January/February are often the coldest months of the year. One effect of the cold is to thicken the blood making it clot more readily leading to an increase in strokes and heart attacks in people with high blood pressure. Many elderly people think that they must go out and get exercise to stay fit. My late df did and had 2 massive strokes in the January and died 3 weeks later. His GP hadn't bothered treating his high blood pressure. But, had it been this year, as he had chronic bronchitis he might well have been vaccinated - he'd have walked a mile and a half to the health centre as the buses/trains weren't reliable - would've had the vaccine and quite probably died from a stroke. He was only 79 and fit enough to walk 3 miles 3 times a day.
I'm nearly 65 and have a compromised immune system and have been ill with hypothermia due to a thyroid problem and I'll be offered the "flu vaccine after my birthday in March which seems a bit pointless as it's after the 'flu season.
I've been told I'm high risk for Covid, but despite an auto-immune disorder I'm way down the list for a vaccine.
The immune system gradually weakens with age, and many people have untreated underactive thyroid problems - the British Thyroid Association said that at least 25% of people who have their blood tested to create the 'normal' range have a problem, it's just not been diagnosed and treated.
So, some dying could have an autoimmune disorder and not be aware of it, some could be like my late DF and have walked to the health centre in the cold causing other problems. As previous posters have said it can be down to spurious correlation.
Testing isn't an exact science, whether for vaccines or computer systems. You do the best you can in line with current best practice. 100% testing isn't practical before launching a vaccine. It's just unknown.