Effects of decentralization based on leaders' turnover.

	Municipal secretary	Mayor
	(1)	(2)
	Log (AQI)
D⁰ × turnover × decentralize	-0.18***	-0.14***
	(-3.68)	(-2.88)
Obs.	78, 010	78, 472
R²	0.48	0.48
	Log (PM_2.5)
D⁰ × turnover × decentralize	-0.23***	-0.19***
	(-3.33)	(-2.76)
Obs.	78, 010	78, 472
R²	0.47	0.46
	Log (PM₁₀)
D⁰ × turnover × decentralize	-0.21***	-0.14***
	(-3.37)	(-2.64)
Obs.	78, 010	78, 472
R²	0.51	0.51
Weather	YES	YES
City-year FE	YES	YES
Week FE	YES	YES
Day of week FE	YES	YES
Note: For simplicity, the table only shows the coefficients of interactions during marathon games. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

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To further disentangle the heterogenous effects of political cycles on reducing air pollution after decentralization, we separately estimate the effects of new or old leaders based on the idea of Liu et al. ^[33] and Li et al. ^[34]. We construct a dummy BEF, which is 1 if the dates of marathon are less than 12 months before the leave of the incumbent leaders, and otherwise 0. The dummy variable AFT is 1 if the dates of marathon are less than 12 months after new leaders take office, and otherwise 0. The results in Table 6 show that after marathon decentralization, leaders that will leave soon have stronger motivation to take actions to improve air quality during the days of marathon games. These findings imply that there is a stronger promotion incentive of local leaders to perform well when the probability of political turnover is higher. The results in Table 6 also prove the asymmetric effects of political turnovers on the improvement of air quality.

Table 6. The effects of decentralization before and after the leaders' leave.

	Municipal secretary		Mayor
	(1) OLS	(2) IV	(3) OLS	(4) IV
	(1) OLS	(2) IV	(3) OLS	(4) IV
	Log (AQI)
D⁰ × BEF × year2015	-0.20***	-0.29***	-0.21***	-0.23***
D⁰ × BEF × year2015	(-3.96)	(-3.86)	(-4.27)	(-2.69)
D⁰ × AFT × year2015	-0.01	-0.05	0.08	-0.08
D⁰ × AFT × year2015	(-0.33)	(-0.73)	(1.52)	(-0.91)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.48	0.48	0.48	0.48
	Log (PM_2.5)
D⁰ × BEF × decentralize	-0.27***	-0.43***	-0.31***	-0.37***
D⁰ × BEF × decentralize	(-3.88)	(-4.09)	(-4.37)	(-3.26)
D⁰ × AFT × decentralize	-0.01	-0.13	0.14*	-0.11
D⁰ × AFT × decentralize	(-0.13)	(-1.28)	(1.96)	(-0.87)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.47	0.47	0.46	0.46
	Log (PM₁₀)
D⁰ × BEF × decentralize	-0.22***	-0.39***	-0.22***	-0.28***
	(-3.42)	(-4.03)	(-3.67)	(-2.74)
D⁰ × AFT × decentralize	-0.01	-0.02	0.10	-0.06
D⁰ × AFT × decentralize	(-0.27)	(-0.20)	(1.60)	(-0.56)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.51	0.51	0.51	0.51
Weather	YES	YES	YES	YES
City-year FE	YES	YES	YES	YES
Week FE	YES	YES	YES	YES
Day of week FE	YES	YES	YES	YES
Note: The instrumental variable is temperature dummy with 5–25–degree interval. For simplicity, the table only shows the coefficients of interactions at the marathon date. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. F statistic is for the Kleibergen-Paap rk Wald test. * p < 0.01, p < 0.05, * p < 0.1.

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4.3. Career concerns

As have been proved in previous sections, the effects of authority decentralization on air pollution might be affected by political returns, which reflects the career concerns of city leaders. In this section, we use leaders' age as a proxy to measure career concern and its effects on reducing air pollution during marathon games after decentralization. In Chinese political system, prefectural leaders who are not promoted to higher levels usually will retire at the age of 65. Therefore, local leaders will have stronger motivation to reduce air pollution after authority decentralization with the increase of age before retirement. The results in Columns (1) and (2) of Table 7 indicate that air quality during the dates of marathon game will significantly improve in cities with the increase of leaders' age after marathon decentralization. Specifically, local AQI will decrease by 0.2% with the increase of leaders' age after decentralization. The results based on IV model in Table A4 of the appendix are similar.

Table 7. Effects of decentralization based on leaders' career concerns.

	Municipal secretary	Mayor
	(1)	(2)
	Log (AQI)
D⁰ × age × decentralize	-0.002***	-0.002***
	(-3.43)	(-3.32)
Obs.	78, 010	78, 472
R²	0.48	0.48
	Log (PM_2.5)
D⁰ × age × decentralize	-0.003***	-0.002***
	(-3.09)	(-3.16)
Obs.	78, 010	78, 472
R²	0.47	0.47
	Log (PM₁₀)
D⁰ × age × decentralize	-0.002***	-0.002***
	(-3.36)	(-2.66)
Obs.	78, 010	78, 472
R²	0.51	0.51
Weather Controls	YES	YES
City-year FE	YES	YES
Week FE	YES	YES
Day of week FE	YES	YES
Note: For simplicity, the table only shows the coefficients of interactions at the marathon date. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

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Overall, the empirical results suggest that the impact of decentralization on reducing air pollution during the dates of marathon has a close relationship with the political incentives of local leaders. Some explanations are in order. While air quality improves significantly after decentralization, the duration of the effects is short. Almost at the end of marathon games, the coefficients of the interaction terms are not significant anymore. The U-shaped dynamic effects imply the necessity to adjust the decentralization policy to overcome the possible opportunistic behaviours of local governments.

5. Conclusions

In this study, we investigate the impacts of authority decentralization on reducing air pollution based on the policy of decentralizing the right to hold marathon games by local governments. The empirical results show that during marathon games, local air quality improves significantly. Moreover, the reduction of local air pollution during the days of marathon is mainly caused by the authority decentralization since 2015. We also find that the effect of authority decentralization on reducing air pollution is closely linked to the incentives of local leaders.

