The author has declared that no competing interests exist.
Analyzed the data: GB. Wrote the paper: GB.
The Transmission Disequilibrium Test (TDT) compares frequencies of transmission of two alleles from heterozygote parents to an affected offspring. This test requires all genotypes to be known from all members of the nuclear families. However, obtaining all genotypes in a study might not be possible for some families, in which case, a data set results in missing genotypes. There are many techniques of handling missing genotypes in parents but only a few in offspring. The robust TDT (rTDT) is one of the methods that handles missing genotypes for all members of nuclear families [with one affected offspring]. Even though all family members can be imputed, the rTDT is a conservative test with low power. We propose a new method, Mendelian Inheritance TDT (MITDT-ONE), that controls type I error and has high power. The MITDT-ONE uses Mendelian Inheritance properties, and takes population frequencies of the disease allele and marker allele into account in the rTDT method. One of the advantages of using the MITDT-ONE is that the MITDT-ONE can identify additional significant genes that are not found by the rTDT. We demonstrate the performances of both tests along with Sib-TDT (S-TDT) in Monte Carlo simulation studies. Moreover, we apply our method to the type 1 diabetes data from the Warren families in the United Kingdom to identify significant genes that are related to type 1 diabetes.
The Transmission Disequilibrium Test (TDT) is the most widely used family-based test for linkage disequilibrium
The TDT compares frequencies of the transmission of two alleles from heterozygote parents to an affected offspring. The TDT requires complete genotypes from parents and offspring. However, sometimes genotypes may not be available. If genotypes of parents are missing, including only complete cases
The robust TDT (rTDT) was proposed to handle any missing genotypes in a nuclear family with one affected offspring and bi-allelic marker
We demonstrate the features of rTDT and MITDT-ONE with an example. We assume that we have genotypes of nuclear families with one affected offspring, and bi-allelic markers with alleles 1 and 2. In a given data set, there are (1,1), (1,2), or (2,2) complete genotypes or (0,0) missing genotypes. For each family, there are three genotypes with the first two genotypes for parents and the last genotype for offspring (e.g., (1,2)(1,1)(1,2)). If at least one of the genotypes is unknown, then the data is called incomplete. Otherwise it is called complete. Hence, a whole data set has two parts for a given marker: complete and incomplete trio genotypes.
The TDT considers transmission from heterozygote parents (
We construct interval estimates of MITDT-ONE and rTDT as follows: (1) compute maximum and minimum increments in
For complete families, let us assume that we have 50 heterozygote parents (
Family | Parents | Children |
1 | (0,0)(1,2) | (0,0) |
2 | (1,2)(1,1) | (0,0) |
The first step of imputing missing cases involves only possible admissible completions. The MITDT-ONE and rTDT (as does TDT) consider families with at least one heterozygote parent. For example, if the incomplete case is (1,1)(0,0)(1,2), we do not consider the completion (1,1)(2,2)(1,2) because both parents have homozygous genotypes. Moreover, in family 2 above, (1,2)(1,1)(2,2) is not a possible admissible completion because the only possible completions for offspring are (1,1) or (1,2). All possible admissible genotypes are defined in
Family | Scenario | Parent | Children |
|
|
1 | 1 | (1,1)(1,2) | (1,1) | 1 | 0 |
2 | (1,1)(1,2) | (1,2) | 0 | 1 | |
3 | (2,2)(1,2) | (1,2) | 1 | 0 | |
4 | (2,2)(1,2) | (2,2) | 0 | 1 | |
5 | (1,2)(1,2) | (1,1) | 2 | 0 | |
