Epidemiological data

The present study focused on two pieces of information: the seroprevalence of infection with H. pylori in Japan and the snapshot case number of peptic ulcer in Japan. Regarding the seroprevalence of infection with H. pylori, a prior study by the authors estimated the time-dependent force of infection with H. pylori in Japan using systematically collected data ([Reference Fujisawa18–Reference Malaty24] as analysed in [Reference Kayano, Lee and Nishiura25]). The year of survey, serological testing method, ages of subject and sample size are summarised in Supplementary Table S1. Briefly, survey years broadly ranged from 1974 to 2012, and the majority of surveys used serum IgG antibody, while only Akamatsu et al. used urine antibody among adolescents [Reference Akamatsu19] and Okuda et al. used stool antigen and PCR [Reference Okuda23]. Studies by Akamatsu et al. from 2007-9 [Reference Akamatsu19] and Okuda et al. from 2010–11 [Reference Okuda23] respectively focused on adolescents and school-age children, but other included studies examined the entire age spectrum involving both children and adults [Reference Fujisawa18, Reference Asaka20–Reference Kumagai22, Reference Malaty24]. Despite such differences, our earlier study has shown that the observed antibody data over age and time, as extracted from all included studies, were well captured by a simple integral equation model and heterogeneity did not matter [Reference Kayano, Lee and Nishiura25]. Using the collected dataset and estimating the hazard of infection [Reference Kayano, Lee and Nishiura25], the best-fit model did not identify any age dependence in the hazard of infection and estimated that the hazard of infection decreased over time beginning in the year 1937; the exponential decay in the hazard was 0.047 per year [Reference Kayano, Lee and Nishiura25]. We used these published estimates and adopted the resulting prevalence of infection with H. pylori as a function of time and age. There was no distinction in the force of infection by sex [Reference Kayano, Lee and Nishiura25]; thus, we assumed that men and women shared an identical force of infection.

Regarding the snapshot case number of peptic ulcer, data were retrieved from a patient survey that is performed every 3 years by the Ministry of Health, Labour and Welfare in Japan (conducted in 1981, 1984, 1987, 1990, 1993, 1996, 1999, 2002, 2005, 2008, 2011 and 2014) [26]. This nationwide survey samples subject hospitals using a block randomisation method in which the blocking unit is the secondary medical region, defined as the geographic region in which healthcare facilities can offer a complete set of acute care services that require hospital admission (in 2019, n = 344 secondary medical regions in Japan). The principles of the survey method did not change over time. The survey collects information regarding patients' primary diagnoses, along with information regarding sex, date of birth, postal address, inpatient or outpatient status and treatment details; this data collection is performed to obtain an overview of the spectrum of diseases of both inpatients and outpatients in a single cross-sectional survey throughout Japan [27]. The survey is conducted on a single day in October of the survey year. The data were collected across age groups, regardless of a birth cohort. The total numbers of peptic ulcer cases derived from this survey, including both outpatients and inpatients, were 164 300 and 34 600, respectively, in 1984 and 2014. For this study, we retrieved the age-dependent number of peptic ulcer cases by sex, inpatient/outpatient information and survey year.

Important events that lead to abrupt changes

In the present analysis, we captured the time-dependent case patterns of peptic ulcer by birth year cohort using mathematical models (see Statistical models); for this purpose, two important time events that likely affected the epidemiology of peptic ulcer are briefly described here. First, Japanese national health insurance began to cover the diagnosis and treatment of H. pylori infection for patients with peptic ulcer in 2000 (importantly, the implementation of coverage began in 1999) [Reference Asaka and Takeda28, Reference Asaka29]. The treatment guidelines for eradication therapy for H. pylori infection were also published during the same period [Reference Asaka29]. The impact of change in 1999 was explored by statistical models 2-1, 2-2, 3-1 and 3-2. Second, prior to eradication therapy, cimetidine (an H2-receptor antagonist) was commercially introduced in Japan in 1982, and other H2-receptor antagonists (e.g. famotidine and ranitidine) were also introduced during the early 1980s [Reference Asaka and Takeda28]. This event was explored by our statistical models 3-1 and 3-2 in the present study. Accordingly, we set 1982 and 1999 as the years in which the epidemiological dynamics of peptic ulcer may have abruptly changed.