In the future, more detailed data need to be used to consider to what extent authority decentralization can have influence on the behaviours of local governments. Firstly, the long-term impact of authority decentralization on air pollution can be identified based on updated data related to local air pollution. Secondly, the incentives of local governments need to be further studied by considering spill-over effects and competing effects across different cities. Finally, the incentives of air pollution reduction induced by decentralization may exist in other field related to city management such as driving restriction, which can also be studied to better understand the effects of authority decentralization on air pollution.

Acknowledgments

This study was financially supported by the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20220384).

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix

Figure A1. Average AQI in marathon game cities and marathon game dates.

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Figure A2. Values of AQI in cities that held new marathon games before and after decentralization.

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Table A1. Dynamic effects of marathon game on Log (AQI).

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
D^-5	-0.024	-0.024	-0.023	-0.023	-0.011	-0.028	-0.031
	(-1.11)	(-1.11)	(-1.08)	(-1.08)	(-0.53)	(-1.35)	(-1.44)
D^-4	-0.003	-0.004	-0.002	-0.002	0.003	-0.012	-0.013
	(-0.12)	(-0.18)	(-0.09)	(-0.10)	(0.11)	(-0.54)	(-0.54)
D^-3	-0.045**	-0.047**	-0.044*	-0.044*	-0.044*	-0.052**	-0.055**
	(-1.98)	(-2.08)	(-1.94)	(-1.94)	(-1.96)	(-2.48)	(-2.41)
D^-2	-0.050**	-0.052**	-0.049**	-0.049**	-0.050**	-0.057***	-0.061**
	(-2.05)	(-2.14)	(-2.02)	(-2.02)	(-2.04)	(-2.69)	(-2.53)
D^-1	-0.027	-0.029	-0.027	-0.027	-0.023	-0.028	-0.041*
	(-1.25)	(-1.35)	(-1.22)	(-1.22)	(-1.03)	(-1.45)	(-1.88)
D⁰	-0.056**	-0.056**	-0.055**	-0.055**	-0.043*	-0.042**	-0.057**
	(-2.47)	(-2.46)	(-2.44)	(-2.44)	(-1.89)	(-2.01)	(-2.49)
D⁺¹	-0.052**	-0.051**	-0.051**	-0.051**	-0.035	-0.024	-0.044**
	(-2.37)	(-2.33)	(-2.34)	(-2.34)	(-1.61)	(-1.22)	(-1.99)
D⁺²	-0.024	-0.025	-0.024	-0.024	-0.012	-0.016	-0.022
	(-1.16)	(-1.17)	(-1.13)	(-1.13)	(-0.58)	(-0.85)	(-1.05)
D⁺³	-0.027	-0.029	-0.026	-0.026	-0.019	-0.013	-0.020
	(-1.21)	(-1.30)	(-1.18)	(-1.19)	(-0.86)	(-0.62)	(-0.90)
D⁺⁴	-0.006	-0.009	-0.006	-0.006	-0.005	0.007	0.003
	(-0.28)	(-0.40)	(-0.24)	(-0.25)	(-0.21)	(0.31)	(0.13)
D⁺⁵	-0.010	-0.012	-0.009	-0.009	-0.012	-0.004	-0.011
	(-0.39)	(-0.49)	(-0.37)	(-0.37)	(-0.49)	(-0.18)	(-0.43)
Weather	YES	YES	YES	YES	YES	YES	YES
Holiday	YES	YES	YES	YES	YES		YES
Year-City FE	YES	YES	YES	YES	YES		YES
Week FE	YES	YES	YES	YES			YES
Day of week FE	YES	YES	YES	YES	YES		YES
Month FE					YES
Date FE						YES
Marathon date dummy							YES
City time trends	No	1st	2nd	3rd	1st	1st	1st
Obs.	83, 578	83, 578	83, 578	83, 578	83, 578	83, 589	83, 578
Adj. R²	0.481	0.481	0.481	0.481	0.467	0.548	0.483
Note: Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

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Figure A3. Distribution of temperature at marathon day. (Note: Figure A3(A) is the distribution of temperature in cities during marathon games which were first held before 2015; Figure A3(B). is the distribution of temperature in cities during marathon games which were first held after 2015.).

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Table A2. Effects of decentralization based on leaders' heterogeneous promotion statuses.

	Municipal secretary		Mayor
	(1)	(2)	(3	(5)
	OLS	IV	OLS	IV
	Log (AQI)
D⁰ × promote × decentralize	-0.171***	-0.217*	-0.132***	-0.153*
D⁰ × promote × decentralize	(-3.05)	(-1.92)	(-2.68)	(-1.82)
Obs.	50, 883	50, 883	54, 673	54, 673
R²	0.474	0.474	0.484	0.484
	Log (PM_2.5)
D⁰ × promote × decentralize	-0.256***	-0.372***	-0.174**	-0.252**
D⁰ × promote × decentralize	(-3.30)	(-2.66)	(-2.53)	(-2.25)
Obs.	50, 883	50, 883	54, 673	54, 673
R²	0.460	0.460	0.470	0.470
	Log (PM₁₀)
D⁰ × promote × decentralize	-0.191***	-0.278**	-0.142**	-0.242**
D⁰ × promote × decentralize	(-2.69)	(-2.23)	(-2.53)	(-2.38)
Obs.	50, 883	50, 883	54, 673	54, 673
R²	0.502	0.502	0.515	0.515
	First stage results
Temp × promote × decentralize		0.508***		0.448***
		(6.97)		(8.96)
F-Stat.		48.60		80.23
Weather Controls	YES	YES	YES	YES
City-year FE	YES	YES	YES	YES
Week FE	YES	YES	YES	YES
Day of week FE	YES	YES	YES	YES
Note: The results are based on the equation as follows: $\log \left(P_{i t}\right)=\alpha_{i \text{t}}+\beta_i D_i^0 { decentralize } \times { incentive }_i+ { age }+ { edu }+ { tenure }+f\left(t_i\right)+\Gamma_t+W_{i t}+\varepsilon_{i t}$ The instrumental variable is 5–25–degree temperature dummy. For simplicity, the table only shows the coefficients of interactions during marathon games. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

| Show Table

DownLoad: CSV

Table A3. Effects of decentralization based on leaders' turnover.