6 | (1,2)(1,2) | (1,2) | 1 | 1 | |
7 | (1,2)(1,2) | (2,2) | 0 | 2 | |
2 | 8 | (1,2)(1,1) | (1,1) | 1 | 0 |
9 | (1,2)(1,1) | (1,2) | 0 | 1 |
Under the null hypothesis
All these families have equal probabilities of being considered under the null hypothesis of no linkage. However, MITDT-ONE and rTDT consider increments in
Both tests use the same admissible cases and consider lower limits to identify significant genes. Both methods reject the null hypothesis of no linkage at 5% nominal level in the above example. The interval estimate of MITDT-ONE is always contained in the interval estimate of rTDT (see in Construction of the MITDT-ONE and rTDT for more details). It is important to note that MITDT-ONE and rTDT have the same minimum values for
There are 17 admissible missing cases in a nuclear family with one affected offspring (
If
If
In all other cases:
The value of
Offspring Genotype | ||||||
Case | Parental Genotype | (0,0) | (1,1) | (1,2) | (2,2) | Total |
1 | (0,0) (0,0) | + | + | + | + | 4 |
2 | (0,0) (1,1) | + | + | + | − | 3 |
3 | (0,0) (1,2) | + | + | + | + | 4 |
4 | (0,0) (2,2) | + | − | + | + | 3 |
5 | (1,1) (1,2) | + |
|
|
|
1 |
6 | (1,2) (1,2) | + |
|
|
|
1 |
7 | (1,2) (2,2) | + |
|
|
|
1 |
Total number of admissible incomplete trios | 17 |
The symbols
Case | Incomplete Genotypes | Admissible Completions | Increments | |||
k | Parents | Offspring | Parents | Offspring |
|
|
1 | (0, 0)(0, 0) | (0, 0) | (1,1) (1,1) | (1,1) | 0 | 0 |
(1,1) (1,2) | (1,1) | 1 | 0 | |||
(1,1) (1,2) | (1,2) | 0 | 1 | |||
(1,1) (2,2) | (1,2) | 0 | 0 | |||
(1,2) (1,2) | (1,1) | 2 | 0 | |||
(1,2) (1,2) | (1,2) | 1 | 1 | |||
(1,2) (1,2) | (2,2) | 0 | 2 | |||
(2,2) (1,2) | (1,2) | 1 | 0 | |||
(2,2) (1,2) | (2,2) | 0 | 1 | |||
(2,2) (2,2) | (2,2) | 0 | 0 | |||
2 | (0, 0)(0, 0) | (1, 1) | (1,1) (1,1) | (1,1) | 0 | 0 |
(1,1) (1,2) | (1,1) | 1 | 0 | |||
(1,2) (1,2) | (1,1) | 2 | 0 | |||
3 | (0, 0)(0, 0) | (1, 2) | (1,1) (1,2) | (1,2) | 0 | 1 |
(1,1) (2,2) | (1,2) | 0 | 0 | |||
(1,2) (1,2) | (1,2) | 1 | 1 | |||
(1,2) (2,2) | (1,2) | 1 | 0 | |||
4 | (0, 0)(0, 0) | (2, 2) | (1,2) (1,2) | (2,2) | 0 | 2 |
(1,2) (2,2) | (2,2) | 0 | 1 | |||
(2,2) (2,2) | (2,2) | 0 | 0 | |||
5 | (0, 0)(1, 1) | (0, 0) | (1,1) (1,1) | (1,1) | 0 | 0 |
(1,2) (1,1) | (1,1) | 1 | 0 | |||
(1,2) (1,1) | (1,2) | 0 | 1 | |||
(2,2) (1,1) | (1,2) | 0 | 0 | |||
6 | (0, 0)(1, 1) | (1, 1) | (1,1) (1,1) | (1,1) | 0 | 0 |
(1,2) (1,1) | (1,1) | 1 | 0 | |||
7 | (0, 0)(1, 1) | (1, 2) | (1,2) (1,1) | (1,2) | 0 | 1 |
(2,2) (1,1) | (1,2) | 0 | 0 | |||
8 | (0.0) (1,2) | (0,0) | (1,1) (1,2) | (1,1) | 1 | 0 |
(1,1) (1,2) | (1,2) | 0 | 1 | |||
(1,2) (1,2) | (1,1) | 2 | 0 | |||
(1,2) (1,2) | (1,2) | 1 | 1 | |||
(1,2) (1,2) | (2,2) | 0 | 2 | |||
(2,2) (1,2) | (1,2) | 1 | 0 | |||
(2,2) (1,2) | (2,2) | 0 | 1 |
Case | Incomplete Genotypes | Admissible Completions | Increments | |||
k | Parents | Offspring | Parents | Offspring |
|
|
9 | (0, 0)(1, 2) | (1, 1) | (1,1) (1,2) | (1,1) | 1 | 0 |
(1,2) (1,2) | (1,1) | 2 | 0 | |||
10 | (0, 0)(1, 2) | (1, 2) | (1,1) (1,2) | (1,2) | 0 | 1 |
(1,2) (1,2) | (1,2) | 1 | 1 | |||
(2,2) (1,2) | (1,2) | 1 | 0 | |||
11 | (0, 0)(1, 2) | (2, 2) | (1,2) (1,2) | (2,2) | 0 | 2 |
(2,2) (1,2) | (2,2) | 0 | 1 | |||
12 | (0, 0)(2, 2) | (0, 0) | (1,1) (2,2) | (1,2) | 0 | 0 |
(1,2) (2,2) | (1,2) | 1 | 0 | |||
(1,2) (2,2) | (2,2) | 0 | 1 | |||
(2,2) (2,2) | (2,2) | 0 | 0 | |||
13 | (0, 0)(2, 2) | (1, 2) | (1,1) (2,2) | (1,2) | 0 | 0 |
(1,2) (2,2) | (1,2) | 1 | 0 | |||
(2,2) (2,2) | (1,2) | 0 | 0 | |||
14 | (0, 0)(2, 2) | (2, 2) | (1,2) (2,2) | (2,2) | 0 | 1 |
(2,2) (2,2) | (2,2) | 0 | 0 | |||
15 | (1, 1)(1, 2) | (0, 0) | (1,1) (1,2) | (1,1) | 1 | 0 |
(1,1) (1,2) | (1,2) | 0 | 1 | |||
16 | (1, 2)(1, 2) | (0, 0) | (1,2) (1,2) | (1,1) | 2 | 0 |
