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An anonymized approach
I'm interested in your reaction to the privacy flaws in this approach (assuming technology permits).
Hypothesis: Cell phone usage changes accident rates based on whether the phone is in use at the time of the accident. (With subcategorization by severity and kind of roadway, 3 categories of each).
Field data gathering:
At every accident where it is possible to collect the correct time and location of the accident, do so. This should cover a moderately large but uniform area. For example, the entire SF Bay area or LA county. Do this without regard to severity, location, or indicated cell phone use. Categorize each accident by severity (low, medium, high) and by kind of roadway (freeway, major, minor).
Once per month, provide every covering cell carrier with a list of locations, times, and categories (1-10). The tenth category is created by going to highway locations where there is no accident. Pick times and locations with statistics similar to accident occurrences. Based on the roll of dice, make a cell phone call or not. Record the location and time. The categories given to the carriers are randomized each month. The carriers are to respond with ten numbers: the number times that a cell phone from one of their subscribers was in use at a location and time in each category.
The analysis re-bins the categories. The non-accident category is used to determine the accuracy of the carrier's time and location analysis, because the correct number that should be returned is known. It can also be used to assess the extent to which other cell phone usage by nearby automobiles will distort the data.
The monthly numbers can be used together with other statistics on likelihood of cell phone use while driving to determine the impact on accident rate.
I see no financial motivation for the carrier to do this, so they will demand payment. It might be a large payment if they do not normally keep time and location records. I don't see a motivation for the insurers to make this payment. Police and government are not likely to have budget for this. But perhaps you could find someone to cover the costs.
I think that this would sufficiently anonymize the data, and I'm interested in your analysis. This is an example of what you need to do to create a test plan based on the question to be answered, rather than create a massive database and subsequent data mining.