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A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma.

Chaib E, Amaku M, Coutinho FA, Lopez LF, Burattini MN, D'Albuquerque LA, Massad E - Theor Biol Med Model (2013)

Bottom Line: This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes.With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria.We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Medical Informatics, LIM 01, School of Medicine, University of Sao Paulo, Av,Dr, Arnaldo 455, Sao Paulo CEP 01246-903, Brazil. edmassad@usp.br.

ABSTRACT

Background: The criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes.

Methods: We propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500.

Results: With 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria.

Conclusion: We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.

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Related in: MedlinePlus

Frequency distribution of tumor size. Dots represent actual values from references [9-11] and the line is the exponential fitting to the real data (R2 = 0.92). Parameter λ = 0.3 which implies in an average tumor size of 3.3 cm.
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Figure 2: Frequency distribution of tumor size. Dots represent actual values from references [9-11] and the line is the exponential fitting to the real data (R2 = 0.92). Parameter λ = 0.3 which implies in an average tumor size of 3.3 cm.

Mentions: In Figure 2 we show the actual distribution of tumor size, fitted to an exponential distribution. The parameter λ in this case is equal to 0.3. As the total number of patients in these samples was 327 patients, this implies in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7] [9-11].


A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma.

Chaib E, Amaku M, Coutinho FA, Lopez LF, Burattini MN, D'Albuquerque LA, Massad E - Theor Biol Med Model (2013)

Frequency distribution of tumor size. Dots represent actual values from references [9-11] and the line is the exponential fitting to the real data (R2 = 0.92). Parameter λ = 0.3 which implies in an average tumor size of 3.3 cm.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4016553&req=5

Figure 2: Frequency distribution of tumor size. Dots represent actual values from references [9-11] and the line is the exponential fitting to the real data (R2 = 0.92). Parameter λ = 0.3 which implies in an average tumor size of 3.3 cm.
Mentions: In Figure 2 we show the actual distribution of tumor size, fitted to an exponential distribution. The parameter λ in this case is equal to 0.3. As the total number of patients in these samples was 327 patients, this implies in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7] [9-11].

Bottom Line: This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes.With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria.We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Medical Informatics, LIM 01, School of Medicine, University of Sao Paulo, Av,Dr, Arnaldo 455, Sao Paulo CEP 01246-903, Brazil. edmassad@usp.br.

ABSTRACT

Background: The criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes.

Methods: We propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500.

Results: With 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria.

Conclusion: We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.

Show MeSH
Related in: MedlinePlus