(1,2) (1,2) | (1,2) | 1 | 1 | |||
(1,2) (1,2) | (2,2) | 0 | 2 | |||
17 | (1, 2)(2, 2) | (0, 0) | (1,2) (2,2) | (1,2) | 1 | 0 |
(1,2) (2,2) | (2,2) | 0 | 1 |
Case | Parents | Offspring | Increment |
Min. | Max. | |||||
(0,0) | (1,0) | (2,0) | (1,1) | (0,1) | (0,2) | Inc | Inc | |||
1 | (0,0) (0,0) | (0,0) | + | + | + | + | + | + | 0 | 2 |
2 | (1,1) | + | + | + | − | − | − | 0 | 2 | |
3 | (1,2) | + | + | − | + | + | − | 0 | 2 | |
4 | (2,2) | + | − | − | − | + | + | 0 | 2 | |
5 | (0,0) (1,1) | (0,0) | + | + | − | − | + | − | 0 | 1 |
6 | (1,1) | + | + | − | − | − | − | 0 | 1 | |
7 | (1,2) | + | − | − | − | + | − | 0 | 1 | |
8 | (0,0) (1,2) | (0,0) | − | + | + | + | + | + | 1 | 2 |
9 | (1,1) | − | + | + | − | − | − | 1 | 2 | |
10 | (1,2) | − | + | − | + | + | − | 1 | 2 | |
11 | (2,2) | − | − | − | − | + | + | 1 | 2 | |
12 | (0,0) (2,2) | (0,0) | + | + | − | − | + | − | 0 | 1 |
13 | (1,2) | + | + | − | − | − | − | 0 | 1 | |
14 | (2,2) | + | − | − | − | + | − | 0 | 1 | |
15 | (1,1) (1,2) | (0,0) | − | + | − | − | + | − | 1 | 1 |
16 | (1,2) (1,2) | (0,0) | − | − | + | + | − | + | 2 | 2 |
17 | (1,2) (2,2) | (0,0) | − | + | − | − | + | − | 1 | 1 |
In
Sebastiani et al.
Since TDT provides better power when linkage disequilibrium is at its maximum (
The lowest values of the interval estimates of rTDT and MITDT-ONE find significant genes when they are actually not. The way the interval estimate for MITDT-ONE constructed guarantees that its lowest interval estimate
We claimed that rTDT is a conservative test. We have observed this through simulation study but not theoretically. The reason rTDT becomes conservative is that the value of
We replicated the simulation study in
Our simulation study demonstrates realistic complex disease models. We generated 5,000 data sets for four different missing models and three genetics models (additive, dominant and recessive). In each simulation, we generated 100 families and each family consisted of one affected and one unaffected offspring, and 50 heterozygote fathers and 50 heterozygote mothers. In disease models, the probabilities of an affected child given the homozygosity (
Missing Rates | |||
MM/MR | Father | Mother | Offspring |
|
|
|
|
1/1 | (0.10,0.10,0.10) | (0.10,0.10,0.10) | (0.10,0.10,0.10) |
2/1 | (0.05, 0.05, 0.10) | (0.05, 0.05, 0.10) | (0.10,0.10,0.10) |
2/2 | (0.05, 0.075, 0.10) | (0.05, 0.075, 0.10) | (0.10,0.10,0.10) |
2/3 | (0.05, 0.10, 0.10) | (0.05, 0.10, 0.10) | (0.10,0.10,0.10) |
2/4 | (0.10, 0.05, 0.05) | (0.10, 0.05, 0.05) | (0.10,0.10,0.10) |
2/5 | (0.10, 0.075, 0.05) | (0.10, 0.075, 0.05) | (0.10,0.10,0.10) |
2/6 | (0.10, 0.10, 0.05) | (0.10, 0.10, 0.05) | (0.10,0.10,0.10) |
3/1 | (0.05, 0.05, 0.10) | (0.05, 0.05, 0.10) | (0.05, 0.05, 0.10) |
3/2 | (0.05, 0.075, 0.10) | (0.05, 0.075, 0.10) | (0.05, 0.075, 0.10) |
3/3 | (0.05, 0.10, 0.10) | (0.05, 0.10, 0.10) | (0.05, 0.10, 0.10) |
3/4 | (0.10, 0.05, 0.05) | (0.10, 0.05, 0.05) | (0.10, 0.05, 0.05) |
3/5 | (0.10, 0.075, 0.05) | (0.10, 0.075, 0.05) | (0.10, 0.075, 0.05) |
3/6 | (0.10, 0.10, 0.05) | (0.10, 0.10, 0.05) | (0.10, 0.10,0.05) |
4/1 | (0.10, 0.10, 0.10) | (0.10, 0.10, 0.10) | (0.05, 0.05, 0.10) |
4/2 | (0.10, 0.10, 0.10) | (0.10, 0.10, 0.10) | (0.05, 0.075, 0.10) |
4/3 | (0.10, 0.10, 0.10) | (0.10, 0.10, 0.10) | (0.05, 0.10, 0.10) |
4/4 | ((0.10, 0.10, 0.10) | (0.10, 0.10, 0.10) | (0.10, 0.05, 0.05) |
4/5 | (0.10, 0.10, 0.10) | (0.10, 0.10, 0.10) | (0.10, 0.075, 0.05) |
4/6 | (0.10, 0.10, 0.10) | (0.10, 0.10, 0.10) | (0.10, 0.10,0.05) |
Missing models:(1) Missing Completely at Random (MCAR) for all genotypes, (2) informative missing for parental genotypes and MCAR for offspring genotypes, (3) informative missing for all genotypes, and (4) MCAR for parental genotypes and informative missing for offspring genotypes.
