I've spend quite a bit of time working on cycling safety. This is the start of me summarising what I know. First of all, I will debunk some abuses of research.
Abused Research: Jensen of Trafitek 2007
Some opponents of cycleways will cite this study and may quote parts like: "The safety effects of bicycle tracks in urban areas are an increase of about 10 percent in both crashes and injuries. The safety effects of bicycle lanes in urban areas are an increase of 5 percent in crashes and 15 percent in injuries. Bicyclists’ safety has worsened on roads, where bicycle facilities have been implemented." rather than link to the study which shows that those percentages are against the researcher's predictions (an approach that even the author calls a "second-best methodology" and I feel that second is ranking it a bit high) and not the pre-implementation figures. The predictions in Table 2 are debatable but seem to be a linear continuation of whatever the previous casualty trend was, multiplied by a traffic volume factor estimated from general data rather than traffic modelling.
In short, the data shows a decrease but it is presented as an increase because it's a smaller decrease than predicted! (source discussion)
Abused Research: Lund University 1987
This is not online or widely available, so what is often cited is a graphic from a conference presentation which summarised it and was put online by cycleway opponent John S Allen at German Cycling Federation ADFC background information on bicycling #173.
The headline figures draw no distinctions for cycleway types, junction layouts and so on and are used to wrap it all up into one answer which is "clear, simple and wrong." It falls into the oft-repeated trap of lumping crossroads in with forks and so on, then ignoring those differences, so it gives only generalities.
Flawed Research: Franklin 1988 and 1989
I reply to this in more details on one of my Redways pages, but in short they contain many basic factual errors, the usage data is very weak so the casualty rates may be wildly inaccurate and there is no attempt to distinguish between route types.
Cycling Fallacies has more descriptions of abused and flawed research in its pages.