Department of Medico-Biocybernetics, Faculty of Medico-Biology, Russian State Medical University, Moscow 117437, Russia
Received 30 December 1998; accepted 18 May 1999
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ABSTRACT |
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INTRODUCTION |
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Although the experimental approach has been successful in defining the relationship between the ALDH2 allele and flushing symptoms, it is difficult to assess the issue of the extent to which ALDH2*2/*2 alleles promote flushing more than ALDH2*1/*2 alleles. Various mathematical methods can be used for such assessment; however the deterministic approach is difficult to use because the intensity of flushing induced by ALDH2*2 varies (Enomoto et al., 1991; Higuchi et al., 1992
).
Cross-impact analysis is a probabilistic approach developed for system analysis, forecasting, etc. (Gordon and Hayward, 1968; Gordon, 1969
; Enzer, 1970
, 1971
, 1972
; Sage, 1977
), which could be useful for analysis of the relationship between the ALDH2 allele and the flushing syndrome. The aim of the present study was to attempt to apply this method to the relationship between the ALDH2 allele and flushing symptoms.
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METHODOLOGY AND RESULTS |
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Bayes'law states that the probabilities of occurrences of two events, 1 and 2, can be related by
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Figure 1 shows the simplest coupled relationship regarding the occurrence of ALDH2 alleles and flushing. At the genotype level, the probabilities of the occurrence of homozygotes (ALDH2*2/*2 and ALDH2*1/*1) and heterozygotes (ALDH2*1|*2) are P(2) and P(
). At the phenotype level, the impacted probability of the occurrence of flushing given ALDH2*1/*2 is P(1|
), the impacted probability of the non-occurrence of flushing given ALDH2*1/*2 is P(
|
), the impacted probability of the occurrence of flushing given ALDH2*2/*2 is P(1|2), and the impacted probability of the non-occurrence of flushing given ALDH2*1/*1 is P(
|
). At the level of combination of genotype and phenotype, the probability of occurrences of ALDH2*1/*2 and flushing is P(1
), the probability of occurrence of ALDH2*1/*2 and non-occurrence of flushing is P(
2), the probability of the occurrences of ALDH2*2/*2 and flushing is P(12), and the probability of the occurrence of ALDH2*1/*1 and the non-occurrence of flushing is P(
).
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Calculation with cross-impact analysis
Calculation of probability of P(1).
P(1) is the probability of the occurrence of flushing. This probability is essential, because otherwise it would be impossible to find any relationship between ALDH2 and flushing; the term flushing would not exist if humans had a zero probability of flushing.
Table 1 shows two simple experimental examples on ALHD2 and flushing in Asians. With the data in the first column, we have P(2) = 2/189 + 96/189 = 0.52 and P(
) = 1 P(2) = 0.48. Putting P(2) and P(
) into the equations in Appendix 1, we have P(1) = 1 and 0.01
P(1)
0.02. Similarly, with the data in the second column, we have 0.6
P(1)
1 and 0.04
P(1)
0.06. To the best of our knowledge, neither the probability of flushing nor the genotype of flushing have been documented, thus it is impossible to compare these results with experimental data. However, it may be reasonable to consider Asians as having a probability of flushing from 0.6 to 1 as some people might never flush.
