For pedigree-based association analysis, several methods have been developed that utilize information about transmission of alleles, such as the orthogonal test for within-family variation (quantitative transmission-disequilibrium test, or QTDT) 12. The quantitative trait linkage-disequilibrium test (QTLD) is a modification of the QTDT method that assigns the founder genotypes to the within-family component rather than to the between-family component 3. The measured genotype (MG) model is a simple fixed-effects regression for which non-independence in the data is accounted for by polygenic effects 45. All three approaches, QTDT, QTLD, and MG, can be applied to the association analysis of quantitative traits in extended pedigrees. They differ in the amount and type of marker information used for testing association. The MG model uses all individuals with available phenotype and genotype data. The family-based models use a subset of this sample. The effective sample size of QTDT is further reduced because founders and spouses are not use to estimate the within-component effect. Thus, QTDT may lack of power compared with QTLD and/or MG but, on the other hand, both MG and QTLD tests may be affected by allelic association due to population stratification. The relative merit of these approaches has been investigated in a few instances 36. Here, we extend these studies to explore type I error and relative power of QTDT, QTLD, and MG tests in a large pedigree-based sample, i.e., Genetic Analysis Workshop 16 Problem 3 Framingham Heart Study (FHS) simulated data set. Our investigation was performed with knowledge of the answers.

Table 2 shows empirical estimates of the mean chi-square statistics and type I error rates, at a nominal p-value of 5%, of QTDT, QTLD, and MG tests when the studied SNP is not associated to the trait. The three association tests were roughly similar in empirical estimates, whether or not the studied SNP is linked to a major gene. In general, error rates were lower or close to the nominal values, except for QTDT with two SNPs. As expected, accounting for population stratification decreased the mean chi-square statistics of both QTLD and MG models. Interestingly, in these data, departure from normality did not yield inflated error rates, except with QTDT for TG and rs4244457. Error rates remained unchanged when diet was included into the model (results not shown).

Table 3 shows empirical estimates of the three association models when the studied SNP is the functional polymorphism. For QTLD and MG models, we chose to report the results obtained after accounting for population stratification. Across the three association models, the power was the lowest for the functional SNP with smallest size effects (i.e., α2), and for the less heritable trait (i.e., TG). For TG, mean chi-square estimates were slightly increased when diet was included into the model. For QTDT and MG_S models, estimates were also increased when the trait was normal (i.e., using TG_Rob), relative to when the trait was non-normal. Reverse trends were observed for QTLD_S. The direction of the association parameters was consistent across the three association models (results not shown). Overall, for a given trait and SNP, the mean chi-square statistic was always the highest with MG_S and the lowest with QTDT. The mean chi-square of QTDT was 1.6 to 6.2 times lower than that of MG_S. For QTLD_S the ratios ranged from 1.0 to 2.4. This is consistent with the amount of marker and trait information used by each association model. For MG, the effective sample sizes (Ne) ranged from 5854 (α4) to 5995 (α2 and δ1) subjects. For QTLD and QTDT, Ne values ranged from 2436 (α4) to 2839 (δ1), and from 1846 (α4) to 2240 (δ1), respectively. It is worth noting that across the three functional variants, the drops in Ne values relative to that of MG varied little: they were the lowest with δ1 (2.11 vs. 2.68 for QTLD vs. QTDT), and the highest with α4 (2.40 vs. 3.17 for QTLD vs. QTDT). In contrast, and for HDL, differences in the performances of the models were more marked with δ1 than with α4. Indeed, mean chi-square statistic of QTLD_S was 1.73 lower than that of MG_S with δ1, whereas both tests showed same performances with α4. Similarly, drops of the mean QTDT statistic, relative to MG_S, were much greater with α2 (6.25) or δ1 (2.37) than with α4 (1.56). It is worth noting that α4 and δ1 explained similar amount of HDL variability. Thus, these results suggest that the relative performance of the association models can not be simply related to differences in the effective sample sizes.

In conclusion, our results showed that MG outperformed the two orthogonal-based association models (QTLD, QTDT), even after accounting for population stratification. QTDT had the lowest power rates. Similar conclusions were reached by two previous simulation studies 36. It is worth noting that our investigation was conducted in a relatively large pedigree-based sample (>5,850 subjects with known phenotype and genotype status; out of these ~10% are founders). Thus, although the major gene-specific effects were very modest (<0.4%), the three association models showed good power (>80%, at p = 5%) to detect direct association for HDL and two (α4 and δ1) of the three functional variants. At a lower tabulated threshold (p = 0.1%), the power remained good using the MG model only. For TG, good power was obtained with the MG model with one functional SNP (δ1) and using transformed TG values.

FHS: Framingham Heart Study; HDL: High-density lipoprotein; QTLD: Quantitative trait linkage disequilibrium; QTDT: Quantitative transmission-disequilibrium test; MG: Measured genotype; SNP: Single-nucleotide polymorphism; STRAT: Population stratification; TG: Triglyceride.

The authors declare that they have no competing interests.

ASP carried out the statistical genetic analyses and drafted the manuscript. ZV contributed in the statistical analysis and helped to draft the manuscript. MM conceived the study, coordinated it, and contributed to the draft the manuscript. All authors read and approved the final manuscript.