Quantitative genetics has evolved dramatically in the past century, and the proliferation of genetic data enables the characterization of complex interactions beyond the scope of its theoretical foundations. In this paper, we lay the foundations of an alternative formulation of quantitative genetics based on information theory. Information theory can provide sensitive measures of statistical dependencies among variables, and provides a natural mathematical language for an alternative view of quantitative genetics. In previous work we examined the information content of discrete functions and applied this formalism to the analysis of genetic data. We present here a set of relationships that both unifies the information measures for the set of discrete functions, and uses them to express key quantitative genetic relationships. Information theory measures of variable interdependency are used to identify significant interactions, and a general approach is described for inferring functional relationships within genotype and phenotype data. We present information-based measures of the genetic quantities: penetrance, heritability and degrees of statistical epistasis. Our scope here includes the consideration of three variable dependencies and independently segregating variants, which captures two locus effects, genetic interactions, and two phenotype pleiotropy. However, this formalism and general theory naturally applies to multi-variable interactions and higher-order complex dependencies, and can be adapted to account for population structure, linkage and non-randomly segregating markers. This paper therefore lays the initial groundwork for a full formulation of quantitative genetics based in information theory.

Background. Fetuin-A (α₂-Heremans Schmid glycoprotein) has recently been identified as a circulating inhibitor of calcification and is regulated as a negative acute phase protein. However, its relationships with cardiac valvular calcification and atherosclerosis and outcome have not been evaluated in peritoneal dialysis (PD) patients. Method. We performed a prospective follow-up study in 238 PD patients with echocardiography done at baseline to detect cardiac valvular calcification and biochemical analysis performed for serum fetuin-A, albumin and C-reactive protein (CRP). Results. Baseline serum fetuin-A concentration was (mean±SD) 0.309±0.068 g/l (normal range 0.4–0.95). Across the three tertiles of increasing serum fetuin-A, a significant trend effect was observed for age (P = 0.023), diabetes (P = 0.008), background atherosclerotic vascular disease (P = 0.010), cardiac valvular calcification (P = 0.002), serum albumin (P<0.001), subjective global assessment (P = 0.005) and CRP (P<0.001). Adjusting for CRP and calcium × phosphorus product, every 0.01 g/l increase in serum fetuin-A remained independently associated with a 6% decrease in the risk of valvular calcification (95% confidence intervals, 0.90–0.99; P = 0.028). Furthermore, serum fetuin-A showed a significant decrease across the four groups of patients with increasing components of the malnutrition, inflammation, atherosclerosis/calcification (MIAC) syndrome (P<0.001) and was the lowest among patients with all components of the MIAC syndrome (0.263±0.055 g/l) and highest among those who do not have the MIAC syndrome at all (0.338±0.063 g/l). Lower serum fetuin-A was associated with greater all-cause mortality (P = 0.0011) and fatal and non-fatal cardiovascular events (P = 0.0017), but its significance was lost when atherosclerotic vascular disease, valvular calcification, inflammation and malnutrition were included in the model. Conclusions. Serum fetuin-A showed important associations with valvular calcification, atherosclerosis, malnutrition and inflammation, and was linked to mortality and cardiovascular events in PD patients via its close relationships with the MIAC syndrome.

Vitamin D seems to protect against cardiovascular disease, but the reported effects of vitamin D on patient outcomes in CKD are controversial. We conducted a prospective, double blind, randomized, placebo-controlled trial to determine whether oral activated vitamin D reduces left ventricular (LV) mass in patients with stages 3–5 CKD with LV hypertrophy. Subjects with echocardiographic criteria of LV hypertrophy were randomly assigned to receive either oral paricalcitol (1 μg) one time daily (n=30) or matching placebo (n=30) for 52 weeks. The primary end point was change in LV mass index over 52 weeks, which was measured by cardiac magnetic resonance imaging. Secondary end points included changes in LV volume, echocardiographic measures of systolic and diastolic function, biochemical parameters of mineral bone disease, and measures of renal function. Change in LV mass index did not differ significantly between groups (median [interquartile range], −2.59 [−6.13 to 0.32] g/m² with paricalcitol versus −4.85 [−9.89 to 1.10] g/m² with placebo). Changes in LV volume, ejection fraction, tissue Doppler-derived measures of early diastolic and systolic mitral annular velocities, and ratio of early mitral inflow velocity to early diastolic mitral annular velocity did not differ between the groups. However, paricalcitol treatment significantly reduced intact parathyroid hormone (P<0.001) and alkaline phosphatase (P=0.001) levels as well as the number of cardiovascular-related hospitalizations compared with placebo. In conclusion, 52 weeks of treatment with oral paricalcitol (1 μg one time daily) significantly improved secondary hyperparathyroidism but did not alter measures of LV structure and function in patients with severe CKD.

C-reactive protein (CRP), the prototype marker of inflammation, and cardiac hypertrophy are important prognostic indicators in dialysis patients. Residual renal function (RRF) has also been shown to influence survival of peritoneal dialysis (PD) patients. This study examined the relations between inflammation, RRF, and left ventricular hypertrophy (LVH) and determined whether inflammation, RRF, and LVH combine adversely to predict the outcomes of PD patients. A prospective observational study was performed in 231 chronic PD patients. Left ventricular mass index (LVMi), residual glomerular filtration rate (GFR), CRP, hemoglobin, serum albumin, and BP were determined at study baseline and related to outcomes. On univariate analysis, age (P = 0.002), dialysis duration (P = 0.004), coronary artery disease (P < 0.001), pulse pressure (P < 0.001), hemoglobin (P < 0.001), serum albumin (P = 0.032), log-CRP (P < 0.001), and GFR (P < 0.001) were significantly associated with log-LVMi. Log-CRP was positively correlated with pulse pressure (R = 0.218, P = 0.001) and negatively correlated with GFR (R = −0.272, P < 0.001). Multivariate analysis showed that log-CRP (P = 0.008) and RRF (P = 0.003) remained associated with log-LVMi independent of hemoglobin, serum albumin, arterial pulse pressure, and coronary artery disease. After follow-up for 30 ± 14 mo, 34.2% patients had died. CRP, RRF, and LVMi each were significantly predictive of all-cause mortality and cardiovascular death. Kaplan-Meier analysis showed a significant increase in all-cause (P < 0.0001) and cardiovascular mortality (P < 0.0001) as the number of risk factors, namely CRP ≥50th percentile, no RRF, and LVMi≥ 50th percentile increased with the 2-yr all-cause mortality and cardiovascular death reaching as high as 61% and 46%, respectively, for patients who had all three risk factors. Compared with patients with none of the three risk factors, those with all three risk factors had an adjusted hazards ratio of 6.94 (P < 0.001) and 5.43 (P = 0.001) for all-cause mortality and cardiovascular mortality, respectively. In conclusion, inflammation, RRF, and LVH are interrelated and combine adversely to increase mortality and cardiovascular death risk of PD patients.