https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(21)02183-8/fulltextThis study doesn't completely fill in the gaps, but it does have a much larger sample set (n = 3,436,957) and the study ran from Dec 14, 2020 to Aug 8, 2021, so it does attempt to measure effectiveness over time.
From the data/results: 184,041 participants contracted covid and 12,130 ended up in the hospital.
Over the entire study period, fully vaccinated individuals had an adjusted vaccine effectiveness of 73% (95% CI 7274) against SARS-CoV-2 infections and 90% (8992) against COVID-19-related hospital admissions (appendix pp 67). Stratified by age group, the vaccine effectiveness against infection of those who were fully vaccinated was 91% (95% CI 8893) for those aged 1215 years and 61% (5765) for those aged 65 years and older (appendix p 6). The age stratified vaccine effectiveness against hospital admissions was 92% (95% CI 8895) for those aged 1644 years, and 86% (8288) for those aged 65 years and older (appendix p 6).
Vaccine effectiveness against infection for the fully vaccinated decreased with increasing time since vaccination, declining from 88% (95% CI 8689) during the first month after full vaccination to 47% (4351) after 5 months (157 days after second dose, p<00001; figure 2A; appendix p 9). Individuals aged 65 years and older had a vaccine effectiveness of 80% (95% CI 7385) within 1 month after being fully vaccinated, decreasing to 43% (3054; p<00001) at 5 months after full vaccination (figure 2A; appendix p 9). Among fully vaccinated individuals of all ages, overall adjusted vaccine effectiveness estimates for COVID-19 hospital admissions were 87% (95% CI 8291) within 1 month after being fully vaccinated, and 88% (8292) at 5 months after full vaccination, showing no significant waning (p=080; figure 2B; appendix pp 910).
Overall vaccine effectiveness against infection with the delta variant for the fully vaccinated was 75% (95% CI 7178), while overall vaccine effectiveness for other variants was 91% (8892; appendix pp 910). Estimates against both delta and other variants were high within 1 month after full vaccination (vaccine effectiveness against delta 93% [95% CI 8597] vs other variants 97% [9599]; p=029). At 4 months after full vaccination, vaccine effectiveness against delta infections declined to 53% (95% CI 3965) and vaccine effectiveness against other variants declined to 67% (4580; p=025).Bold emphasis added. There is a lot to unpack in this article, but the data is a much better set for drawing conclusions from.