The number of people needed to be treated to prevent one case of pneumococcal bacteraemia was 161, but the confidence interval included vaccination causing more pneumococcal bacteraemia. There are two main conclusions to be drawn from this. The first is that the weight of evidence is that polysaccharide pneumococcal vaccines have yet to be shown to work in the types of people given them in industrialised countries. The only real evidence that they do comes from two improperly randomised studies from the 1940s. A similarly improperly randomised but large study done in the 1990s in Finland showed no benefits.
Much resource is put into increasing pneumococcal vaccination in at-risk groups.
Perhaps it is time to consider whether this is doing more harm than good. The other point is one of consistency in systematic reviews and meta-analysis. The review of breast cancer screening made great play of improper randomisation affecting results. Part of the ethos of evidence-based medicine is not choosing trials to suit your own biases, but this can be hard. There are perhaps two other useful insights here.