Artificial neural network approach for selection of susceptible single nucleotide polymorphisms and construction of prediction model on childhood allergic asthma
© Tomita et al; licensee BioMed Central Ltd. 2004
Received: 01 March 2004
Accepted: 01 September 2004
Published: 01 September 2004
Screening of various gene markers such as single nucleotide polymorphism (SNP) and correlation between these markers and development of multifactorial disease have previously been studied. Here, we propose a susceptible marker-selectable artificial neural network (ANN) for predicting development of allergic disease.
To predict development of childhood allergic asthma (CAA) and select susceptible SNPs, we used an ANN with a parameter decreasing method (PDM) to analyze 25 SNPs of 17 genes in 344 Japanese people, and select 10 susceptible SNPs of CAA. The accuracy of the ANN model with 10 SNPs was 97.7% for learning data and 74.4% for evaluation data. Important combinations were determined by effective combination value (ECV) defined in the present paper. Effective 2-SNP or 3-SNP combinations were found to be concentrated among the 10 selected SNPs.
ANN can reliably select SNP combinations that are associated with CAA. Thus, the ANN can be used to characterize development of complex diseases caused by multiple factors. This is the first report of automatic selection of SNPs related to development of multifactorial disease from SNP data of more than 300 patients.
In recent years, the number of patients suffering from allergic asthma has increased , and allergic diseases including asthma have become a social problem affecting medical costs and quality of life. Allergic asthma is a complex disorder characterized by airway inflammation, bronchial hyperresponsiveness and reversible airway obstruction. Elevated numbers of activated Th2 cells, mast cells and eosinophils in the bronchial mucosa cause certain features of asthma, including increased serum IgE levels in allergic asthma. The available data suggest that there are many potential susceptible genes for allergic asthma, including genes for cytokines, receptors, transcription factors, immune recognition and regulation of lipid mediator generation. A few susceptible genes for allergic asthma have been identified that may be associated with the asthmatic phenotype [2–4], but definite susceptible genes have not been identified yet. Thus, large-scale analysis of gene markers is needed, along with identification of association between these genetic polymorphisms and the asthmatic phenotype, and its development mechanism. It has been reported that the human genome has 3 to 10 million single nucleotide polymorphisms (SNPs). A SNP in a coding region can cause amino acid substitution, resulting in functional modification of the protein; a SNP in a promoter region can affect transcriptional regulation; and a SNP in an intron region can affect splicing and expression of the gene. Thus, SNPs can be highly informative for identifying genetic factors of multifactorial disease such as allergic asthma.
In the present study, we analyzed associations between SNPs and childhood allergic asthma (CAA), which is more strongly influenced by genetic factors than other types of allergic asthma. We performed this analysis using an artificial neural network (ANN), which is a computer-based algorithm that can be trained to recognize and categorize complex patterns [5–8]. ANNs have been used for discrimination between subtly different clinical disease lesions; e.g., premalignant lesion Barrett's versus esophageal cancer, based on microarray data . In a previous study, we performed severity assessment of senile dementia of Alzheimer type using ANN modeling of electroencephalogram data. The average error of the ANN model for assessment scale (HDS-R) score was 2.64 points out of 30 . We have also used an ANN for prediction of 4 allergic diseases using SNP data ; 82 subjects with data for 6 SNPs were analyzed, and the ANN model predicted diagnosis with accuracy of more than 78%. Thus, we have achieved sufficiently high accuracy with ANNs using relatively little SNP data.
Polymorphisms used in the present study.
