# Impact of genotyping errors on the type I error rate and the power of haplotype-based association methods

- Vivien Marquard
^{1}, - Lars Beckmann
^{1}, - Iris M Heid
^{2, 3}, - Claudia Lamina
^{2, 4}and - Jenny Chang-Claude
^{1, 5}Email author

**10**:3

**DOI: **10.1186/1471-2156-10-3

© Marquard et al; licensee BioMed Central Ltd. 2009

**Received: **30 September 2008

**Accepted: **29 January 2009

**Published: **29 January 2009

## Abstract

### Background

We investigated the influence of genotyping errors on the type I error rate and empirical power of two haplotype based association methods applied to candidate regions. We compared the performance of the Mantel Statistic Using Haplotype Sharing and the haplotype frequency based score test with that of the Armitage trend test.

Our study is based on 1000 replication of simulated case-control data settings with 500 cases and 500 controls, respectively. One of the examined markers was set to be the disease locus with a simulated odds ratio of 3. Differential and non-differential genotyping errors were introduced following a misclassification model with varying mean error rates per locus in the range of 0.2% to 15.6%.

### Results

We found that the type I error rate of all three test statistics hold the nominal significance level in the presence of nondifferential genotyping errors and low error rates. For high and differential error rates, the type I error rate of all three test statistics was inflated, even when genetic markers not in Hardy-Weinberg Equilibrium were removed. The empirical power of all three association test statistics remained high at around 89% to 94% when genotyping error rates were low, but decreased to 48% to 80% for high and nondifferential genotyping error rates.

### Conclusion

Currently realistic genotyping error rates for candidate gene analysis (mean error rate per locus of 0.2%) pose no significant problem for the type I error rate as well as the power of all three investigated test statistics.

## Background

The influence of measurement errors in explanatory variables on the properties of a test statistic, like its type I error rate or power, has always been important to investigate. For example, Bross [1] discovered that in a case-control study with nondifferential errors independent of the disease status, the type I error rate of the Chi-Squared test is not increased, whereas the power to detect an association is reduced.

In genetic association studies, where a large amount of genotype data is produced, measurement errors in the data are almost inevitable. Genotyping errors are reported to occur with different frequencies and for different reasons [2–4]. For candidate region association studies they are mostly caused for example by contamination of the DNA extract, low quality reagents or by human artefacts, and occur with a frequency between 0.1% and 15% [3, 4]. They are known to influence important issues, like the selection of tagging SNPs [5, 6] or haplotype frequency estimation [7–9], and the properties of test statistics, e.g. [10, 11]. For family based studies, it has been shown that the false-positive rate (type I error rate) of the Transmission/Disequilibrium Test (TDT) is dramatically inflated due to undetectable genotyping errors causing an overtransmission of common alleles [12]. Therefore, test statistics that account for genotyping errors have been developed, e.g. TDTae [13, 14]. Additionally, methods to detect and deal with genotyping errors [3, 15, 16] have been of great interest, for example the use of double-sampling procedures [17, 18]. Furthermore, it is still a matter of controversy as to whether deviation from Hardy-Weinberg-Equilibrium (HWE) should be used to identify genotyping errors [19–21].

So far, few studies have investigated the impact of genotyping errors on haplotype-based association methods, while there are reports on their impact on haplotype frequency estimation. It was previously shown that the type I error rate of a haplotype-based TDT (HS-TDT) is inflated in the presence of genotyping errors [22], but that the test statistic can be robustified [23]. Moskvina et al. [24] discovered in a theoretical approach that "genotyping errors tend to make the genotype distribution more similar to the stable distribution", which in genetic case-control association studies generally leads to a loss in power for nondifferential errors and to an increased type I error rate in the presence of differential errors. The type I error rate of a likelihood ratio test of independence of haplotype frequency and affection status, based on two marker haplotypes, was examined in a simulation study and found to be inflated given differential genotyping errors even with error rates lower than 1% for markers with small minor allele frequencies (MAF) and markers in strong LD [25].

Our aim is to explore the impact of genotyping errors on the type I error rate and the power of two haplotype-based association test statistics for candidate regions. The commonly used haplotype-based score test (haplo.score, [26]) relies on estimates of haplotype frequencies. Thus, since the influence of genotyping errors on haplotype frequency estimation is known, they might also have a large impact on the performance of haplo.score. The other haplotype-based test statistic is the Mantel Statistic Using Haplotype Sharing [27], which is of particular interest, since haplotype-sharing based association methods have not been investigated in the presence of genotyping errors. Haplotype-sharing is a nonparametric approach that does not rely on estimates of haplotype frequencies and assumptions on the underlying disease models, and may thus be more robust against errors concerning the haplotype distribution. Both investigated test statistics use haplotype information, but the Mantel Statistic Using Haplotype Sharing is actually a pointwise test. Therefore, we additionally investigated the single-point Armitage trend test as a comparison.

