Suppose you have genotyped 20 members of an experimental backcross population at five markers spanning two chromosomes, and you have also recorded the disease resistance status of each subject as resistant or not resistant. You are interested in finding whether there are BTL in the genetic region spanned by your marker set, and if so, where those BTL are and how strongly linked they are to the disease resistance locus. The first step is to input the data, and then to use PROC BTL with the appropriate options to request all single-marker models of the data to be calculated, as in the following program:
data MarkerDat; input (m1-m5) ($) trait; datalines; A B B A B 1 B A B B A 1 A B A B B 1 A A B B A 1 A B A B B 1 B A A A B 1 A A B A A 1 B B A B A 1 A A B B A 1 A A A B A 1 A B A A B 0 B A B A A 0 B A A A B 0 B B A B B 0 B A A B B 0 B B A A B 0 A B B A A 0 B A B A A 0 A B A A B 0 B A B A B 0 ;
proc btl data=MarkerDat; marker m1-m5 /all=1; model trait; run;
The results from the analysis are shown in Figure 3.1.
Figure 3.1: Single-Marker Model Statistics
Model Statistics | ||||||
---|---|---|---|---|---|---|
Marker Effect |
DF | Chi- Square |
Pr > ChiSq | AIC | AICC | BIC |
M4 | 1 | 6.8470 | 0.0089 | 29.2 | 30.7 | 32.2 |
M1 | 1 | 4.5129 | 0.0336 | 31.5 | 33.0 | 34.5 |
M5 | 1 | 2.9321 | 0.0868 | 33.1 | 34.6 | 36.1 |
M2 | 1 | 1.2289 | 0.2676 | 34.8 | 36.3 | 37.8 |
M3 | 1 | 1.2289 | 0.2676 | 34.8 | 36.3 | 37.8 |
Similarly, all two-marker models can be calculated as follows, with the results shown in Figure 3.2.
proc btl data=MarkerDat; marker m1-m5 /all=2; model trait; run;
Figure 3.2: Two-Marker Model Statistics
Model Statistics | ||||||
---|---|---|---|---|---|---|
Marker Effect |
DF | Chi- Square |
Pr > ChiSq | AIC | AICC | BIC |
M1*M4 | 3 | 11.0214 | 0.0116 | 29.0 | 33.3 | 34.0 |
M4*M5 | 3 | 10.0860 | 0.0178 | 30.0 | 34.3 | 35.0 |
M3*M4 | 3 | 8.3508 | 0.0393 | 31.7 | 36.0 | 36.7 |
M1*M2 | 3 | 7.6224 | 0.0545 | 32.4 | 36.7 | 37.4 |
M2*M4 | 3 | 7.1383 | 0.0676 | 32.9 | 37.2 | 37.9 |
M1*M5 | 3 | 6.3399 | 0.0962 | 33.7 | 38.0 | 38.7 |
M1*M3 | 3 | 5.0764 | 0.1663 | 35.0 | 39.3 | 40.0 |
M3*M5 | 3 | 4.4450 | 0.2172 | 35.6 | 39.9 | 40.6 |
M2*M5 | 3 | 3.6150 | 0.3061 | 36.4 | 40.7 | 41.4 |
M2*M3 | 3 | 1.3136 | 0.7259 | 38.7 | 43.0 | 43.7 |
Since m1
m4
appears to be the best two-marker effect, you can then estimate the recombination and penetrance parameters for this BTL
model. First you have to enter the mapping information for the markers as follows:
data MarkerMap; input marker $ chromosome position location; datalines; m1 1 1 0 m2 1 2 4.3 m3 1 3 16 m4 2 1 0 m5 2 2 5.5 ;
Now you can use the PARMEST statement to request the parameter estimates to be calculated, as in the following code. PROC BTL estimates penetrance values with each recombination parameter set to 0.5.
proc btl data=MarkerDat map=MarkerMap; marker m1 m4 /group=chromosome; model trait; parmest cross=b gen=1 r=0.5; run;
Figure 3.3 displays information about the model that includes the two-marker effect m1
m4
. The “Parameter Estimates” table shows that penetrance values are not in the valid range (between 0 and 1) for this model with the given values of .
Figure 3.3: Model Statistics, Marker Class Means, and Parameter Estimates for m1*m4 Model
Model Statistics | ||||||
---|---|---|---|---|---|---|
Marker Effect |
DF | Chi- Square |
Pr > ChiSq | AIC | AICC | BIC |
M1*M4 | 3 | 11.0214 | 0.0116 | 29.0 | 33.3 | 34.0 |
Marker Class Means | ||||
---|---|---|---|---|
Marker Class |
Marker Genotype |
N | Mean | Standard Error |
pi11 | AA | 5 | 0.4000 | 0.0480 |
pi12 | AB | 5 | 1.0000 | 0.0000 |
pi21 | BA | 6 | 0.1667 | 0.0231 |
pi22 | BB | 4 | 0.5000 | 0.0625 |
Parameter Estimates | |
---|---|
Parameter | Estimate |
r1 | 0.0000 |
r2 | 0.0000 |
p11 | 1.6000 |
p12 | 4.0000 |
p21 | 0.6667 |
p22 | 2.0000 |
theta | 0.5000 |
NOTE: The r and theta parameters are fixed. |