TECHNICAL APPENDIX Accompanying the manuscript: Development of an Empirically Calibrated Model of Gastric Cancer in Two High-Risk Countries Jennifer M. Yeh, PhD 1 Karen M. Kuntz, ScD 2 Majid Ezzati, PhD 3 Chin Hur, MD, MPH 4 Chung Yin Kong, PhD 4 Sue J. Goldie, MD, MPH 1 From the 1 Program in Health Decision Science, Department of Health Policy and Management, Harvard School of Public Health, Boston, MA; 2 Division of Health Policy and Management, School of Public Health, University of Minnesota, Minneapolis, MN; 3 Department of Population and International Health and Department of Environmental Health, Harvard School of Public Health, Boston, MA; 4 Institute of Technology Assessment, Massachusetts General Hospital, Boston, MA.
Model Assumptions Exploratory Analyses After identifying parameters for a natural history model of gastric cancer (GC and Helicobacter pylori (Hp infection and their respective plausible ranges based on a broad literature review, we ranked the transitions a priori to determine the order of manipulation and established the following targets for model output to approximate: 1 age-specific prevalence of precancerous lesions, 2 age-specific symptomatic gastric cancer incidence, 3 lifetime risk of gastric cancer, 4 proportion of gastric cancers that are Hp-positive, and 5 conditional probabilities of developing gastric cancer given Hp status. We then systematically varied each eligible parameter, one at a time, with the goal of a close visual fit to both age-specific prevalence of precancerous lesions and incidence of cancer and approximation (±1% to the other three targets. For these exploratory analyses, we allowed all progression probabilities to vary by age and Hp status and we assumed that regression probabilities were similar in both countries so that differences between countries were reflected in progression probabilities. We then compared the transition probabilities derived from these analyses to determine what could be inferred about the natural history of gastric cancer. Within China, where sex-specific epidemiologic data on precancerous lesions prevalence were available, progression probabilities were higher among men. Between countries, the probabilities of progression among precancerous states were higher in China. This was true for both men and women. The relative risk of progression to atrophy for Hp infection ranged from 10.0-15.0 in China and 7.3-8.0 in Colombia, which was similar to a relative risk of 9.5 reported in a prospective chronic gastritis study in the Netherlands. 1 2
We also found that we were unable to achieve reasonable visual fits to epidemiologic data without assuming that the probability of progression from gastritis to atrophy was higher for Hp infection individuals. In contrast, an assumption of higher progression rates to more advanced precancerous lesions for Hp infection individuals was not necessary. We also we found that disease progression probabilities varied within and between countries by subgroup. Except for the probabilities of progressing to atrophy for Hp positive individuals in Colombia and to intestinal metaplasia for individuals in China, parameter values were within their plausible ranges. The majority of transition probabilities were constant across age, although it was necessary to allow the probability of progressing to pre-symptomatic cancer to vary by age. As the age-specific probabilities for this transition were similar between countries by sex, we estimated an age pattern for the transition for which data are unavailable in the literature. 3
Parameterization (1 Initial Distribution Calculation Described below are details for calculating the initial distribution of the model cohort: Fraction of gastritis that is Hp+ (f 1 f 1 =, Gastritis = Pr( Gastritis p 1 4 2 pifi where Pr(Hp+ = seroprevalence of Hp infection p i = prevalence of i f i = fraction of i that is Hp+ i = 1 2 3 4 5 gastritis atrophy intestinal metaplasia dysplasia cancer Prevalence of gastritis, atrophy, intestinal metaplasia and dysplasia for a 10 Hp+ cohort Pr(i Hp+ = pifi where Pr(Hp+ = seroprevalence of Hp infection i = 1 2 3 4 5 gastritis atrophy intestinal metaplasia dysplasia cancer 4