We simulated case-control scenarios with differential and nondifferential genotyping errors, incorporated by following the unrestricted misclassification model, proposed by Heid et al. [28]. Heid et al. estimated the occurrence of genotyping errors by assessing genotypes in duplicates and fitting several misclassification models given as the 3 × 3 misclassification matrix. We used their observed mean error rate per locus of around 0.2% in a simulation scenario to analyze the influence of a realistic amount of genotyping errors, and additionally, investigated higher error rates of 8 and 15.6% that are in the range of rates already used in previous simulation studies [3, 19, 29]. The simulated haplotype data was based on haplotypes across 15 SNPs as described in Heid et al. [30] to provide realistic haplotype scenarios. We estimated the type I error rate and empirical power for the Mantel Statistic Using Haplotype Sharing [27] and the haplotype-based score test (based on haplotype frequencies) [26]) and compared them with those of the Armitage trend test for all examined scenarios.

## Methods

### Data

*APM1*gene, the adiponectin encoding gene [30]. We standardized the given estimated haplotype frequencies to achieve an overall frequency of 1 (see Table 1). Each haplotype consists of 15 carefully selected tagging SNPs. We simulated genotype data for different scenarios, containing either no, differential or nondifferential genotype errors, respectively. For each scenario, we generated 1000 replications with each 500 cases and 500 controls. Two haplotypes were drawn randomly to form an individual. For the analysis of type I error rate, without loss of generality the first 500 randomly drawn haplotype pairs were chosen to be cases and the last 500 haplotype pairs to be controls. For the analysis of empirical power, case-control status was assigned based on a logistic regression model with a recessive mode of inheritance. Here, we assumed a baseline odds ratio for the disease to be 1.017 and an odds ratio for carriers with two copies of the disease allele to be 3. Via the logistic regression model a probability to develop the disease based on their genetic components can be determined for each individual. According to these probabilities an individual was stated to be a case or a control. Haplotype pairs were drawn until the sample size of 500 cases and 500 controls was obtained. Marker 13 with a minor allele frequency of 0.028 (see Table 1) was chosen to be the putative disease locus.

Haplotype distribution

Haplotypes | Frequencies | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.026 |

0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.021 |

0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0.012 |

0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0.035 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0.074 |

0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0.044 |

0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0.139 |

0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0.049 |

0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0.108 |

0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0.011 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0.061 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0.112 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0.074 |

0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0.028 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0.105 |

0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0.021 |

1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0.060 |

1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0.018 |

0.078 | 0.108 | 0.099 | 0.329 | 0.29 | 0.338 | 0.157 | 0.061 | 0.727 | 0.074 | 0.309 | 0.401 | 0.028 | 0.55 | 0.092 | MAF* |

### Genotyping error

Genotype misclassification was incorporated independently at every marker for a haplotype pair following the unrestricted misclassification model described by Heid et al. [28]. A SNP genotype misclassification model is described by a 3 × 3 misclassification matrix with each cell containing the probability to assess a true genotype of 0, 1, 2 (coding the number of minor alleles of a SNP) as an observed genotype of 0, 1, 2. The mean error rate per locus is then calculated as the sum of frequencies of all discordant genotypes [3].

Misclassification matrix

Observed genotype | Mean error rate per locus (%) | ||||
---|---|---|---|---|---|

0 | 1 | 2 | |||

0 | 0.99951 | 0.00039 | 0.00010 | ||

1 | 0.00243 | 0.99602 | 0.00155 | 0.2 | |

2 | 0.00138 | 0.00023 | 0.99839 | ||

True Genotype | 0 | 0.975 | 0.018 | 0.007 | |

1 | 0.02 | 0.97 | 0.01 | 8 | |

2 | 0.01 | 0.018 | 0.972 | ||

0 | 0.95 | 0.039 | 0.011 | ||

1 | 0.035 | 0.945 | 0.02 | 15.6 | |

2 | 0.015 | 0.036 | 0.949 |

In previous studies, different genotype mean error rates per locus between 0.1% and 15% have been reported and used in simulation studies [3, 19, 29]. Therefore, we investigated the influence of genotyping errors with the observed rate of 0.2% by Heid et al. [28], but also high error rates of 8% and 15.6%. The influence of nondifferential errors was investigated by incorporating genotype errors in cases and controls following the same error model with the same misclassification probabilities. Differential genotype errors might occur, e.g. when cases and controls were genotyped in different laboratories or when data from different sites or different populations were combined. These differential errors were simulated by introducing errors (1) in cases, but not in controls, or (2) in the first seven markers in cases and in the last seven markers in controls.