148 G/A (Val50Ile)
924 T/C (synonym)
265 A/G (Arg16Gly)
811 A/G (Glu237Gly)
2446 A/C (Ile816Leu)
3214 T/A (Cys1072Ser)
3473 C/T (Pro1158Leu)
329 G/A (Arg110Gln)
SNPs selected for diagnostic prediction with ANN
Several reports have suggested linkage between asthma and chromosomes. For example, genes in the 5q31-5q33 region code for Th2-type cytokines (IL-4, IL-13, which regulate B cell heavy-chain class-switching to IgE production)  and ADRB2 (which mediates airway smooth muscle relaxation and protects against bronchial hyperreactivity) [11, 12]. IL-4 operates via the IL-4 receptor (IL-4R), which is encoded by a gene in chromosomal region 16q12. Mice deficient in the IL-4Rα chain lack IgE production and Th2 inflammatory reactions, and it has been shown that total IgE level is dependent on Ile50Val substitution . In the present study, we analyzed 25 SNPs (Table 1) in 17 genes known to be associated with development of asthma. Association between these SNPs and CAA was assessed by P-value. As shown in Table 1, 21 of these 25 SNPs had a P-value greater than 0.1. The P-values of CysLT2 (108 C/A), IL-4Rα (148 G/A), ADRB2 (265 A/G) and C5 (4266 G/A) were 0.0036, 0.0155, 0.0541 and 0.0581, respectively. When CysLT2 (108 C/A), which had the lowest P-value of 25 SNPs, was used for discrimination between case and control as a sole factor, prediction accuracy was 54.4%, and the sensitivity and specificity was 12.8% and 95.9%, respectively, compared with the number of case and control subjects to assess discrimination performance (genotype CC; case 150, control 165, genotype CA or AA; case 22, control 7). Thus, we constructed a susceptible marker-selectable ANN model, which can discriminate between cases and controls using the selected susceptible SNPs, and which can include the association between combinations of SNPs and development of CAA.
Diagnostic prediction using 25 SNPs
Accuracy, sensitivity and specificity of ANN and LR.
Selection of susceptible SNPs for CAA
Ranking of SNPs selected by PDM.
IL-4Rα (148 G/A)
CysLT2 (2534 A/G)
IL-10 (-571 C/A)
C 3 (4896 C/T)
C 3 (1692 G/A)
IKAP (2446 A/C)
IL-13 (329 G/A)
C 3 (912 G/A)
STAT6 (2964 G/A)
IL-4 (-590 C/T)
IKAP (3473 C/T)
ADRB2 (265 A/G)
IKAP (3214 T/A)
C5aR (1289 C/A)
C 5 (4266 G/A)
CysLT2 (108 C/A)
C3aR (1526 G/A)
The results of diagnostic prediction using the 10 SNPs selected by PDM are shown in Figure 2c, and the accuracy, sensitivity and specificity are shown in Table 2b. In the ANN model, the accuracy, sensitivity and specificity with evaluation data were again sufficiently high, and were somewhat similar to the results from the analysis using 25 SNPs, although the number of input variables was markedly smaller than in the analysis using 25 SNPs. In particular, sensitivity was significantly high (77.9%), indicating that case subjects were more correctly diagnosed by this model. To compare with the LR model, LR model consisting of 10 SNPs selected by ANN was constructed (Figure 2d). As shown in Table 2b, the LR model constructed showed low accuracy. This result indicates high performance of ANN modeling for CAA prediction although selected SNPs would not be suitable for LR analysis. We concluded that the ANN model constructed with 10 SNPs could discriminate between cases and controls as precisely as the model constructed with 25 SNPs.
Interaction between SNP and another SNP for CAA
To understand the importance of the 10 SNPs selected, we analyzed combinations of these 10 SNPs. We paid particular attention to SNP combinations associated with CAA, and assessed whether any combinations consisting of SNPs selected by ANN were associated with CAA. The relationships between 2-SNP or 3-SNP combinations and CAA development were examined by calculating P-value using the χ2 test. In models using 10 SNPs selected by PDM or the other 15 SNPs, the total number of 2-SNP combinations and 3-SNP combinations (N comb ) is 90 (10P2) or 210 (15P2), and 360 (10P3/2) or 1365 (15P3/2), respectively. With respect to 2-SNP combination between the SNP of interest and SNP A, P-value was calculated as follows. When patients were limited with certain pattern of another SNP, such as AA major homozygote of SNP A, patient distribution of the SNP of interest was investigated. With respect to 3-SNP combination, between the SNP of interest, and SNP A and B, P-value was calculated as follows. When patients were limited with certain pattern of two other SNPs, such as AA major homozygote of SNP A and BB major homozygote of SNP B, patient distribution of the SNP of interest was investigated.
Selection of effective combinations evaluated with two bases P-value and ECV among the 10 selected SNPs.
Number of effective combinations (N ef ) and its concentration ratio.
