||At the beginning of the 21st century, primary liver cancer (PLC) remains the fifth most common malignancy in men worldwide, and the eighth in women. Central Africa and South East of Asia are high risk geographic areas for PLC, whereas developed countries appear to be generally low risk. Infections with hepatitis B (HBV) and C (HCV) viruses are the main risk factors for PLC, accounting for well over 80% of PLC cases detected worldwide. The recently detected increase in both incidence and mortality by PLC in developed countries is strongly related to these viral infections. The evaluation of PLC time trends needs to take into consideration the geographic distribution and effect of these viruses. This thesis presents three studies which the aim to describe PLC incidence and mortality issues in different geographic areas, each addressing several epidemiological and methodological issues. For each study, different statistical methods on the basis of the Bayesian inference have been proposed, evaluated and discussed in order to cope with extra-Poisson variability. The first study, entitled «Meta-analysis of cohort studies of risk of liver cancer death among HBV carriers«, evaluates the variability in PLC mortality reported in 11 cohort studies of male HBV carriers, taking into consideration the effects of geographic area and the choice of the general population versus a more comparable group such as HBV-negative workers or blood donors as the comparison group. The statistical methods of this study focuses on mixtures of Poisson distributions. The «stickbreaking» method has been used to estimate the number of components of the mixture of Poisson distributions, and, thus to obtain a pooled relative risk (RR) of death for PLC among male HBV carriers. The pooled RR of death by PLC related to HBV infection was 23. 5 (95% Credibility Interval (CRI): 14. 9 - 44. 5). Studies carried out in high risk areas for PLC (China and Taiwan) showed RRs 2 to 5-fold higher than those of studies carried out in Europe, Japan and the U. S. . In low risk areas for PLC, studies which used workers or blood donors as comparison groups had RRs 1. 9-fold higher (95% CRI: 1. 2 - 3. 1) than studies which used the general population. However, in high risk areas, the ratio of RRs was 5. 3-fold (95% CRI: 3. 4 - 7. 9). This is the first time that a «healthy donor effect» has been quantified in longitudinal studies. The second study, entitled «Geographic distribution of primary liver cancer in Europe in 2002» evaluates the effect of HBV and HCV seroprevalence in 38 European countries on PLC incidence and mortality. Mixed Poisson models based on Bayesian inference have been used to smooth Standardized Incidence (SIR) and Mortality (SMR) ratios for PLC accounting for the effect of HBV and HCV prevalences. This approach enabled us to both examine the effect of different levels of HBV and HCV, and to identify remaining variability in PLC after accounting for infection rates. Bayesian inference allowed the determination of posterior probabilities for the somoothed SIRs and SMRs (hereafter RRs). The Deviance Information Criterion (DIC) and the «effective number of parameters» (pD) have been used as tools for model choice. The highest mortality and incidence PLC RRs were found in Southern European countries (RR range 0. 9-2. 4), whereas Northern European countries showed the lowest RRs (RR range: 0. 3-0. 9). The effect of HBV infection was not found to be statistically significant in the model which accounted for both HBV and HCV prevalence. Countries with a prevalence of HCV higher than 2% (e. g. : Italy and Spain) had a higher risk of incidence and mortality (RR range: 1. 28 - 1. 78) than countries with HCV prevalence below 1%. Thus, the high risk of PLC detected in Southern Europe appears to be explained, in part, by HCV infection. The high HCV seroprevalence in this area could be associated with exposure 30-50 years ago. There may be an underestimation of PLC incidence and mortality rates in Eastern European countries given the low PLC RRs reported, despite high HBV and HCV seroprevalences observed. The implementation of population-based cancer registries in Eastern European countries is warranted, as well as HCV prevalence studies across Europe, to better determine the distribution of PLC in Europe and its relationship with that virus. The last study, entitled «Time trends in liver disease in Spain during the period 198397», describes incidence and mortality trends in hepatocellular carcinoma and cholangiocarcinoma as well as mortality trends in liver cirrhosis in Spain. Autoregressive age-period-cohort (APC) models have been used to evaluate the time trends. We found that APC models performed well for those liver diseases with large number of cases, whereas the age-period models did for those liver diseases with low number of cases. We found an increase in incidence and mortality of hepatocellular carcinoma in Spain (annual percent change (APCH) in men's incidence: 6. 6%, 95% CRI: 5. 8, 8. 1: APCH in women's incidence: 4. 5%, 95% CRI: 1. 4%, 7. 3%; APCH in men's mortality: 6. 8%, 95% CRI: 5. 8%, 8. 1%; APCH in women's mortality: 5. 1%, 95% CRI: 3. 5%, 6. 3%), that appear to be related to HCV exposure 30 years ago, as described in other studies of PLC. We also found an increasing trend in cholangiocarcinoma mortality (APCH in men: 17. 1%, 95% CRI: 13. 5%, 21. 2%; APCH in women: 15. 0%, 95% CRI: 11. 5%, 19. 5%) similar to that found in some developed countries, that could be attributed to improvement in diagnosis resulting from better imaging and diagnostic techniques. However, we did not detect a significant increasing trend in cholangiocarcinoma incidence, perhaps due to the low number of cases reported by the Spanish cancer registries. We have observed a decreasing trend in cirrhosis mortality in both sexes during the study period (APCH in men: -3. 1%, 95% CRI: -5. 1, -1. 9%; APCH in women: -2. 9%; 95% CRI: -6. 2%, -1. 3%), although younger cohorts did not show this pattern. This cohort effect suggests the possibility that younger cohorts could be exposed to some additional risk factors besides alcohol consumption. HIV and HCV or HBV co-infection and intravenous drug addiction could explain the increase in liver cirrhosis mortality among younger cohorts. The flexibility of the Bayesian approach allowed us to cope with extra-Poisson variability in three statistical analyses, applying different models, and addressing relevant methodological aspects specific to each problem. Challenging statistical issues in the framework of Bayesian applied modelling are: i) the selection of prior distributions for model parameters, which is related to convergence of the model; and ii) model selection procedures, and these remain important considerations for future research.