Estimates for Hp- prevalence estimates follow similar calculations. For China: For a cohort of 1000 individuals in China with 1 7 Hp seroprevalence, 2 distribution of 65%, 18%, 12%, and 5% among gastritis, atrophy, intestinal metaplasia and dysplasia, and 3 92% of atrophy, intestinal metaplasia and dysplasia are assumed to be Hp+: Health state Gastritis IM Dysplasia (i = 1 (i = 2 (i = 3 (i = 4 Hp+ 378 166 110 46 700 Hp- 272 14 10 4 300 Total 650 180 120 50 1000 p i.65.18.12.05 f i.58.92.92.92 Fraction of gastritis that is Hp+ (f 1 f 1 = 700- (180*.92- (120*.92- (50*.92 650 = 700-166-110-46 650 378 = 650.58 Prevalence of gastritis, atrophy, intestinal metaplasia and dysplasia for a 10 Hp+ cohort Pr(Gastritis = Pr( = 650 *.58 1000.70 180 *.92 1000.70 =.539 or 53.9% =.237 or 23.7% 5
Pr(IM = Pr(DYS = 120 *.92 1000.70 50 *.92 1000.70 =.158 or 15.8% =.066 or 6.6% (2 Estimation of the Proportion of Gastric Cancers that are Hp positive in Colombia To estimate the relative risk (RR of gastric cancer (GC given Hp infection, we first calculated the lifetime risk of developing noncardia intestinal type gastric cancer between the ages of 20 and 80 using age-specific incidence rates. 2 We then calculated the conditional probabilities of cancer given Hp status using the probabilities of Hp infection and estimated that the relative risk of gastric cancer given Hp infection was 4.46. Using this relative risk, we estimated that 98.9% of gastric cancers in Colombia are Hp positive. To estimate the distribution among precancerous lesions at age 20 for Hp+ and Hp- individuals, we conducted similar calculations as those for China. Described below are details for calculating the relative risk (RR of gastric cancer given exposure to Hp in China and percentage of Hp+ gastric cancers in Colombia. Lifetime risk of gastric cancer between ages 20 and 80 Pr( GC 1 exp( 80 20 ri where r i = annual gastric cancer incidence rate for age i 6
Conditional probabilities of gastric cancer Pr( GC Hp GC * Pr( GC Pr( GC Hp GC *Pr( GC Relative risk of gastric cancer given exposure to Hp Relative Risk ( RR Pr( GC Pr( GC Hp Hp For China: RR Pr( GC Pr( GC Hp Hp 0.0431 0.0097 4.46 Estimating the proportion of gastric cancers that are Hp+ in Colombia Relative Risk ( RR Pr( GC Pr( GC Hp Hp RR GC * Pr( GC GC * Pr( GC RR GC * Pr( GC * GC *Pr( GC RR GC * 1 GC RR * *(1 GC GC 7
RR * RR * * GC GC RR * GC RR * * GC RR * GC 1 RR * GC RR * 1 RR * For Colombia: Given Pr(Hp. 95and a RR 4. 46 (generalized from China data: GC 98.9% 8
Estimation of Hp Treatment Effectiveness Based on evidence from clinical studies, we assumed that Hp treatment reduced disease progression only among individuals with gastritis or atrophy; individuals with more advanced lesions did not benefit from treatment. 3-5 As all individuals infected with Hp enter the model with gastritis or more advanced precancerous lesions, we assumed Hp treatment did not affect gastritis development. We estimated treatment effectiveness using data on the prevalence of precancerous lesions in the treatment and placebo group after 7.3 years from the Hp treatment study in Linqu, County. 5 In the study, compared with the placebo group, individuals with gastritis in the treatment group had a higher probability of having gastritis versus progressing to more advanced lesions (60. with treatment vs. 47.2% with placebo; relative risk = 1.27. Similarly, individuals with atrophy also had a higher likelihood of having gastritis (42. with treatment vs. 18.8% with placebo; relative risk = 2.23. We operationalized treatment effectiveness by systematically varying the transition probabilities between gastritis and atrophy in our natural history model until output matched post-treatment prevalence data from the Linqu Hp treatment study. 5 This process was repeated for each of the 50 good-fitting parameter sets for both each subgroup. We estimated that the average relative risk of progression to atrophy was 0.5 for men (range, 0.1 0.7 and 0.3 for women (range, 0.1 0.7 in China and 0.08 (range, 0.01-0.13 for both men and women in Colombia. The average relative risk of regression to gastritis was 2.1 (range, 2.0-2.4 and 2.3 (2.1-2.4 for both sexes in China and Colombia, respectively. 9
