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Appendix A Methods,A 1 Overall modelling framework for GBD 2013. Figure S1 GBD 2013 data and model flow chart,A 2 Using DisMod to estimate acute infections. DisMod MR produces consistent estimates of disease incidence prevalence remission and. mortality using a non linear mixed effects model to bring together all available data on the. descriptive epidemiology of the disease of interest DisMod MR is an integrative systems model. which combines a system dynamics model of process with a statistical model of data In DisMod. MR 2 0 the model of process is a two compartment stock and flow model described by two. ordinary differential equations with the age specific flows between a susceptible and a with. condition population The model of data is an offset log normal model with hierarchical random. effects on geography age standardized to address age group heterogeneity DisMod MR model. results include estimates of seroprevalence and instantaneous seroconversion rates i e the. incidence of seroconversion among the seronegative population We converted these. instantaneous seroconversion rates to population incidence rates i e the number of infections per. number in the total population using the formula, population incidence rate instantaneous seroconversion rate 1 seroprevalence. A 3 Hepatitis B chronic to acute conversion, HBsAg seropositivity typically persists only among chronic carriers and by estimating incidence. from a model of HBsAg seroprevalence we are effectively modelling the incidence of HBV. infections that result in chronic carriage We therefore need to adjust these incidence estimates. to estimate the incidence of all HBV infections i e including those that result in chronic carriage. and those that result in clearance Knowing the proportion of infections that lead to the carrier. state we can simply divide our initial estimates by that proportion to estimate the total It is. clear however that this proportion varies enormously with age so we must age specific. proportions to produce accurate estimates Here we use equations estimated by Edmunds et al1. to calculate the probability that a new HBV infection will result in carriage by age. 6 25 0 645, The oldest age group included in Edumunds s meta analysis included people ages 20 to 30 years.
treated as age 25 years in their model We are therefore not confident that their equation. will hold for those older than 25 years of age and take the conservative approach of assuming. that the probability of developing the carrier state does not change with increasing age above 25. 25 0 645 25 0 061,A 4 Acute hepatitis proportion symptomatic. We used published age specific formulae to estimate the probability of symptomatic infection for. HAV2 and HEV3,P Symptomatic HAV 0 852 1 0 01244,P Symptomatic HEV 1 0 011. Where Prmax is the maximum probability of symptomatic acute infection among adults and was. assumed to be 0 6 4, For HBV we developed a non linear model of the age specific probability of symptomatic acute. infection based on data from McMahon et al5,P Symptomatic HBV age 6 days 0 098. 1 0 358 29 6, Figure S2 The probability that hepatitis B infection will result in chronic carriage by age of infection.
McMahon et al did not report the probability of symptomatic acute infections among perinatal. cases but it is known to be a rare outcome occurring in approximately only 1 of perinatal. infections 6 We therefore assumed a probability of symptomatic acute infection of 0 01 in the. first week of life,P Symptomatic HBV age 6 days 0 01. For HCV we assumed that 25 of acute infections would be symptomatic based on a combination. of expert opinion and published estimates 7,A 5 Acute hepatitis E case fatality. We estimated the prevalence of pregnancy Ppreg among women for each country year and age. group based on age specific fertility rates We then estimated the acute hepatitis E case fatality. among women as weighted average of the case fatalities among non pregnant population CFnon. preg and among pregnant women CFpreg, Where CFpreg was assumed to be 0 039 and CFnon preg was assumed to be 0 0038 3 Case fatalities. were assumed to be equal for males and non pregnant females or 0 38. A 6 Severity splits and disability weights, Symptomatic cases of acute HAV HBV HCV and HEV were split between mild moderate and. severe sequelae Each sequela was assigned the disability of the most closely matching health. state from the 235 GBD 2013 health states For mild moderate and severe acute hepatitis these. health states were Infectious disease acute episode mild disability weight 0 006 0 002. 0 012 Infectious disease acute episode moderate disability weight 0 051 0 032 0 074. and Infectious disease acute episode severe disability weight 0 133 0 088 0 19. respectively 8, Table S1 Proportion of symptomatic cases assigned to each of the three severity states with the mean disability.