Statistical model

Here, to explain the abrupt changes that are described in subsection ‘Important events that lead to abrupt changes’, we modelled the snapshot number of peptic ulcer and compared the model fit by including and excluding the following components: (i) seroprevalence of H. pylori infection; (ii) effect of birth year, proportional to H. pylori infection (hereafter referred to as the ‘cohort effect’); (iii) eradication therapy; and (iv) natural decline in the risk of infection. Let i be the index of birth year, such that i = {1925, 1935, 1945, 1955 and 1965}, and let c _i(t) be the snapshot number of peptic ulcer in year t; then, the chronological age is given by t-i. Let h _i(t) represent the seroprevalence of H. pylori infection in year t, which was previously parameterised in a published study [Reference Kayano, Lee and Nishiura25]. Let k be a constant, expected value of the cases, such that the prototype model (M0) that does not include any event is as follows:

(1)$$E( {c_i( t ) } ) = k$$

for t − a ≥ i. It should be noted that for the following models, we assume that the case number of peptic ulcer is dependent on the time series of H. pylori infection due to the established causal link to peptic ulcer, thus, all models other than (1) consider H. pylori seroprevalence. Assuming that H. pylori seroprevalence h _i(t) is proportional to the risk of peptic ulcer, we have M1-1 as follows:

(2)$$E( {c_i( t ) } ) = c_i( {t-1} ) + w( h_i( t ) -h_i( {t-1} ) ) , \;$$

where w is the scaling factor of H. pylori infection. Extending M1-1 by considering the birth cohort effect in the element that is proportional to H. pylori infection, perhaps reflecting birth-cohort-specific susceptibility to H. pylori infection and associated complications, we have M1-2 as follows:

(3)$$E( {c_i( t ) } ) = c_i( {t-1} ) + w_i( h_i( t ) -h_i( {t-1} ) ) .$$

Additionally, considering an abrupt decline in the risk of peptic ulcer, possibly attained by eradication therapy, M2-1 was extended from M1-1 by a factor of (1 − ɛ), as follows:

(4)$$E( {c_i( t ) } ) = \left\{{\matrix{ {c_i( {t-1} ) + w( {h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t < 1999} \cr {c_i( {t-1} ) + w( {( {1-\varepsilon } ) h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t = 1999} \cr {c_i( {t-1} ) + w( {1-\varepsilon } ) ( {h_i( t ) -h_i( {t-1} ) } ). \;\;\;t \ge 2000} \cr } } \right.$$

Accounting for the cohort effect in (3) onto M2-1, we have M2-2, as follows:

(5)$$E( {c_i( t ) } ) = \left\{{\matrix{ {c_i( {t-1} ) + w_i( {h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t < 1999} \cr {c_i( {t-1} ) + w_i( {( {1-\varepsilon } ) h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t = 1999} \cr {c_i( {t-1} ) + w_i( {1-\varepsilon } ) ( {h_i( t ) -h_i( {t-1} ) } ) .\;\;\;t \ge 2000} \cr } } \right.$$

Adding the potential of a natural decline in peptic ulcer, which we assume was based on the introduction of H2-receptor antagonist therapy in 1982, expressed by the decay rate δ to the model in (4), we have M3-1, as follows:

(6)$$E( {c_i( t ) } ) = \left\{{\matrix{ {c_i( {t-1} ) + w\exp ( {-{\rm \delta }( {t-1982} ) } ) ( {h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t < 1999} \cr {c_i( {t-1} ) + w\exp ( {-{\rm \delta }( {t-1982} ) } ) ( {( {1-{\rm \varepsilon }} ) h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t = 1999} \cr {c_i( {t-1} ) + w\exp ( {-{\rm \delta }( {t-1982} ) } ) ( {1-{\rm \varepsilon }} ) ( {h_i( t ) -h_i( {t-1} ) } ) .\;\;\;t \ge 2000} \cr } } \right.$$

