Development of an Empirically Calibrated Model of Gastric Cancer in Two High-Risk Countries

Gastric cancer is the second leading cause of cancer-related deaths worldwide, responsible for an estimated 700,000 deaths each year (1). With its high case fatality rate, poor prognosis, and limited treatment options, finding effective strategies for primary or secondary prevention of gastric cancer is a public health priority. Although epidemiologic studies have established the relationship between Helicobacter pylori and gastric cancer and promising results that H. pylori treatment can reduce cancer incidence among individuals without preexisting precancerous lesions, there is no consensus on whether screening for H. pylori should be conducted. From the perspective of developing countries, such as China, where more than 40% of the world's gastric cancer cases occur, implementation of a H. pylori screening program may offer a feasible option to reduce gastric cancer mortality.

Ideally, the strongest evidence on the effectiveness of H. pylori treatment to prevent gastric cancer would come from randomized controlled trials that use gastric cancer incidence or mortality as the primary outcome. Several clinical trials are under way (2) and results from the first of such studies suggest that after 7.5 years, H. pylori treatment reduces cancer incidence among individuals without atrophy, intestinal metaplasia, or dysplasia at time of treatment (3).

To estimate the public health benefits of a H. pylori screening program, several factors must be considered: the underlying natural history of H. pylori-associated disease; the heterogeneity of risk conferred by gender, age, and country; the effectiveness of H. pylori treatment in interrupting the pathway to cancer; and the feasibility of implementing a secondary prevention program at the population level. No clinical trial or single longitudinal cohort study will be able to consider all of these factors and assess all possible strategies in all populations. Integrating the best available biological, epidemiologic, and economic data, mathematical simulation models in a decision-analytic framework can assist in decision-making by estimating the avertable burden of disease expected with different strategies, identifying factors most likely to influence outcomes, and providing qualitative insight into the potential cost-effectiveness of different strategies (4).

We used available data from cross-sectional surveys, cohort studies, and surveillance of cancer cases to develop a natural history model of H. pylori-associated gastric cancer and empirically calibrated this model to epidemiologic data in China and Columbia. We sought to identify a series of good-fitting parameter sets that provided model predictions consistent with epidemiologic data in the two countries and to use the model to assess the health and economic outcomes associated with primary prevention strategies. These analyses, conducted with multiple, equally good-fitting parameter sets, directly reflect the influence of parameter uncertainty, within the constraints of the model structure, about the natural history of gastric cancer on the policy results.

We chose to parameterize and calibrate the model to China and Colombia for the following reasons: (a) gastric cancer is a leading cause of cancer-related deaths (1), (b) the vast majority are infected with H. pylori according to serology-based point prevalence studies (5-7), and (c) data from prospective cohort studies on the development of gastric cancer are available (8-11). Although both countries have high gastric cancer rates, they differ in prevalence rates of H. pylori infection (6, 7) and smoking (12, 13). The model development process included definition of model structure, specification of model parameters and assumptions, and estimation of parameters by calibrating the model to epidemiologic data. Because progression rates of the underlying biological process are unavailable, we relied on calibration, the process of inferring unobservable parameter values by comparing how well model output compares with empirical data, to inform these parameters. We used a likelihood-based calibration approach to identify a series of good-fitting parameter sets that provided model predictions that were consistent with descriptive epidemiologic data. Using this empirically calibrated model, we then estimated a range of likely outcomes associated with H. pylori screening.

We developed a Markov state transition simulation model of gastric carcinogenesis, in which the natural history of noncardia intestinal type gastric adenocarcinomas is represented as a sequence of monthly transitions among health states (Fig. 1). In this cohort model, health states are stratified by H. pylori status and include normal gastric mucosa, chronic nonatrophic gastritis, gastric atrophy, intestinal metaplasia, dysplasia, gastric cancer, and death. At the start of the simulation, a cohort of 20-year-old individuals enters the model and is distributed among H. pylori+ and H. pylori− precancerous health states. Each month, all individuals residing in one state have a probability to transition to another state. For example, individuals with intestinal metaplasia can regress to atrophy, progress to dysplasia, or remain with intestinal metaplasia. Individuals who develop cancer face disease-specific mortality rates, and all individuals face an age-dependent risk of dying from other causes. Individuals are followed throughout their lifetime and, to allow disease progression to vary by sex, the model is run separately for men and women. We conducted analyses for each country separately.