The performances of the methods were demonstrated by validity and power analysis. The S-TDT, which ignores genotypes of the parents and compares frequencies of the affected and unaffected offspring
In validity and power analysis tables, the TDT ignores missing cases and considers only complete cases, S-TDT ignores parental genotypes and considers only genotypes of affected and unaffected offspring of all 100 families (genotypes are all known), and MITDT and rTDT use all 100 families after construction of all possible admissible genotypes.
The most positive value of linkage disequilibrium is defined as
When
All testing procedures (TDT, MITDT-ONE, rTDT) except S-TDT were valid tests at 1% and 5% significance levels (
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
D, A, R | 1/1 | 0.024 | 0.009 | 0 | 0.007 |
2/1 | 0.024 | 0.009 | 0 | 0.007 | ||
2/2 | 0.01 | 0 | 0.007 | |||
2/3 | 0.009 | 0 | 0.007 | |||
2/4 | 0.009 | 0 | 0.006 | |||
2/5 | 0.009 | 0 | 0.007 | |||
2/6 | 0.009 | 0 | 0.007 | |||
3/1 | 0.024 | 0.01 | 0 | 0.007 | ||
3/2 | 0.011 | 0 | 0.007 | |||
3/3 | 0.01 | 0 | 0.007 | |||
3/4 | 0.009 | 0 | 0.007 | |||
3/5 | 0.01 | 0 | 0.008 | |||
3/6 | 0.01 | 0 | 0.009 | |||
4/1 | 0.024 | 0.01 | 0 | 0.007 | ||
4/2 | 0.01 | 0 | 0.007 | |||
4/3 | 0.01 | 0 | 0.007 | |||
4/4 | 0.01 | 0 | 0.009 | |||
4/5 | 0.01 | 0 | 0.009 | |||
4/6 | 0.01 | 0 | 0.009 | |||
|
D, A, R | 1/1 | 0.022 | 0.007 | 0 | 0.006 |
2/1 | 0.022 | 0.007 | 0 | 0.004 | ||
2/2 | 0.007 | 0 | 0.005 | |||
2/3 | 0.007 | 0 | 0.006 | |||
2/4 | 0.008 | 0 | 0.004 | |||
2/5 | 0.008 | 0 | 0.004 | |||
2/6 | 0.008 | 0 | 0.005 | |||
3/1 | 0.022 | 0.009 | 0 | 0.005 | ||
3/2 | 0.009 | 0 | 0.005 | |||
3/3 | 0.008 | 0 | 0.006 | |||
3/4 | 0.008 | 0 | 0.005 | |||
3/5 | 0.009 | 0 | 0.006 | |||
3/6 | 0.008 | 0 | 0.007 | |||
4/1 | 0.022 | 0.008 | 0 | 0.006 | ||
4/2 | 0.008 | 0 | 0.006 | |||
4/3 | 0.008 | 0 | 0.006 | |||
4/4 | 0.008 | 0 | 0.007 | |||
4/5 | 0.008 | 0 | 0.007 | |||
4/6 | 0.008 | 0 | 0.007 |
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
D, A, R | 1/1 | 0.104 | 0.05 | 0 | 0.04 |
2/1 | 0.104 | 0.048 | 0 | 0.036 | ||
2/2 | 0.048 | 0 | 0.037 | |||
2/3 | 0.05 | 0 | 0.04 | |||
2/4 | 0.047 | 0.001 | 0.034 | |||
2/5 | 0.047 | 0.001 | 0.034 | |||
2/6 | 0.05 | 0.001 | 0.037 | |||
3/1 | 0.104 | 0.052 | 0.001 | 0.035 | ||
3/2 | 0.052 | 0 | 0.036 | |||
3/3 | 0.052 | 0 | 0.041 | |||
3/4 | 0.048 | 0.003 | 0.036 | |||
3/5 | 0.053 | 0.002 | 0.04 | |||
3/6 | 0.053 | 0.001 | 0.042 | |||
4/1 | 0.104 | 0.053 | 0.001 | 0.039 | ||
4/2 | 0.052 | 0 | 0.04 | |||
4/3 | 0.052 | 0 | 0.041 | |||
4/4 | 0.053 | 0.001 | 0.042 | |||
4/5 | 0.053 | 0 | 0.043 | |||
4/6 | 0.053 | 0 | 0.045 | |||
|
D, A, R | 1/1 | 0.102 | 0.045 | 0 | 0.036 |
2/1 | 0.102 | 0.043 | 0 | 0.031 | ||
2/2 | 0.043 | 0 | 0.034 | |||
2/3 | 0.045 | 0 | 0.036 | |||
2/4 | 0.042 | 0.001 | 0.028 | |||
2/5 | 0.042 | 0.001 | 0.03 | |||
2/6 | 0.045 | 0.001 | 0.034 | |||
3/1 | 0.102 | 0.045 | 0 | 0.032 | ||
3/2 | 0.046 | 0 | 0.034 | |||
3/3 | 0.047 | 0 | 0.037 | |||
3/4 | 0.041 | 0.003 | 0.033 | |||
3/5 | 0.047 | 0.002 | 0.037 | |||
3/6 | 0.045 | 0.001 | 0.038 | |||
4/1 | 0.102 | 0.046 | 0 | 0.036 | ||
4/2 | 0.046 | 0 | 0.037 | |||
4/3 | 0.047 | 0 | 0.037 | |||
4/4 | 0.045 | 0 | 0.038 | |||
4/5 | 0.046 | 0 | 0.039 | |||
4/6 | 0.047 | 0 | 0.039 |
In column 2, D, A, and R represent dominant, additive, and recessive genetic models (GM), respectively.