	Municipal secretary		Mayor
	(1)	(2)	(3)	(4)
	OLS	IV	OLS	IV
	Log (AQI)
D⁰ × turnover × decentralize	-0.178***	-0.216***	-0.134***	-0.221***
D⁰ × turnover × decentralize	(-3.63)	(-2.99)	(-2.90)	(-2.79)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.480	0.480	0.479	0.479
	Log (PM_2.5)
D⁰ × turnover × decentralize	-0.220***	-0.360***	-0.183***	-0.324***
D⁰ × turnover × decentralize	(-3.28)	(-3.67)	(-2.79)	(-2.96)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.465	0.465	0.464	0.464
	Log (PM₁₀)
D⁰ × turnover × decentralize	-0.205***	-0.289***	-0.141***	-0.230**
D⁰ × turnover × decentralize	(-3.31)	(-3.06)	(-2.66)	(-2.51)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.508	0.507	0.506	0.506
	First stage results
Temp × turnover × decentralize		0.568***		0.570***
		(9.43)		(10.27)
F-Stat.		88.89		105.50
Weather Controls	YES	YES	YES	YES
City-year FE	YES	YES	YES	YES
Week FE	YES	YES	YES	YES
Day of week FE	YES	YES	YES	YES
Note: The results are based on the equation as follows: $\log \left(P_{i t}\right)=\alpha_{i \text{t}}+\beta_i D_i^0 { decentralize }_i \times { incentive }_i+ { age }+ { edu }+ { tenure }+f\left(t_i\right)+\Gamma_t+W_{i t}+\varepsilon_{i t}$ The instrumental variable is temperature dummy with 5-25-degree interval. For simplicity, the table only shows the coefficients of interactions at the marathon date. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

| Show Table

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Table A4. Effects of decentralization with leaders' heterogeneous promotion statuses.

	Municipal secretary		Mayor
	(1)	(2)	(3)	(4)
	OLS	IV	OLS	IV
	Log (AQI)
D⁰ × age × decentralize	-0.002***	-0.004***	-0.002***	-0.004***
D⁰ × age × decentralize	(-3.39)	(-3.45)	(-3.29)	(-3.14)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.480	0.480	0.479	0.479
	Log (PM_2.5)
D⁰ × age × decentralize	-0.003***	-0.006***	-0.003***	-0.006***
D⁰ × age × decentralize	(-3.06)	(-3.95)	(-2.97)	(-3.70)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.465	0.465	0.464	0.464
	Log (PM₁₀)
D⁰ × age × decentralize	-0.002***	-0.004***	-0.002***	-0.004***
D⁰ × age × decentralize	(-3.33)	(-3.56)	(-3.11)	(-3.12)
Obs.	78, 010	78, 010	78, 472	78, 472
R²	0.508	0.507	0.506	0.506
	First stage results
Temp × age × decentralize		0.464***		0.439***
		(13.24)		(12.89)
F-Stat.		175.28		166.08
Weather Controls	YES	YES	YES	YES
City-year FE	YES	YES	YES	YES
Week FE	YES	YES	YES	YES
Day of week FE	YES	YES	YES	YES
Note: The results are based on the equation as follows: $\log \left(P_{i t}\right)=\alpha_{i \text{t}}+\beta_i D_i^0 { decentralize }_i \times { incentive }_i+ { age }+ { ed }+ { tenure }+f\left(t_i\right)+\Gamma_t+W_{i t}+\varepsilon_{i t}$ The instrumental variable is 5-25-degrees temperature dummy. For simplicity, table only shows the coefficients of interactions during marathon games. Robust t-statistics are reported in parentheses. Standard errors are clustered at the city level. * p < 0.01, p < 0.05, * p < 0.1.

