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This paper examines how estimates of the deterrent effect of capital punishment depend on alternate choices of assumptions concerning the homicide process. Specific models of the homicide process represent bundles of these assumptions, which involve the unobserved heterogeneity, the relevant penalty probabilities for homicide choices, possible cross-polity parameter variation, and exchangeability between polity-time pairs that do and do not experience positive numbers of murders. We demonstrate how various assumptions have driven the conflicting findings from studies on capital punishment, and isolate a particular set of assumptions that are required to find a positive deterrent effect.

<b><i>Introduction:</i></b> The objective of this study was to examine the association between type 2 diabetes mellitus (T2DM) and genes identified in previous genome-wide association studies (GWASs) in rural Han Chinese adults. <b><i>Methods:</i></b> This prospective study included 1,832 adults aged ≥18 years in Deqing without diabetes at baseline. The subjects were followed up for 8.7 years on average. We selected 45 susceptible tag single-nucleotide polymorphisms (SNPs) for T2DM that have been identified in GWASs and genotyped. A Cox model was constructed to calculate the adjusted hazard ratios (aHRs) for the association between SNPs and incident T2DM. <b><i>Results:</i></b> The incidence rate of T2DM was 12.0 per 1,000 person-years. After adjustment for covariates and a Bonferroni correction, rs17584499 of protein tyrosine phosphatase, receptor-type D (PTPRD), rs11257655 and rs10906115 of cell division cycle 123 gene (CDC123), and rs12970134 of melanocortin-4 receptor (MC4R) were significantly associated with incident T2DM. The aHRs for incident T2DM were 1.75 (95% confidence interval [CI]: 1.28–2.40) and 1.61 (95% CI: 1.27–2.04) in association with an increasing number of T alleles in rs17584499 and rs11257655 under an additive genetic model, and the aHR was 1.72 (95% CI: 1.33–2.22) with an increasing number of A alleles in rs10906115. The aHRs under the dominant model were 1.82 (95% CI: 1.25–2.66) for TT + CT versus CC of rs17584499 and 2.04 (95% CI: 1.47–2.86) for AA + AG versus GG of rs10966115. The aHRs under the recessive model were 2.99 (95% CI: 1.30–6.89) for TT versus CT + CC of rs17584499, 1.92 (95% CI: 1.39–2.70) for TT versus CT + CC of rs11257655, and 2.54 (95% CI:1.22–5.29) for AA versus AG + GG of rs12970134. In addition, an increased incidence of T2DM was significantly associated with the TA haplotype of rs11257655 and rs10906115 (aHR = 1.81, 95% CI: 1.12–2.92), while a decreased incidence was associated with the CG haplotype (aHR = 0.49, 95% CI: 0.35–0.68) and the CT haplotype of rs1111875 and rs5015480 (aHR = 0.61, 95% CI: 0.37–0.98). <b><i>Conclusion:</i></b> Variants of the PTPRD, CDC123, and MC4R genes were associated with the T2DM incidence in a rural Han Chinese population.