10 SNPa:15 SNPb
2 : 0
1 : 1
0 : 2
10 SNPa : 15 SNPb
3 : 0
2 : 1
1 : 2
0 : 3
Two-SNP interactions among the 10 selected SNPs (P-value < 0.05 and ECV2 < 0.5)
SNP 1 genotype
Pb × Pc
Pa/(Pb × Pc)
C 3 (4896 C/T)
C 3 (1692 G/A)
CysLT2 (2534 A/G)
IL-4Rα (148 G/A)
C 3 (1692 G/A)
C 3 (4896 C/T)
C 3 (912 G/A)
C 3 (4896 C/T)
C 3 (4896 C/T)
C 3 (912 G/A)
C 3 (1692 G/A)
CysLT2 (2534 A/G)
STAT6 (2964 G/A)
IL-10 (-571 C/A)
C 3 (4896 C/T)
IL-4Rα (148 G/A)
C 3 (912 G/A)
IL-4Rα (148 G/A)
IL-4 (-590 C/T)
IL-4Rα (148 G/A)
In the next step, 3-SNP combinations were analyzed. The effective rate, the random selection rate, and the concentration ratio were calculated as well as the case of 2-SNP combination (Table 5). It was found to be 2.28 for each of the 10 selected SNPs alone (3:0 in Table 5), 1.33 for 2 of the 10 selected SNPs and 1 of the remaining 15 SNPs (2:1 in Table 5), 0.67 for 1 of the 10 selected SNPs and 2 of the remaining 15 SNPs (1:2 in Table 5), and 0.94 for the remaining 15 SNPs alone (0:3 in Table 5). The concentration ratio was higher for combinations among the 10 selected SNPs than for other combinations, so we can select 3-SNP combinations associated with CAA with high rate. The combination with the lowest ECV3 consisted of the genes IL-4Rα, and C3 (0.03526). This is about 3% of the value multiplied each P-value of 2-SNP combination (0.5060). For patients with genotype GA of IL-4Rα (148 G/A: Val50Ile) and genotype CT of C3 (4896 C/T), patient frequency against genotype of C3 (1692 G/A) had a P-value of 0.01784. For C3 (1692 G/A) alone, a P-value of 0.6993 was obtained, which was 40 times greater than the P-value of the 3-SNP combination. Thus the rate of correct identification of effective combinations evaluated by adjusted P-value and ECV selected based on PDM trials was higher than the corresponding randomized rate, implying that the ANN can reliably select SNP combinations that are associated with CAA.
The present findings also indicate that the 3-SNP combination consisting of IL-10 (-571 C/A), IL-4 (-590 C/T) and C3 (1692 G/A) is a susceptible factor of CAA (P = 0.00426). No association with CAA was found for any of these 3 SNPs alone (P = 0.1074, 0.9085, 0.6993, respectively; Table 1) or for any 2-SNP combinations of them (P = 0.1851, and 0.3002, respectively). Subjects with genotype CA at IL-10 (-571 C/A), genotype CT at IL-4 (-590 C/T) (CAA, 34 subjects; healthy controls, 38 subjects) and genotype GG at C3 (1692 G/A) (CAA, 12 subjects; healthy controls, 6 subjects) were estimated to be at high risk for pathogenesis of CAA. Furthermore, among the subjects with the same genotype pattern, the number of subjects with genotype AA at C3 (1692 G/A) were CAA, 3 and healthy controls, 13, respectively (Figure 5b).
Other remarkable combinations shown in Table 6 were also found among the 10 selected SNPs. For example, the number of cases with GG genotype at IL-4R α ( 148G/A) and TT genotype at C3 (4896C/T) was 4 times the number of controls with that genotype combination (CAA, 20 subjects; healthy controls, 5 subjects) (P = 0.00271). There are no previous reports of association between these genotype combinations and CAA. The combination of IL-4Rα (148 G/A: Val50Ile) and IL-4 (-590 C/T) was also associated with CAA (P = 0.00689); association between allergic asthma and this combination has previously been reported [15, 16].
