honestly, these stats mean nothing without knowing individual intervals between vaccine, its effective date and community exposure prior to effective date.
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That issue is addressed in the first line of the first table highlighted in yellow.
The chart lists 4,000 single-dose deaths within 21 days of vaccination, and 9,500 after 21 days but before the second dose (which I guess is 21 days or more after the first dose). That's within the averaged death window and points to an incubating infection prior to the first dose. Without looking at community exposure pre and post first dose, and, antibody levels at time of death, we can't say definitively the vaccine caused those deaths.
There are another 4,000 that died up to or 14 days after the second dose, or, on a 21-day dosing, 35 days plus to death from the first dose. That's still within the averaged death window but also points to inadequate antibody production of the first dose, and community infection between the first and second dose dates. That is, given an average 28 day death cycle, infection would have occurred just prior to or anytime after the first dose when antibodies were still building.
Does this mean that the UK should not have extended time to second dose to three weeks, so as to reach more people with the first dose, but leaving some people with inadequate antibody level buildup from the first dose? People with a false sense of security more likely to return to community settings before the 21-28 day caution window while antibodies are building? Should antibody testing be part of the dose 2 regime?