Nonrandom sampling in genetic epidemiology: Maximum likelihood methods for multifactorial analysis of quantitative data ascertained through truncation

Abstract

Three types of nonrandom sampling of family data are described, and appropriate maximum likelihood methods are proposed for each. The three types arise depending on whether the selection of probands, based on truncation, is applied directly to the phenotypic distribution, to the distribution of a correlated trait, or to the liability distribution of an associated disease. Family data ascertained through random and nonrandom sampling can be analyzed together in a unified approach. Results of a Monte Carlo study are presented that demonstrate the utility of the proposed methods. In particular, likelihood ratio tests of null hypotheses are shown to be distributed as chi-square, even in samples as small as 50 families (with variable sibship size).

Familial Aggregation of Lipids and Lipoproteins in Families Ascertained through Random and Nonrandom Probands in the Iowa Lipid Research Clinics Family Study

“…The 8 path coefficients, up to 20 Ps, 6 means and 6 variances (I each for a phenotype and an index for each of a father, mother and child) are estimated us ing maximum likelihood methods for multifactorial analysis of quantitative data ascertained through in direct truncation (17]. Briefly, for a random sample, the likelihood is a function of X, the column vector of dimension m of deviations from the means of the ob served phenotypes and indices in the jlh family.…”

“…differ ent traits measured at 2 different times (such as when visit I CH is the selection variable and visit 3 TG is the phenotype). For nonprobands, however, |5", (j * proband) is defined as a 'partial' correlation between the selection variable of a proband and the pheno type of the nonproband relative, given the proband's phenotype (17].…”

“…Although some methods are available for analysis of nonrandom samples of family data [14][15][16], none of them are geared to take advantage of the specific LRC sampling protocol. Accord ingly, we recently developed new methods appropriate for this purpose [17]. One of these methods, based on selection through indirect truncation on a correlated trait (in which the likelihood function is condi tioned on the actual event that the pro band's value is beyond a certain threshold [17] ), has recently been incorporated into a path analysis program for nuclear families [18] .…”

“…Accord ingly, we recently developed new methods appropriate for this purpose [17]. One of these methods, based on selection through indirect truncation on a correlated trait (in which the likelihood function is condi tioned on the actual event that the pro band's value is beyond a certain threshold [17] ), has recently been incorporated into a path analysis program for nuclear families [18] . This method provides nearly unbi ased and efficient parameter estimates, and powerful likelihood ratio tests of null hypotheses [17,19].…”

“…One of these methods, based on selection through indirect truncation on a correlated trait (in which the likelihood function is condi tioned on the actual event that the pro band's value is beyond a certain threshold [17] ), has recently been incorporated into a path analysis program for nuclear families [18] . This method provides nearly unbi ased and efficient parameter estimates, and powerful likelihood ratio tests of null hypotheses [17,19]. The method also al lows for analysis of both random and noi random samples jointly and separately fo assessing heterogeneity between samples which may lead to inferences regardin the similarity of risk factors for CHD ii randomly ascertained pedigrees versu those obtained through hyperlipidemk probands, which is the main focus of this study.…”