To characterize the development mechanism, we investigated several relationships between SNPs and development of CAA, referring to previous papers, as described below. IL-4 is produced by Th2 cells, and exerts its activity by interacting with the receptor IL-4Rα, located on the surface of B cells. It has been reported that the V50 (148G)/R551(1827G) combination of IL-4Rα polymorphisms may be associated with enhancement of IL-4Rα function . As concerns the polymorphisms on IL-4, it was reported that the -590T allele increases the strength of the IL-4 promoter compared with the -590C allele . C3 is a proinflammatory mediator that binds to specific cell surface receptors and causes leukocyte activation, smooth muscle contraction and vascular permeability . C3-deficient mice challenged with allergen show diminished airway hyperresponsiveness and lung eosinophilia, with dramatic reduction of the number of IL-4-producing cells and attenuation of IgE responses . In the present study, we found that interaction between genotype TT at C3 (4896 C/T) and genotype GG at IL-4Rα (148 G/A) may be associated with CAA, but details of interaction between these polymorphisms combinations and development mechanisms have not been clarified. The present findings indicate that, among subjects with an IL-10 (-571 C/A) genotype of CA and an IL-4 (-590 C/T) genotype of CT, there is important correlation with a C3 (1692 G/A) genotype of GG or AA (Figure 5b).
CysLTs, which are produced by inflammatory cells including eosinophils, are mediators of leukotrienes, and have been implicated in the pathogenesis of allergic diseases. Recently, it has been reported that CysLTs can act as autocrine or paracrine mediators to stimulate rapid, nonexocytotic release of IL-4 . These findings are consistent with the present results, in which subjects with CT or TT genotype at IL-4 (-590 C/T), AG or GG genotype at CysLT2 (2534 A/G) and GG genotype at IL-4Rα (148 G/A) were estimated to be at high risk for pathogenesis of CAA (P = 0.00022). However, 2-SNP interaction between CysLT2 (2534 A/G) and IL-4Rα (148 G/A) (P = 0.00030) markedly affected the 3-SNP interaction.
In the present study, we examined correlation between CAA and 25 SNPs in 17 genes using an ANN model. We think that there are not a few main effects and interactions which can explain development of multifactorial disease like CAA, because it is thought that interactions of genetic risk factors might be different individually among CAA patients in spite of same disease. So it is very important to select multiple genetic factor models associated with multifactorial disease like CAA with high concentration ratio. We found that 10 of these SNPs are important factors in development of CAA. Important combinations among these 10 SNPs were also extracted. As described above, several of these combinations (listed in Table 6 etc.) have been found to be important factors in allergic disease, in previous biological and epidemiological studies. We also found several novel important combinations. The present data about important combinations suggests multiple patterns of CAA development. It should be noted that these findings were obtained automatically using an ANN model constructed without priori knowledge. Using an ANN model with 10 SNPs, we were able to discriminate between cases and controls with more than 70% accuracy. We concluded that the ANN is an effective tool for predicting development of CAA, using SNP data. However, further investigation of other genetic and environmental factors associated with CAA is needed. We previously constructed an advanced modeling method, the fuzzy neural network [20, 21], which is an ANN model. When this model is applied to analysis, the susceptibility rules of interaction can be explicitly and linguistically described. Also, it can be used to describe susceptible interaction between genetic factors such as SNPs and environmental factors such as favorite foods and life style. Using the rules obtained with this model, we can plan protocols for preventive treatment of subjects with high-risk genetic profiles. Network analysis tools such as ANNs can be applied to analysis of multifactorial disease using SNP data such as selection of important SNPs or description of interactions between SNPs.
Relationships between CAA and 25 SNPs in 17 candidate genes were analyzed using an ANN. In diagnostic prediction, ANN discriminated cases from controls more precisely than LR. From among the 25 original SNPs analyzed, we selected 10 SNPs that were closely associated with CAA. Calculating P-value using the χ2 test, we found that 2-SNP and 3-SNP combinations of these 10 SNPs were associated with CAA. The ANN was able to represent associations between CAA and these 2-SNP or 3-SNP combinations using complicated nonlinear relations. Thus, the ANN can be used to characterize development of complex diseases caused by multiple factors.
Subjects and SNP data
SNP data were kindly provided by the ethics committees of Tohoku University and RIKEN. We analyzed the SNP data for 25 polymorphisms in the 17 genetic regions listed in Table 1. Each SNP was detected using the established method based on TaqMan PCR . The study population comprised 172 subjects with childhood allergic asthma (CAA) who were under 17 years of age and 172 healthy subjects with no signs or symptoms of atopy-related diseases selected from general population, all of whom gave written informed consent for SNP analysis. The subjects were diagnosed by experienced doctors, as "positive" (with allergic asthmatic symptoms) or "negative" (without allergic asthmatic symptoms). In the present paper, the subjects with CAA are referred to as "cases" and the healthy subjects are referred to as "controls". Genotype patterns of the 25 SNPs were compared between cases and controls. None of the cases had genotype patterns coinciding with those of controls.