In power analysis, the null hypothesis is that there is a complete linkage (
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
Dominant | 1/1 | 0.291 | 0.769 | 0.072 | 0.829 |
2/1 | 0.291 | 0.782 | 0.102 | 0.833 | ||
2/2 | 0.785 | 0.098 | 0.835 | |||
2/3 | 0.769 | 0.072 | 0.829 | |||
2/4 | 0.78 | 0.18 | 0.815 | |||
2/5 | 0.782 | 0.175 | 0.819 | |||
2/6 | 0.767 | 0.145 | 0.823 | |||
3/1 | 0.291 | 0.764 | 0.136 | 0.815 | ||
3/2 | 0.776 | 0.111 | 0.826 | |||
3/3 | 0.769 | 0.072 | 0.829 | |||
3/4 | 0.795 | 0.449 | 0.83 | |||
3/5 | 0.812 | 0.385 | 0.838 | |||
3/6 | 0.778 | 0.294 | 0.833 | |||
4/1 | 0.291 | 0.761 | 0.094 | 0.821 | ||
4/2 | 0.762 | 0.08 | 0.823 | |||
4/3 | 0.769 | 0.072 | 0.829 | |||
4/4 | 0.769 | 0.298 | 0.826 | |||
4/5 | 0.77 | 0.266 | 0.829 | |||
4/6 | 0.777 | 0.244 | 0.835 | |||
Additive | 1/1 | 0.257 | 0.72 | 0.053 | 0.788 | |
2/1 | 0.257 | 0.729 | 0.077 | 0.792 | ||
2/2 | 0.735 | 0.074 | 0.795 | |||
2/3 | 0.72 | 0.053 | 0.788 | |||
2/4 | 0.724 | 0.143 | 0.772 | |||
2/5 | 0.731 | 0.139 | 0.774 | |||
2/6 | 0.716 | 0.113 | 0.781 | |||
3/1 | 0.257 | 0.714 | 0.105 | 0.77 | ||
3/2 | 0.726 | 0.083 | 0.786 | |||
3/3 | 0.72 | 0.053 | 0.788 | |||
3/4 | 0.751 | 0.383 | 0.788 | |||
3/5 | 0.767 | 0.327 | 0.795 | |||
3/6 | 0.731 | 0.248 | 0.793 | |||
4/1 | 0.257 | 0.713 | 0.068 | 0.778 | ||
4/2 | 0.715 | 0.059 | 0.781 | |||
4/3 | 0.72 | 0.053 | 0.788 | |||
4/4 | 0.721 | 0.253 | 0.785 | |||
4/5 | 0.724 | 0.218 | 0.788 | |||
4/6 | 0.729 | 0.197 | 0.795 |
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
Recessive | 1/1 | 0.231 | 0.68 | 0.042 | 0.756 |
2/1 | 0.231 | 0.688 | 0.064 | 0.755 | ||
2/2 | 0.693 | 0.061 | 0.761 | |||
2/2 | 0.68 | 0.042 | 0.756 | |||
2/2 | 0.686 | 0.119 | 0.734 | |||
2/2 | 0.69 | 0.117 | 0.737 | |||
2/2 | 0.676 | 0.097 | 0.746 | |||
3/1 | 0.231 | 0.671 | 0.089 | 0.731 | ||
3/2 | 0.682 | 0.068 | 0.748 | |||
3/3 | 0.68 | 0.042 | 0.756 | |||
¾ | 0.714 | 0.342 | 0.753 | |||
3/5 | 0.728 | 0.287 | 0.76 | |||
3/6 | 0.693 | 0.207 | 0.761 | |||
4/1 | 0.231 | 0.673 | 0.055 | 0.744 | ||
4/2 | 0.676 | 0.048 | 0.747 | |||
4/3 | 0.68 | 0.042 | 0.756 | |||
4/4 | 0.683 | 0.218 | 0.753 | |||
4/5 | 0.686 | 0.186 | 0.756 | |||
4/6 | 0.69 | 0.167 | 0.764 | |||
|
Dominant | 1/1 | 0.021 | 0.009 | 0 | 0.007 |
2/1 | 0.021 | 0.009 | 0 | 0.006 | ||
2/2 | 0.009 | 0 | 0.006 | |||
2/3 | 0.009 | 0 | 0.007 | |||
2/4 | 0.009 | 0 | 0.005 | |||
2/5 | 0.009 | 0 | 0.005 | |||
2/6 | 0.009 | 0 | 0.007 | |||
3/1 | 0.021 | 0.01 | 0 | 0.007 | ||
3/2 | 0.01 | 0 | 0.007 | |||
3/3 | 0.009 | 0 | 0.007 | |||
¾ | 0.009 | 0 | 0.007 | |||
3/5 | 0.01 | 0 | 0.007 | |||
3/6 | 0.009 | 0 | 0.007 | |||
4/1 | 0.021 | 0.009 | 0 | 0.007 | ||
4/2 | 0.009 | 0 | 0.007 | |||
4/3 | 0.009 | 0 | 0.007 | |||
4/4 | 0.01 | 0 | 0.008 | |||
4/5 | 0.009 | 0 | 0.008 | |||
4/6 | 0.009 | 0 | 0.008 |
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
Additive | 1/1 | 0.015 | 0.012 | 0 | 0.016 |