weight by sub type, Sub type Mild Moderate Severe Mean Disability Weight. Hepatitis A 0 14 0 85 0 01 0 046,Hepatitis B 0 00 0 98 0 02 0 053. Hepatitis C 0 00 0 96 0 04 0 054,Hepatitis E 0 00 0 97 0 03 0 053. For liver cancer the person years for the four general sequelae were estimated Cases that die. within ten years experience only three sequelae diagnosis treatment metastatic phase and. terminal phase Cases that survive beyond ten years experience disability due to diagnosis and. treatment and remission Duration of sequela 1 Diagnosis and treatment was four months. sequela 2 controlled phase was ten years for the survivors minus the duration of the other. sequelae Duration of sequela 3 disseminated phase was based on SEER data for median. survival of patients with stage IV liver cancer 2 51 months 9. A 7 CODEm models, We used the Cause of Death Ensemble Model CODEm tool to model mortality from cirrhosis. liver cancer and all acute hepatitides combined For each cause the modeller specifies a list of. potential covariates that may help inform the model CODEm then tests combinations of. covariates using both linear and spacetime models and with both mortality rate and cause. fraction as possible dependent variables Each of these separate models is considered a sub. model Each sub model is trained on 70 of the data and the remaining 30 are held out for. out of sample prediction testing The final predictions are based on combining results from. multiple sub models in which sub models are weighted based on the out of sample prediction. performance the best performing sub models have the strongest influence on the final. predictions and poor performers have little or no influence For each cause models are built. separately for males and for females Detailed information about CODEm was published. previously 10, We used two models for liver cancer one model that included data from all countries was used.
to estimate liver cancer mortality for developing countries and one model that included only. data from developed countries and was used to estimate liver cancer mortality for developed. countries Cancer data from developed countries are substantially better than from developing. countries The poorer data from developing countries produces greater uncertainty in all. estimates and thus erroneously inflates the uncertainty in estimates for developed countries. The two model approach avoids this problem and allows uncertainty to be correctly estimated in. developed countries There are therefore four liver cancer mortality models separate all country. models for males and females and separate developed country models for males and females. For cirrhosis hepatitis and all country liver cancer both the male and female models included 55. sub models each The male and female developed country liver cancer models included 34 and. 44 sub models respectively The model types and dependent variables for these sub models are. given in Table S2 The potential covariates for each cause and the number of included sub. models that contained each covariate are given in Table S3. Table S2 The number of sub models in which the dependent variable was cause fraction versus mortality rate by. model type for each cause and sex,Dependent Variable. Sex Model Type Cause Fraction Rate Both,Linear 13 0 13. Females Spacetime 42 0 42,Both 55 0 55,Linear 13 0 13. Males Spacetime 42 0 42,Both 55 0 55,Linear 0 0 0,Females Spacetime 24 31 55. Both 24 31 55,Linear 0 0 0,Males Spacetime 20 35 55.
Both 20 35 55,Liver Cancer all countries,Linear 6 20 26. Females Spacetime 6 23 29,Both 12 43 55,Linear 3 11 14. Males Spacetime 10 31 41,Both 13 42 55,Liver Cancer developing countries. Linear 8 14 22,Females Spacetime 8 14 22,Both 16 28 44. Linear 7 10 17,Males Spacetime 7 10 17,Both 14 20 34.
Table S3 The number of models in which each covariate was used among those models that were included in the. final ensemble For each cause covariate combination we give the number of models for which that covariate was. included and in parentheses the percent of all models in the ensemble that contained that covariate Hyphens. indicate that a given covariate was not specified as a potential covariate for that cause i e sanitation was considered. as a potential covariate in the cirrhosis model whereas zeros indicate that the covariate was included as a potential. predictor for that cause but that none of the models that included that covariate performed well enough to be. included in the final ensemble,Liver Cancer Liver Cancer. Cirrhosis Hepatitis,all countries developed, Females Males Females Males Females Males Females Males. Alcohol 25 26 35 35 26 12,liters per capita 45 5 47 3 63 6 63 6 59 1 35 3. Animal fat 0 0 0 0,kcal per capita 0 0 0 0 0 0 0 0. BMI 17 18 6 29 6 6,mean 30 9 32 7 10 9 52 7 13 6 17 6.