### Association statistics

We compared the type I error rate and the empirical power of three different statistics testing association in candidate regions or genes.

#### Mantel Statistic Using Haplotype Sharing

We applied the pointwise Mantel Statistic Using Haplotype Sharing [27] which uses the information of neighbouring markers. It correlates genetic and phenotypic similarity across all pairs of haplotypes, where the genetic similarity is measured as the shared length between haplotypes and the phenotypic similarity is the mean-corrected cross product based on the coded phenotypes (the disease status). Significance was assessed by Monte Carlo permutation of the disease status, while the haplotype pair of an individual was kept together.

Haplotypes used for the Mantel Statistic Using Haplotype Sharing were estimated from the genotypes via the EM algorithm, implemented in R [31]. For comparison we additionally estimated haplotypes via fastPHASE [32].

#### Armitage Trend Test

The second pointwise test we applied was the Armitage trend test. The Armitage trend test is a 2 × 3 (1 df) Chi-squared test for independence and was calculated via logistic regression with the count of the minor alleles (0, 1, 2) as the independent variable.

#### Haplo.score

The third statistic we used was a haplotype-based score test (haplo.score, [26, 31]). The test describes haplotype association in a generalized linear model framework. It is carried out under the global null hypothesis of no haplotype association and relies on the probability distribution of haplotype pairs conditional on the observed individual genotype.

### Test for deviation from Hardy-Weinberg Equilibrium

We used the standard asymptotic Chi-squared test with 1 degree of freedom to test for deviations from Hardy-Weinberg-Equilibrium at a nominal significance level of 0.05 ([33], p.64f). This test was applied to each marker for each replication on controls only. As a data quality check on genotyping errors, all markers not in Hardy-Weinberg-Equilibrium (HWE) were then excluded from the analysis for the corresponding replication.

### Type I error rate and power

For each replication, we determined the pointwise p-value for the Armitage trend test and the Mantel Statistic Using Haplotype Sharing as well as the global p-value for the haplo.score test. Significance was then defined with a p-value less than the significance level of α = 0.05. The number of significant replications was counted and divided by the number of total replications. When no disease locus was simulated, this number reflects the type I error rate. If there is a disease locus, it represents the empirical power at the disease locus.

## Results

### Quality of haplotype estimation

#### Comparison of estimated haplotypes based on genotypes with or without errors

We counted the number of correctly estimated SNPs per haplotype as a measure for quality of haplotype estimation. When no genotyping errors or errors with a low error rate of 0.2% are incorporated, we observed for both phasing algorithms that nearly all 1000 haplotype pairs (for each replication) are estimated correctly. With increasing genotype error rate, the number of accurately estimated haplotypes decreases. For an error rate of 8%, on average 800 haplotype pairs are correctly estimated, whereas with an error rate of 15.6%, only 600 are. This effect is independent of differential and non-differential error scenarios. However, at least 10 of 15 SNPs are estimated correctly for all scenarios, i.e. the estimated haplotypes did not differ from the true haplotypes (without genotype errors) at more than five SNPs

#### Estimated haplotype frequencies and number of estimated haplotypes

### Type I error rate is inflated only for differential genotyping error rates

Results on Type I error rate of haplo.score

Mean error rate per locus (%) | Nondifferential | Differential (errors only in cases) | Differential (cases: first 7 markers, controls: last 7 markers) |
---|---|---|---|

Without errors | 0.047 | ||

0.2 | 0.047 | 0.384 | 0.057 |

8 | 0.049 | 1 | 0.333 |

15.6 | 0.037 | 1 | 0.973 |

In summary, the type I error rate is only increased for higher genotyping error rates with differential genotyping errors, but its magnitude depends on the sample size.

### Power is reduced in the presence of high, non-differential genotype error

In summary, with low genotyping error rates, the empirical power of all three association test statistics remains high at around 89% to 94%. But power is decreased by high, nondifferential genotype errors.

### Test for deviation from Hardy-Weinberg Equilibrium

Amount of genotype errors

SNP | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Number of replications with at least 1 genotype error | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |

Number of replications with deviation from HWE | 804 | 534 | 830 | 43 | 58 | 122 | 247 | 602 | 64 | 424 | 69 | 108 | 874 | 80 | 437 |

