Regressive logistic models for familial diseases: a formulation assuming an underlying liability model

Area of Science:

• Biostatistics
• Genetic Epidemiology
• Complex Disease Modeling

Background:

• Familial aggregation of complex diseases is influenced by major genes and non-major-gene factors.
• Existing statistical models, such as mixed models and regressive logistic models, offer different approaches to delineate these influences.
• An analytical equivalence between these models has been challenging to establish.

Purpose of the Study:

• To formulate regressive logistic models based on an underlying liability model of disease.
• To establish a direct correspondence between mixed models and regressive logistic models.
• To provide a unified and parsimonious framework for analyzing complex disease genetics.

Main Methods:

• Proposed a formulation of regressive logistic models assuming an underlying liability threshold model.
• Modeled correlated liabilities among relatives, with affection defined by exceeding a threshold.
• Expressed regression coefficients in terms of familial correlations under a regressive model for liability structure.

Main Results:

• Established a one-to-one correspondence between the parameters of the proposed regressive logistic model and the mixed model.
• Demonstrated that the liability model leads to a parsimonious parameterization.
• Showed that the derived logits can accommodate various family dependence patterns and gene-environment interactions.

Conclusions:

• The proposed unified framework reconciles regressive logistic and mixed models for complex disease analysis.
• This approach offers a more parsimonious and flexible method for dissecting genetic and environmental contributions to disease.
• The model is extendable to complex family structures and gene-environment interactions.