Relative risk (RR) estimates in recent epidemiologic studies1–5 of call-crash association are near one, whereas those of earlier studies6,7 are near 4. Because RR estimates calculated from different study designs should be very close for small risks in the absence of biases,8 (p. 61) this large discrepancy implies some source of bias. This report examines possible bias arising from a confounding third variable (driving) that could affect both cell phone use and crash frequency and that may have been only partially matched between case and control windows in earlier studies.6,7
These studies6,7 used a case-crossover design to compare cell phone use at various time intervals before a crash (the case window) with cell phone use during the same period on a previous day (the control window). (The term “use” refers here solely to conversation time, the only phone-related task information in billing records.6,7) Crash occurrence ensures that a person was driving during the case window, but the person may not have been driving during all (or a part) of the control window. Nondriving during a control window confounds RR estimates because it eliminates the possibility of a crash and can reduce the probability of a call. Reduced call probability when not driving cannot be rejected based on existing data because epidemiologic studies, to date, have good accuracy for driving times from GPS data1,3–5 or calling times from cellular billing records,2,6,7 but not both in the same study. Nondriving during a control but not a case window would make it seem (erroneously) that cell phone usage was less during control periods, making the denominator smaller and leading to the (false) conclusion that calling while driving has an RR above 1.
Earlier studies6,7 attempted to reduce confounding by nondriving in control windows by asking subjects to recall their driving at that time, retaining only subjects6 or control windows7 with recalled driving. Redelmeier and Tibshirani6 interviewed 100 people who were not in the original study, and only 65% recalled driving during a “selected period.” They multiplied their crude RR (and confidence range) of 6.54 (95% confidence interval [CI] = 4.5–9.9) by this 65% “driving consistency” factor, yielding an adjusted RR of 4.3 (3–6.5). Similarly, McEvoy et al7 found that drivers who crashed recalled driving in only 36% of control windows and analyzed only those control windows to yield an RR estimate of 4.1 (2.2–7.7).
However, neither study6,7 controlled for those who may have been driving for only part of the control window. Part-time driving in a control window biases RR estimates upwards, just as complete nondriving does. The present study accounts for the full range of driving in control windows and adjusts the earlier RR estimates6,7 accordingly.
Day-to-day driving consistency was calculated from 100 days of GPS data collected from 439 vehicles during 2005–2006 in Puget Sound, Washington.9 The data had been previously deidentified and made publicly available.10 To ensure that all vehicles were matched on day of week, the analysis for each vehicle was started on the first Monday for which it had GPS data.
Driving consistency was calculated for each vehicle for a “day-pair.” The number of driving minutes during the day 2 window that overlapped with driving minutes during the corresponding day 1 window was tabulated. (Day 2 is analogous to the “case” or crash day, and day 1 is analogous to the “control” day in the case-crossover studies.6,7) An array was created for each day containing 1440 bins, each representing a 1-minute period from 3:00 AM to 2:59 AM the next day. A bin was assigned a value of “1” if driving occurred during that minute and “0” otherwise. Each bin for day 2 was compared with its corresponding bin for day 1. The number of bins with overlapping 1s, divided by the total driving minutes during day 2, defines the driving consistency for a given vehicle,
where day1 (i) and day2 (i) are the bin entries for the first and second days, respectively.
Driving consistency was then tabulated for every vehicle with GPS data in the day-pair. Because Redelmeier and Tibshirani6 eliminated subjects for whom no driving occurred at the same clock time during days 1 and 2 (ie, drivers for whom driving consistency was 0), the current analysis retained only vehicles with driving-consistency values exceeding 0. The mean of this value over all vehicles for a given day-pair is the mean part-time driving consistency. This calculation was repeated for the 100 consecutive day-pairs.