A number of assumptions were necessary for the model and we informed these in three ways. First, we established initial ranges for most model parameters by conducting a literature review on the precancerous process of gastric cancer for each country and selecting the highest and lowest values among all available studies (7-11, 14-17). Second, we conducted a series of sensitivity analyses to identify influential parameters, followed by calibration exercises in which we manipulated one uncertain variable at a time and visually examined the influence of that parameter on model output approximation to empirical data. This iterative process is described in the online supplemental data. Third, we then convened an expert panel to review these analyses and to elicit opinion on reasonable model assumptions in which data were lacking. As a result of this process, the following assumptions were made:

• H. pylori epidemiology. Individuals acquire H. pylori infection during childhood and, unless treated with antibiotics, remain infected (18). New infections and reinfection in adulthood are rare (19) and were not allowed in our model. All infected individuals develop gastritis and face a higher risk of developing atrophy (20).

• Gastric cancer epidemiology. Gastric carcinogenesis is a multifactorial and multistep process for noncardia intestinal type gastric adenocarcinomas (21). Disease progression among precancerous lesions varies by sex and country, with possible regression to less advanced lesions. The risk of progressing from dysplasia to presymptomatic cancer increases with age and varies by sex. In the absence of other causes of death, all cancers become symptomatic within 2 years (median time = 4 months). Among all gastric cancers, 95% are adenocarcinomas; 95% of adenocarcinomas are distal to the cardia; and 40%, 50%, and 60% of noncardia adenocarcinomas are intestinal type for individuals younger than 44 years, between 45 and 65 years, and older than 65 years, respectively (22).

To establish plausible ranges for each transition probability in the model, we conducted a comprehensive literature search that included prospective cohort studies on the progression of precancerous lesions and the association between H. pylori infection and gastric cancer (Table 1; refs. 7-11, 14-18, 20, 23-26). For comparability across studies, we defined atrophy as severe atrophy and, for intestinal metaplasia and dysplasia, collapsed subtypes into one broad category. The initial distribution among H. pylori+ and H. pylori− health states was based on H. pylori seroprevalence, age-specific prevalence of precancerous lesions, and the proportion of gastric cancers that are H. pylori+.

In China, 70% of the population in Linqu are infected with H. pylori (6). We estimated age-specific prevalence of precancerous health states at age 20 years by extrapolating cross-sectional trend data on individuals between the ages of 35 and 65 years (9). A meta-analysis of 12 case-control studies nested in prospective cohorts in multiple countries, including the United States, the United Kingdom, Japan, and China, found that 91.5% of all gastric cancers were H. pylori+ among controls with a H. pylori prevalence of 64.6% using blood samples collected more than 10 years before cancer diagnosis and case-control sets matched on sex, age, and date of sampling (26). Based on this epidemiologic evidence, we assumed that 92% of gastric cancers would be H. pylori+ in Linqu, where 70% are H. pylori infected. We then calculated the distribution among the precancerous health states for a cohort of 100% H. pylori+ individuals by assuming that 92% of dysplasia, intestinal metaplasia, and atrophy prevalence was attributable to those who were infected with H. pylori. Similar calculations were conducted to estimate the distribution for a cohort of H. pylori− individuals. In accordance with having a higher risk of gastric cancer, H. pylori+ individuals had a higher percentage of advanced precancerous lesions compared with H. pylori− individuals. We assumed that, at age 20 years, the prevalence among the health states was similar for both men and women given their similar rates of H. pylori infection during childhood.