Additional Results Among a total of 65,536 parameter sets simulated for each subgroup, we identified a best fitting parameter set for which all but 2 to 3 model outputs fell within the 95% confidence intervals of the calibration targets. With a log likelihood ratio test, we identified 811 to 2475 additional parameter sets with goodness-of-fit scores that were statistically indistinguishable to the best fitting parameter set (goodness-of-fit score ranged from 35 to 48 depending on subgroup. In total, these parameter sets represented 1.2% to 3.8% of all simulated parameter sets and had model outputs which were consistent with our multiple calibration targets. Figures A1 to A4 provide model output for prevalence of precancerous lesions and incidence of gastric cancer for 50 randomly-selected good-fitting parameter sets for each subgroup. Figure A5 depicts distribution of values for each parameter among all good-fitting parameter sets. Tables A1 to A4 show the pairwise correlation coefficients among all good-fitting parameter sets for each subgroup, with statistically significant correlation coefficients starred. 10
Incidence of gastric cancer (per 100,000 Prevalence of intestinal metaplasia Prevalence of dysplasia Prevalence of gastritis Prevalence of atrophy An Empirically Calibrated Model of Gastric Cancer Figure A1. Model fit to calibration targets on precancerous lesions prevalence and gastric cancer incidence using 50 randomly selected good-fitting parameter sets for China men. Bold lines, 95% confidence intervals. Non-bold lines, model output for each 50 randomly-selected good-fitting parameter sets. 10 10 8 8 6 6 10 35-39 40-44 45-49 50-54 55-59 60-64 10 35-39 40-44 45-49 50-54 55-59 60-64 8 8 6 6 35-39 40-44 45-49 50-54 55-59 60-64 35-39 40-44 45-49 50-54 55-59 60-64 500 400 300 200 100 0 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 11
Incidence of gastric cancer (per 100,000 Prevalence of intestinal metaplasia Prevalence of dysplasia Prevalence of gastritis Prevalence of atrophy An Empirically Calibrated Model of Gastric Cancer Figure A2. Model fit to calibration targets on precancerous lesions prevalence and gastric cancer incidence using 50 randomly selected good-fitting parameter sets for China women. Bold lines, 95% confidence intervals. Non-bold lines, model output for each 50 randomly-selected good-fitting parameter sets. 10 10 8 8 6 6 35-39 40-44 45-49 50-54 55-59 60-64 35-39 40-44 45-49 50-54 55-59 60-64 10 10 8 8 6 6 35-39 40-44 45-49 50-54 55-59 60-64 35-39 40-44 45-49 50-54 55-59 60-64 300 200 100 0 20-24 25-29 30-34 35-39 40-44 45-50- 49 54 55-59 60-64 65-69 70-74 75-79 80-84 12
Incidence of gastric cancer (per 100,000 Prevalence of intestinal metaplasia Prevalence of dysplasia Prevalence of gastritis Prevalence of atrophy An Empirically Calibrated Model of Gastric Cancer Figure A3. Model fit to calibration targets on precancerous lesions prevalence and gastric cancer incidence using 50 randomly selected good-fitting parameter sets for Colombia men. Bold lines, 95% confidence intervals. Non-bold lines, model output for each 50 randomly-selected good-fitting parameter sets. 10 10 8 8 6 6 25-34 35-44 45-54 55-65 25-34 35-44 45-54 55-65 10 10 8 8 6 6 25-34 35-44 45-54 55-65 25-34 35-44 45-54 55-65 500 400 300 200 100 0 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 13
Incidence of gastric cancer (per 100,000 Prevalence of intestinal metaplasia Prevalence of dysplasia Prevalence of gastritis Prevalence of atrophy An Empirically Calibrated Model of Gastric Cancer Figure A4. Model fit to calibration targets on precancerous lesions prevalence and gastric cancer incidence using 50 randomly selected good-fitting parameter sets for Colombia women. Bold lines, 95% confidence intervals. Non-bold lines, model output for each 50 randomly-selected good-fitting parameter sets. 10 10 8 8 6 6 25-34 35-44 45-54 55-65 25-34 35-44 45-54 55-65 10 10 8 8 6 6 25-34 35-44 45-54 55-65 25-34 35-44 45-54 55-65 500 400 300 200 100 0 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 14