## Conclusion

We investigated the impact of genotyping errors on the performance of the Mantel Statistic Using Haplotype Sharing and the haplotype-based score test, haplo.score. Both are haplotype-based tests that have been applied to case-control data in population-based candidate gene association studies. The haplo.score is based on genotypes incorporated in a generalized linear model framework, but accounts for the uncertainty of haplotype phase within the calculations. On the other hand, the Mantel Statistic Using Haplotype Sharing needs the complete phase information of the individuals under study, i.e. the corresponding haplotype pair for each individual. For better comparison of the two haplotype-based methods we used the individuals' haplotype pairs determined via the EM-algorithm, implemented in R (haplo.em) [31]. This algorithm is also used by haplo.score and provides the same haplotype frequency distribution as incorporated in the haplo.score procedure. Haplo.score tests the global hypothesis of whether an association between any examined haplotype exists, whereas the Mantel Statistic Using Haplotype Sharing is a pointwise test that only incorporates the information of neighbouring markers. Hence, the comparison of these two methods might be hampered by the fact that they test different null hypotheses. We therefore additionally investigate the pointwise Armitage trend test as a third association test statistic. It has been shown that the trend test achieves greatest power, compared to other Chi-Squared tests, when there is no prior knowledge of the underlying disease model or in the presence of deviation from HWE [29]. Since the disease model in this simulation study is known to be recessive, the 2 × 2 (1 df) Chi-Squared test for independence with the count of the homozygote minor alleles (0, 0, 1) should be the most powerful test [34]. However, in the presence of genotyping errors, the advantage in power of this 1 df Chi-Squared-test over the Armitage trend test, for a known recessive disease model, could not be confirmed [29].

We find that in the presence of genotyping errors, with a mean error rate per locus of 0.2%, the type I error rate and the empirical power of all three statistics are not affected at all. The type I error rate is highly inflated only for high and differential genotyping error rates (8% and 15.6%). The magnitude of increase in type I error rate depends on the sample size, i.e. type I error rate is more inflated with a larger than with a smaller sample size, which was also previously reported by Moskvina et al. [25] and can be explained by the fact that differential errors are systematic errors ([35], p. 116). In the presence of high differential error rates, the two haplotype-based approaches were more sensitive, i.e. showed clearly higher type I error rates compared to the Armitage trend test.

Genotyping errors affect the number of haplotypes and shift the haplotype distribution towards an increased number of rare haplotypes. The amount of rare haplotypes increases with higher genotype error rates. The size of the study sample is also positively correlated with the number of additional haplotypes due to genotype errors. Our results indicate that this large amount of rare haplotypes is the reason for the inflation of the type I error rate of the Mantel Statistic Using Haplotype Sharing, since the statistic is based on all haplotypes, including the many rare ones. Our results agree with the previously reported observations of an inflated type I error rate in the presence of undetectable or sample-specific errors (differential errors) of former investigations [6–8, 29].

The power gain for all three association test statistics for high and differential genotype errors is coherent in view of the above mentioned inflated type I error rate. We also observe a loss in power for nondifferential genotyping errors, as reported by Heid et al. [28]. On the other hand, the observation of Moskvina et al. [25] that the type I error rate of a haplotype-based association statistic is highly inflated even in the presence of a small genotyping error rate of less than 1% cannot be confirmed with this simulation. Moskvina et al. [25] draw this conclusion for markers in high LD and a relatively low minor allele frequency, whereas the markers we examined comprise haplotypes in two blocks of high LD and have MAFs of between 0.028 and 0.45. Nevertheless, we are able to confirm the effect of sample size on the type I error rate in the presence of genotyping errors, which Moskvina et al. [25] reported.

There has been a lively discussion on whether the exclusion from data analysis of markers that are not in HWE is an appropriate way to deal with genotyping errors [19–21]. Our results support the criticism of this approach, showing that the proportion of genotyping errors detected by testing for deviation from HWE can be quite low. Especially, in the case of common alleles, deviation of HWE is not a sufficient indicator for genotyping errors. We should point out that the chosen cut-off of p < 0.05 to indicate significant deviation from HWE is already very strict. Choosing a less stringent cut-off, as often suggested and conducted in practice, would further decrease the number of genotyping errors detected. Differential errors have been simulated to occur either only in cases or in different markers for cases and controls, as in most real situations. Thus, the test of deviation from HWE applied to controls only is not at all appropriate to detect such differential errors. Hence, the exclusion of markers not in HWE does not reduce the inflated type I error rate substantially. Furthermore, the exclusion of markers leads to a general loss in power, since markers truly associated with disease may also be eliminated.

We show that in the presence of a realistic amount of genotype errors (with a mean error rate per locus of 0.2%), all three examined methods to test association in candidate regions perform well. The Mantel Statistic Using Haplotype Sharing and the Armitage trend test hold their pointwise and the haplo.score its global nominal significance level of 5%. The power to detect the putative disease locus or a haplotype specific association remained high with 89%–94%.

## Declarations

### Acknowledgements

This work was supported by the National Genome Research Net (VM, IMH, CL) and the Munich Center of Health Sciences as part of LMUinnovativ (IMH, CL). Furthermore, it was supported by the Deutsche Forschungsgemeinschaft Grant BE 3906/2-1 (LB).

## Authors’ Affiliations

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