For Nariño, Colombia, no published estimate studies were available to determine the proportion of gastric cancers that are H. pylori+ in a population with a H. pylori prevalence greater than 90%. Therefore, we estimated the percentage by calculating the relative risk of gastric cancer given H. pylori infection in China (equal to 4.5), made the simplifying assumption that the relative risk was generalizable given that epidemiologic studies suggest relative risk estimates for risk factors with well-defined exposure indicators are similar across populations ([27]), and estimated that 98.9% of gastric cancers in Colombia were H. pylori+. We then calculated the initial distribution among H. pylori+ and H. pylori− precancerous health states using prevalence estimates for H. pylori and precancerous lesions at age 20 years (7, 11). Table 1 provides a summary of the initial distributions for each country. Further details can be found in the online supplemental data.

We established calibration targets using epidemiologic data that included age-specific prevalence of gastritis, age-specific prevalence of atrophy, age-specific prevalence of intestinal metaplasia, age-specific prevalence of dysplasia, and age-specific symptomatic gastric cancer incidence (Table 2; refs. 9, 11, 28). The specific number of calibration targets differed between China and Columbia as a result of differences in the number of age groups for which data on prevalence of precancerous lesions were available. For each target, we determined a 95% confidence interval using data arising from population-based studies and cancer registries.

1. Cross-sectional studies on prevalence of precancerous lesions. In each country, a cohort of individuals representing the population of a high-risk region was followed for 4.5 years (Linqu county, Shandong province, China) or 5.1 years (Nariño, Colombia; refs. 8-11). At baseline, seven and four gastric biopsies per individual were taken in China and Colombia, respectively, to determine the presence of gastritis, atrophy, intestinal metaplasia, and dysplasia, and provided age-specific prevalence of precancerous lesions for the population. Given the dependence of detection sensitivity on the number of biopsies taken and the variation in the number of biopsies between countries, we adjusted the prevalence of precancerous lesions in Colombia using data from Linqu that reported prevalence estimates with both seven and four biopsies (9, 15). We estimated that with seven biopsies, the prevalence of intestinal metaplasia and dysplasia would be 10% and 33%, respectively, higher in Colombia. This estimate was similar to the 5% to 29% lower prevalence reported in a diagnostic yield comparison study between three to five biopsies and a seven-biopsy protocol (29).

2. Cancer databases on gastric cancer incidence. For each country, Cancer Incidence in Five Continents Volume VIII provided age-specific gastric cancer rates for 5-year age groups between the ages of 20 and 84 years (28). For China, data from the Jiashan cancer registry were used given that, of the seven available cancer registries, the region was most similar to Linqu county in terms of cumulative gastric cancer rates for males and females (29.3 per 1,000 versus 22.0 per 1,000), H. pylori seroprevalence (62.5% versus 52.6%), and percentage of population living in rural areas (90% versus 80%; refs. 28, 30).

Because we cannot directly estimate the transition probabilities among the health states, we use calibration to identify parameter sets of transition probabilities that produce model output that are consistent with observed data on the prevalence of precancerous lesions and cancer incidence. We identify multiple parameter sets that are all consistent with the epidemiologic data and refer to ranges of values within the identified sets as parameter uncertainty throughout the article.

For this process, we allowed all disease progression and regression parameters between gastritis and presymptomatic cancer to vary simultaneously; all other parameters were held constant. We conducted a multidimensional search of the parameter space defined by the plausible ranges of the model parameters (as described above) using a grid search and identified 65,000 unique parameter sets. We then simulated the model for each parameter set. Model outcomes associated with each parameter set (i.e., combination of parameter values) were compared with empirically based epidemiologic targets on the age-specific prevalence of precancerous lesions and incidence of gastric cancer. Using data from cross-sectional prevalence studies and cancer registries, we defined a total of 36 and 28 calibration targets for China (24 precancerous, 12 cancer) and Colombia (16 precancerous, 12 cancer), respectively. We specified likelihood functions for each target, assuming each follows an independent binomial distribution.