| Show Table

DownLoad: CSV

References

[1]	C. Ball, D. Izadi, L. Verjee, J. Chan, J. Nanchahal, Systematic review of non-surgical treatments for early Dupuytren's disease, BMC Musculoskeletal Disord., 17 (2016), 345. https://doi.org/10.1186/s12891-016-1200-y doi: 10.1186/s12891-016-1200-y
[2]	R. Grazina, S. Teixeira, R. Ramos, H. Sousa, A. Ferreira, R. Lemos, Dupuytren's disease: where do we stand?, EFORT Open Rev., 4 (2019), 63–69. https://doi.org/10.1302/2058-5241.4.180021 doi: 10.1302/2058-5241.4.180021
[3]	G. Rayan, Dupuytren disease: anatomy, pathology, presentation, and treatment, J. Bone Joint Surg., 89 (2007), 190–198. https://doi.org/10.2106/00004623-200701000-00026 doi: 10.2106/00004623-200701000-00026
[4]	C. Eaton, Dupuytren disease and related diseases - The cutting edge, Springer International Publishing Switzerland, 2017. https: //doi.org/10.1007/978-3-319-32199-8
[5]	R.B. Shaw. Jr., A.K.S. Chong, A. Zhang, V. R. Hentz, J. Chang, Dupuytren's disease: history, diagnosis, and treatment, Plast. Reconstr. Surg., 120 (2007), 44e. https://doi.org/10.1016/s0363-5023(10)80134-0 doi: 10.1016/s0363-5023(10)80134-0
[6]	R. McFarlane, Dupuytren's disease: Relation to work and injury, J. Hand Surg. Am., 16 (1991), 775–779. https://doi.org/10.1016/s0363-5023(10)80134-0 doi: 10.1016/s0363-5023(10)80134-0
[7]	E. Critchley, S. Vakil, H. Hayward, V. Owen, Dupuytren's disease in epilepsy: result of prolonged administration of anticonvulsants, J. Neurol. Neurosurg. Psychiatry, 39 (1976), 498–503. https://doi.org/10.1136/jnnp.39.5.498 doi: 10.1136/jnnp.39.5.498
[8]	P. Burge, G. Hoy, P. Regan, R. Milne, Smoking, alcohol and the risk of Dupuytren's contracture, J. Bone Joint Surg. Br., 79 (1997), 206–210. https://doi.org/10.1302/0301-620x.79b2.6990 doi: 10.1302/0301-620x.79b2.6990
[9]	K. Denkler, Surgical complications associated with fascietomy for Dupuytren's disease: A 20-year review of the English literature, Eplasty, 10 (2010), e15.
[10]	H. Khan, F. Verrijp, S. Hovius, C. van Nieuwenhoven, D. D. Group, R. Selles, Recurrence of Dupuytren's contracture: a consensus-based definition, PLoS One, 12 (2017), e0164849. https://doi.org/10.1371/journal.pone.0164849 doi: 10.1371/journal.pone.0164849
[11]	R. Meek, S. McLellan, J. Crossan, Dupuytren's disease: A model for the mechanisms of fibrosis and its modulation by steroids, J. Bone Joint Surg. Br., 81 (1999), 732–738. https://doi.org/10.1302/0301-620x.81b4.9163 doi: 10.1302/0301-620x.81b4.9163
[12]	L. Verjee, J. Verhoekx, J. Chan, T. Krausgruber, V. Nicolaidou, D. Izadi, et al., Unraveling the signaling pathways promoting fibrosis in Dupuytren's disease reveals TNF as a therapeutic target, Proc. Natl. Acad. Sci. USA, 110 (2013), E928–E937. https://doi.org/10.1073/pnas.1301100110 doi: 10.1073/pnas.1301100110
[13]	S. Iqbal, M. Hayton, J. Watson, P. Szczypa, A. Bayat, First identification of resident and circulating fibrocytes in Dupuytren's disease shown to be inhibited by Serum Amyloid P and Xiapex, PLoS One, 9 (2014), e99967. https://doi.org/10.1371/journal.pone.0099967 doi: 10.1371/journal.pone.0099967
[14]	J. Neumüller, J. Menzel, H. Millesi, Prevalence of HLA-DR3 and autoantibodies to connective tissue components in Dupuytren's contracture, Clin. Immunol. Immunopathol., 71 (1994), 142–148. https://doi.org/10.1006/clin.1994.1064 doi: 10.1006/clin.1994.1064
[15]	R. Pereira, C. Black, S. Turner, J. Spencer, Antibodies to collagen types I-VI in Dupuytren's contracture, J. Hand Surg. Br., 11 (1986), 58–60. https://doi.org/10.1016/0266-7681(86)90014-8 doi: 10.1016/0266-7681(86)90014-8
[16]	J. Wilkinson, R. Davidson, T. Swingler, E. Jones, A. Corps and P. Johnston, et al., MMP-14 and MMP-2 are key metalloproteases in Dupuytren's disease fibroblast-mediated contraction, Biochim. Biophys. Acta, 1822 (2012), 897–905. https://doi.org/10.1016/j.bbadis.2012.02.001 doi: 10.1016/j.bbadis.2012.02.001
[17]	B. Costas, S. Coleman, G. Kaufman, R. James, B. Cohen, R. Gaston, Efficacy and safety of collagenase clostridium histolyticum for Dupuytren disease nodules: a randomized controlled trial, BMC Musculoskeletal Disord., 18 (2017), 374. https://doi.org/10.1186/s12891-017-1713-z doi: 10.1186/s12891-017-1713-z
[18]	G. Caravalhana, I. Auquit-Auckbur, P. Y. Miliez, Maladie de Dupuytren : état des connaissances et de la recherche en physiopathologie, Chirurgie de la Main, 30 (2011), 239–245. https://doi.org/10.1016/j.main.2011.03.002 doi: 10.1016/j.main.2011.03.002
[19]	K. Gudmunsson, R. Amgrimsson, N. Sigfússon, T. Jónsson, Increased total mortality and cancer mortality in men with Dupuytren's disease: a 15-year follow-up study, J. Clin. Epidem., 55 (2002), 5–10. https://doi.org/10.1016/s0895-4356(01)00413-9 doi: 10.1016/s0895-4356(01)00413-9
[20]	S. Karkampouna, P. Kloen, M. Obdejin, S. Riester, A. van Wijnen, M. K. de Julio, Human Dupuytren's ex vivo culture for the study of myofibroblasts and extracellular matrix interactions, J. Vis. Exp., 98 (2015), 52534. https://doi.org/10.3791/52534 doi: 10.3791/52534