2/1 | 0.015 | 0.009 | 0 | 0.014 | ||
2/2 | 0.01 | 0 | 0.014 | |||
2/3 | 0.012 | 0 | 0.016 | |||
2/4 | 0.01 | 0 | 0.011 | |||
2/5 | 0.01 | 0 | 0.011 | |||
2/6 | 0.012 | 0 | 0.014 | |||
3/1 | 0.015 | 0.009 | 0 | 0.012 | ||
3/2 | 0.01 | 0 | 0.013 | |||
3/3 | 0.012 | 0 | 0.016 | |||
¾ | 0.011 | 0.001 | 0.014 | |||
3/5 | 0.013 | 0 | 0.015 | |||
3/6 | 0.013 | 0 | 0.016 | |||
4/1 | 0.015 | 0.012 | 0 | 0.015 | ||
4/2 | 0.012 | 0 | 0.015 | |||
4/3 | 0.012 | 0 | 0.016 | |||
4/4 | 0.012 | 0 | 0.017 | |||
4/5 | 0.012 | 0 | 0.018 | |||
4/6 | 0.013 | 0 | 0.018 | |||
Recessive | 1/1 | 0.014 | 0.014 | 0 | 0.021 | |
2/1 | 0.014 | 0.012 | 0 | 0.017 | ||
2/2 | 0.013 | 0 | 0.019 | |||
2/3 | 0.014 | 0 | 0.021 | |||
2/4 | 0.013 | 0 | 0.015 | |||
2/5 | 0.013 | 0 | 0.015 | |||
2/6 | 0.013 | 0 | 0.018 | |||
3/1 | 0.014 | 0.012 | 0 | 0.014 | ||
3/2 | 0.013 | 0 | 0.017 | |||
3/3 | 0.014 | 0 | 0.021 | |||
¾ | 0.013 | 0.001 | 0.017 | |||
3/5 | 0.016 | 0.001 | 0.019 | |||
3/6 | 0.015 | 0 | 0.021 | |||
4/1 | 0.014 | 0.012 | 0 | 0.02 | ||
4/2 | 0.012 | 0 | 0.02 | |||
4/3 | 0.014 | 0 | 0.021 | |||
4/4 | 0.014 | 0 | 0.022 | |||
4/5 | 0.014 | 0 | 0.023 | |||
4/6 | 0.015 | 0 | 0.023 |
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
Dominant | 1/1 | 0.571 | 0.911 | 0.249 | 0.941 |
2/1 | 0.571 | 0.919 | 0.295 | 0.942 | ||
2/2 | 0.919 | 0.287 | 0.943 | |||
2/3 | 0.911 | 0.249 | 0.941 | |||
2/4 | 0.919 | 0.484 | 0.938 | |||
2/5 | 0.92 | 0.469 | 0.938 | |||
2/6 | 0.913 | 0.402 | 0.937 | |||
3/1 | 0.571 | 0.912 | 0.366 | 0.935 | ||
3/2 | 0.916 | 0.314 | 0.939 | |||
3/3 | 0.911 | 0.249 | 0.941 | |||
¾ | 0.928 | 0.734 | 0.941 | |||
3/5 | 0.933 | 0.67 | 0.944 | |||
3/6 | 0.916 | 0.553 | 0.941 | |||
4/1 | 0.571 | 0.909 | 0.309 | 0.936 | ||
4/2 | 0.911 | 0.274 | 0.937 | |||
4/3 | 0.911 | 0.249 | 0.941 | |||
4/4 | 0.911 | 0.57 | 0.939 | |||
4/5 | 0.913 | 0.535 | 0.94 | |||
4/6 | 0.914 | 0.507 | 0.944 | |||
Additive | 1/1 | 0.524 | 0.885 | 0.198 | 0.92 | |
2/1 | 0.524 | 0.894 | 0.243 | 0.92 | ||
2/2 | 0.893 | 0.234 | 0.922 | |||
2/3 | 0.885 | 0.198 | 0.92 | |||
2/4 | 0.894 | 0.421 | 0.914 | |||
2/5 | 0.894 | 0.407 | 0.916 | |||
2/6 | 0.885 | 0.343 | 0.914 | |||
3/1 | 0.524 | 0.883 | 0.313 | 0.91 | ||
3/2 | 0.89 | 0.262 | 0.916 | |||
3/3 | 0.885 | 0.198 | 0.92 | |||
3/4 | 0.904 | 0.681 | 0.918 | |||
3/5 | 0.909 | 0.608 | 0.924 | |||
3/6 | 0.89 | 0.489 | 0.918 | |||
4/1 | 0.524 | 0.881 | 0.254 | 0.914 | ||
4/2 | 0.883 | 0.221 | 0.916 | |||
4/3 | 0.885 | 0.198 | 0.92 | |||
4/4 | 0.885 | 0.504 | 0.917 | |||
4/5 | 0.886 | 0.468 | 0.919 | |||
4/6 | 0.888 | 0.44 | 0.923 |
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
Recessive | 1/1 | 0.498 | 0.862 | 0.168 | 0.905 |
2/1 | 0.498 | 0.873 | 0.205 | 0.907 | ||
2/2 | 0.873 | 0.198 | 0.909 | |||
2/3 | 0.862 | 0.168 | 0.905 | |||
2/4 | 0.873 | 0.378 | 0.899 | |||
2/5 | 0.872 | 0.365 | 0.9 | |||
2/6 | 0.863 | 0.302 | 0.898 | |||
3/1 | 0.498 | 0.86 | 0.272 | 0.895 | ||
