Introduction

Lung cancer is the leading cause of cancer death in both men and women in the U.S and an estimated 158,040 Americans are expected to die from lung cancer in 2015, accounting for approximately 27% of all cancer deaths (CDC, 2014). The most common environmental risk factor for sporadic lung cancer is smoking and radon (Alberg and Samet, 2003). However, there are large variations in an individual’s susceptibility to lung cancer and the heritability of lung cancer is estimated to be 8–14% (Czene et al., 2002; Hemminki et al., 2001). Only a fraction of smokers (~15%) will develop lung cancer in their lifetime, and non-smokers also can develop lung cancers (Spitz et al., 2003). A number of cancer genes such as K-ras, p53, Rb, EGFR, HER2-neu have been identified whose mutations contribute to lung cancers (Ding et al., 2008; Iggo et al., 1990; Johnson et al., 2001; Paez et al., 2004; Takahashi et al., 1989).

Efforts to identify quantitative susceptibility loci in lung cancer have mostly involved genome-wide association studies (GWAS) and identified a number of lung cancer risk single-nucleotide polymorphisms (SNPs; Amos et al., 2008; Landi et al., 2009; Ryan et al., 2015; Zhu et al., 2008). However, they account for a very small fraction of lung cancer cases and their mechanisms of action remain largely unknown (Gibson, 2012).

Known predictive models of lung cancers mostly use smoking status, radon exposure, and family history (Spitz et al., 2007). However, these models cannot predict pre-birth risk or risk long before incidence. Researchers have also used a set of susceptibility loci to create a genetic risk score to better predict lung cancer risk (Jostins and Barrett, 2011; Li et al., 2012; Weissfeld et al., 2015). But these predictions were generally poor and not meaningful for clinical use. It has been shown that many complex traits or diseases are associated with an accumulation of enormously large numbers of variants of small effects (Boyle et al., 2017; Purcell et al., 2009).

An allele can be a major allele or minor allele (MA) according to its frequency in the population and the minor allele has frequency <0.5. Most known risk alleles are MAs (Park et al., 2011). We have shown that the collective effects of a genome-wide collection of MAs in an individual are linked with risk for Parkinson’s disease (Zhu et al., 2015), reproductive fitness (Yuan et al., 2014), diabetes (Gui et al., 2017; Lei and Huang, 2017) and schizophrenia (He et al., 2017). The MA content (MAC) of an individual may be at optimal balance with negative selection on both too high or too low MAC values (Yuan et al., 2014). MAC has also been linked with lung cancer in a mouse lung cancer model (Yuan et al., 2014). Lung cancer is a complex disease with causal factors not yet completely identified. Thus, we suspected that MAC may play a role in lung cancer. If a few major effect mutations can cause cancer, it is not unexpected that numerous minor effect mutations or the so called passenger mutations may also increase cancer risk (Gibson, 2012; McFarland et al., 2017).

We here aimed to study the overall level of genome-wide randomness in lung cancer cases relative to controls as measured by total MA amounts in an individual. We also attempted to identify a set of MAs that can predict lung cancer risks.

Materials and methods

SNPs data sets

We downloaded from database of Genotypes and Phenotypes (dbGaP) (https://www.ncbi.nlm.nih.gov/gap) one case control GWAS data set, phs000336.p1.v1. Its dbGaP web page described 5699 cases and 5818 controls, but in fact, only ~3900 controls and ~3800 cases were available to be downloaded, and it consisted of SNPs data sets from five Illumina platforms: (1) HumanHap240Sv1.0 (genotyping ~30 cases and ~1100 controls at 243,991 Oligos/SNPs), (2) HumanHap300v1.1 (genotyping the same individuals as HumanHap240Sv1.0 at 317,503 Oligos/SNPs), (3) HumanHap550v3.0 (genotyping ~770 cases and ~850 controls at 561,466 Oligos/SNPs), (4) Human610_Quadv1_B (genotyping ~3000 cases and ~1800 controls at 620,901 Oligos/SNPs), (5) Human1M-Duov3_B (genotyping ~150 controls at 1,199,187 Oligos/SNPs).