For each parameter set, we computed a goodness-of-fit score equal to −2 × the sum of the log-likelihood scores for all of the calibration targets. We defined the best-fitting parameter set as the set with the lowest goodness-of-fit score. We then identified a subset of good-fitting parameter sets, defined as those whose fit was statistically indistinguishable from the goodness-of-fit score of the best-fitting set (α = 0.05), using a likelihood ratio test and assuming that the distribution of the goodness-of-fit scores approximate a χ² distribution (degrees of freedom-number of calibration targets). This process was repeated for each subgroup. Because the minimum and the maximum values included in the grid search for all unknown parameters were similar across all four subgroups, we compared the distributions of good-fitting values for each parameter to gain qualitative insight into potential disease progression differences by subgroup.

Using the empirically calibrated model, we then assessed the implications of our calibration approach in terms of the uncertainty in modeled outcomes by examining the range of model-projected cancer incidence reduction that could be expected using 50 randomly selected good-fitting parameter sets to simulate the reduction in lifetime gastric cancer risk associated with a H. pylori screening program (Table 1; refs. 31-33). Based on clinical studies that evaluated the effect on precancerous gastric lesions or gastric cancer incidence, we assumed that the effectiveness of H. pylori treatment is dependent on the absence of advanced precancerous lesions and that treatment reduces disease progression probabilities among individuals with gastritis or atrophy (3, 7, 34). Using posttreatment data on the prevalence of precancerous lesions from a H. pylori treatment study in Linqu, China, we operationalized treatment effectiveness by systematically varying the transition probabilities between gastritis and atrophy in our natural history model until the output matched posttreatment data on the relative risk of gastritis versus advanced precancerous lesions (see online supplemental data; ref. 34). This process was repeated for each of the 50 good-fitting parameter sets for each subgroup.

Figure 2 depicts the model output for select precancerous and cancer targets using a random sample of 50 sets from the subset of good-fitting parameter sets. Gastric cancer incidence showed the largest variation, reflecting the wide 95% confidence intervals of the Cancer Incidence in Five Continents Volume VIII data. Accordingly, the lifetime risk and conditional probabilities of gastric cancer also varied among the good-fitting parameter sets (Table 3).

We compared the distributions of good-fitting values for each parameter to gain insight on subgroup differences. Within China, the probability of progressing to atrophy for H. pylori+ individuals and progressing to intestinal metaplasia for all individuals seemed to be higher for men. Similarly, the probability of regressing to intestinal metaplasia was lower among men. In Colombia, no differences by sex were apparent, reflecting their similar calibration targets. Between countries, progression to atrophy given H. pylori infection and progression to intestinal metaplasia were higher in China for both sexes. For all subgroups, the probability of progressing to dysplasia and regressing to intestinal metaplasia were similar except for men in China, who seemed to have higher and lower values, respectively (Fig. 3).

Across parameter sets, some general patterns emerged. Several parameter sets were similar except for the multiplier value dictating the rate of progression from dysplasia to presymptomatic cancer, reflecting the wide 95% confidence intervals of the cancer targets and the use of a grid search algorithm. In addition, the probabilities of progressing to and regressing from a specific health state were positively correlated. For example, if the probability of regressing to intestinal metaplasia increased, the probability of progressing to dysplasia also increased. Additional details are provided in the online supplemental data.

Using a randomly selected sample of 50 good-fitting parameter sets for each subgroup, we projected the reduction in lifetime risk of gastric cancer associated with a once-per-lifetime H. pylori screening at age 20 years. Figure 4 depicts the mean and range identified by simulating the effect of the intervention with multiple good-fitting parameter sets. The implementation of a H. pylori screening program was projected to provide a mean reduction of 15% in the lifetime risk of gastric cancer among men in China. The range produced across all good-fitting parameter sets varied from 7% to 30%. The reduction was greater among subgroups in Colombia, reflecting the higher proportion of individuals who had gastritis or atrophy at age of screening and benefited from treatment.

Motivated to generate policy discussion about potential secondary prevention programs for gastric cancer, we synthesized the available data to develop a model of H. pylori infection and gastric cancer, and empirically calibrated this model to data in China and Colombia. This process identified multiple good-fitting parameter sets that fit equally well to epidemiologic data. By conducting comparative analyses of different gastric cancer prevention strategies using a random sample of the good-fitting parameter sets, the model allows for a description of the uncertainty in policy outcomes that follows from uncertainty in model parameters. As such, in our illustrative example, although we projected that a once-per-lifetime H. pylori screen could significantly reduce cancer risk in all subgroups, we also find that estimates of the absolute magnitude of benefit vary considerably when we explicitly consider the underlying uncertainty around disease progression and regression.