To use SNP data as input data for the ANN, we converted the genotyping data into 2-numeral data. In ANN modeling, input and output variables are normalized into 0.1–0.9 . In SNP data, there are 3 genotypes per locus. Therefore, we provided 2 inputs per SNP: (0.1, 0.1) for homozygote of the major allele, (0.1, 0.9) for heterozygote, and (0.9, 0.9) for homozygote of the minor allele. Since from the genetic point of view it may be difficult to estimate that heterozygote affects a disease by half the extent that homozygote affects it, the coding of (0.1), (0.5) and (0.9) was never used. The diagnosis data were also converted into numerical data, referred to hereafter as "teacher" values: 0.9 for "positive (case)", and 0.1 for "negative (control)".
For LR, we converted SNP data into numerical input data as follows: (0.1, 0.1) for homozygote of the major allele, (0.1, 0.9) for heterozygote, and (0.9, 0.9) for homozygote of the minor allele. Positive and negative diagnoses were also converted into numerical data: 0.9 and 0.1, respectively.
ANN model and model construction
For SNP analysis, we used a three-layered ANN with input, hidden and output layers (Figure 1). For model construction, the performance index of the ANN was assessed using a method we previously proposed [7, 8], with slight modifications. N error (number of missed points) and Er (sum of squared error) were defined and calculated for learning data and evaluation data as follows:
N error = Nerror,l+ Nerror,e (3)
where Y and T represent the predicted value and the teacher value, respectively. N l and N e represent the number of subjects as learning and evaluation data, respectively. N error is the number of output data with an error of >0.4 between the predicted value and teacher value as shown above. Er is calculated with the square of error as shown above. For ANN learning, the connection weights were initially randomly set from 0 to 1, and were altered using the back propagation methods  with learning data so as to minimize the value of Er l . Learning rates of 0.1, 0.2, 0.3, 0.4 and 0.5 were examined. The maximum learning time was 2000 iterations. The best ANN model (selected for SNP analysis) was that in which N error reached minimum within the maximum learning time. When minimum N error was equal to that of other models within the maximum learning time, the model with minimum Er value was selected.
Prediction accuracy of the constructed model was defined as follows. Threshold was set at 0.5. If the teacher value was 0.9, and the predicted value was greater than 0.5, the prediction was true (true positive; TP); for predicted values lower than 0.5, the prediction was false (false negative; FN). If the teacher value was 0.1, and the predicted value was lower than 0.5, the prediction was true (true negative; TN); for predicted values greater than 0.5, the prediction was false (false positive; FP).
We calculated the prediction accuracy (Ac) as follows:
The sensitivity (Se) and specificity (Sp) of predicted values were defined as follows:
where N TP , N FN , N TN and N FP are the number of TN, FN, TN and FP subjects, respectively. N case and N control are the number of case and control subjects, respectively.
Parameter Decreasing Method (PDM)
In order to extract SNPs closely associated with CAA, we selected the input variables by parameter decreasing method (PDM) after the ANN model with 25 SNPs was constructed. In PDM, 1 SNP was excluded from input variables in turn, and ANN models were constructed with the remaining 24 SNPs by performing the cross-validation described below. From among the 25 models thus constructed, the model with minimum N error averaged in the cross-validation step was selected. When minimum N error was equal to that of other models within the maximum learning time, the model with minimum Er value was selected as described above. The PDM step was repeated until 1 SNP remained as input variable. The PDM procedure was performed 5 times with unifying learning rates of 0.1 and learning time of 2000, and the rank of importance of selected SNPs was determined as described in Results section. We performed 5 PDM trials so that the effects of randomized initial connection weights might be minimized. In 5 PDM trials, data set for cross-validation mentioned below was reconstructed every time.
Cross-validation allows estimation of the prediction error of a model by leaving out a portion of the data as an evaluation data . In the present study, to investigate the flexibility of the ANN, learning and evaluation were performed using the ANN and 5-fold cross-validation. With 5-fold cross-validation, the data set for the 172 cases and 172 controls was divided into 5 groups with randomizing and alternating the data. In each group, the number of cases was equal to that of controls. Four groups were assigned as learning data, and 1 group was assigned as evaluation data; this learning and evaluation process was repeated 5 times, so that each group was assessed once as evaluation data. Then, the prediction accuracy of evaluation data across all 5 trials was calculated and averaged for the overall prediction accuracy of the ANN model shown in Table 2. Sensitivity and specificity were also calculated.
