Power comparisons between the TDT and two likelihood-based methods

Abstract

We compare the statistical power of the transmission disequilibrium test (TDT) with that of two likelihood‐based linkage tests, the classical LOD score and a modified LOD score in which a linkage disequilibrium (LD) parameter is incorporated into the likelihood (LD‐LOD). We hypothesize that, when LD is present, the LD‐LOD will have the greatest power of the three tests because the TDT breaks a multiplex pedigree into triads, and the LOD score has previously been shown to have lower power when LD is present but not accounted for. We test this hypothesis using a simulation study in which we generate affected sib‐pair (ASP) pedigrees under a range of genetic models, varying the genotypic relative risk (GRR) from 6 to 16. Because the likelihood‐based tests require that a genetic model be specified, we compare the tests under two scenarios. First, we assume the true genetic model in the analysis, and second, we compare the tests when the LD‐LOD (LOD) is maximized over two wrong genetic models. For the generating models we considered, we find that the LD‐LOD has greater power than the TDT even when the genetic models is mis‐specified and the results corrected for multiple tests. Extreme differences occur under the multiplicative and dominant models, for which the difference in power is as high as 40% at complete LD. The LOD score provides the lowest power in the presence of LD for the range of GRR considered here. Genet. Epidemiol. 20:192–209, 2001. © 2001 Wiley‐Liss, Inc.

Detecting linkage disequilibrium in the presence of locus heterogeneity

“…However, the power of the LD‐Het method can be improved by considering the maximum of LD‐Het statistics derived under different models. For example, following the MMLS‐C method (Greenberg et al 1998, Slager et al 2001), we can consider a “LD‐Het‐C” statistic which is the maximum of a recessive LD‐Het statistic and a dominant LD‐Het statistic. The power of such an “LD‐Het‐C” statistic should be more robust with respect to the (unknown) underlying genetic models.…”

“…However, for simplicity and concreteness, we first derive an LD‐Het statistic based on a working model of recessive mode of inheritance with complete penetrance. This is motivated by the result that the TDT can be considered a score statistic corresponding to the likelihood ratio test, assuming a recessive model with complete penetrance with trio data (Slager et al 2001; Huang & Jiang, 2001). In the appendices, we describe the LD‐Het method for general data configuration and model assumptions.…”

Detecting linkage disequilibrium in the presence of locus heterogeneity

“…However, the power of the LD‐Het method can be improved by considering the maximum of LD‐Het statistics derived under different models. For example, following the MMLS‐C method (Greenberg et al 1998, Slager et al 2001), we can consider a “LD‐Het‐C” statistic which is the maximum of a recessive LD‐Het statistic and a dominant LD‐Het statistic. The power of such an “LD‐Het‐C” statistic should be more robust with respect to the (unknown) underlying genetic models.…”

“…However, for simplicity and concreteness, we first derive an LD‐Het statistic based on a working model of recessive mode of inheritance with complete penetrance. This is motivated by the result that the TDT can be considered a score statistic corresponding to the likelihood ratio test, assuming a recessive model with complete penetrance with trio data (Slager et al 2001; Huang & Jiang, 2001). In the appendices, we describe the LD‐Het method for general data configuration and model assumptions.…”

The effect of ascertainment on penetrance estimates for rare variants: Implications for establishing pathogenicity and for genetic counselling

“…The third form of penetrance estimate we consider is based on an “ascertainment assumption free” [ 10 ] approach, which involves conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score [ 11 – 13 ], and also the LOD score allowing for linkage disequilibrium or LD-LOD [ 6 , 14 , 15 ], and in principle any program that allows calculation of the LOD score will support this method. The calculation is done here assigning the VOI (which plays the role of the “marker”) and the disease allele the same (rare) frequency (we have used 0.001 in the simulations), assuming complete linkage disequilibrium between the two (D′ = 1), and also assuming 0 recombination between the marker and the disease allele.…”

“…The third form of penetrance estimate we consider is based on an "ascertainment assumption free" [10] approach, which involves conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score [11][12][13], and also the LOD score allowing for linkage disequilibrium or LD-LOD [6,14,15], and in principle any program that allows calculation of the LOD score will support this method. The calculation is done here…”

The effect of ascertainment on penetrance estimates for rare variants: implications for establishing pathogenicity and for genetic counselling

“…We close by noting that there is one essentially “ascertainment assumption free” (12) method for estimating the penetrance, viz., by conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score (13–15), and also the LOD score allowing for linkage disequilibrium or LD-LOD (6, 16, 17), and in principle any program that allows calculation of the LOD score will support this method. As in Thompson (6) the calculation is done here assigning the VOI (which plays the role of the “marker”) and the disease allele the same (rare) frequency (we have used 0.001 in the simulations), assuming complete linkage disequilibrium between the two (D’ = 1), and also assuming 0 recombination between the marker and the disease allele.…”

