As most imputation approaches use a healthy control population as reference, we first conducted imputation of the masked genotypes using an independent set of healthy controls as reference. When imputing integer genotypes, discordance (D_int) at each SNP was defined as the percentage of samples where genotype was mistakenly inferred by imputation, and D_int = D_M + D_m(where D_M is the percent of genotypes where imputation over-estimated the major allele by one or two copies, and D_m is the percent of genotypes where imputation mistakenly over-estimated the minor allele by one or two copies). In other words, D_int is percent of genotypes which do not match imputation, composed of the cases where minor allele is mistakenly predicted D_m and cases where the major allele is mistakenly predicted D_M. When imputing fractional genotypes, discordance (D_frac) at each SNP was defined as the average of the absolute difference between the imputed fractional genotype and the “true” genotype (coded as 0, 1, or 2; where 2 = homozygous for the major allele) across all samples, where the “true” genotype is given by SNP-chip. In general, the average D_int = 15–20% across all diseases and D_frac = 0.19 and 0.24 (Table 1). Interestingly, the lowest overall discordance rate was found in CD, the dataset with the largest sample size.

We observed that the imputation discordance rate (either D_int or D_frac) was significantly higher for DAM than for NAM. For example, in the ALS dataset, D_int = 19.65% ± 1.16 (mean ± 2 × standard error) for DAM and D_int = 17.4% ± 1.11 for NAM, a statistically significant difference (p = 0.005) (Table 1). Similarly, imputation of PD samples was significantly less accurate (p = 0.0002) for the 100 DAM (D_int = 19.12% ± 1.3) than for 100 NAM (D_int = 15.74% ± 1.23). We found no difference in D_int between DAM and NAM in the CD dataset (p = 0.95). A similar pattern was found when using fractional genotypes (D_frac) (Table 1).

When independent cases were used as a reference for imputation (instead of controls), a significant reduction in D_int or D_frac was observed. For example, in the ALS dataset, the average discordance at DAM (D_int = 18.04% ± 1.15) using cases as reference was significantly lower (matched pairs t-test, p = 10⁻⁴) than the average discordance at the same SNPs using controls as reference (D_int = 19.65% ± 1.16), suggesting that more accurate imputation is obtained when matched cases are used as reference for imputation. The average D_int in the ALS dataset using independent ALS cases as a reference was 18.04% (± 1.15) for DAM and 17.6% (± 1.2) for NAM, a non-significant difference (p = 0.6) (Table 1).

Similar results were obtained in the PD dataset, in which the average discordance at DAM using controls as reference (D_int = 19.12% ± 1.3) was significantly higher than that observed when matched cases were used instead (D_int = 18.22% ± 1.4) (matched pairs t-test, p = 0.002). Although using independent cases as a reference reduces the discordance in imputation, a significant drop in imputation accuracy was still observed in the PD dataset for DAM (D_int = 18.22% ± 1.4) compared with NAM (D_int = 15.89% ± 1.21) (p = 0.01) (Table 1). We observed similar results using fractional imputation metrics.

In summary, the average total discordance rate of imputation on each data set ranged from 15 to 20% and SNPs with large effect sizes were significantly more discordant than SNPs with small effect sizes (up to 3.5%) in two of three datasets (PD and ALS). This discordance was attenuated when cases, instead of controls, were used as reference for imputation.

In order to determine whether the discordance observed was random or systematic, we looked at bias. For integer imputation, we defined bias (B) as the difference in imputation discordance when predicting the major (M) and minor (m) alleles, B_int = D_M − D_m. When using fractional imputation, bias (B_frac) is defined at each SNP as the average of the signed difference between the imputed fractional genotype and the true genotype (coded as 0, 1, or 2; where 2 is homozygous for the major allele) across all samples. According to these definitions, a positive bias means imputation favors the major allele, and a negative bias means imputation favors the minor allele.

Before discussing the difference between using cases or controls as a reference, or between DAM and NAM, it is important to note that imputation is inherently biased toward the minor allele. For integer genotypes, when using controls as a reference to impute NAM (markers not associated with disease), there is a small significant bias toward the major allele of 1–2% in all three datasets (ALS p = 0.0067; PD p < 10⁻⁶; and CD p < 10⁻⁷), Table 2. This effect was reduced by using fractional imputation (Table 2). This inherent bias is the reason that we defined bias in terms of major or minor allele, and the reason that we split the DAM (disease markers) into two groups for further analysis: markers where the major allele is the susceptibility (“risk”) allele, and markers where the minor allele is the risk allele.