In addition to developing country-specific models of gastric cancer through calibration, we gained insight into how disease progression may vary within countries by sex and between countries. A comparison of the distributions of good-fitting values for each individual parameter by subgroup suggests that disease progression may vary within and between countries, reflecting the multifactorial etiology of the disease. Most striking are the lower regression probabilities among men in China from dysplasia to intestinal metaplasia. A cross-sectional study on the cohort from which our precancerous calibration targets were based found that 80% of men but only 5% of women smoked, and that smokers had higher relative risks of intestinal metaplasia (odds ratio, 1.2-1.4) or dysplasia (odds ratio, 1.6-2.2; ref. 16). Smoking may therefore explain in part the differential rates of disease progression. As smoking prevalence data for both high-risk regions were not available, we were unable to explicitly incorporate the role of smoking into our model. Along with the uncertainty surrounding our prevalence calibration targets, these findings are therefore suggestive, and additional data are needed before these effects can be formalized.

Our calibration methods have several limitations. With multiple parameters being varied simultaneously, the search space is extensive, and more efficient optimization algorithms might guide the parameter search more systematically. There is also no consensus for how “good” the model fit must be to ensure adequate representation of disease natural history and, thus, the strict definition of a “good-fitting parameter set” is subject to analytic choices. In this analysis, we used a likelihood ratio test to identify parameter sets that were statistically similar to the best-fitting parameter set and then randomly selected 50 good-fitting sets to conduct the analysis. We recognize that this approach relies on the assumption that the best set itself achieves an acceptable fit to the empirical data. Our likelihood-based approach for model calibration has been used to develop models for several cancers, including hepatitis C virus and liver cancer by Salomon et al. (35), human papilloma virus and cervical cancer by Kim et al. (36) and Goldhaber-Fiebert et al. (37), and colorectal cancer by Knudsen et al. (38). Although this approach has the ability to reflect the strength of evidence for each calibration target, other calibration approaches have also been used to parameterize models. For example, McMahon et al. (39) have developed a natural history model of lung cancer using a χ² approach in which the overall goodness of fit of a parameter set is assessed by summing individual χ² statistics for all calibration targets. Fryback et al. have developed a breast cancer modeling using an “acceptance window” approach in which intervals around each calibration targets are specified heuristically or by 95% confidence intervals, and goodness of fit for a parameter set is measured by summing the number of model output that fall outside of the targeted intervals (40). Model calibration using a Bayesian approach has also been used for other disease models (41, 42). The use of a variety of methods implies that there is no consensus on a single best approach and, often, the analytic choice depends on the nature of the question, the data available, and the complexity of the model; we anticipate that as empirical work on calibration methods evolves, the advantages and disadvantages of different approaches will be more clearly refined.

Our choice of approach reflected tradeoffs and consideration of data availability, ease of implementation, computer capacity, and our relatively modest goal of generating broad qualitative insight for decision-making. There are several steps that could improve the search methods, such as exploring the parameter space more thoroughly with a finer grid search. Although cross-sectional prevalence studies provide the best available data on precancerous lesions, we know that they are imperfect given their reliance on gastric biopsies, which have low sensitivity and are subject to histological misclassification. As a result, we may overestimate the importance of point estimates for each of our calibration targets. To address the varying levels of sensitivity with biopsies, fit to calibration targets for certain lesions could be weighed more than others in the goodness-of-fit score calculation. As additional data on H. pylori infection and its role in the developmental process of gastric cancer emerge, our model can be recalibrated, modifying our calibration approach if necessary, to ensure its output are consistent with the new empirical data.