Detecting linkage disequilibrium in the presence of locus heterogeneity

“…However, the power of the LD‐Het method can be improved by considering the maximum of LD‐Het statistics derived under different models. For example, following the MMLS‐C method (Greenberg et al 1998, Slager et al 2001), we can consider a “LD‐Het‐C” statistic which is the maximum of a recessive LD‐Het statistic and a dominant LD‐Het statistic. The power of such an “LD‐Het‐C” statistic should be more robust with respect to the (unknown) underlying genetic models.…”

“…However, for simplicity and concreteness, we first derive an LD‐Het statistic based on a working model of recessive mode of inheritance with complete penetrance. This is motivated by the result that the TDT can be considered a score statistic corresponding to the likelihood ratio test, assuming a recessive model with complete penetrance with trio data (Slager et al 2001; Huang & Jiang, 2001). In the appendices, we describe the LD‐Het method for general data configuration and model assumptions.…”

The effect of ascertainment on penetrance estimates for rare variants: Implications for establishing pathogenicity and for genetic counselling

“…The third form of penetrance estimate we consider is based on an “ascertainment assumption free” [ 10 ] approach, which involves conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score [ 11 – 13 ], and also the LOD score allowing for linkage disequilibrium or LD-LOD [ 6 , 14 , 15 ], and in principle any program that allows calculation of the LOD score will support this method. The calculation is done here assigning the VOI (which plays the role of the “marker”) and the disease allele the same (rare) frequency (we have used 0.001 in the simulations), assuming complete linkage disequilibrium between the two (D′ = 1), and also assuming 0 recombination between the marker and the disease allele.…”

“…The third form of penetrance estimate we consider is based on an "ascertainment assumption free" [10] approach, which involves conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score [11][12][13], and also the LOD score allowing for linkage disequilibrium or LD-LOD [6,14,15], and in principle any program that allows calculation of the LOD score will support this method. The calculation is done here…”

The effect of ascertainment on penetrance estimates for rare variants: implications for establishing pathogenicity and for genetic counselling

“…We close by noting that there is one essentially “ascertainment assumption free” (12) method for estimating the penetrance, viz., by conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score (13–15), and also the LOD score allowing for linkage disequilibrium or LD-LOD (6, 16, 17), and in principle any program that allows calculation of the LOD score will support this method. As in Thompson (6) the calculation is done here assigning the VOI (which plays the role of the “marker”) and the disease allele the same (rare) frequency (we have used 0.001 in the simulations), assuming complete linkage disequilibrium between the two (D’ = 1), and also assuming 0 recombination between the marker and the disease allele.…”

Detecting linkage disequilibrium in the presence of locus heterogeneity

“…However, the power of the LD‐Het method can be improved by considering the maximum of LD‐Het statistics derived under different models. For example, following the MMLS‐C method (Greenberg et al 1998, Slager et al 2001), we can consider a “LD‐Het‐C” statistic which is the maximum of a recessive LD‐Het statistic and a dominant LD‐Het statistic. The power of such an “LD‐Het‐C” statistic should be more robust with respect to the (unknown) underlying genetic models.…”

“…However, for simplicity and concreteness, we first derive an LD‐Het statistic based on a working model of recessive mode of inheritance with complete penetrance. This is motivated by the result that the TDT can be considered a score statistic corresponding to the likelihood ratio test, assuming a recessive model with complete penetrance with trio data (Slager et al 2001; Huang & Jiang, 2001). In the appendices, we describe the LD‐Het method for general data configuration and model assumptions.…”

The effect of ascertainment on penetrance estimates for rare variants: Implications for establishing pathogenicity and for genetic counselling

“…The third form of penetrance estimate we consider is based on an “ascertainment assumption free” [ 10 ] approach, which involves conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score [ 11 – 13 ], and also the LOD score allowing for linkage disequilibrium or LD-LOD [ 6 , 14 , 15 ], and in principle any program that allows calculation of the LOD score will support this method. The calculation is done here assigning the VOI (which plays the role of the “marker”) and the disease allele the same (rare) frequency (we have used 0.001 in the simulations), assuming complete linkage disequilibrium between the two (D′ = 1), and also assuming 0 recombination between the marker and the disease allele.…”

“…The third form of penetrance estimate we consider is based on an "ascertainment assumption free" [10] approach, which involves conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score [11][12][13], and also the LOD score allowing for linkage disequilibrium or LD-LOD [6,14,15], and in principle any program that allows calculation of the LOD score will support this method. The calculation is done here…”

The effect of ascertainment on penetrance estimates for rare variants: implications for establishing pathogenicity and for genetic counselling

“…We close by noting that there is one essentially “ascertainment assumption free” (12) method for estimating the penetrance, viz., by conditioning on all of the phenotypic data. This is the ascertainment correction implicit in the usual LOD score (13–15), and also the LOD score allowing for linkage disequilibrium or LD-LOD (6, 16, 17), and in principle any program that allows calculation of the LOD score will support this method. As in Thompson (6) the calculation is done here assigning the VOI (which plays the role of the “marker”) and the disease allele the same (rare) frequency (we have used 0.001 in the simulations), assuming complete linkage disequilibrium between the two (D’ = 1), and also assuming 0 recombination between the marker and the disease allele.…”