[21]	S. Ud-Din, A. Bayat, Non-animal models of wound healing in cutaneous repair: in silico, in vitro, ex vivo, and in vivo models of wounds and scars in human skin, Wound Repair Regen., 25 (2017), 164–176. https://doi.org/10.1111/wrr.12513 doi: 10.1111/wrr.12513
[22]	C. Jean-Quartier, F. Jeanquartier, I. Jurisica, A. Holzinger, In silico cancer research towards 3R, BMC Cancer, 18 (2018), 408. https://doi.org/10.1186/s12885-018-4302-0 doi: 10.1186/s12885-018-4302-0
[23]	N. Menke, J. Cain, A. Reynolds, D. Chan, R. Segal, T. W. Witten, et al., An in silico approach to the analysis of acute wound healing, Wound Repair Regen., 18 (2010), 105–113. https://doi.org/10.1111/j.1524-475X.2009.00549.x doi: 10.1111/j.1524-475X.2009.00549.x
[24]	C. A. Alfonso-Rodríguez, I. Garzón, J. Garrido-Gómez, A. C. X. Oliveira, M. A. Martín-Piedra, G. Scionti, et al., Identification of histological patterns in clinically affected and unaffected palm regions in Dupuytren's disease, PLoS One, 9 (2014), e112457. https://doi.org/10.1371/journal.pone.0112457 doi: 10.1371/journal.pone.0112457
[25]	S. Rehman, Y. Xu, W. Dunn, P. Day, H. Westerhoff, R. Goodacre, et al., Dupuytren's disease metabolite analyses reveals alterations following initial short-term fibroblast culturing, Mol. BioSyst., 8 (2012), 2274–2288. https://doi.org/10.1039/c2mb25173f doi: 10.1039/c2mb25173f
[26]	J. Luck, Dupuytren's contracture: a new concept of the pathogenesis correlated with surgical management, J. Bone Joint Surg., 41 (1959), 635–664.
[27]	T. Layton, J. Hanchahal, Recent advanced in the understanding of Dupuytren's disease, F1000Res, 8 (2019), 231. https://doi.org/10.12688/f1000research.17779.1 doi: 10.12688/f1000research.17779.1
[28]	K. Moyer, D. Banducci, W. Graham, H. Ehrlich, Dupuytren's disease: physiologic changes in nodule and cord fibroblasts through aging in vitro, Plast. Reconstr. Surg., 110 (2002), 187–196. https://doi.org/10.1097/00006534-200207000-00031 doi: 10.1097/00006534-200207000-00031
[29]	L. Vi, L. Feng, R. Zhu, Y. Wu, L. Satish, B. Gan, et al., Periostin differentially induces proliferation, contraction and apoptosis of primary Dupuytren's disease and adjacent palmar fascia cells, Exp. Cell Res., 315 (2009), 3574–3586. https://doi.org/10.1016/j.yexcr.2009.07.015 doi: 10.1016/j.yexcr.2009.07.015
[30]	M. van Beuge, E. J. ten Dam, P. Werker, R. Bank, Matrix and cell phenotype differences in Dupuytren's disease, Fibrogenesis Tissue Repair, 9 (2016), 9. https://doi.org/10.1186/s13069-016-0046-0 doi: 10.1186/s13069-016-0046-0
[31]	E. Bianchi, S. Taurone, L. Bardella, A. Signore, E. Pompili and V. Sessa, et al., Involvement of pro-inflammatory cytokines and growth factors in the pathogenesis of the Dupuytren's contracture: a novel target for a possible future therapeutic strategy?, Clin. Sci., 129 (2015), 711–720. https://doi.org/10.1042/CS20150088 doi: 10.1042/CS20150088
[32]	J. Verhoekx, K. Beckett, M. Bisson, D. McGrouther, A. Grobbelaar, V. Mudera, The mechanical environment in Dupuytren's contracture determines cell contractility and associated MMP-mediated matrix remodeling, J. Orthop. Res., 31 (2013), 328–334. https://doi.org/10.1002/jor.22220 doi: 10.1002/jor.22220
[33]	J. Andrew, S. Andrew, A. Ash, B. Turner, An investigation into the role of inflammatory cells in Dupuytren's disease, J. Hand Surg. Br., 16 (1991), 267–271. https://doi.org/10.1016/0266-7681(91)90051-o doi: 10.1016/0266-7681(91)90051-o
[34]	C. Mayerl, B. D. Frari, W. Parson, G. Boeck, H. Piza-Katzer, G. Wick, et al., Characterisation of the inflammatory response in Dupuytren's disease, J. Plast. Surg. Hand Surg., 50 (2016), 171–179. https://doi.org/10.3109/2000656X.2016.1140054 doi: 10.3109/2000656X.2016.1140054
[35]	M. Tripoli, A. Cordova, F. Moschella, Updates on the role of molecular factors and fibroblasts in the pathogenesis of Dupuytren's disease, J. Cell Commun Signal., 10 (2016), 315–330. https://doi.org/10.1007/s12079-016-0331-0 doi: 10.1007/s12079-016-0331-0
[36]	T. Wynn, T. Ramalingam, Mechanisms of fibrosis: therapeutic translation for fibrotic disease, Nat. Med., 18 (2012), 1028–1040. https://doi.org/https://doi.org/10.1038/nm.2807
[37]	L. Verjee, K. Midwood, D. Davidson, D. Essex, A. Sandison, J. Nanchahal, Myofibroblast distribution in Dupuytren's cords: correlation with digital contracture, J. Hand Surg. Am., 34 (2009), 1785–1794. https://doi.org/10.1016/j.jhsa.2009.08.005 doi: 10.1016/j.jhsa.2009.08.005
[38]	B. Behm, P. Babilas, M. Landthaler, S. Schreml, Cytokines, chemokines and growth factors in wound healing, J. Eur. Acad. Dermatol Venerol, 26 (2012), 812–820. https://doi.org/10.1111/j.1468-3083.2011.04415.x doi: 10.1111/j.1468-3083.2011.04415.x
[39]	G. Landskron, M. D. L. Fuente, P. Thuwajit, C. Tuwajit, M. Hermoso, Chronic inflammation and cytokines in the tumour microenvironment, J. Immunol. Res., 2014 (2014), 149185. https://doi.org/10.1155/2014/149185 doi: 10.1155/2014/149185