Since the data set 1 above shared only ~330,000 SNPs with other platforms data sets, it was excluded. In addition, identical individuals were also removed, who were genotyped by both Human610_Quadv1_B and HumanHap550v3.0 platforms. The remaining samples (6576 individuals [3782 cases and 2794 controls] with 551,741 SNPs overlapped) were genotyped by Illumina Human610_Quadv1_B or Human1M-Duov3_B or HumanHap550v3.0 platforms. They came from three studies: (1) the Cancer Prevention Study II Nutrition Cohort (CPS-II) (enrolled in the U.S.), (2) the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study (ATBC) (enrolled in Finland), and (3) the Prostate, Lung, Colon and Ovary Study (PLCO) (enrolled in the U.S.) (1994; Calle et al., 2002; Hayes et al., 2005; Landi et al., 2009). So, these individuals were from US and Finland. Cases were admitted based on chest X ray examination. Participants are all European descendant. We also downloaded from 1000 Genomes Project (1kGP) (http://www.internationalgenome.org) involving 2504 individuals from multiple population groups with a total of ~84.4 million variants (Auton et al., 2015).

Subjects selection

Principal components analysis (PCA) is common in assessing population structure and genetic background. While the chosen thresholds based on PCA to exclude outliers were somewhat arbitrary in common practice, our priority was to include as many samples as possible when no clear genetic substructures could be found as visually judged from the PCA plot. We used the software GCTA to calculate the value of principal components of each sample and figures were plotted with R version 3.2.2. We removed individuals that appeared to be outliers. As illustrated in Supplementary Figure S1, even though all individuals are of European descent, US samples and Finland samples were clustered differently. So we performed separate analyses for these two different sets of samples. For the 3580 US samples, we selected these PC value ranges: −0.005 < PC1 < 0.015, −0.01 < PC2 < 0.005, and −0.04 < PC3 < 0.01 (Supplementary Figure S2A and S2B). For the 2996 Finland samples, we selected these PC value ranges: −0.02 < PC1 < 0.03, −0.03 < PC2 < 0.02, and −0.04 < PC3 < 0.04 (Supplementary Figure S3A and S3B). For 1kGP samples, PCA was also performed (Supplementary Figure S2C and S2D, Supplementary Figure S3C and S3D).

SNPs quality control (QC)

We next performed a SNP-level set of QC steps. SNPs were filtered by removing those with >5% non-informative calls in the population, and those not following the Hardy-Weinberg equilibrium in either the case group or the control group (P < 0.0001 chi square test), and those with MAF < 0.01. Only autosome SNPs were used. Samples with >10% missing SNPs and non-founders were excluded (i.e. only parents were retained in cases where their children were also sampled). Overall, these steps resulted in two data sets with ~510,000 SNPs (from 551,741 in phs000336.p1.v1). The description of cleaned up data sets is shown in Table 1.

Table 1 Number of individuals and SNPs in the final (post-QC) data set
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Statistical analysis

Minor allele frequency (MAF) refers to the frequency at which the second most common allele occurs in a given population. MAs were defined as those alleles with MAF < 0.5 in the control group. The MAC of an individual is the number of MAs divided by the total number of SNPs examined (Yuan et al., 2014). We used a custom script to calculate the MAC values of case and control groups (https://github.com/health1987/dist). Difference in the average MAC value was compared by t test. PLINK was used to calculate a linkage disequilibrium (LD) (r2) score for each pair of SNPs in a window of 200 kb SNPs, and one SNP from the pair was excluded if r2 > 0.4. To justify this r2 threshold, we also tested the results at other r2 levels (i.e. r2 = 0.05, r2 = 0.1, r2 = 0.2, r2 = 0.3, r2 = 0.4, r2 = 0.5, r2 = 0.6, r2 = 0.7, r2 = 0.8 r2 = 0.9 and r2 = 1).

For each GWAS data set (the US data set and the Finland data set), we used PLINK (Purcell et al., 2007) to perform logistic regression test, which allows for multiple covariates when testing for disease trait SNP association, and obtained regression coefficient (beta) and asymptotic P-value for each SNP. A positive regression coefficient (beta) means that the minor allele increases risk mean. Logistic regression details including getting beta of SNPs using PLINK (Purcell et al., 2007) have been reported previously (Hagenaars et al., 2017).