Accounting for cohort effect, we have M3-2, as follows:

(7)$$E( {c_i( t ) } ) = \left\{{\matrix{ {c_i( {t-1} ) + w_i\exp ( {-{\rm \delta }( {t-1982} ) } ) ( {h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t < 1999} \cr {c_i( {t-1} ) + w_i\exp ( {-{\rm \delta }( {t-1982} ) } ) ( {( {1-{\rm \varepsilon }} ) h_i( t ) -h_i( {t-1} ) } ) , \;\;\;t = 1999} \cr {c_i( {t-1} ) + w_i\exp ( {-{\rm \delta }( {t-1982} ) } ) ( {1-{\rm \varepsilon }} ) ( {h_i( t ) -h_i( {t-1} ) } ) .\;\;\;t \ge 2000} \cr } } \right.$$

Assuming that the observed snapshot case number follows a Poisson distribution, unknown parameters (i.e. w (or w _i), ɛ and δ) were estimated by means of maximum likelihood estimation using the likelihood function, as follows:

(8)$$L = \mathop \prod \limits_i \mathop \prod \limits_t \displaystyle{{E{( {c_i( t ) } ) }^{x_i( t ) }{\rm exp}( {-E( {c_i( t ) } ) } ) } \over {x_i( t ) !}}.$$

where x _i(t) is the observed number of peptic ulcer cases in birth cohort i in year t. Fitted models were compared using the Akaike information criterion (AIC). Moreover, the coefficient of determination was computed to elucidate the percentage of observed time-dependent cases that could be described by the abovementioned simple components. Identifying the first and second best-fit models, we used the difference in the coefficient of determination to decompose the observed components into the abovementioned (i) through (iv), that is,

$$R^2 = 1-\displaystyle{{\mathop \sum \nolimits_t \mathop \sum \nolimits_i {( {x_i( t ) -E( {c_i( t ) } ) } ) }^2} \over {\mathop \sum \nolimits_t \mathop \sum \nolimits_i {( {x_i( t ) -\bar{x}( t ) } ) }^2}}$$

where $\bar{x}( t )$ represents the mean of the observed data in year t.

Parametric bootstrapping was performed using the Hessian matrix H(θ). To do so, we have randomly drawn model parameters sampled from the normal distribution with the mean θ and standard deviation σ was obtained from the square root of diagonal elements of the inverse Hessian matrix. Then, for each set of parameters, we obtain a possible variation in epidemiological dynamics of peptic ulcer. By taking 2.5th and 97.5th percentile points of the simulated distributions, we obtain 95% confidence intervals of incidence.

Apart from the abovementioned time- and age-dependent models, it is critical to independently verify the presence of change in time trend in 1999 because of eradication therapy. To test our hypothesis that the frequency of peptic ulcer in Japan changed in 1999, we quantified the time trend using the following two models. First, if the frequency of peptic ulcers in Japan has been changing over time, independent of the event in 1999, the estimated case number c should be expressed as a simple linear function, such that

(9)$$E( {c_i( t ) } ) = at + b, \;$$

where a is the linear time-dependent trend and b is a constant parameter (intercept). Alternatively, if there was a changing point in 1999 due to the introduction of eradication therapy, the estimated frequency of peptic ulcers should be better described by

(10)$$E( {c_i( t ) } ) = \left\{{\matrix{ {at + b, \;\;\;t < 1999} \cr {\;at + b + k, \;\;\;\;\;\;\;t \ge 1999} \cr } } \right.$$

where k represents the change in the trend from 1999. Modelling c with those simple approaches, we performed a likelihood ratio test, comparing models (9) and (10), to identify a better-fit model for the empirically observed data.

Ethical considerations

The present study used publicly available data [Reference Kayano, Lee and Nishiura25, 27]. The datasets did not contain any information associated with individual identity; therefore, ethical approval was not required for this study.