1. Overview
The transition probabilities among health states of EC were estimated based on established Markov models for the natural history of EC. It is known that the natural history model can predict the incidence of EC based on the EC mortality, all-cause mortality, the prevalence of each pathological stage of EC, and transition probability. Similarly, as the above incidence/mortality/prevalence was available, we could estimate transition probability.
2. Study design
Based on the project of early diagnosis and treatment of EC which began in 2005 and is detailed described in our previous paper[11], this study through cluster sampling selected Hejian Town as the screening site in Linzhou County, Henan Province, and the population aged 40-69 in this town as the target screening population, among which those without contraindications for endoscopy were examined by endoscopic iodine staining, and those with positive results were examined by pathology, and their pathological results, age, gender, and other basic information were recorded in detail. For precancerous lesions and esophageal cancer diagnosed by screening, the treatment principals were as follows: (1) for severe dysplasia, carcinoma in situ and intramucosal carcinoma, endoscopic mucosal resection (EMR) or argon plasma coagulation (APC)was recommended; in the first year after treatment, they should be followed up by endoscopy; (2) for submucosal carcinoma (T1N0M0), esophagectomy was recommended; (3) for invasive carcinoma, common treatment modalities were chosen depending on disease severity and could include surgery, radiotherapy, or chemotherapy, or a combination. At the same time, the incidence of EC in each age group(every 10 years)from 40 to 69 years old in Linzhou County in 2005 and the statistical monitoring data of 321,737 deaths in 2004-2006 were obtained from Linzhou County Cancer Registry.
3. Markov models
3.1 Natural history of EC
We developed an 8-state Markov model simulating the natural history of esophageal carcinogenesis: normal (EC-free), mild dysplasia (mD), moderate dysplasia (MD), severe dysplasia/carcinoma in situ (SD/CIS), intramucosal carcinoma (IC), submucosal carcinoma (T1N0M0) (SC), invasive carcinoma (INC), and death[12,13]. The state-transition Markov model based on the natural history of EC has been described in the literature and also showed in Figure 1 [14]. At the start of the model, a hypothetical cohort is distributed in these health states except the “death” state. During each Markov cycle (1 year), a person may remain in the same health state, progress to another state or regress to lesser stages, and die from other reasons or EC. The health state of EC in the next year relied only on the health state of this year and the corresponding transition probabilities [15]. Consider that in the real world, the eligible screening age is 40-69 years and the average life expectancy is 73 years[16], so in the Markov model, we assume that 100,000 participants enter the model at age 40 years and are followed up until age 70 years. TreeAge Pro 2009 Suite by TreeAge Software Inc, was used for all analysis.
3.2 Parameters used in the Markov model
To establish the Markov model of natural history for EC, the following parameters were needed: initial probability, transition probability, and death probability. Initial probability refers to the prevalence of each health state for cohort members at the start of the modeling [17]. Transition probability denotes the likelihood of progression or regression from one health state to another in a Markov cycle. Death probability represents the probability that the population dies from EC or other causes in each model cycle.
3.3 Parameter sources
3.3.1 Initial probability
Initial probabilities were calculated in terms of Linzhou County’s screening results in the project called “Early Detection and Early Treatment of EC in Demonstration Centers in China” (EDETEC) during the years 2005-2008.
The project EDETEC was launched by the Chinese Central Government in 2005, aimed at increasing the early detection and treatment rate, the five-year survival rate of EC, and so forth [18]. Until 2008, 8267 participants aged 40-69 years have received endoscopic and nearly 3000 performed the pathological examination. Most of the esophageal cancer was Squamous carcinoma while only 5% of them were Barrett's esophagus. The initial distribution probabilities of 7 Markov states except death (from “normal” to “INC”) were respectively 88.95%, 8.2%, 1.8%, 0.9%, 0.08%, 0.05%, and 0.02% in the 40-44 year age group [14].
3.3.2 Death probability
The previous study has demonstrated that persons with SD/CIS or lesser may not die from EC; that IC or SC cases may die from all causes including EC; INC patients were assumed to mainly die from EC [14]. Therefore, in the natural-history model, the corresponding death probabilities for the three kinds of the population above were converted from non-esophageal-cancer mortality, all-cause mortality, and case fatality rate of EC, respectively. And they all were obtained from the published data, which were counted according to Linzhou County Cancer Registry during 2004-2006, and the results of our prospective cohort study based on the EC chemoprevention trial of selenomethionine and celecoxib in “Early Detection of EC” (EDEC) program [14,19]. Table 1 demonstrates the age-specific death probabilities of different Markov states.
Table 1 Death probabilities for each health state of EC*
Age
|
Normal to SD/CIS
|
IC/SC
|
INC
|
40-
|
0.002270
|
0.002438
|
0.581700
|
45-
|
0.003073
|
0.003383
|
0.581700
|
50-
|
0.007054
|
0.007967
|
0.581700
|
55-
|
0.017061
|
0.019559
|
0.581700
|
60-
|
0.019744
|
0.021985
|
0.581700
|
65-
|
0.024105
|
0.027370
|
0.581700
|
*: death probabilities were obtained from published literature[13]. SD/CIS: severe dysplasia/ carcinoma in situ; IC/SC: intramucosal carcinoma/submucosal carcinoma; INC: invasive carcinoma.
3.3.3 transition probability
The transition probabilities among health states were estimated using the approach taken by others [20-23]. Firstly, transition probability ranges were determined from published studies [6,7,24-30], cohort data in the chemoprevention trial of EDEC program mentioned previously [19], and experts’ opinions serving as an initial data set. Due to the limited sample size, the transition probabilities were significantly different among published literature, and even some parameters for progression and regression of the disease were unavailable. Thus, in the second step, the transition probabilities were hierarchically calibrated to make the modeled age-specific EC incidence curves fit the empirical ones observed in real-world settings. In the third step, we further adjusted the transition probabilities to obtain a distribution of each pathological stage for EC similar to that of surveillance data. Observed data from Linzhou County Cancer Registry during 2004-2006 and the screening results in the above EDETEC [18] project during 2005-2008 were used for the model calibration.
3.4 Model validation
Incidence and prevalence of EC were highly associated with the transition probabilities among its precancerous lesions. Internal validation of our results was performed by comparing the model predictions with observed epidemiological data from Linzhou County Cancer Registry during 2004-2006 and the screening results in the above EDETEC project during 2005-2008. Validation outcomes included the age-specific incidence of EC and the distribution of pathological stages of EC.