Risk prediction model

Since the US cohort includes 2177 individuals (1209 cases and 968 controls) and was a bit more than the 1999 individuals (1139 cases and 860 controls) in the Finland cohort, so we only performed risk prediction analysis in the former data set. The US data set was randomly separated into training (716 cases/590 controls), validation 1 (242 cases/193 controls), and validation 2 (251 cases/185 controls) cohorts at a ratio of 6:2:2.

Using logistic regression test, we obtained regression coefficient (beta) for each SNP in the GWAS data set that was used as the training set. Since a positive beta means that the minor allele increases risk mean, we used four methods to create genetic risk score (GRS): (1) adding up the weighted value of each risk allele regardless whether the beta was positive or negative, (2) adding up the non-weighted value of each risk allele regardless whether the beta was positive or negative, (3) adding up the weighted value of each risk allele with positive beta, and (4) adding up the non-weighted value of each risk allele with positive beta.

$${\mathrm{wGRS}} = \mathop {\sum}\limits_{{\mathrm{i}} = 1}^{\mathrm{n}} {{\mathrm{beta}}_{{\mathrm{SNPi}}}} + 0.5 \ast \mathop {\sum}\limits_{{\mathrm{j}} = 1}^{\mathrm{m}} {{\mathrm{beta}}_{{\mathrm{SNPj}}}}$$
(1)

SNPi represents MAs in homozygous state and SNPj represents MAs in heterozygous state. A custom script was used to calculate the total weighted genetic risk score (wGRS) according to equation (1).

$${\mathrm{GRS}} = \mathop {\sum}\limits_{{\mathrm{i}} = 1}^{\mathrm{n}} {{\mathrm{SNP}}_{\mathrm{i}}},$$
(2)

where the GRS was the total number of MAs of SNPs chosen. For each locus, SNPi is 0, 1 or 2 depending on whether the site was homozygous major alleles, heterozygous, or homozygous minor alleles. We obtained GRS of individuals by using a custom script according to equation (2) (Supplementary Materials).

$${\mathrm{wGRS}}_{\mathrm {positive}} = \mathop {\sum}\limits_{{\mathrm{i}} = 1}^{\mathrm{n}} {{\mathrm{beta}}_{{\mathrm{SNPi}}}} + 0.5 \ast \mathop {\sum}\limits_{{\mathrm{j}} = 1}^{\mathrm{m}} {{\mathrm{beta}}_{{\mathrm{SNPj}}}}$$
(3)

Only SNPs with positive beta were considered for equation (3).

$${\mathrm{GRS}}_{\mathrm {positive}} = \mathop {\sum }\limits_{{\mathrm{i}} = 1}^{\mathrm{n}} {\mathrm{SNP}}_{\mathrm{i}}$$
(4)

Only SNPs with positive beta were considered for equation (4).

Based on the logistic regression test, we also obtained asymptotic P-value for each SNP in the GWAS training set. In order to obtain a best model for risk prediction, SNPs at 19 different P-values (<0.001, <0.003, <0.005, <0.007, <0.009, <0.01, <0.02, <0.03, <0.04, <0.05, <0.06, <0.07, <0.08, <0.09, <0.1, <0.3, <0.5, <0.7 and <1) in training data set were chosen at first among all SNPs studied here (i.e. 19 risk prediction models were created). In addition, to avoid overfitting of the prediction model on the training set from which the SNPs set was derived, LD clumping was performed in the training cohort. Different SNPs were chosen to construct the genetic risk score (GRS) at different P-value thresholds (same as above) and different LD r2 thresholds (r2 = 1, r2 = 0.9, r2 = 0.8, r2 = 0.7, r2 = 0.6, r2 = 0.5, r2 = 0.4, r2 = 0.3, r2 = 0.2, r2 = 0.1 and r2 = 0.05) (i.e, 19 × 11 = 209 models were created). Here, 19 + 209 = 228 models were built. So, the final total number of models was 4 × 228 = 912 models for the US training data set (716 cases/590 controls), taking into account of four methods (wGRS, GRS, wGRSpositive and GRSpositive) and 228 models per method.

