BACKGROUND: We investigate the power of heterogeneity LOD test to detect linkage when a trait is determined by several major genes using Genetic Analysis Workshop 13 simulated data. We consider three traits, two of which are disease-causing traits: 1) the rate of change in body mass index (BMI); and 2) the maximum BMI; and 3) the disease itself (hypertension). Of interest is the power of "HLOD2", the maximum heterogeneity LOD obtained upon maximizing over the two genetic models. RESULTS: Using a trait phenotype Obesity Slope, we observe that the power to detect the two markers closest to the two genes (S1, S2) at the 0.05 level using HLOD2 is 13% and 10%. The power of HLOD2 for Max BMI phenotype is 12% and 9%. The corresponding values for the Hypertension phenotype are 8% and 6%. CONCLUSION: The power to detect linkage to the slope genes is quite low. But the power using disease-related traits as a phenotype is greater than the power using the disease (hypertension) phenotype

Finch, Stephen

Gordon, Derek

Huo, Yanling

Mendell, Nancy R

Ning, Yuming

Yoo, Yun Joo

BMC Genetics

English

PubMed

Yun Yoo

Yanling Huo

Yuming Ning

Derek Gordon

Stephen Finch

Nancy R Mendell

Crossref

Power of maximum HLOD tests to detect linkage to obesity genes

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BioMed CentralBMC Genetics
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Power of maximum HLOD tests to detect linkage to obesity genes
Yun Joo Yoo*1, Yanling Huo1, Yuming Ning2, Derek Gordon3, 
Stephen Finch1 and Nancy R Mendell1
Address: 1Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, New York, USA, 2Chung 
Yu College of Business Administration, Keelung, Taiwan and 3Laboratory of Statistical Genetics, The Rockefeller University, New York, New York, 
USA
Email: Yun Joo Yoo* - yjyoo@ams.sunysb.edu; Yanling Huo - yhuo@ams.sunysb.edu; Yuming Ning - ymning@ms15.hinet.net; 
Derek Gordon - gordon@linkage.rockefellor.edu; Stephen Finch - sfinch@gis.net; Nancy R Mendell - nmendell@notes.cc.sunysb.edu
* Corresponding author    
Abstract
Background: We investigate the power of heterogeneity LOD test to detect linkage when a trait
is determined by several major genes using Genetic Analysis Workshop 13 simulated data. We
consider three traits, two of which are disease-causing traits: 1) the rate of change in body mass
index (BMI); and 2) the maximum BMI; and 3) the disease itself (hypertension). Of interest is the
power of "HLOD2", the maximum heterogeneity LOD obtained upon maximizing over the two
genetic models.
Results: Using a trait phenotype Obesity Slope, we observe that the power to detect the two
markers closest to the two genes (S1, S2) at the 0.05 level using HLOD2 is 13% and 10%. The
power of HLOD2 for Max BMI phenotype is 12% and 9%. The corresponding values for the
Hypertension phenotype are 8% and 6%.
Conclusion: The power to detect linkage to the slope genes is quite low. But the power using
disease-related traits as a phenotype is greater than the power using the disease (hypertension)
phenotype.
Background
One of the issues in analysis of complex diseases is the
power of considering an disease related trait as a pheno-
type than the disease itself [1]. Another issue considered
here is the method of analysis, which allows for heteroge-
neity when one or more major genes determine a trait [2].
The Genetic Analysis Workshop 13 (GAW13) simulated
longitudinal data on obesity provide an example of a dis-
ease-related phenotype. According to the simulation
model, the Obesity Slope, the rate of increase in BMI
(body mass index) over time is determined by only two
major genes (S1, S2). Also, Obesity Slope in turn is a risk
factor for hypertension, and it is also implied in the simu-
lation model that these two genes for obesity are in fact
two of many hypertension-causing genes.
In this work, we want to investigate the power of HLOD
maximized over two genetic models (dominant and reces-
sive) to detect linkage with the Obesity Slope phenotype
and also with the hypertension phenotype, i.e., the dis-
ease itself. We also consider another trait, the individual's
maximum observed BMI (Max BMI), which is related to
both obesity and hypertension.
from Genetic Analysis Workshop 13: Analysis of Longitudinal Family Data for Complex Diseases and Related Risk Factors
New Orleans Marriott Hotel, New Orleans, LA, USA, November 11–14, 2002
Published: 31 December 2003
BMC Genetics 2003, 4(Suppl 1):S16
<supplement> <title> <p>Genetic Analysis Workshop 13: Analysis of Longitudinal Family Data for Complex Diseases and Related Risk Factors</p> </title> <editor>Laura Almasy, Christopher I Amos, Joan E Bailey-Wilson, Rita M Cantor, Cashell E Jaquish, Maria Martinez, Rosalind J Neuman, Jane M Olson, Lyle J Palmer, Stephen S Rich, M Anne Spence, Jean W MacCluer</editor> </supplement>
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(page number not for citation purposes)
BMC Genetics 2003, 4 http://www.biomedcentral.com/1471-2156/4/s1/S16Methods
Definition of disease phenotypes
The first phenotype considered is Obesity Slope. For each
individual, we regressed BMI values on log of age values at
each time where the BMI was recorded, using the follow-
ing model: E(BMI ij) = αj + βjlog10(Xij), for i = 1,2,..., tj.
Here Xij denotes the jth individual's age at the ith measure-
ment; BMIij denotes the jth individual's BMI at age Xij; and
tj denotes the number of time points for which we have
BMI values on the jth individual. The value of BMIij is com-
puted, again following the model described in the simula-
tion as BMIij = Wij/Hij2, where Wij denotes jth individual's
weight in kilograms and Hij denotes the jth individual's
