Previous research on estimation of the progression of chronic disease, from the normal preclinical screen-detectable phase (PCDP) to the final clinical phase, has usually assumed constant transition rates and has rarely addressed how relevant covariates affect multi-state transitions. The present study proposes two non-homogeneous models using the Weibull distribution and piecewise exponential model, together with covariate functions of the proportional hazard form, to tackle these problems. We illustrate the models by application to a selective breast cancer screening programme. The results of the Weibull model yield estimates of scale and shape parameters for annual preclinical incidence rate as 0.0000058 (SE=0.0000019) and 2.4755 (SE=0.1153), the latter being significantly higher than 1. Annual transition rate was estimated as 0.3153 (SE=0.1385). Relative risks for the effects of late age at first pregnancy (AP) and high body mass index (BMI) on preclinical incidence rate were 1.98 and 2.59, respectively. The corresponding figures on the transition from the PCDP to clinical phase were 1.56 and 1.99, respectively. Non-homogeneous Markov models proposed in this study can be easily applied to rates of progression of chronic disease with increasing or decreasing rates with time and to model the effect of relevant covariates on multi-state transition rates.

Schizophrenia and human leukocyte antigen (HLA) matching between couples or between mothers and offspring have independently been associated with prenatal/obstetric complications, including preeclampsia and low birth weight. Here, we report the results of a family-based candidate-gene study that brings together these two disparate lines of research by assessing maternal-fetal genotype matching at HLA-A, -B, and -DRB1 as a risk factor of schizophrenia. We used a conditional-likelihood modeling approach with a sample of 274 families that had at least one offspring with schizophrenia or a related spectrum disorder. A statistically significant HLA-B maternal-fetal genotype-matching effect on schizophrenia was demonstrated for female offspring (P=.01; parameter estimate 1.7 [95% confidence interval 1.22-2.49]). Because the matching effect could be associated with pregnancy complications rather than with schizophrenia per se, these findings are consistent with the neurodevelopmental hypothesis of schizophrenia and with accumulating evidence that the prenatal period is involved in the origins of this disease. Our approach demonstrates how genetic markers can be used to characterize the biology of prenatal risk factors of schizophrenia.

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The MFG test is a family-based association test that detects genetic effects contributing to disease in offspring, including offspring allelic effects, maternal allelic effects and MFG incompatibility effects. Like many other family-based association tests, it assumes that the offspring survival and the offspring-parent genotypes are conditionally independent provided the offspring is affected. However, when the putative disease-increasing locus can affect another competing phenotype, for example, offspring viability, the conditional independence assumption fails and these tests could lead to incorrect conclusions regarding the role of the gene in disease. We propose the v-MFG test to adjust for the genetic effects on one phenotype, e.g., viability, when testing the effects of that locus on another phenotype, e.g., disease. Using genotype data from nuclear families containing parents and at least one affected offspring, the v-MFG test models the distribution of family genotypes conditional on offspring phenotypes. It simultaneously estimates genetic effects on two phenotypes, viability and disease. Simulations show that the v-MFG test produces accurate genetic effect estimates on disease as well as on viability under several different scenarios. It generates accurate type-I error rates and provides adequate power with moderate sample sizes to detect genetic effects on disease risk when viability is reduced. We demonstrate the v-MFG test with HLA-DRB1 data from study participants with rheumatoid arthritis (RA) and their parents, we show that the v-MFG test successfully detects an MFG incompatibility effect on RA while simultaneously adjusting for a possible viability loss.