Risk prediction evaluation

We performed the internal validation twice to estimate the predictive power of the models; in the first phase, a models’ performance was evaluated based on validation 1 data set (242 cases/193 controls); only those performing well could enter the second phase in which the models were evaluated based on validation 2 data set (251 cases/185 controls); results from validation 2 were used to quantify model performance. Each experiment’s discriminatory capability was evaluated using the receiver operating characteristic (ROC) curve. We then calculated the AUC using GraphPad Prism 6 and the “pROC” R package. In order to obtain a MA set performing well in risk prediction by using one of the four methods (wGRS, GRS, wGRSpositive and GRSpositive), 228 models were respectively constructed for each method based on P-value from logistic regression test and LD clumping r2 or no LD clumping. We then obtained AUC of each model in the validation 1 data set.

The model performing well and stably in two internal validation experiments was chosen as the final prediction model for each method. The Hosmer–Lemeshow test is a statistical test for goodness of fit for logistic regression models, which is used frequently in risk prediction models (Alba et al., 2017; Hosmer et al., 1997; Krag et al., 1998). We used “RSADBE” R packages and “pscl” R packages to perform the Hosmer–Lemeshow goodness-of-fit test (HL test) for assessing this model calibration; calibration refers to the accuracy of absolute risk estimates (Alba et al., 2017); when the P-value from this test is larger than 0.05, the model can be considered as well calibrated.

Comparison with existing methods

Since GRS proposed above is also a sort of polygenic risk score (PRS) (Purcell et al., 2009), assuming the collective effect of many SNPs, we compared its prediction accuracy with other PRS-based methods (such as PRSice (Euesden et al., 2015), LDpred (Vilhjalmsson et al., 2015), and AnnoPred (Hu et al., 2017)). For PRSice (Euesden et al., 2015; Hagenaars et al., 2017), SNPs were first chosen based on passing both LD pruning (0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1) and GWAS p-value thresholding (0.001, 0.003, 0.005, 0.007, 0.009, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.3, 0.5, 0.7, 1). Polygenic scores were then calculated by summing up alleles associated with lung cancer, weighted by odds ratio from logistic regression test. For LDpred (Vilhjalmsson et al., 2015), SNPs were screened first using different fractions of causal variants (1, 0.3, 0.1, 0.03, 0.01, 0.003, 0.001, 0.0003, 0.0001); the posterior effect size of each SNP was then inferred based on odds ratio and LD information followed by risk score calculations. AnnoPred (Hu et al., 2017) is similar to LDpred but leverages functional annotations to reevaluate SNPs effect. All the evaluation and identification for models were performed in the two phased internal validation as we did for GRS.

Pathway enrichment analysis

We used ANNOVAR (Wang et al., 2010) to annotate the genes associated with the set of risk SNPs identified by the above analysis. We used WebGestalyR (Wang et al., 2013) tool to check the pathways associated with these genes in the Kyoto Encyclopedia of Genes and Genomes database (KEGG). The enriched pathways in the risk SNPs set were compared by chi square test with a group of SNPs chosen randomly.

Risk prediction in other population

For the model performing the best in the US population, its predictive value was also estimated in another independent cohort (the Finland population).

Results

Enrichment of minor alleles in lung cancer cases

We used a previously published GWAS data set of lung cancer case and control cohorts for our studies (Landi et al., 2009). The cleaned data sets after removing genetic outliers were described in Table 1. Total number of samples used here was 2348 cases and 1828 controls including the US cohort and the Finland cohort. In each cohort, we used the control data set for identifying minor allele status, and calculated the MAC value of each individual.

For the US samples who were all of European descent, there were 511,807 autosomal SNPs after QC. For SNPs set with MAF < 0.5 (including 511,547 SNPs), the average MAC value of controls was significantly lower than that of cases (Fig. 1a and Table 2). We further performed the MAC analyses by using subsets of SNPs. After filtering by LD at different r2 levels (Table 2), we obtained many subsets of autosomal SNPs. For example, when r2 = 0.05, there were 21,974 SNPs, and the average MAC value of controls was also significantly lower than that of cases (Table 2). The results were similar in other subsets of various r2 levels (Table 2).

