Cancer Causesand Control, 2,

147 - 155

• Evaluation of cancer p r e v e n t i o n strategies by computemzed simulation model: an approach to lung cancer

Naohito Yamaguchi, Yoshiyasu Tamura, Tomotaka Sobue, Suminori Akiba, Megu Ohtaki, Yasumasa Baba, Shoichi Mizuno, and Shaw Watanabe (Received 4 January 1991; accepted in revisedforrn 7 March 1991) A computerized simulation model was developed to evaluate the potential impact of primary and secondary prevention on lung cancer mortality in Japan. The natural history of lung cancer was modeled as a Markovian stochastic process from cancer-free to preclinical, clinical, and finally to terminal states. The increase in mortality rate of lung cancer among males aged 75 to 79 years has been the major force of increase in the total number of lung cancer deaths in Japan. The simulation showed that this tendency would continue until the late 1990s, presumably due to the increase in the proportion of ever-smokers in that cohort, who started smoking at an earlier age than did prior generations. It was shown that the number of lung cancer deaths can be reduced either by smoking cessation or screening programs, and that the reduction is proportional to the increase in the annual smoking-cessation rate and to the annual increment in the screening rate. However, only two to three percent reduction of lung cancer deaths in the year 2001 can be expected when the annual smoking-cessation rate is raised from the current value of 0.46 percent to five percent during the period from 1991 to 2000 or when the screening rate is increased by three percent annually for the same period.

Key words: Lung cancer, Japan, modeling, screening, smoking.

Introduction In Japan, cancer has been the leading cause of death since 1981, with approximately 200,000 people dying from this disease each year. 1Among the sites of cancer prevailing in Japan, lung cancer has received the most attention because of the marked increase in the death rate of both females and males. 2 Mass screening programs for lung cancer using miniature X-ray examination and sputum cytology

have been supported by the Japanese Government, and over four million individuals were screened by this program in 1988, corresponding approximately to 10 percent of the population aged 40 years o r o v e r . 3'4 It was reported, however, in three randomized controlled trials in the United States, that there was no significant decrease in lung cancer deaths among screening participants as compared to a less-inten-

Drs Yamaguchi, Mizumo, and Watanabe are with the Epidemiology Division, National Cancer Center Research Institute, Tokyo, Japan. Drs Tamura and Baba are with the Institute of Statistical Mathematics, Tokyo, Japan. Dr Sobue is with the Center for Adult Diseases, Osaka, Japan. Dr Akita is at the Radiation Effect Research Foundation, Hiroshima, Japan. Dr Ohtaki is at the Research Institute for Nuclear Medicine and Biology, Hiroshima University. Address correspondence to Dr Yamaguchi at the National Cancer Center Research Institute, 5-1-1 Tsukiji, Chuo-ku, Tokyo 104, Japan. This study was supported in part by a grant-in-aid for Cancer Research from the Ministry of Health and Welfare, Japan. © 1991 Rapid Communications of Oxford Ltd

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Figure 1. The stochastic model of the natural history of lung cancer. sively screened comparison group. 5'6'z When the data in these trials were further analyzed using mathematical modeling, the reduction in mortality by annual X-ray screening was estimated to be 18 percent in New York and five percent in Baltimore for adenocarcinoma and large cell carcinoma of the lung. s Antismoking efforts, on the other hand, seemed to have received less support from government policy makers, partly, perhaps, because of the monopoly of tobacco sales by the government until 1984. The smoking rates among Japanese males and females were reported to be approximately 60 percent and 15 percent, respectively, as of 1989.9 The overall smoking rate has been declining but an increasing trend in young women has been noted. 9'1°Since it is unrealistic to expect that all smokers will quit smoking immediately, it is necessary to assess, quantitatively, how a gradual decline of smoking rate affects lung cancer mortality in the future. In addition, it has been recognized in recent studies that the risk of lung cancer among ex-smokers remains at a high level for decades after cessation, longer than previously reported. 11'12'13 This remaining effect of smoking among ex-smokers also has to be considered when projecting future trends of lung cancer mortality. Public concern about the prevention and control of lung cancer is increasing, but the effects of such activities on lung cancer deaths in the future remain to be assessed quantitatively. The objective of this project is to develop a computer-based simulation model to evaluate the potential impact of primary and secondary prevention on lung cancer deaths in Japan in the future. The simulation model, called CANSAVE 148

Cancer Causes and Control. Vol 2. 1991

(Cancer Strategy Analysis and Validation of Effect), is based on a Markovian stochastic model for cancer progression leading to death, in which the transition probabilities are estimated based on various sources of information from epidemiology and biomathematical sciences.

Materials and methods To extrapolate future lung cancer deaths using the simulation model CANSAVE, the initial population has to be specified for age and gender structure, smoking history, and screening rate. In addition, the screening rate and the mortality rate for all-causes in the target population have to be given for the entire simulation period as external information. The proportions of current smokers, ex-smokers, and nonsmokers during the simulation period are given as a result of simulation, and the number of new cases of lung cancer and the number of deaths from lung cancer and other causes are calculated by the simulation model.

