The duration of protection afforded by coronavirus disease 2019 (Covid-19) vaccines in the United States is unclear. Whether the increase in postvaccination infections during the summer of 2021 was caused by declining immunity over time, the emergence of the B.1.617.2 (delta) variant, or both is unknown. We extracted data regarding Covid-19–related vaccination and outcomes during a 9-month period (December 11, 2020, to September 8, 2021) for approximately 10.6 million North Carolina residents by linking data from the North Carolina Covid-19 Surveillance System and the Covid-19 Vaccine Management System. We used a Cox regression model to estimate the effectiveness of the BNT162b2 (Pfizer–BioNTech), mRNA-1273 (Moderna), and Ad26.COV2.S (Johnson & Johnson–Janssen) vaccines in reducing the current risks of Covid-19, hospitalization, and death, as a function of time elapsed since vaccination. For the two-dose regimens of messenger RNA (mRNA) vaccines BNT162b2 (30 μg per dose) and mRNA-1273 (100 μg per dose), vaccine effectiveness against Covid-19 was 94.5% (95% confidence interval [CI], 94.1 to 94.9) and 95.9% (95% CI, 95.5 to 96.2), respectively, at 2 months after the first dose and decreased to 66.6% (95% CI, 65.2 to 67.8) and 80.3% (95% CI, 79.3 to 81.2), respectively, at 7 months. Among early recipients of BNT162b2 and mRNA-1273, effectiveness decreased by approximately 15 and 10 percentage points, respectively, from mid-June to mid-July, when the delta variant became dominant. For the one-dose regimen of Ad26.COV2.S (5×10¹⁰ viral particles), effectiveness against Covid-19 was 74.8% (95% CI, 72.5 to 76.9) at 1 month and decreased to 59.4% (95% CI, 57.2 to 61.5) at 5 months. All three vaccines maintained better effectiveness in preventing hospitalization and death than in preventing infection over time, although the two mRNA vaccines provided higher levels of protection than Ad26.COV2.S. All three Covid-19 vaccines had durable effectiveness in reducing the risks of hospitalization and death. Waning protection against infection over time was due to both declining immunity and the emergence of the delta variant. (Funded by a Dennis Gillings Distinguished Professorship and the National Institutes of Health.)

Major depressive disorder (MDD) is a common complex trait with enormous public health significance. As part of the Genetic Association Information Network initiative of the US Foundation for the National Institutes of Health, we conducted a genome-wide association study of 435 291 single nucleotide polymorphisms (SNPs) genotyped in 1738 MDD cases and 1802 controls selected to be at low liability for MDD. Of the top 200, 11 signals localized to a 167 kb region overlapping the gene piccolo (PCLO, whose protein product localizes to the cytomatrix of the presynaptic active zone and is important in monoaminergic neurotransmission in the brain) with P-values of 7.7 × 10⁻⁷ for rs2715148 and 1.2 × 10⁻⁶ for rs2522833. We undertook replication of SNPs in this region in five independent samples (6079 MDD independent cases and 5893 controls) but no SNP exceeded the replication significance threshold when all replication samples were analyzed together. However, there was heterogeneity in the replication samples, and secondary analysis of the original sample with the sample of greatest similarity yielded P=6.4 × 10⁻⁸ for the nonsynonymous SNP rs2522833 that gives rise to a serine to alanine substitution near a C2 calcium-binding domain of the PCLO protein. With the integrated replication effort, we present a specific hypothesis for further studies.

Summary: Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. We present several classes of semiparametric regression models, which extend the existing models in important directions. We construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters. The maximum likelihood estimators are consistent and asymptotically normal with efficient variances. We develop simple and stable numerical techniques to implement the corresponding inference procedures. Extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings. Applications to three medical studies yield important new insights. We conclude that there is no reason, theoretical or numerical, not to use maximum likelihood estimation for semiparametric regression models. We discuss several areas that need further research.