Fig. 1
figure 1

Comparison of average MAC values. Shown are US samples (a, b) and Finland samples (c, d). Either all autosomal SNPs (a, c) or only those shared with 1 kGP were used for analysis (b, d). *** P < 0.001, and * P < 0.05. Student’s t test. Standard error of mean (SEM) values are shown

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Table 2 MAC (mean ± SD) comparison in the US samples
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In addition, we repeated the MAC analysis by comparing the cases of the US cohort with a different control group, the European group of 1kGP (Auton et al., 2015). The US cohort shared 398,279 with 1kGP. Based on PCA (Supplementary Figure S2C and S2D), 210 unrelated individuals from 1kGP remained after removal of outliers. They were similar to the US group in genetic background and mostly Northern and Western European ancestry (CEU) and Iberian ancestry of Spain (IBS). Among the 398,279 SNPs shared with 1kGP, only 7348 SNPs showed different MA status between the US control group and 1kGP. The majority of these 7348 SNPs had MAFs near 0.5 (~99.8% SNPs with MAF > 0.4), which would make the MA assignment less certain, and were hence excluded. We further removed those SNPs with MAF = 0.5 or MAF = 0 in the US control group or 1kGP group. For the remaining 389,969 SNPs (MAF > 0 and < 0.5 in 1kGP), the average MAC of cases was significantly higher than controls (Fig. 1b and Supplementary Table S1). Therefore, the result of higher MAC in cases could be verified by using a cohort not associated with the original case control studies. For subsets of SNPs based on LD clumping at many r2 levels (Supplementary Table S1), no difference in MAC was found for some subsets that had lower numbers of SNPs (19,954 SNPs remained at r2 = 0.05 and 42,958 SNPs remained at r2 = 0.1). However, for subsets with relatively more SNPs, the average MAC of cases was again significantly higher than controls (Supplementary Table S1). We also examined SNPs with MAF <0.5 but >0.05, and found the average MAC of cases to be more significantly higher than that of controls (data shown in Supplementary Table S2).

For the Finland samples, there were 512,363 autosomal SNPs after QC. For SNPs set with MAF <0.5 (including 512,106 SNPs), the average MAC value of control was significantly lower than that of cases (Fig. 1c and Table 3). We further performed the MAC analyses on subsets of SNPs based on LD clumping and observed higher MAC in cases in all subsets (Table 3).

Table 3 MAC (mean ± SD) comparison in the Finland samples
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We also compared the cases of the Finland cohort with another control group, the European group of 1kGP. The Finland cohort shared 398,138 SNPs with 1kGP. Based on PCA (Supplementary Figure S3C and S3D), 98 unrelated individuals from 1kGP remained after removal of outliers, and were mainly of Finish ancestry (FIN). Among the 398,138 SNPs shared with 1kGP, 10,885 SNPs showed different MA status between the Finland control group and 1kGP. The majority of these 10,885 SNPs had MAFs near 0.5 (~99.9% SNPs with MAF > 0.4), which would make the MA assignment less certain, and were hence deleted. We also removed those SNPs with MAF = 0.5 or MAF = 0 in the Finland control group. For the remaining 385,616 SNPs (MAF > 0 and MAF < 0.5 in 1kGP), the average MAC of cases was significantly higher than controls (Fig. 1d and Supplementary Table S3). Therefore, the result of higher MAC in cases could be verified by using a cohort not associated with the original case control studies. We further analyzed subsets of SNPs-based LD clumping at many different r2 levels (Supplementary Table S3). Higher MAC in cases were observed for all SNPs subsets with relatively large number of SNPs (>37,120). We also examined SNPs with MAF < 0.5 but >0.05 (removed rare SNPs), and found the average MAC of cases to be more significantly higher than that of controls (data shown in Supplementary Table S4).

Distinguish cases from controls

Since the MAC of cases was higher than that of controls, we aimed to distinguish cases from controls based on MAC values. However, although the average MAC of cases was significantly higher than controls (P < 0.0001), MAC values alone could not produce clear separation of cases from controls (Fig. 2a, b). We therefore generated a wGRS by taking into account of beta values from logistic regression analyses. The total MA number of each individual was then converted into a total wGRS by adding the coefficient of each MA (major alleles were not counted). By converting MAC into the wGRS, the results showed clear separation of cases and controls in both the US and the Finland data sets (Fig. 2c, d).

Fig. 2
figure 2

The distribution pattern of MAC and wGRS. MAC (a and b) and wGRS (c and d) values in the US data set (a and c) and the Finland data set (b and d) were plotted against the number of individuals

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Risk prediction

We next aimed to obtain a specific set of MAs from a training data set that could be used to predict lung cancer risk for an unrelated data set (validation data set). Since the US data set and Finland data set were genetically different groups (see PCA plot Supplementary Figure S1) and the US data set had larger sample size, we only performed risk prediction studies on the US cohort.