When controls were used as a reference for imputation DAM, a consistent bias against the risk allele was observed for all three diseases. For example, when the major allele was the risk allele, integer imputation was biased toward the minor allele (p < 10⁻⁷ for each disease) and when the minor allele was the risk allele, imputation was biased toward the major allele (p < 10⁻¹⁵ for each disease). Similar results were observed when fractional imputation was used.

Interestingly, when independent cases were used as a reference to impute DAM, the bias against risk alleles remained. Similarly to what we observed using controls as a reference, when the major allele was the risk allele, imputation was significantly biased toward the minor allele (p < 10⁻⁸ in ALS; p = 3 × 10⁻⁴ in PD; and p = 0.012 in CD). Conversely, when the minor allele was the risk allele, imputation was significantly biased toward the major allele (p < 10⁻⁶ for each disease).

Figure 1 shows the bias (Y-axis) when controls (left) or cases (right) are used as a reference to impute SNPs in the ALS dataset. With either reference population the bias is consistently against the risk allele and can be observed for all DAM (circles) including the most significantly associated SNPs (dark gray) as well as for more modestly associated (light gray). However, the magnitude of the bias is lower when cases are used as reference. We observed similar results in the PD and CD data sets (Supplementary Figures S1, S2). Of note, results were largely unchanged when the call tolerance parameter T was changed from 0.5 to 0.3 or 0.1 (data not shown), or when fractional genotypes were used (Supplementary Figures S3–S5).

To evaluate the potential effect of imputation on a genome-wide association study (GWAS), the same three datasets (PD, ALS, and CD) were used to perform three parallel association studies. For this analysis, imputation was performed using the CEU subset of the 1000 Genomes as a reference for imputation (Abecasis et al., 2010). For any SNP, the odds ratio (OR) was defined by logistic regression (OR = exp(b), where b is the estimate of the logit coefficient in the logistic regression). Odds ratios computed from imputed genotypes (imputed OR) were compared to those obtained using data from experimentally determined genotypes (from SNP chip; termed “true” OR). Imputed OR were compared to true OR for each DAM. Figure 2 shows the distribution of imputed/true OR for the top 100 DAM in each dataset. Using integer imputation, the magnitude of the mean imputed OR was only 64.2% ± 2.8 (mean ± 2 × standard error) as high as the magnitude of the true OR in ALS, 71.1% ± 3.2 in PD, and 73.8% ± 2.4 in CD. In all cases, it is evident that the distribution of OR is shifted toward the left of 1.0, a vertical dotted line which represents equality between imputed OR and true OR. Using fractional genotypes yielded similar results (Figure 2). Using another commonly used imputation software algorithm (Beagle) yielded similar results (Figure 2). However, in contrast to Mach imputation, the magnitude of the mean imputed OR was closer to the magnitude of the true OR in each dataset. In summary, the observed effect size after imputation is considerably lower for both types of imputation although in the second analysis using Beagle and a larger reference dataset improves the accuracy of imputation. It should be noted that for a few SNPs, the imputed OR is nearly equal or greater than the true OR (imputed OR/true OR ≥ 1). That is, for these SNPs, there is no decrease in observed magnitude of association with disease when imputed genotypes are used.

Quality controlled, genotype-level data from three previously published independent case-control GWAS in individuals of European ancestry in Amyotrophic Lateral Sclerosis (ALS), Crohn's Disease (CD), and Parkinson's Disease (PD) were obtained from dbGAP (Mailman et al., 2007) (Supplementary Table S1). In CD (Rioux et al., 2007) and PD (Fung et al., 2006), cases and controls were matched by sex, age (or year of birth), and ancestry (Rioux et al., 2007; Simon-Sanchez et al., 2009). For ALS cases (Schymick et al., 2007), a sample from neurologically normal controls (Simon-Sanchez et al., 2007) were matched for age and gender and ancestry (Schymick et al., 2007). After quality control done by the original authors, we performed a second layer of quality control on markers (MAF > 0.05, HWE p-value > 10⁻⁶ in controls, genotype success rate > 95%).