3/2 | 0.87 | 0.221 | 0.901 | |||
3/3 | 0.862 | 0.168 | 0.905 | |||
¾ | 0.885 | 0.633 | 0.902 | |||
3/5 | 0.891 | 0.562 | 0.908 | |||
3/6 | 0.869 | 0.448 | 0.904 | |||
4/1 | 0.498 | 0.858 | 0.22 | 0.899 | ||
4/2 | 0.86 | 0.19 | 0.901 | |||
4/2 | 0.862 | 0.168 | 0.905 | |||
4/2 | 0.863 | 0.459 | 0.902 | |||
4/2 | 0.865 | 0.425 | 0.904 | |||
4/2 | 0.866 | 0.395 | 0.909 | |||
|
Dominant | 1/1 | 0.104 | 0.04 | 0 | 0.038 |
2/1 | 0.104 | 0.043 | 0 | 0.034 | ||
2/2 | 0.042 | 0 | 0.034 | |||
2/3 | 0.04 | 0 | 0.038 | |||
2/4 | 0.042 | 0 | 0.032 | |||
2/5 | 0.042 | 0 | 0.03 | |||
2/6 | 0.04 | 0 | 0.037 | |||
3/1 | 0.104 | 0.045 | 0 | 0.032 | ||
3/2 | 0.046 | 0 | 0.033 | |||
3/3 | 0.042 | 0 | 0.039 | |||
¾ | 0.041 | 0.004 | 0.033 | |||
3/5 | 0.044 | 0.002 | 0.037 | |||
3/6 | 0.042 | 0.001 | 0.039 | |||
4/1 | 0.104 | 0.042 | 0 | 0.039 | ||
4/2 | 0.043 | 0 | 0.039 | |||
4/3 | 0.042 | 0 | 0.039 | |||
4/4 | 0.042 | 0.001 | 0.04 | |||
4/5 | 0.043 | 0.001 | 0.039 | |||
4/6 | 0.042 | 0 | 0.041 |
|
GM | MM/MR | S-TDT | TDT | rTDT | MI-TDT |
|
Additive | 1/1 | 0.08 | 0.055 | 0 | 0.07 |
2/1 | 0.08 | 0.054 | 0 | 0.061 | ||
2/2 | 0.056 | 0 | 0.065 | |||
2/3 | 0.055 | 0 | 0.07 | |||
2/4 | 0.053 | 0.002 | 0.055 | |||
2/5 | 0.055 | 0.002 | 0.058 | |||
2/6 | 0.055 | 0.001 | 0.062 | |||
3/1 | 0.08 | 0.052 | 0 | 0.055 | ||
3/2 | 0.056 | 0 | 0.06 | |||
3/3 | 0.055 | 0 | 0.07 | |||
¾ | 0.056 | 0.007 | 0.059 | |||
3/5 | 0.065 | 0.005 | 0.069 | |||
3/6 | 0.059 | 0.003 | 0.068 | |||
4/1 | 0.08 | 0.055 | 0 | 0.065 | ||
4/2 | 0.055 | 0 | 0.066 | |||
4/3 | 0.055 | 0 | 0.07 | |||
4/4 | 0.057 | 0.003 | 0.07 | |||
4/5 | 0.058 | 0.003 | 0.071 | |||
4/6 | 0.058 | 0.002 | 0.075 | |||
Recessive | 1/1 | 0.077 | 0.066 | 0 | 0.084 | |
2/1 | 0.077 | 0.064 | 0 | 0.078 | ||
2/2 | 0.066 | 0 | 0.081 | |||
2/3 | 0.066 | 0 | 0.084 | |||
2/4 | 0.063 | 0.002 | 0.07 | |||
2/5 | 0.065 | 0.002 | 0.072 | |||
2/6 | 0.065 | 0.001 | 0.075 | |||
3/1 | 0.077 | 0.061 | 0.001 | 0.068 | ||
3/2 | 0.065 | 0 | 0.075 | |||
3/3 | 0.066 | 0 | 0.083 | |||
¾ | 0.067 | 0.008 | 0.074 | |||
3/5 | 0.078 | 0.006 | 0.083 | |||
3/6 | 0.07 | 0.004 | 0.083 | |||
4/1 | 0.077 | 0.064 | 0.001 | 0.077 | ||
4/2 | 0.065 | 0 | 0.079 | |||
4/2 | 0.066 | 0 | 0.083 | |||
4/2 | 0.067 | 0.004 | 0.084 | |||
4/2 | 0.068 | 0.003 | 0.086 | |||
4/2 | 0.07 | 0.002 | 0.09 |
When the linkage disequilibrium was at its moderate level (
We illustrate the robustness of the MITDT-ONE for type 1 diabetes at insulin dependent diabetes mellitus 2 locus (IDDM2) on chromosome 11p15. At our request, Neil Walker of the Juvenile Diabetes Research Foundation/Wellcome Trust Diabetes and Inflammation Laboratory (JDRF/WT DIL) compiled data from 475 families with
We considered the same U.K. Warren Families but chose the first affected child from each family to have only
The percentage of missing genotypes ranged from low (4% for DIL977) to high (52% for DIL997).
