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To derive diagnostic criteria for evaluating at-risk subjects from families with unknown genotype, we first performed bootstrap sampling to create replicate datasets that simulate the ratio of PKD1 to PKD2 as well as affected to unaffected subjects seen in clinic. To create each replicate, a subject was randomly drawn one at a time from the pool of subjects. After each draw, the selected subject was replaced in the same pool and the draw was repeated until a designated sample size was reached. Weights were assigned to each subject to control for the increasing probability of prior clinical diagnosis with increasing age and to ensure a constant ratio of unaffected PKD1 to unaffected PKD2 of 85:15.
Prior clinical diagnosis probabilities were obtained for nine 5-year age groups starting at age 15-19 up to age 55-59. Let i=1, 2,
, 9 represent the 9 age groups. Let j=1,2 represent the PKD1 and PKD2 families, respectively, and k=1,2 represent unaffected and affected subjects. The total number of subjects in the ith age group is represented as ni.. with the total number of unaffected PKD1 and unaffected PKD2 subjects in the ith age group represented by ni11 and ni21 respectively.
To maintain a constant ratio of unaffected PKD1 to unaffected PKD2 subjects of 85:15, unaffected PKD1 subjects were given a weight of 85 x ni.. / ni11 and unaffected PKD2 subjects were given a weight of 85 x ni.. / ni21. The additional factors for total number of subjects within each age group were included to control for the effect of sampling variability since there were unequal numbers of PKD1 and PKD2 subjects within each age group as well as varying ratios of unaffected to affected subjects.
Weights were also assigned so that the probability that an affected patient was selected by the bootstrap sample declined with increasing age to reflect the increasing probability of clinical diagnosis with age. A further assumption was made that only affected subjects who met the ultrasound diagnostic criterion being examined could carry a prior clinical diagnosis. Therefore, affected subjects who did not meet the ultrasound criterion being examined were assigned similar weights to those used for unaffected subjects, that is, affected PKD1 subjects who did not meet the ultrasound criterion were given a weight of 85 x ni.. / ni12 and similarly, weights of 85 x ni.. / ni22 were used for affected PKD2 subjects who did not meet the given ultrasound diagnosis.
Finally, each bootstrap sample needed to select the appropriate number of affected subjects meeting the ultrasound criterion for diagnosis in order to achieve the correct balance of unaffect to affected subjects within each age group. Age-specific cumulative probability of diagnosis resulting from investigation of an ADPKD-related symptom using data derived from a large natural history study are given as pi1 for PKD1 subjects in the ith age group and pi2 for PKD2 subjects. Let m=1,2 indicate subjects who meet and those who fail to meet the given ultrasound criterion. Then, ni121 represents the total number of affected PKD1 subjects in the ith age group who meet the ultrasound criterion and ni122 represents the total number of affected PKD1 subjects in the ith age group who do not meet the ultrasound criterion. The weight assigned to each affected PKD1 subject meeting a given ultrasound criterion in the ith age group is given by:
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Weights were examined to ensure that none were less than zero, which would have occurred had there been more affected subjects failing to meet a given ultrasound criterion than the number of subjects predicted to be undiagnosed by the model.
Each weight was then divided by the sum of all the weights in the PKD1 and PKD2 cohorts for the PKD1 and PKD2 analyses respectively, and by the sum of the weights in both cohorts for the combined analysis. The process was repeated for each of the 5 ultrasound criteria examined.
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