Abstract
Studies about the genetic basis for disease are routinely conducted through family studies under response-dependent sampling in which affected individuals called probands are sampled from a disease registry, and their respective family members (non-probands) are recruited for study. The extent to which the dependence in some feature of the disease process (e.g., presence, age of onset, severity) varies according to the kinship of individuals reflects the evidence of a genetic cause for disease. When the probands are selected from a disease registry, it is common for them to provide quite detailed information regarding their disease history, but non-probands often simply provide their disease status at the time of contact. We develop conditional second-order estimating equations for studying the nature and extent of within-family dependence which recognizes the biased sampling scheme employed in family studies and the current status data provided by the non-probands. Simulation studies are carried out to evaluate the finite sample performance of different estimating functions and to quantify the empirical relative efficiency of the various methods. Sensitivity to model misspecification is also explored. An application to a motivating psoriatic arthritis family study is given for illustration.
Highlights
1.1 IntroductionThe heritable nature of disease can be inferred from the structure of the within-family dependence in disease manifestation [19]
The incidence of psoriatic arthritis (PsA) is reported to be between 0.3 and 1.0% [9] and hereditary factors are thought to be important, as some studies have suggested that close blood relatives of individuals affected by psoriatic arthritis are at higher risk of developing the disease compared to the general population
Based on our previous findings regarding asymptotic relative efficiency and robustness, here we focus our attention on the preferred estimating functions Gi and full covariance matrix Wi (G–W) and GI-working partial independence (WPI)
Summary
The heritable nature of disease can be inferred from the structure of the within-family dependence in disease manifestation [19]. Li et al [20], Hsu et al [15], and Shih and Chatterjee [27] proposed likelihood methods based on disease onset time for case–control family study and Chatterjee et al [6] proposed methods to estimate the relative risk, cumulative risk, and residual familial aggregation for case– control family data and modified method for case-only family data In their methods, modeling and estimation of the residual familial aggregation is key to adjustment for ascertainment bias, but this is done using an exchangeable dependence structure in which the association is the same for different pairs of relatives. More elaborate dependence modeling plays a central role when studying the “parent-of-descent” hypothesis, where the primary goal is to estimate and compare the strength of father–child and mother–child associations in phenotype to elucidate the role of the sex chromosomes in disease transmission [30] With this in mind, we consider copula models [22] as a basis for modeling the joint risk of disease among family members. A supplementary estimating equation is incorporated to extract limited information about the marginal onset time distribution from the proband
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