Logistic Regression (LR) Model
An LR model was constructed using SPSS 11.5J statistic software for Windows (SPSS Japan Inc., Tokyo), for comparison with the ANN model. All 25 SNPs were used as input variables of LR. For LR analysis, we used 50 main effects plus an intercept but not any interaction terms. As with the ANN model, the data set was divided into 5 groups and the cross-validation was performed. Prediction accuracy, sensitivity and specificity were calculated.
Determination of differences in frequency of alleles and genotypes
We also examined association between CAA and combinations of SNPs by calculating P-value using a χ2 test. The χ2 test was used to evaluate the differences in frequencies of alleles or genotypes between cases and controls. The P-values shown in Table 1 were calculated using 172 cases and 172 controls. Degree of freedom (D.F.) (shown in Table 1) was 2 for 3 types of subjects; e.g., homozygote of the major allele, heterozygote, and homozygote of the minor allele. In the test with one SNP, when the expectancy for subjects homozygous for the minor allele (calculated from the frequency of the genotype) was less than 5 subjects for both case and control, we regarded the homozygote of the minor allele and the heterozygote as identical and defined degree of freedom as 1. In the tests with 2-SNP and 3-SNP combinations, we used the D.F. shown in Table 1 to find the change of differences in frequency under the same condition of SNP alone. If, in more than 5 subjects, all expectancies for subjects satisfied the test conditions, we calculated P-value with χ2 test. In order to determine important combinations, we use two evaluation bases (P-value and effective combination value (ECV)) mentioned in Results section.
- Mannino DM, Homa DM, Akinbami LJ, Moorman JE, Gwynn C, Redd SC: Surveillance for asthma-United States, 1980–1999. MMWR CDC Surveill Summ 2002, 51: 1–13.Google Scholar
- Thomas NS, Wilkinson J, Holgate ST: The candidate region approach to the genetics of asthma and allergy. Am J Respir Crit Care Med 1997, 156: S144–151.View ArticlePubMedGoogle Scholar
- Nanavaty U, Goldstein AD, Levine SJ: Polymorphisms in candidate asthma genes. Am J Med Sci 2001, 321: 11–16. 10.1097/00000441-200101000-00003View ArticlePubMedGoogle Scholar
- Steinke JW, Borish L, Rosenwasser LJ: 5. Genetics of hypersensitivity. J Allergy Clin Immunol 2003, 111: S495–501. 10.1067/mai.2003.143View ArticlePubMedGoogle Scholar
- Ritchie MD, White BC, Parker JS, Hahn LW, Moore JH: Optimization of neural network architecture using genetic programming improves detection and modeling of gene-gene interactions in studies of human diseases. BMC Bioinformatics 2003, 4: 28. 10.1186/1471-2105-4-28PubMed CentralView ArticlePubMedGoogle Scholar
- Yan X, Selaru FM, Jing Y, Zou TT, Shustova V, Mori Y, Sato F, Liu TC, Olaru A, Wang S, Kimos MC, Perry K, Desai K, Greenwald BD, Krasna MJ, Shibata D, Abraham JM, Meltzer SJ: Artificial neural networks and gene filtering distinguish between global gene expression profiles of Barrett's esophagus and esophageal cancer. Cancer Research 2002, 62: 3493–3497.Google Scholar
- Hanai T, Hibino S, Nagata E, Matsubara M, Fukagawa K, Shirataki T, Honda H, Kobayashi T: Assessment of senile dementia of Alzheimer type using artificial neural networks. Jpn J Med Electro Biol Eng 1999, 37: 178–183. (in Japanese).Google Scholar
- Tomida S, Hanai T, Koma N, Suzuki Y, Kobayashi T, Honda H: Artificial neural network predictive model for allergic disease using single nucleotide polymorphisms data. J Biosci Bioeng 2002, 93: 470–478.View ArticlePubMedGoogle Scholar
- Bishop CM: Neural networks for pattern recognition. Oxford: Clarendon Press 1995.Google Scholar