height in meters at the ith time point observed. Ordinary
least-squares regression resulted in estimates of βj for each
of our subjects. We treated an individual as "missing"
slope information if he had too few measurements. Indi-
viduals in Cohort 1 with less than three measurements
were treated as missing. Individuals in Cohort 2 with less
than two measurements were treated as missing. Cohort 1
has 21 time points with two-year intervals and Cohort 2
has five time points with eight- or four-year intervals. We
then defined individuals as "Obese" if βj ≥ b90 and "Nor-
mal" if βj < b90, where b90 denotes the 90th percentile of the
slopes observed in each replicate being analyzed.
The second disease-related phenotype considered here is
the maximum of jth individual's BMI over all ages (Max
BMI). We defined individuals as "High" if Max BMI ≥ m90
and "Normal" if Max BMI < m90, where m90 denotes the
90th percentile of the Max BMI values observed in each
replicate being analyzed. The third phenotype is "Hyper-
tension." Individuals defined as "affected" are those with
diastolic BP ≥ 90 and/or systolic BP ≥ 140, and "Normal"
are those having diastolic BP < 90 and systolic BP < 140.
Methods of linkage analysis
Single-point linkage analysis was done for the two mark-
ers closest to the two genes S1 and S2, and for five
unlinked markers. One marker linked to S1 is 11g6 and
the other, linked to S2, is 7g7. We also considered five
unlinked markers on chromosomes 2, 4, 6, 8, and 10
(2g5, 4g4, 6g3, 8g2, 10g1), on which none of the disease
genes were located.
We used the linkage test specified on Abreu et al. [3]. We
obtained a value "HLOD-D" by maximizing over all val-
ues of the recombination fraction and heterogeneity
parameter assuming disease allele frequency 0.01 and
dominance with penetrance 0.5. Then we obtained a
value "HLOD-R" by maximizing over all values of the
recombination fraction and heterogeneity parameter
assuming disease allele frequency 0.01 and recessive
model with penetrance 0.5. The test statistic HLOD2 was
obtained as the maximum of HLOD-D and HLOD-R.
Also, for the comparison, we considered LOD2, the maxi-
mum of LOD-D and LOD-R using the same two analysis
models without heterogeneity parameter. To calculate
HLOD values, we used HOMOG program combining
with LINKAGE package.
Results and Discussion
With the results of analysis of five unlinked markers using
the Obesity Slope phenotype, the empirical critical values
for a 0.05 level test are 0.947 for HLOD2 and 0.730 for
LOD2 from the null distribution of size N = 500. Then we
obtained power values for the three phenotypes by com-
puting the percentage of replicates with higher HLOD2
(or LOD2) values than the critical value in all 100 repli-
cates. Highest power is 13% for Obesity Slope phenotype
at the 11g6 marker. Power values for three phenotypes are
presented in the Table 1.
Table 1: Power of HLOD2 and LOD2 test for three phenotypes 
Critical values of 0.947 for HLOD2 and 0.730 for LOD2 are used 
for both of markers.
Marker 11g6 (S1) 7g7 (S2)
Phenotype HLOD2 LOD2 HLOD2 LOD2
Obesity Slope 13% 10% 10% 10%
Max BMI 12% 11% 9% 9%
Hypertension 8% 8% 6% 4%
Distribution of HLOD2 scores of three phenotypes with marker 11g6Figure
Distribution of HLOD2 scores of three phenotypes 
with marker 11g6. With the critical value 0.947 obtained 
from the 95% percentile of null distribution (dotted line), 
Obesity Slope (blue line) has power of 13%, Max BMI (red 
line) has power of 12%, and Hypertension (green line) has 
power of 8%.Page 2 of 3
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The Obesity Slope phenotype resulted in the highest
power. The second highest is the Max BMI (Figure 1). At a
certain level it is not surprising that the Max BMI gives
closer results to the Obesity Slope phenotype than Hyper-
tension does. There is a strong association between being
in the top 10% for the Obesity Slope and Max BMI pheno-
types (χ2 = 19.5). On the other hand, there is no associa-
tion in this sample between being in the top 10% for the
Slope Phenotype and having hypertension (χ2 = 2.66).
There are several possible explanations for the low power
to detect linkage observed here. The most likely one is that
we lose power by dichotomizing the values rather than
analyzing these traits as quantitative phenotypes using
model-free methods. Second, even though we are focus-
ing on the slope itself, which is the direct product of the
gene, we do have error in our estimate of an individuals'
slope due to the combination of random noises in the
simulations models.
Conclusions
The overall power values for HLOD2 analysis are quiet
low in the case of the analysis of dichotomized BMI slope
values and dichotomized BMI values. However, they are
higher than those obtained using the hypertension
phenotype.
References
1. Rice JP, Saccone NL, Rasmussen E: Definition of the phenotype.
Adv Genet 2001, 42:69-76.
2. Greenberg DA, Abreu PC: Determining trait locus position
from multipoint analysis: accuracy and power of three differ-
ent statistics. Genet Epidemiol 2001, 21:299-314.
3. Abreu PC, Hodge SE, Greenberg DA: Quantification of type I
error probabilities for heterogeneity LOD scores. Genet
Epidemiol 2002, 22:156-169.Page 3 of 3
(page number not for citation purposes)


Abreu PC: Determining trait locus position from multipoint analysis: accuracy and power of three different statistics. Genet Epidemiol

E: Definition of the phenotype. Adv Genet

Greenberg DA: Quantification of type I error probabilities for heterogeneity LOD scores. Genet Epidemiol

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Power of maximum HLOD tests to detect linkage to obesity genes

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