[40]	K. Baird, J. Crossan, S. Ralston, Abnormal growth factor and cytokine expression in Dupuytren's contracture, J. Clin. Pathol., 46 (1993), 425–428. https://doi.org/10.1136/jcp.46.5.425 doi: 10.1136/jcp.46.5.425
[41]	K. Augoff, J. Kula, J. Gosk, R. Rutowski, Epidermal growth factor in Dupuytren's disease, Plast Reconstr. Surg., 115 (2005), 128–133. https://doi.org/10.1097/01.PRS.0000146038.61595.4A doi: 10.1097/01.PRS.0000146038.61595.4A
[42]	K. Augoff, R. Tabola, J. Kula, J. Gosk, R. Rutowski, Epidermal growth factor receptor (EGF-R) in Dupuytren's disease, J. Hand Surg. Br., 30 (2005), 570–573. https://doi.org/10.1016/j.jhsb.2005.06.008 doi: 10.1016/j.jhsb.2005.06.008
[43]	S. Sigismund, D. Avanzato, L. Lanzetti, Emerging functions of the EGFR in cancer, Mol. Oncol., 12 (2018), 3–20. https://doi.org/10.1002/1878-0261.12155 doi: 10.1002/1878-0261.12155
[44]	N. Jain, J. Moeller, V. Vogel, Mechanobiology of macrophages: how physical factors coregulate macrophage plasticity and phagocytosis, Ann. Rev. Biomed. Eng., 21 (2019), 267–297. https://doi.org/10.1146/annurev-bioeng-062117-121224 doi: 10.1146/annurev-bioeng-062117-121224
[45]	J. Lim, B. Choi, S. Lee, Y. Jang, J. Choi, Y. Kim, Regulation of wound healing by granulocyte-macrophage colony-stimulating factor after vocal fold injury, PLOS ONE, 8 (2013), e54256. https://doi.org/10.1371/journal.pone.0054256 doi: 10.1371/journal.pone.0054256
[46]	R. McFarlane, Patterns of the diseased fascia in the fingers in Dupuytren's contracture, Plast. Reconstr. Surg., 54 (1974), 31–44. https://doi.org/
[47]	D. Schwartz, Dupuytren's diathesis revisited: evaluation of prognostic indicators for risk of disease recurrence, J. Hand Ther., 20 (2007), 280–281. https://doi.org/https://doi.org/10.1197/j.jht.2007.04.014 doi: 10.1197/j.jht.2007.04.014
[48]	C. Eaton, Evidence-based medicine: Dupuytren contracture, Plast Reconstr. Surg., 133 (2014), 1239. https://doi.org/10.1097/PRS.0000000000000089 doi: 10.1097/PRS.0000000000000089
[49]	F. Syed, A. Thomas, S. S. ad V. Kolluru, S. Hart, A. Bayat, In vitro study of novel collagenase (XIAFLEX) on Dupuytren's disease fibroblasts displays unique drug related properties, PLOS ONE, 7 (2012), e31430. https://doi.org/10.1371/journal.pone.0031430 doi: 10.1371/journal.pone.0031430
[50]	A. Mantovani, M. Locati, Tumor-associated macrophages as a paradigm of macrophage plasticity, diversity, and polarization: lessons and open questions., Arterioscler. Thromb. Vasc. Biol., 33 (2013), 1478–1483. https://doi.org/10.1161/ATVBAHA.113.300168 doi: 10.1161/ATVBAHA.113.300168
[51]	C. Ferrante, S. Leibovich, Regulation of macrophage polarisation and wound healing, Adv. Wound Care, 1 (2012), 10–16. https://doi.org/10.1089/wound.2011.0307 doi: 10.1089/wound.2011.0307
[52]	S. Yotsukura, H. Mamitsuka, Evaluation of serum-based cancer biomarkers: a brief review from a clinical and computational viewpoint, Critical Reviews in Oncology/Hematology, 93 (2015), 103–115. https://doi.org/10.1016/j.critrevonc.2014.10.002 doi: 10.1016/j.critrevonc.2014.10.002
[53]	A. Bayat, D. McGrouther, Management of Dupuytren's disease - clear advice for an elusive condition, Ann. R. Coll. Surg. Engl., 88 (2006), 3–8. https://doi.org/10.1308/003588406X83104 doi: 10.1308/003588406X83104
[54]	G. Dolmans, P. Werker, H. Hennies, D. Furniss, E. Festen, L. Franke, et al., Wnt signaling and Dupuytren's disease, N. Engl. J. Med, 365 (2011), 307–317. https://doi.org/10.1056/NEJMoa1101029 doi: 10.1056/NEJMoa1101029
[55]	Y. Kim, J. Wallace, F. Li, M. Ostrowski, A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumour: a mathematical model and experiments, J. Math. Biol., 61 (2010), 401–421. https://doi.org/10.1007/s00285-009-0307-2 doi: 10.1007/s00285-009-0307-2
[56]	Y. Kim, A. Friedman, Interaction of tumour with its micro-environment: a mathematical model, Bull. Math. Biol., 72 (2010), 1029–1068. https://doi.org/10.1007/s11538-009-9481-z doi: 10.1007/s11538-009-9481-z
[57]	A. Friedman, Y. Kim, Tumour cell proliferation and migration under the influence of their microenvironment, Math. Biosci. Eng., 8 (2011), 371–383. https://doi.org/10.3934/mbe.2011.8.371 doi: 10.3934/mbe.2011.8.371
[58]	K. Norton, K. Jin, A. Popel, Modeling triple-negative breast cancer heterogeneity: effects of stromal macrophages, fibroblasts and tumour vasculature, J. Theor. Biol., 452 (2018), 56–68. https://doi.org/10.1016/j.jtbi.2018.05.003 doi: 10.1016/j.jtbi.2018.05.003
[59]	N. Picco, E. Sahai, P. Maini, A. Anderson, Integrating models to quantify environment-mediated drug resistance, Cancer Res., 77 (2017), 5409–5418. https://doi.org/10.1158/0008-5472.CAN-17-0835 doi: 10.1158/0008-5472.CAN-17-0835
[60]	R. Wadlow, B. Wittner, S. Finley, H. Bergquist, R. Upadhyay and S. Finn, et al., Systems-level modelling of cancer-fibroblast interaction, PLoS One, 4 (2009), e6888. https://doi.org/10.1371/journal.pone.0006888 doi: 10.1371/journal.pone.0006888