Cigarettes per capita,0 0 0 0 0 0 0 0,Cumulative cigarettes 0 0 0 0. 15 year 0 0 0 0 0 0 0 0,Cumulative cigarettes 0 0 0 0. 20 year 0 0 0 0 0 0 0 0,10 18 28 8 6 8,Diabetes prevalence. 18 2 32 7 50 9 14 5 13 6 23 5,Education 21 19 33 16 20 13 14 14. years per capita 38 2 34 5 60 0 29 1 36 4 23 6 31 8 41 2. 0 0 1 1 0 0 0 0,Health system access,0 0 0 0 1 8 1 8 0 0 0 0 0 0 0 0.
Hepatitis A seroprevalence,0 9 34 29 20 21 16 14,Hepatitis B seroprevalence. 0 0 16 4 61 8 52 7 36 4 38 2 36 4 41 2,34 32 19 22 28 33 28 16. Hepatitis C seroprevalence,61 8 58 2 34 5 40 0 50 9 60 0 63 6 47 1. Hepatitis E seroprevalence,Log lag distributed income 16 22 23 18 13 16 0 0. LDI per capita 29 1 40 0 41 8 32 7 23 6 29 1 0 0 0 0. Red meat 0 0 0 0,kcal per capital 0 0 0 0 0 0 0 0,Sanitation 23 14.
proportion with access 41 8 25 5,Schistosomiasis prevalence. Water proportion with 13 17,access to improved source 23 6 30 9. A 8 Aetiology splits, We conducted literature reviews for studies that reported the prevalence of risk factors among. those with cirrhosis or liver cancer From each study we extracted the proportion of participants. with evidence of chronic HBV infection chronic HCV infection history of excessive alcohol. use or other identifiable causes e g non alcoholic steatohepatitis NASH genetic causes We. excluded those with cryptogenic disease In many studies some proportion of participants. present with multiple possible aetiologies e g an individual with cirrhosis may be infected with. both HBV and HCV Unfortunately data on comorbidities were too sparse to model each. combination of aetiologies as separate aetiological entities We therefore attempted to assign. each case to a single cause Where a study reports patients with multiple aetiologies we split. those patients between the possible aetiologies proportionally As an example we ll take a. hypothetical study of 100 cirrhosis patients that reported 60 patients having a chronic hepatitis. infection 20 with HBV 30 with HCV and 10 with both HBV and HCV We would split those. 10 patients between HBV and HCV in a 20 30 ratio giving us a 24 patients with cirrhosis due to. HBV and 36 patients with cirrhosis due to HCV, For both cirrhosis and liver cancer we run four separate DisMod models corresponding to each. of the four potential aetiologies i e alcohol HBV HCV and other Within each age sex year. and location we rescale the four proportion estimates to ensure that they sum to one by dividing. each proportion by the sum of the four,A 9 Uncertainty.
We propagate uncertainty through the modeling chain using posterior simulation For all. estimates we take 1 000 draws from the posterior distribution of the estimate We then perform. all subsequent calculations at the draw level For example for the natural history model of acute. hepatitis B deaths for each age sex location year we take 1 000 random draws from the. posterior distribution of our incidence estimate and 1 000 random draws from the distribution of. our estimate of case fatality based on a beta distribution We then calculate 1 000 mortality. rate draws where draw one is equal to the product of the first incidence draw and the first case. fatality draw The mean of the 1 000 draws is then taken as the point estimate the 2 5th and. 97 5th percentile draws are taken as the lower and upper bounds of the 95 uncertainty interval. A 10 Trend Decomposition, We decomposed overall trends in DALYs to determine the effects of population growth changes. in age structure and changes in age specific rates using a . liver cancer and all acute hepatitides combined For each cause the modeller specifies a list of potential covariates that may help inform the model CODEm then tests combinations of covariates using both linear and spacetime models and with both mortality rate and cause fraction as possible dependent variables

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