- Marsh DG, Neely JD, Breazeale DR, Ghosh B, Freidhoff LR, Ehrlich-Kautzky E, Schou C, Krishnaswamy G, Beaty TH: Linkage analysis of IL4 and other chromosome 5q31.1 markers and total serum immunoglobulin E concentrations. Science 1994, 264: 1152–1156.View ArticlePubMedGoogle Scholar
- Green SA, Turki J, Bejarano P, Hall IP, Liggett SB: Influence of beta 2-adrenergic receptor genotypes on signal transduction in human airway smooth muscle cells. Am J Respir Crit Care Med 1995, 13: S25–33.Google Scholar
- Ulbrecht M, Hergeth MT, Wjst M, Heinrich J, Bickeboller H, Wichmann HE, Weiss EH: Association of β2-adrenoreceptor variants with bronchial hyperresponsiveness. Am J Respir Crit Care Med 2000, 161: 469–474.View ArticlePubMedGoogle Scholar
- Mitsuyasu H, Izuhara K, Mao XQ, Gao PS, Arinobu Y, Enomoto T, Kawai M, Sasaki S, Dake Y, Hamasaki N, Shirakawa T, Hopkin JM: Ile50Val variant of IL4R alpha upregulates IgE synthesis and associates with atopic asthma. Nat Genet 1998, 19: 119–120. 10.1038/472View ArticlePubMedGoogle Scholar
- Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR: A simulation study of the number of events per variable in logistic regression analysis. J Clin Epidemiol 1996, 49: 1373–1379. 10.1016/S0895-4356(96)00236-3View ArticlePubMedGoogle Scholar
- Rosenwasser LJ, Klemm DJ, Dresback JK, Inamura H, Mascali JJ, Klinnert M, Borish L: Promoter polymorphisms in the chromosome 5 gene cluster in asthma and atopy. Clin Exp Allergy 1995, 25: 74–78.View ArticlePubMedGoogle Scholar
- Risma KA, Wang N, Andrews RP, Cunningham CM, Ericksen MB, Bernstein JA, Chakraborty R, Hershey GK: V75R576 IL-4 receptor α is associated with allergic asthma and enhanced IL-4 receptor function. J Immunol 2002, 169: 1604–1610.View ArticlePubMedGoogle Scholar
- Humbles AA, Lu B, Nilsson CA, Lilly C, Israel E, Fujiwara Y, Gerard NP, Gerard C: A role for the C3a anaphylatoxin receptor in the effector phase of asthma. Nature 2000, 406: 998–1001. 10.1038/35023175View ArticlePubMedGoogle Scholar
- Drouin SM, Corry DB, Kildsgaard J, Wetsel RA: The absence of C3 demonstrates a role for complement in Th2 effector function in a murine model of pulmonary allergy. J Immunol 2001, 167: 4141–4145.View ArticlePubMedGoogle Scholar
- Bandeira-Melo C, Hall JC, Penrose JF, Weller PF: Cysteinyl leukotrienes induce IL-4 release from cord blood-derived human eosinophils. J Allergy Clin Immunol 2002, 109: 975–979. 10.1067/mai.2002.124269View ArticlePubMedGoogle Scholar
- Horikawa S, Furuhashi T, Uchikawa Y, Tagawa T: A study on fuzzy modeling using fuzzy neural networks. Proceedings of International Fuzzy Engineering Symposium '91 1991, 562–573.Google Scholar
- Ando T, Suguro M, Kobayashi T, Seto M, Honda H: Multiple fuzzy neural network system for outcome prediction and classification of 220 lymphoma patients on the basis of molecular profiling. Cancer Sci 2003, 94: 906–913.View ArticlePubMedGoogle Scholar
- Fujii K, Matsubara Y, Akanuma J, Takahashi K, Kure S, Suzuki Y, Imaizumi M, Iinuma K, Sakatsume O, Rinaldo P, Narisawa K: Mutation detection by TaqMan-allele specific amplification: application to molecular diagnosis of glycogen storage disease type Ia and medium-chain acyl-CoA dehydrogenase deficiency. Hum Mutat 2000, 15: 189–196. 10.1002/(SICI)1098-1004(200002)15:2<189::AID-HUMU8>3.3.CO;2-8View ArticlePubMedGoogle Scholar
- Rumelhart DE, Hinton GE, Williams RJ: Learning representation by back-propagation errors. Nature 1986, 323: 533–536.View ArticleGoogle Scholar
- Hastie T, Tibshirani R, Friedman J: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics 2001.Google Scholar
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