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 following model: E(BMI ij) = αj + βjlog10(Xij), for i = 1,2,..., tj.
Here Xij denotes the jth individual's age at the ith measurement; 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 computed, again following the model described in the simulation 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. Individuals 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 "Normal" 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 "Hypertension." 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 markers 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 values 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 maximum 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.