Modeling of the natural history of lung cancer The natural history of lung cancer was modeled as a sequential multistep disease process from cancer-free state (state 0) to preclinical state (state 1), clinical state (state 2) and, finally, to death state caused by cancer (state 4) 14 as shown in Figure 1. Death from other causes was also considered in the model. The transition probability from state i to state j will be denoted by Pii in this paper. All the transition probabilities were given as annual rates shown in Table 1.

Evaluation of cancer prevention strategies Table 1. Transition matrix for the natural history of lung cancer

State

0 Cancer-free

1 Preclinical

2 Clinical

3 Death (lung cancer)

4 Death (other causes)

0 Cancer-free

P00 a

P01

0

0

P04

1 Preclinical

P]0( = 0.16)

P)I b

PIE(= 0.64)

0

P14

2 Clinical 3 Death (lung cancer) 4 Death (other causes)

P20(=0.13) 0 0

0 0 0

P22c 0 0

P23(=0.69) 1 0

P24 0 1

~P00 = 1 - P01 - P04. b p . = 1 - P10 - P12 - P14' ~P22 = 1 - P20 - P23 - P24"

The transition probability from cancer-free to preclinical state was considered age-dependent, reflecting the complex, multistage cancer-forming process. It was assumed that smoking influenced only this transition in the natural history of lung cancer. Based on epidemiologic observations of British physicians, is the death rate from lung cancer was assumed to increase with age as follows:

assumed that growth of lung-cancer mass occurs independently of cigarette smoking. The a 0 term was estimated on a birth cohort basis by Mizuno et a116 as shown in Figure 2. It should be noted that the value of a 0was influenced by the shortage of tobacco during the 1940s in certain birth cohorts. The parameter r. was also reported for Japanese males. 16 The parameter r~ was estimated in the present study on a birth cohort basis by fitting simulation results to the observed agespecific death rates among Japanese males during the period from 1975 to 1987. The functional forms for the transition probability P01 were derived by incorporating the preclinical and clinical periods into Equations (1) and (2):

Equation (1) death r a t e = r . (age) 4 (nonsmokers), Equation (2) death rate = r s ( a g e - a0)4"5 (smokers), where r., r s, and a 0 are constants. Equation (2) is based on an idea that the risk of death from lung cancer increases with the 4.5th power of the effective year of smoking) 5 The a0 term is the sum of the period prior to cigarette smoking and the growth period following the cancer-forming process. It was

Equation (3) Po] = r. (age + D ) 4 (nonsmokers), Equation (4) Pol = r~ (age - a 0+ D) 4s (smokers),

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Figure 2. Year to be subtracted from age at observation of lung cancer death to calculate the effective year of smoking. Cancer Causes and Control. Vo12. 1991

149

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where D is the sum of the preclinical and clinical periods which can be calculated using the following equation:

Equation (5) D = 1/P~2+ 1/P23. It was assumed that the relative risk (RR) of lung cancer among ex-smokers to current smokers was reduced at a rate of three percent per year, based on an estimate from a case-control study conducted recently in Japan. 13 The transition probabilities from preclinical to clinical, clinical to recovery, and clinical to death were estimated simultaneously by the least square method, minimizing the departure of survival functions in the model from the observed survival curves in cases detected by screening and through symptoms) 7 The observed and assumed survival curves are illustrated in Figure 3. The estimated transition probabilities were 0.64/year, 0.13/year and 0.69/year for preclinical to clinical, clinical to recovery, and clinical to death, respectively. The transition probability from preclinical to recovery was estimated to be 0.16/year for participants of annual screening and was assumed to be zero for nonparticipants. It was assumed that the sensitivity of the screening test was 0.62. TMThe screening rate in Japanese males aged 55 to 79 was assumed to be 10 percent during the period 1973 t o 1 9 8 9 . 4 The rate thereafter was modified in various ways to observe the impact of secondary prevention. The probability of death from other causes was assumed to be independent of lung cancer. For the 150

Cancer Causes and Control. Vol 2. 1991

period 1973 to 1989, age-specific death rates were obtained from the Vital Statistics Database. 19 For the period 1990 to 2001, the age-specific death rates in 1989 were used, assuming that they would not change thereafter. Death rates from other causes were estimated for smokers, ex-smokers, and nonsmokers based on the RR of death from all causes, except for lung cancer among smokers when compared with nonsmokers and the proportions of smokers and ex-smokers obtained by simulation. The RR was assumed to be proportional to the exponential of the duration of smoking as follows :2o

Equation (6) RR = 1.02 x exp(smoking duration). It was assumed that the risk of death in ex-smokers was reduced to half of the level of smokers in one year, and to the level of nonsmokers in two years after smoking cessation? 1 In formulating the model described thus far, time was treated as a discrete variable with one-year intervals. The discrete function was adopted because most epidemiologic data referred to in setting parameters were provided as yearly aggregates.

Simulation procedure The male population in 1973 was chosen as the initial population for the simulation which was generated for 28 years until the year 2001. Since death rates from lung cancer were available through 1987, the period 1975-87 was selected for the fitting procedure to estimate r s. The number of deaths from lung cancer among

Evaluation of cancerprevention strategies 80

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Figure 4. Projected smoking rate in Japanese males aged 55 to 79. males aged 55 to 79 was the index used to evaluate the impact of antismoking and screening programs.

