Computing optimal sampling designs for two-stage studies

Stata Technical Bulletin

Figure 2. Schematic illustration of a three-generation family.

Generation 1

Generation 2

Figure 1. Schematic illustration of a two-generation family.

Syntax

simuped2 #Ag_e1 #S_td1 #Ag_e2 #S_td2 [, r eps(#) saving filename) alle(#) sib(#) ]

simuped3 #Age1 #Std1 #Age2 #Std2 #Age3 #Std3 [. E®ps(#) saving (filename) alle(#) sib(#) si3(#) ]

Description

simuped2 and simuped3 are immediate commands used for generating two- and three-generation family data, respectively.
For each person in a family, the sex is generated by a probability of 0.5. The age of a person is generated according to a normal
distribution, with means #Ag_eb #Ag_e2, and #Ag_e3 for the first, second, and third generations. The standard deviations of the ages
are given by #s_mi, #Std2, and #S_t<_β, respectively.

The number of siblings in a generation is a random number, distributed according to a Poisson distribution. The mean sizes
of the siblings in the second- and third-generation are given by sib(#) and si3(#), respectively.

Hardy-Weinberg equilibrium is assumed for the genotypic distribution of people in the first generation (see, for example,
Elandt-Johnson 1971). The allele frequency of a biallelic locus A is given by the argument alIe ##), denoted as p. The frequencies
of genotypes AA, Aa and aa in the first generation are given by p², 2p(l — p) and (1 — p)², respectively. The genotype of
a person in the second- and third-generation is generated according to the Mendelian inheritance, that is, a person inherits the
allele A from the father (or mother) with probability 0.5.

The simulated family data are saved in a file specified by savingfilename), and the number of replications is specified by
reps (#).

Options

reps (#) specifies the number of simulated families. The default value is 100.

savingfilename) specifies the file into which the simulated data are saved. The default file name is temp.dta.

allé (#) specifies the allele frequency of a biallelic locus A. The default value is 0.1.

sib(#) specifies the mean number of siblings in the second generation. The default value is 3.

si3(#) specifies the mean number of siblings in the third generation. It is only used in simuped3. The default value is 3.

Remarks

simuped2 and simuped3 simulate the basic quantities of a person, such as age, sex, and genotype, which are useful in
genetic epidemiology research. Further quantities of interest, such as the disease status of a person, can be simulated based
on these basic family data. However, it sometimes requires specific models for the affect of a disease and the model of the
natural mortality of a person. We do not include the disease status in the programs because that would not make simuped2 and
simuped3 of as general use.

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