How many people have to be vaccinated to prevent one flu hospitalization, and how many get side effects?

The honest answer: the retrieved studies never directly measured how many flu shots prevent one hospitalization, and the side-effect numbers vary wildly by vaccine, age, and how they were counted.

The core question is unanswerable from these records. No retrieved study reports a number-needed-to-vaccinate for flu hospitalization. What the records do show is that flu vaccine effectiveness swings by year, strain, and age, with children 6 months to 8 years doing best and adults 18-49 and 65+ doing worse [1]. Effectiveness is also consistently lower against the H3N2 strain than H1N1 [1]. Without a stable effectiveness figure, no honest NNT can be calculated.

Side effects are better documented, but they are not one number. In a placebo-controlled trial of older adults, about 11 in 100 vaccinated people had local reactions versus 5 in 100 with placebo, while systemic complaints were actually slightly lower in the vaccinated group [5]. In cancer patients on immune checkpoint inhibitors, 7 of 24 (about 29 in 100) developed new immune-related adverse events within 60 days, including two severe cases [3]. A 12-year VAERS review of children found about 5 in 100 reported adverse events were serious, with 67 deaths total, but VAERS is passive surveillance that misses most events by design [4]. Guillain-Barré syndrome showed a statistical signal in children [4], and a 1991-1999 VAERS analysis found flu vaccine GBS rates of roughly 5-18 per 10 million, several times higher than a tetanus-diphtheria control group [2].

The evidence is fragmented and mostly passive surveillance or small special populations. No retrieved study compares vaccinated versus unvaccinated people on hospitalization outcomes, which is the design that would actually answer your question.

My call: the number-needed-to-vaccinate for flu hospitalization cannot be stated from this evidence, and side-effect rates range from about 1 in 10 for local reactions to roughly 1 in 200 for serious immune events in vulnerable patients. Confidence: low.