SNP | Variant | % |
|
|
DIL997 | C/T | 52 | 4 | 0.0455003 |
DIL996 | C/T | 28 | 4.2631579 | 0.0389475 |
DIL989 | C/T | 26 | 4.7407407 | 0.0294564 |
DIL985 | C/T | 42 | 6.1084337 | 0.0134538 |
DIL984 | G/A | 22 | 3.8571429 | 0.0495346 |
DIL977 | G/A | 4 | 17.386831 |
|
DIL976 | T/G | 36 | 10.940828 | 0.0009407 |
DIL975 | C/T | 30 | 11.571429 | 0.0006697 |
DIL974 | A/C | 30 | 16.568966 |
|
DIL973 | T/C | 16 | 14.069767 |
|
DIL971 | G/C | 20 | 10.971429 |
|
DIL969 | A/T | 6 | 23.027397 |
|
DIL967 | VNTR | 6 | 21.300341 |
|
DIL965 | T/C | 20 | 14.901478 |
|
DIL963 | A/C | 22 | 10.414286 | 0.0012504 |
DIL954 | C/T | 36 | 6.2857143 | 0.0121715 |
DIL3872 | C/G | 18 | 7.4745763 | 0.0062576 |
DIL2048 | C/T | 12 | 3.7815126 | 0.0518218 |
The third, fourth, and fifth columns show the percentages of missing data, the TDT statistics for complete data, and uncorrected p-values at 5% significance level. The significance SNPs are shown by underlined
The MITDT-ONE and rTDT could verify if the significant SNPs for complete data are also significant when missing genotypes are taken into account. However, if either method could not reach significant result as in complete case, it does not mean that these SNPs are insignificant. It simply means that both methods reach an inconclusive decision. Moreover, the number of significant SNPs could be smaller when either test is employed, compared to the number of significant SNPs for complete data. Out of 18 significant SNPs in complete cases, MITDT-ONE (rTDT) verified seven (three) to be significant (
SNP | Variant | Name | dbSNP |
|
|
|
|
DIL977 |
G/A | +1,428 |
rs3842756 | 17.39 | 16.82 | 0.0000305 | 0.0000412 |
DIL973 | T/C | +1,127 |
rs3842752 | 14.07 | 8.00 | 0.0001762 | 0.0046696 |
DIL971 | G/C | +805 |
rs3842748 | 10.98 | 6.13 | 0.0009253 | 0.0133311 |
DIL969 |
A/T | −23 |
rs689 | 23.03 | 21.44 | 15.97× |
36.48×10−5 |
DIL967 |
VNTR | VNTR | - | 21.30 | 18.27 | 3.93× |
0.0000192 |
DIL965 | T/C | −2,221 |
rs3842729 | 14.90 | 7.97 | 0.0001133 | 0.0047659 |
DIL963 | A/C | −2,733A/C | rs3842727 | 10.41 | 4.68 | 0.0012504 | 0.0306104 |
The third and fourth columns show the name of the SNP defined in Barratt et al. (2004) and the SNP database, respectively. The fifth and sixth columns show the statistics for complete and incomplete data when MITDT-ONE is applied, respectively. The seventh and eight columns show the type I errors of the columns fifth and sixth, respectively.
are SNPs found in association by using rTDT.
Sebastiani et al.
The minimum values of the interval estimates of MITDT-ONE and rTDT make a decision against the null hypothesis of no linkage. One of the advantages of using MITDT-ONE is that significance results achieved by complete data is ratified when the minimum value of the interval estimate is smaller than the value of TDT for complete data. The other advantage of our method is that it allows researchers to implement our method to any missing rates. As discussed in the
In the construction of MITDT-ONE, we consider cases where all genotypes of family members are missing (Case 1). It is intuitive that since these families do not have any information they should be ignored from the study. We suggest that these families be omitted from the data if only one SNP is studied. However, if more than one SNP are studied then we suggest keeping them in the computation of MITDT-ONE to have same number of families for each SNP.
In summary, simulation studies show that MITDT-ONE controls type I error rates very well and produces high power when degree of linkage disequilibrium is mild.
We thank the members of the DNA resource team and Neil Walker of Juvenile Diabetes Research Foundation/Wellcome Trust Diabetes and Inflammation Laboratory (JDRF/WT DIL) for sample and data services (