We calculated GRS by counting minor alleles only or by also taking into account regression coefficient (beta). For a MA, when its frequency in the case group is larger than that in the control group, the beta would be positive. We generated four types of GRS metrics. GRS and GRSpositive were just minor allele counts and GRSpositive only counted MAs with positive beta. wGRS had MA counts weighted by beta of both positive and negative, and wGRSpositive only weighted MAs with positive beta. For each score, 228 models were created according to P-values from logistic regression test and LD r2 levels or no LD clumping (Fig. 3). Then, in the first phase internal validation, we used the ROC curve and AUC to examine the discriminatory capability of each model in validation 1 data set (242 cases/193 controls).

Fig. 3
figure 3

Discriminatory ability of prediction models. Four different scoring methods are shown. a wGRS method; b GRS method; c wGRSpositive method and d GRSpositive method

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For wGRS method in validation 1 data set (Fig. 3a), 30 out of 228 models had AUC ≥ 0.55, and were further evaluated in validation 2 data set (251 cases/185 controls). The model performing the best in the validation 2 data set was identified as LD r2 = 0.2, P = 0.07, AUC = 0.554 [95%CI = 0.4996–0.6075]. Similar analyses identified the best model for the other three methods as shown in Table 4.

Table 4 AUC of different methods
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As shown in Table 4, the model with highest AUC (0.5591, 95% CI:0.5051–0.613) was created by the wGRSpositive method. The wGRSpositive model consisted of 5400 SNPs (LD r2 = 0.3 and GWAS P-value = 0.08) (Supplementary Table S5). Hosmer–Lemeshow goodness-of-fit test found this best model to be well calibrated (P = 0.46). As a comparison, we also similarly analyzed our previous work on Parkinson’s disease (Zhu et al., 2015). Among the ~820,000 SNPs analyzed, there were ~420,000 SNPs with positive beta. The risk prediction model performing the best was a wGRS model containing ~37,000 SNPs with MAF < 0.4 and P-value < 0.05. The AUC (0.5795, 95% CI: 0.5391–0.6199) was higher than of that using only SNPs with positive beta (~20,000 SNPs, AUC = 0.555, 95% CI: 0.5149–0.5951) or that with negative beta (~17,000 SNPs, AUC = 0.5713, 95% CI: 0.5314–0.6112). Therefore, the two scoring methods wGRS and wGRSpositive may perform differently in different diseases.

Comparison with existing methods

We used three previously published PRS methods to create risk scores based on the US training data set, PRSice (Euesden et al., 2015), LDpred (Vilhjalmsson et al., 2015) and AnnoPred (Hu et al., 2017). These methods were similarly evaluated in two internal validation analyses, and the best performing models were shown in Table 4. They all appeared to have lower AUC values than the wGRSpositive model.

Pathway enrichment

Using ANNOVAR (Wang et al., 2010), we identified 4832 genes in the best wGRSpositive model containing 5400 risk SNPs. We then used WebGestalyR (Wang et al., 2013) to look for KEGG pathways associated with each of these genes. A total of 39 KEGG pathways were identified with false discovery rate <0.05 (Supplementary Table S6). We also similarly studied a 5400 SNPs set chosen at random, which corresponded to 4954 genes. These genes were enriched in some pathways (Supplementary Table S7). We identified ten pathways that were enriched in the risk set relative to the random SNPs set (Table 5). Some of these pathways are known to be linked to small cell lung cancer, melanoma, prostate cancer (adherens) (Ramteke et al., 2015), and breast cancer (estrogen) (Yamaguchi et al., 2005).

Table 5 Pathways enrichment
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Risk prediction in other population

In addition, for the 5400 SNPs wGRSpositive model performing the best in the US population, its predictive value was low in the Finland population (AUC = 0.4982, 95% CI: 0.4727–0.5238). Thus, the prediction model identified here was highly population specific.

Discussion

In the present study, we showed enrichment of MAs in lung cancer cases relative to matched controls, suggesting a role for the collective effects of polygenic variations in the risk for lung cancer. We also calculated wGRSpositive of each subject based on MA status of SNPs and did risk prediction. We identified a set of MA of common SNPs that can be used to identify subjects at risk of lung cancer.