[61]	A. B. Tepole, E. Kuhl, Computational modelling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing, Comput. Methods Biomech. Biomed. Engin., 19 (2016), 13–30. https://doi.org/10.1080/10255842.2014.980821 doi: 10.1080/10255842.2014.980821
[62]	R. Cooper, R. Segal, R. Diegelmann, A. Reynolds, Modelling the effects of systemic mediators on the inflammatory phase of wound healing, J. Theor. Biol., 367 (2015), 86–99. https://doi.org/10.1016/j.jtbi.2014.11.008 doi: 10.1016/j.jtbi.2014.11.008
[63]	J. Dallon, J. Sherratt, P. Maini, Mathematical modelling of extracellular matrix dynamics using discrete cells: fiber orientation and tissue regeneration, J. Theor. Biol., 199 (1999), 449–471. https://doi.org/10.1006/jtbi.1999.0971 doi: 10.1006/jtbi.1999.0971
[64]	J. Flegg, S. Menon, P. Maini, D. McElwain, On the mathematical modelling of wound healing angiogenesis in skin as a reaction-transport process, Front. Physiol., 6 (2015), 262. https://doi.org/https://doi.org/10.3389/fphys.2015.00262
[65]	S. Jorgensen, J. Sanders, Mathematical models of wound healing and closure: a comprehensive review, Med. Biol. Eng. Comput., 54 (2016), 1297–1316. https://doi.org/10.1007/s11517-015-1435-z doi: 10.1007/s11517-015-1435-z
[66]	D. Koppenol, F. Vermolen, F. Niessen, P. van Zuijlen, K. Vuik, A biomechanical mathematical model for the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds, Biomech. Model. Mechanobiol., 16 (2016), 345–361. https://doi.org/10.1007/s10237-016-0821-2 doi: 10.1007/s10237-016-0821-2
[67]	S. McDougall, J. Dallon, J. Sherratt, P. Maini, Fibroblast migration and collagen deposition during dermal wound healing: mathematical modelling and clinical implications, Phil. Trans. R. Soc. A, 364 (2006), 1385–1405. https://doi.org/10.1098/rsta.2006.1773 doi: 10.1098/rsta.2006.1773
[68]	L. Olsen, J. Sherratt, P. Maini, A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile, J. Theor. Biol., 177 (1995), 113–128. https://doi.org/10.1006/jtbi.1995.0230 doi: 10.1006/jtbi.1995.0230
[69]	L. Olsen, J. Sherratt, P. Maini, A mathematical model for fibro-proliferative wound healing disorders, Bull. Math. Biol., 58 (1996), 787–808. https://doi.org/10.1007/BF02459482 doi: 10.1007/BF02459482
[70]	R. Tranquillo, J. Murray, Continuum model for fibroblast-driven wound contraction: inflammation mediation, J. Theor. Biol., 158 (1992), 135–172. https://doi.org/10.1016/s0022-5193(05)80715-5 doi: 10.1016/s0022-5193(05)80715-5
[71]	E. Valero, J. Garcia-Aznar, A. Menzel, M. Gomez-Benito, Challenges in the modelling of wound healing mechanisms in soft biological tissues, Ann. Biomed. Eng., 43 (2014), 1654–1665. https://doi.org/10.1007/s10439-014-1200-8 doi: 10.1007/s10439-014-1200-8
[72]	Y. Wang, C. Guerrero‐Juarez, Y. Qiu, H. Du, W. Chen, S. Figueroa, et al., A multiscale hybrid mathematical model of epidermal-dermal interactions during skin wound healing, Exp. Dermatol., 28 (2019), 493–502. https://doi.org/10.1111/exd.13909 doi: 10.1111/exd.13909
[73]	H. Waugh, J. Sherratt, Modelling the effects of treating diabetic wounds with engineered skin substitutes, Wound Rep. Reg., 15 (2007), 556–565. https://doi.org/10.1111/j.1524-475X.2007.00270.x doi: 10.1111/j.1524-475X.2007.00270.x
[74]	C. Xue, A. Friedman, C. Sen, A mathematical mode of ischemic cutaneous wounds, Proc. Natl. Acad. Sci. USA, 106 (2009), 16782–16787. https://doi.org/10.1073/pnas.0909115106 doi: 10.1073/pnas.0909115106
[75]	C. Ziraldo, Q. Mi, G. An, Y. Vodovotz, Computational modeling of inflammation and wound healing, Adv. wound care, 2 (2013), 527–537. https://doi.org/10.1089/wound.2012.0416 doi: 10.1089/wound.2012.0416
[76]	F. Balkwill, M. Capasso, T. Hagemann, The tumour microenvironment at a glance, J. Cell Sci., 125 (2012), 5591–5596. https://doi.org/10.1242/jcs.116392 doi: 10.1242/jcs.116392
[77]	J. Junker, E. Caterson, E. Eriksson, The microenvironment of wound healing, J. Craniofac. Surg., 24 (2013), 12–16. https://doi.org/10.1097/SCS.0b013e31827104fb doi: 10.1097/SCS.0b013e31827104fb
[78]	K. Chen, X. Hu, S. Blemker, J. Holmes, Multiscale computational model of Achilles tendon wound healing: Untangling the effects of repair and loading, PLoS Comput. Biol., 14 (2018), e1006652. https://doi.org/https://doi.org/10.1371/journal.pcbi.1006652
[79]	R. Shuttleworth, D. Trucu, Multiscale modelling of fibres dynamics and cell adhesion within boundary cancer invasion, Bull. Math. Biol., 81 (2019), 2176–2219. https://doi.org/10.1007/s11538-019-00598-w doi: 10.1007/s11538-019-00598-w
[80]	J. Jansen, E. Gaffney, J. Wagg, M. Coles, Combining mathematical models with experimentation to drive novel mechanistic insights into macrophage function, Front. Immunol., 10 (2019), 1283. https://doi.org/10.3389/fimmu.2019.01283 doi: 10.3389/fimmu.2019.01283
[81]	H. Warsinske, A. Wheaton, K. Kim, J. Linderman, B. Moore, D. Kirschner, Computational modeling predicts simultaneous targeting of fibroblasts and epithelial cells is necessary for treatment of pulmonary fibrosis, Front. Pharmacol., 7 (2016), 183. https://doi.org/10.3389/fphar.2016.00183 doi: 10.3389/fphar.2016.00183