Lee et al. also developed a Markov model of the precancerous process of gastric cancer using data from a community-based screening program for gastric cancer in Taiwan (43, 44). Under similar natural history assumptions, the authors estimated transition rates between gastritis, atrophy, intestinal metaplasia, and gastric cancer. In contrast to our model, they assumed no regression among precancerous lesions and that all gastric cancers (intestinal and diffuse) develop through the pathway. Because of the lack of detail on biopsy methods and histologic classification used to detect and categorize precancerous lesions in their screening program, we cannot directly compare our results with their estimates. However, by independently estimating natural history parameters using different data sources and maximum likelihood approaches, both studies are consistent with a multistate and multifactorial model of gastric cancer in which H. pylori plays an important role early on in the precancerous process and other risk factors influence the progression to more advanced lesions (21).

There are several additional limitations to our model. First, our calibrated parameters are population averages and do not reflect heterogeneity between individuals that may stem from differences in other risk factors aside from H. pylori infection. Second, we assumed that the relative risk of developing gastric cancer given H. pylori infection calculated using China data was generalizable to Colombia. We also estimated the proportion of gastric cancers that are H. pylori+ from a meta-analysis of case-control studies that may not have adequately controlled for other risk factors. However, specific studies that controlled for potential confounders concluded that including such variables in their models did not alter the relative risk estimates (45). Third, we extrapolated the relative risk (4.5) for gastric cancer given H. pylori infection to Colombia instead of the absolute risk difference (0.0334). However, given that the lifetime risk for gastric cancer is approximately the same in both countries, our calibration results most likely would not have differed significantly if we instead extrapolated the absolute risk (see online supplemental data).

Fourth, our model relies on the assumption that 92% of gastric cancers in China are positive for H. pylori. This may be an underestimate if H. pylori seropositivity was lost in controls due to intestinal metaplasia already having developed at time of blood sample collection in the case-control studies or an overestimate depending on the quality of controls selected and preservation of case matching in the meta-analysis. Fifth, we assumed that H. pylori infection induces gastritis and promotes atrophy only. However, H. pylori may also promote progression to more advanced precancerous lesions. In this case, our calibrated estimates provide a reasonable approximation because more than 90% of atrophy, intestinal metaplasia, and dysplasia in our model is H. pylori related.

Sixth, to fit calibration targets, we assumed that regression from dysplasia and intestinal metaplasia occurred as reported in the cohort studies. However, we are respectful of the biological uncertainty of this disease, and that there are potentially alternative explanations such as low biopsy sensitivity and misclassification that conceivably could produce good fits. Alternatively, natural history for subtypes of intestinal metaplasia and dysplasia may differ. For example, clinical studies suggest that high-grade dysplasia is a nonreversible lesion whereas spontaneous regression occurs in low-grade dysplasia in one third of the cases (46). Thus, our model may reflect the average regression rates among the various subtypes. In addition, we used cross-sectional data to approximate longitudinal estimates of precancerous lesion prevalence and gastric cancer incidence. As a result, our model may not adequately reflect risk factor changes and their effect on gastric cancer rates over time. Epidemiologic studies suggest that infection rates in high-risk regions have remained unchanged, however; for example, in Linqu, nearly 70% of children are still infected with H. pylori (6). Our model therefore likely provides reasonable approximations. Lastly, our analysis is based on the assumption that intestinal-type gastric cancer develops through the multistate precancerous pathway, and our insights should be viewed within the context of this and other underlying model assumptions.

Model-based policy analyses conducted within a decision-analytic framework allow for exploratory analyses of the potential health and economic outcomes of different gastric cancer prevention strategies. Although respectful of formidable evidence gaps, model calibration to the available empirical data allows for analyses to be conducted with multiple good-fitting parameter sets; as such, the results of our exploratory efforts reflect the uncertainty around the natural history of disease. As new data become available, including data from clinical trials of the effectiveness of H. pylori treatment on gastric cancer, models such as this one can be refined and recalibrated and, as such, provide more accurate projections of the comparative benefits and cost-effectiveness of gastric cancer prevention and treatment policies.

No potential conflicts of interest were disclosed.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

We gratefully thank Dr. Gregory Lauwers and Dr. Daniel Chung of Massachusetts General Hospital and Dr. Sapna Syngal of Dana-Farber Cancer Institute for their help and clinical expertise.