Initial state. The Japanese male population from age 27 to 79 as of 1973 was selected so that ages 55 to 79 were covered during the simulation period from the year 1973 to 2001. The proportions of current smokers and ex-smokers for all ages were estimated from data obtained by the National Health Survey in 1980. 22The numbers of cases with lung cancer at preclinical and clinical states at the start of simulation also were estimated so that the projected numbers of death from lung cancer in 1974 and 1975 were closest to the actual observations.

Sensitivity analysis. To assess the sensitivity of simulation results for a subtle change in parameter values, the value of each parameter was modified to 90 percent and 110 percent, and the changes in number of lung cancer deaths in 2001 were compared with the results of actual simulation.

Impact of primary and secondary prevention. In the National Health Survey data, 22the regression analysis of the increase in ex-smokers by age showed that 0.46 percent per year of ever-smokers quit smoking (r= 0.996). The impact of anti-smoking activity was assessed by modeling the annual smoking-cessation rate at one percent, three percent, and five percent per year from 1991 to 2000. To observe the impact of raising the screening rate in the target population, the screening rate was increased from 10 percent to 20, to

30, and to 40 percent during the 10-year period from 1991 to 2000. The corresponding annual increments were one percent, two percent, and three percent, respectively.

Results Projection The projected smoking rates in different age groups are shown in Figure 4. The overall smoking rate in the target population aged 55-79 did not show a remarkable change until the year 2001. The younger age groups consistently showed higher smoking rates through the simulation period due to higher smoking initiation rates, but they tended to show a decreasing trend sooner than the older groups. When death rates in different age categories were examined, as illustrated in Figure 5, the age group 75-79 showed the greatest increase. The death rate increased from 250 to 450 per 100,000 by around 1995 and then began to decrease. The increase in the age group 70-74 was less marked. The other age groups did not show remarkable increases. The simulation results were in accord with the observed death rates until 1987.

Sensitivity analysis The proportionate change in the predicted number of lung cancer deaths in year 2001 was calculated for - 10 percent and + 10 percent changes for the six parameter Cancer Causes and Control. Vo12. 1991

151

N. Yamaguchi et al values shown in Table 2. The change in transition rate from clinical to recovery caused the largest change in the number of deaths, followed by the transition rate from clinical to lung cancer death. The influences were less marked for the other parameters, annual risk reduction among ex-smokers, the screening sensitivity, the transition rate from preclinical to clinical state, and preclinical to recovery.

Potential impact of primary and secondary prevention The simulation showed that the smoking rate in year 2001 would decrease from 62 percent to 58 percent, to 46 percent, and to 36 percent when the annual smoking-cessation rate increased from 0.46 percent to one percent, three percent, and five percent, respectively. The decrease in lung cancer deaths is shown in relation to the cessation rate in Figure 6a. The predicted numbers of lung cancer deaths in 2001 were 25,078, 25,015, 24,795, and 24,590 for the annual cessation rates of 0.46 percent, one percent, three percent, and five percent, respectively, showing a linear decrease with the cessation rate. The regression equation indicated that the risk of dying from lung cancer will decrease by 0.43 percent when the cessation rate increases by one percent. This corresponds to a decrease of approximately two percent in the number of deaths in 2001 if the cessation rate changes from 0.46 percent to five percent. The predicted decreases in the number of lung cancer deaths when the screening rate was increased by one percent, two percent, and three percent annually

Table2. Relativechanges in the number of lung cancerdeaths in 2001 when the value of a parameter in the CANSAVEis modified to 90% and 110% P a r a m e t e r value Parameter

90%

Pr(clinical to recovery) a Pr(clinical to l u n g cancer death) A n n u a l risk r e d u c t i o n in e x - s m o k e r s Screening sensitivity Pr(preclinical to recovery) Pr(preclinical to clinical)

+ + + + +

1.40% 1.13% 0.86% 0.13% 0.13% 0.07%

for the period from 1991 to 2000 are illustrated in Figure 6b. The predicted numbers of lung cancer deaths were 24,835, 24,597, and 24,363 for the annual increments of screening rate of one, two, and three percent, respectively. A decrease by 0.95 percent for the annual increment of one percent in the screening rate was shown by the regression equation. The predicted number of lung cancer deaths in 2001 decreased approximately by 10 percent, from 25,078 to 22,445, when the screening rate was increased from 10 percent to 100 percent after 1990. Relative decreases in projected numbers of lung cancer deaths are plotted against year in Figure 7 for three cases: (i) the smoking cessation rate was increased to five percent during the period 1991 to 2000; (ii) the screening rate was increased from 10 to 40 percent for the period 1991 to 2000; (iii) both the smoking cessation rate and screening rate were increased by the same magnitude as in cases (i) and (ii).

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Evaluation of cancer prevention strategies by computerized simulation model: an approach to lung cancer.

A computerized simulation model was developed to evaluate the potential impact of primary and secondary prevention on lung cancer mortality in Japan. ...
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