[82]	A. Oppelt, D. Kaschek, S. Huppelschoten, R. Sison-Young, F. Zhang and M. Buck-Wiese, et al., Model-based identification of TNF $\alpha$ -induced IKK $\beta$ -mediated and I $\kappa$ B $\alpha$ -mediated regulation of NF $\kappa$ B signal transduction as a tool to quantify the impact of drug-induced liver injury compounds, NPJ Syst. Biol. Appl., 4 (2018), 23. https://doi.org/10.1038/s41540-018-0058-z doi: 10.1038/s41540-018-0058-z
[83]	J. Moermans, Recurrences after surgery for Dupuytren's disease, Eur. J. Plast. Surg., 20 (1997), 240–245. https://doi.org/10.1007/BF01159481 doi: 10.1007/BF01159481
[84]	S. Rehman, R. Goodacre, P. Day, A. Bayat, H. Westerhoff, Dupuytren's: a systems biology disease, Arthritis Res. Ther., 13 (2011), 238. https://doi.org/10.1186/ar3438 doi: 10.1186/ar3438
[85]	S. Rehman, P. Day, A. Bayat, H. Westerhoff, Understanding Dupuytren's disease using systems biology: a move away from reductionism, Front. Physiol., 3 (2012), 316. https://doi.org/10.3389/fphys.2012.00316 doi: 10.3389/fphys.2012.00316
[86]	M. van Beuge, E. ten Dam, P. Werker, R. Bank, Wnt pathway in Dupuytren disease: connecting profibrotic signals, Transl. Res., 166 (2015), 762–771. https://doi.org/10.1016/j.trsl.2015.09.006 doi: 10.1016/j.trsl.2015.09.006
[87]	W. Du, O. Elemento, Cancer systems biology: embracing complexity to develop better anticancer therapeutic strategies, Oncogene, 34 (2015), 3215–3225. https://doi.org/10.1038/onc.2014.291 doi: 10.1038/onc.2014.291
[88]	I. Korsunsky, K. McGovern, T. LaGatta, L. Loohuis, T. Grosso-Applewhite and N. Griffeth, et al., Systems biology of cancer: a challenging expedition for clinical and quantitative biologists, Front. Bioeng. Biotechnol., 2 (2014), 27. https://doi.org/https://doi.org/10.3389/fbioe.2014.00027
[89]	M. Martins-Green, Y. Vodovotz, P. Liu, Systems biology applied to wound healing, Wound Repair Regen., 18 (2010), 1–2. https://doi.org/10.1111/j.1524-475X.2009.00567.x doi: 10.1111/j.1524-475X.2009.00567.x
[90]	Y. Vodovotz, Translational systems biology of inflammation and healing, Wound Repair Regen., 18 (2010), 3–7. https://doi.org/10.1111/j.1524-475X.2009.00566.x doi: 10.1111/j.1524-475X.2009.00566.x
[91]	H. Baltzer, P. Binhammer, Cost-effectiveness in the management of Dupuytren's contracture, Bone Joint J., 95-B (2013), 1094–1100. https://doi.org/10.1302/0301-620X.95B8.31822 doi: 10.1302/0301-620X.95B8.31822
[92]	M. Brazzelii, M. Cruickshank, E. Tassie, P. McNamee, C. Robertson, A. Elders, et al., Collagenase clostridium histolycum for the treatment of Dupuytren's contracture: a systematic review and economic evaluation, Health Technol. Assess., 19 (2015), 90. https://doi.org/10.3310/hta19900 doi: 10.3310/hta19900
[93]	N. Chen, M. Shauver, K. Chung, Cost-effectiveness of open partial fasciectomy, needle aponeurotomy, and collagenase injection for Dupuytren contracture, J. Hand Surg. Am., 36 (2011), 1826–1834. https://doi.org/10.1016/j.jhsa.2011.08.004 doi: 10.1016/j.jhsa.2011.08.004
[94]	M. Dritsaki, O. Rivero-Arias, A. Gray, C. Ball, J. Nanchahal, What do we know about managing Dupuytren's disease cost-effectively?, BMC Musculoskeletal Disord., 19 (2018), 34. https://doi.org/10.1186/s12891-018-1949-2 doi: 10.1186/s12891-018-1949-2
[95]	C. Sau, M. Bounthavong, J. Tran, R. Wilson, Cost-utility analysis of collagenase clostridium histolycum, limited fasciectomy, and percutaneous needle fasciotomy in Dupuytren's contracture, Value Health, 14 (2011), A128. https://doi.org/10.1016/j.jval.2011.02.714 doi: 10.1016/j.jval.2011.02.714
[96]	M. Khashan, P. Smitham, W. Khan, N. Goddard, Dupuytren's disease: review of the current literature, Open Orthop. J., 5 (2011), 283–288. https://doi.org/10.2174/1874325001105010283 doi: 10.2174/1874325001105010283
[97]	I. Stura, D. Gabriele, C. Guiot, A simple PSA-based computational approach predicts the timing of cancer relapse in prostatectomised patients, Cancer Res., 76 (2016), 4941–4947. https://doi.org/10.1158/0008-5472.CAN-16-0460 doi: 10.1158/0008-5472.CAN-16-0460
[98]	S. Hori, S. Gambhir, Mathematical model identified blood biomarker-based early cancer detection strategies and limitations, Sci. Transl. Med., 3 (2011), 109ra116. https://doi.org/10.1126/scitranslmed.3003110 doi: 10.1126/scitranslmed.3003110
[99]	R. Eftimie, E. Hassanein, Improving cancer detection through combinations of cancer and immune biomarkers: a modelling approach, J. Transl. Med., 16 (2018), 73. https://doi.org/10.1186/s12967-018-1432-8 doi: 10.1186/s12967-018-1432-8
[100]	M. McKenna, J. Weis, V. Quaranta, T. Yankeelov, Leveraging mathematical modeling to quantify pharmacokinetic and pharmacodynamic pathways: equivalent dose metric, Front. Physiol., 10 (2019), 616. https://doi.org/10.3389/fphys.2019.00616 doi: 10.3389/fphys.2019.00616

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