0 10 20 30 40 0 10 20 30 40 0 20 40 60 Percent Percent Percent 0 10 20 30 40 0 10 20 30 40 0 20 40 60 0 10 20 30 40 Percent Percent Percent 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 0 10 20 30 0 20 40 60 80 Percent Percent Percent 0 50 100 0 10 20 30 0 20 40 60 80 An Empirically Calibrated Model of Gastric Cancer Figure A5. Distribution of values for each transition probabilities among all good-fitting parameter sets by subgroup. Progression to among Hp+ China men China women Progression to among Hp- China men China women Progression to China men China women Colombia men Colombia women Colombia men Colombia women Colombia men Colombia women 0 50 100.002.004.006.008.002.004.006.008 Monthly probability Graphs by subgroup.0001.0002.0003.0004.0005.0001.0002.0003.0004.0005 Monthly probability Graphs by subgroup.005.01.015.02.025.005.01.015.02.025 Monthly probability Graphs by subgroup Progression to Dy splasia China men China women Progression to Gastric Cancer among men China Colombia Progression to Gastric Cancer among women China Colombia Colombia men Colombia women.002.004.006.008.002.004.006.008 Monthly probability Graphs by subgroup.5 1 1.5.5 1 1.5 Monthly probability Graphs by subgroup.5 1 1.5.5 1 1.5 Monthly probability Graphs by subgroup Regression to Gastritis China men China women Regression to China men China women Regression to China men China women Colombia men Colombia women Colombia men Colombia women Colombia men Colombia women 0.001.002.003.004 0.001.002.003.004 Monthly probability Graphs by subgroup 0.002.004.006 0.002.004.006 Monthly probability Graphs by subgroup 0.005.01.015 0.005.01.015 Monthly probability Graphs by subgroup 15
Table A1. Pairwise correlation coefficients of parameter values among all good-fitting parameter sets for China men among Hp+ among Hp- to Dysplasia Presymptomatic Gastric Cancer Gastritis among Hp+ 1.0000 among Hp- -0.1741* 1.0000-0.1225* 0.0101 1.0000 to Dysplasia 0.0009 0.0258-0.0065 1.0000 Presymptomatic Gastric Cancer -0.0511* 0.0236 0.0242-0.0253 1.0000 Gastritis 0.5468* 0.0149-0.0122 0.0197 0.0279 1.0000 to 0.0620* -0.0189 0.7490* -0.0154 0.0212-0.0033 1.0000 to -0.0071 0.0288 0.0322 0.8561* 0.0485* 0.0384-0.0334 1.0000 * Statistically significant at the p<0.05 level 16
Table A2. Pairwise correlation coefficients of parameter values among all good-fitting parameter sets for China women among Hp+ among Hp- to Dysplasia Presymptomatic Gastric Cancer Gastritis among Hp+ 1.0000 among Hp- -0.1713* 1.0000-0.2250* 0.0374 1.0000 to Dysplasia 0.0341-0.0024 0.0231 1.0000 Presymptomatic Gastric Cancer -0.0678* 0.0075-0.0387 0.0255 1.0000 Gastritis 0.6507* 0.0266-0.0890* 0.0161-0.0247 1.0000 to -0.1212* 0.0090 0.8700* 0.0315-0.0244-0.0509* 1.0000 to 0.0029-0.0085 0.0469* 0.7773* 0.1206* 0.0137 0.0185 1.0000 * Statistically significant at the p<0.05 level 17
Table A3. Pairwise correlation coefficients of parameter values among all good-fitting parameter sets for Colombia men among Hp+ among Hp- to Dysplasia Presymptomatic Gastric Cancer Gastritis among Hp+. among Hp-.* 1.0000.* 0.0030 1.0000 to Dysplasia.* -0.0019-0.0433 1.0000 Presymptomatic Gastric Cancer.* -0.0007 0.0593-0.0839* 1.0000 Gastritis.* 0.0332 0.1333* 0.0194 0.0390 1.0000 to.* 0.0060 0.8222* -0.0273 0.1651* -0.0572 1.0000 to.* -0.0103 0.0571 0.7293* 0.2816* 0.0155 0.0593 1.0000 * Statistically significant at the p<0.05 level 18
Table A4. Pairwise correlation coefficients of parameter values among all good-fitting parameter sets for Colombia women among Hp+ among Hp- to Dysplasia Presymptomatic Gastric Cancer Gastritis among Hp+. among Hp-.* 1.0000.* 0.0029 1.0000 to Dysplasia.* 0.0028-0.0430 1.0000 Presymptomatic Gastric Cancer.* 0.0007 0.0691* -0.0673 1.0000 Gastritis.* 0.0296 0.1204* 0.0072 0.0366 1.0000 to.* -0.0011 0.8357* -0.0523 0.1711* -0.0310 1.0000 to.* 0.0018 0.0619 0.7234* 0.2709* 0.0175 0.0408 1.0000 * Statistically significant at the p<0.05 level 19
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