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Putting P(2) = 0.52 from the first example into the equations in Appendix 2, we have ranges of P(1|) and P(1|2) with respect to different P(1) in Fig. 2
, which shows that the region of P(1|2) is higher than the region of P(1|
) except for the points P(1) = 0 and P(1) = 1. This means that: (1) an individual would never flush after drinking no matter what genotype they have if their probability of flushing is equal to zero, i.e. neither ALDH2*2/*2 nor ALDH2*1/*2 can enhance the chance of flushing; (2) an individual with ALDH2*2/*2 has a higher probability of flushing after drinking than an individual with ALDH2*1/*2 if both have the same probability of flushing in the range from larger than zero to less than unity, i.e. ALDH2*2/*2 can enhance the chance of flushing more than ALDH2*1/*2; (3) an individual with ALDH2*2/*2 would have the same probability of flushing after drinking as an individual with ALDH2*1/*2 if both have the probability of flushing of unity, i.e. ALDH2*2/*2 can enhance the chance of flushing as much as ALDH2*1/*2. For example, if an individual has the probability of flushing of 0.6 [P(1) = 0.6], the probability of the occurrence of flushing with ALDH2*2/*2 is from 0.6 to 1 [0.6
P(1|2)
1] but the probability of the occurrence of flushing with ALDH2*1/*2 is from 0.17 to 0.6 [0.17
P(1|
)
0.6].
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Putting the data from Fig. 2 into the equations in Fig. 1
, we have P(
|
) and P(
|
) in Fig. 3
, which shows that the region of P(
|
) is higher than the region of P(
|2), except at P(1) = 0 and P(1) = 1. This means that: (1) an individual would never flush after drinking no matter what genotype they have if their probability of flushing is equal to zero, i.e. either ALDH2*1/*2 or ALDH2*1/*1 can inhibit the chance of flushing; (2) an individual with ALDH2*1/*2 has a higher probability of non-flushing after drinking than an individual with ALDH2*1/*1 if both have the same probability of flushing in the range from larger than zero to less than unity, i.e. the first ALDH2*1 allele has a stronger impact on the non-occurrence of flushing than the second ALDH2*1 allele, which is similar to saturable kinetics in biochemistry, (3) an individual with ALDH2*1/*2 would have the same probability of non-flushing after drinking as an individual with ALDH2*1/*1 if both have a probability of flushing of unity, i.e. neither ALDH2*1/*2 nor ALDH2*1/ *1 can inhibit flushing. For example, if an individual has a probability of flushing of 0.6 [P(1) = 0.6], the probability of non-occurrence of flushing with ALDH2*1/*2 is from 0.4 to 0.8 [0.4
P(
|
)
0.8] but the probability of non-occurrence of flushing with ALDH2*1/*1 is from 0 to 0.4 [0
P(
|2)
0.4].
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Putting P(2) = 0.52 into the Bayesian equation, we have the relationship between P(2|1), P(1|2) and P(1) given in Fig. 4. For example, if an individual always flushes after drinking, they would have the probability of flushing from larger than zero to 0.4 [0 < P(1)
0.4], and the impacted probability of P(1|2) from 0.4 to unity [0.4
P(1|2)
1].
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GENERAL DISCUSSION |
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The relationship between ALDH2 and flushing can also be defined as inhibition, i.e. (1) the occurrence of ALDH2*1/*1 inhibits the probability of the occurrence of flushing; (2) the occurrence of ALDH2*2/*2 inhibits the probability of the non-occurrence of flushing; (3) the occurrence of ALDH2*1/*2 inhibits the probability of the occurrence of flushing if ALDH2*2/*2 is related to flushing; (4) the occurrence of ALDH2*1/*2 inhibits the probability of non-occurrence of flushing if ALDH2*1/*1 is related to non-flushing. Cross-impact analysis along these lines would give opposite probabilities. In this study, we used the enhancement relationship, because it is more compatible with the experimental evidence.
The experimental data have been taken from the second and final events (Fig. 1), therefore they can be calculated according to the above steps to obtain useful information. In our simple examples, an interesting result was deduced using cross-impact analysis, i.e. the second ALDH2*2 allele has more effect on the enhancement of flushing than the first ALDH2*2 allele; by contrast, the first ALDH2*1 allele has more effect on the enhancement of non-flushing than the second ALDH2*1 allele. In future studies it will be possible to apply cross-impact analysis to, for example, the relationship between alcohol dehydrogenase (ADH) and liver disease.
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APPENDIX 1 |
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APPENDIX 2 |
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ACKNOWLEDGEMENTS |
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FOOTNOTES |
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