The result of higher MAC in lung cancer cases is a novel finding not expected by known works on human lung cancers. It confirms the previous result showing MAC association with lung cancer in a mouse lung cancer model (Yuan et al., 2014). Published lung cancer risk SNPs are relatively few in numbers. Therefore, even if these known risk alleles are mostly minor alleles, it may not predict that cases should have more MAs when a genome-wide collection of ~500k SNPs are considered. If most MAs are not related to lung cancer except those few published lung cancer alleles, the average MAC of cases should not be significantly different from the controls.

Our study here further strengthened the observation that human genetic diversities are presently at optimum level (Huang, 2008; Huang, 2009; Huang, 2016; Yuan et al., 2017; Zhu et al., 2015). While it may only take one or a few major effect errors to cause diseases, it would require the collective effects of many minor effect errors to achieve a similar outcome. Cancer is known to be a disease of random mutations. Individuals with too many inherited random mutations or MAs may need fewer somatic mutations to pass the cancer threshold and hence have high susceptibility to cancer.

AUC has been used in many studies for gauging performance of prediction model (Alba et al., 2017; Kang et al., 2011; O’Connell et al., 2016). Our predictive model of lung cancer was comparable to previous results as indicated by AUC values (Li et al., 2012). Our best predictor model has a AUC of 0.559 as verified by validation experiment. It seems to be low but may still be meaningful. In addition, calibration is one of the most important metrics for prediction models (Alba et al., 2017). Our best predictor model is well calibrated while many previous models did not take this into consideration (Hagenaars et al., 2017; Kang et al., 2011; Lei and Huang, 2017; Li et al., 2012).

The results here indicate interesting differences in the role of MAC between lung cancer and Parkinson’s disease (Zhu et al., 2015). Some epidemiological work showed that cancer seemed to occur less frequently in the context of Parkinson’s disease (Devine et al., 2011). Only SNPs with positive beta or higher frequency in cases were found useful in prediction models in the case of lung cancer but not Parkinson’s disease. Evidence suggests that there is an optimal balance in MAC of an individual (Yuan et al., 2014). Minor alleles are in general under more negative selection but also essential for certain physiological functions such as immunity. Certain diseases may be linked to collective effects of minor alleles with increased frequency in cases, while certain other diseases may also involve a fraction of minor alleles with decreased frequency in cases. As minor alleles are beneficial for adaptive immunity (Yuan et al., 2014), one may speculate that decreased immunity or some other physiological functions may play a relatively more important role in Parkinson’s disease.

After comparing prediction accuracy of the present wGRSpositive method with that of previous PRS method, we observed slightly improved results (wGRSpositive: 0.5591 [95% CI 0.5051–0.613]; PRSice: 0.5492 [95% CI 0.4952–0.6032]; LDpred: 0.525 [95% CI 0.4707–0.5794]; AnnoPred: 0.5226 [95% CI 0.4677–0.5774]). That these methods showed similar performance may not be unexpected given that all are based on the theory of polygenic inheritance for complex diseases. However, the PRSice method excludes SNPs from transversion mutations, which may decrease its power (Euesden et al., 2015; Lei and Huang, 2017). In addition, we noticed GRSpositive method (AUC: 0.5576 [95% CI 0.5036–0.6116]) showed similar results as wGRSpositive method (AUC: 0.5591 [95% CI 0.5051–0.613]). So, wGRS method only performed slightly better than non-wGRS method. However, since the sample size in our study was relatively small, it remains to be seen how these various risk scoring methods may differ in future studies involving larger sample sizes.

We found the predictive power of our model was population specific (US data set: AUC = 0.5591 [95% CI 0.5051–0.613]; Finland data set: AUC = 0.4982 [95% CI 0.4727–0.5238]). The model was created by using US samples and hence should only work for US samples. This is to be expected since different human populations are known to show group specific SNP profiles (Lei and Huang, 2017).

The 5400 SNPs in our lung cancer prediction model were enriched in small cell lung cancer, melanoma, adherens junction and estrogen signaling pathways. In contrast, randomly chosen SNPs of the same number did not have the same pathway enrichment. Most of these pathways are known to play roles in cancer (Ramteke et al., 2015; Yamaguchi et al., 2005). Our results provide additional evidence for the role of these pathways in lung cancer and may help understand their mechanisms of action in lung cancer.