For each disease dataset, half of the patients and a matched number of controls were extracted (split “A”) while maintaining original ratios of gender and age. This half of the data (split A) was used to perform a association study (using software Plink Purcell et al., 2007), using a genotypic model or a linear dose model. Here we report results using the genotypic model; results for the linear trend model were largely similar and not shown. The 100 markers with the largest absolute effect size (DAM) were considered for imputation (OR > 1.88 in ALS, OR > 1.53 in PD, OR > 1.44 in CD). As a control, 100 SNP markers with the smallest absolute effect size (NAM) were imputed with the same procedure (1 ≤ OR < 1.001).

For each marker of interest (DAM or NAM), genotypes of cases of split A were masked with the goal of predicting them using imputation. Next, imputation of the masked genotypes was carried out using all markers within a 1 Mb window centered on each query SNP. The imputation window size was chosen large enough so as to include neighborhood SNPs that have r² > 0.2 with the query SNP. The imputation was repeated with each of two reference sets: (a) the previously unused healthy controls from split B of the same study, (b) an equal number of the previously unused affected case individuals from split B of the study.

Next, for each marker of interest (DAM or NAM) the genotypes of all cases and all controls from each study (split A and split B) were masked with the goal of predicting them with imputation. Imputation was performed using the CEU subset of the 1000 Genomes as a reference for imputation (Abecasis et al., 2010).

Imputation was carried out using Mach (Li et al., 2006) (see Nothnagel et al., 2009 for an evaluation of the relative performance of this algorithm compared to others), with default settings and default quality control criteria for SNPs (MAF > 0.05, HWE p-value > 10⁻⁶, genotype success rate > 95%). For each imputed genotype, Mach outputs a fractional genotype (G_imp) between zero and two that corresponds to the inferred number of copies of the minor allele, where minor allele is determined using dataset frequencies (cases and controls). The fractional genotype is compared to the genotype by SNPchip (G₀), or “true” genotype.

Using a call tolerance parameter (T), the integer imputed genotype (G_int) is homozygous for the major allele if G_imp < T, heterozygous if 1 − T ≤ G_imp < 1 + T, or homozygous for the minor allele if G_imp ≥ 2 − T; otherwise the genotype is considered missing. Results using T = 0.5 are shown here. Results using stricter tolerance thresholds T = 0.3 and T = 0.1 were largely similar and are not shown. When using integer genotypes, discordance D_int = D_M + D_m is the percent of imputed genotypes that do not match genotypes from SNP chip, where D_M is the percent of samples where rounded imputation mistakenly over-predicts the major allele in the genotype (by one or two copies), and D_m is the percent of samples where imputation mistakenly over-predicts the minor allele in the genotype (by one or two copies). The bias B is defined as B_int = D_M − D_m. The bias B_int is positive when the major allele is over-predicted and negative when the minor allele is over-predicted. The bias cannot exceed the discordance: |B_int| ≤ D_int.

The discordance (or bias) calculated at individual SNPs is the sum (or difference) of two proportions. To compare groups of SNPs, a Gaussian approximation of the discordance (or bias) distribution was employed and t-statistics compared the difference in means between two groups of SNPs. Normality of the distributions were tested by the Anscombe–Glynn test of kurtosis. Further, non-parametric tests of differences in medians were used in parallel to confirm results.

For each SNP, we computed across samples the mean discordance D_frac = mean |G_imp − G₀|, and the mean bias B_frac = mean (G_imp − G₀). The bias B_frac is positive when the major allele is over-predicted and negative when the minor allele is over-predicted across all samples. The bias cannot exceed the discordance: |B_frac|≤D_frac.

The discordance (or bias) calculated at individual markers is a mean across the samples. To compare groups of markers (e.g., DAM vs. NAM), a Gaussian approximation of the discordance (or bias) distribution was employed and t-statistics compared the difference in means between two groups of SNPs. Normality of the distributions were tested by the Anscombe–Glynn test of kurtosis. Further, non-parametric tests of differences in medians were used in parallel to confirm results (not shown).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.