The grand mean part-time driving consistency is the average of the mean part-time driving consistency across the 100 day-pairs. It represents the probability that a vehicle is driven during a minute on a “control” day conditional on it having been driven during the corresponding minute on the next day. Its 95% confidence limits were calculated across the 100 day-pairs. Using Redelmeier and Tibshirani's6 method for removing driving bias with out-of-sample data, the RR estimates and confidence intervals6,7 were adjusted by multiplying with the grand mean part-time driving consistency.
The uncertainty of the consistency estimate expands the adjusted RR uncertainty range because of propagation of uncertainty.11,12 Hence, the confidence limits for the adjusted RR estimate were further adjusted by the percentage of uncertainty in the consistency estimate.
Note that driving consistency generalizes to control windows of any duration at any time of day. Assume that a person was driving for k minutes on day 2 and a crash occurs at clock time t. The expected minutes that the person would have driven in a k-minute control window on day 1 (preceding the corresponding clock time t) would be k × p. For example, with a mean driving consistency of 15%, and a 10-minute case window with known driving, the expected driving during a 10-minute control window would be 1.5 minutes.
Control analyses (see eAppendix, http://links.lww.com/EDE/A535) accounted for missing GPS data, the order of the 2 paired days, driving time per day, and weekday versus weekend driving days.
The Figure illustrates the distribution of average driving consistency values observed across the 100 paired days. An average of 81.9 vehicles (36% of the total vehicles in the Figure) had 0% consistency (left-most bar). This finding is consistent with the 35% recall-based estimate reported by Redelmeier and Tibshirani,6 and is about half the 64% estimate in the McEvoy et al study.7
Note that all vehicles in the Figure with a mean driving consistency above 0 would have been treated as having 100% driving consistency in the earlier studies.6,7 However, as illustrated in the Figure, almost all these vehicles had only part-time driving (ie, consistency values >0% but <100%). Among vehicles with 70% consistency, the grand mean part-time driving consistency across the 100 day-pairs was 26.4% (25.2%–27.6%), with a ±5% uncertainty range.
Multiplying the final RR estimates by 26.4% to adjust for part-time driving consistency (and expanding the uncertainty range to account for the uncertainty in the 26.4% estimate) yielded a final adjusted RR of 1.1 (0.75–1.8) for Redelmeier and Tibshirani6 and 1.1 (0.55–2.1) for McEvoy et al.7
Objective GPS methods confirm that the subjective recall methods in the earlier studies6,7 correctly estimated the percentage of drivers who did not drive at all during a control window, and properly removed those subjects6 or control windows7 from their analyses. However, neither study6,7 corrected for part-time driving during control windows, which is difficult or impossible using recall-based methods because of insufficient accuracy.
Assuming full-time driving6,7 in a control window when only part-time driving occurred inflates the RR estimates, even after discarding subjects with no driving in a control window, because the denominator can still have less cell phone usage than the numerator solely because of lower driving exposure. (The period represented by the numerator has a high probability of driving because it is defined as the time leading up to the crash.)
The current study used objective GPS data to estimate the mean part-time driving consistency in control windows at 26.4%. Using Redelmeier and Tibshirani's6 method for out-of-sample data to adjust the RR estimates for part-time driving consistency yielded RR estimates near 1 for the earlier case-crossover studies6,7 (with a confidence range from slightly below to slightly above 1), resolving the discrepancy with more recent studies.1–5
However, the current study did not use the same drivers as in the case-crossover analyses6,7 and so loses the benefit of controlling for driver differences. Indeed, the current GPS data10 are from a different sample, different countries, and different points in time relative to the earlier studies.6,7 Although a comparable analysis of Chicago GPS data had similar results,13 2 studies are not definitive proof that the high RR estimates in the earlier studies6,7 are entirely attributable to driving exposure overestimates in control windows.
Despite this limitation, the present study establishes a plausible hypothesis that earlier case-crossover studies6,7 overestimated the RR for cell phone conversations while driving because they did not adjust for part-time driving exposure in control windows. This part-time driving hypothesis likely accounts for much of the discrepancy between recent and earlier RR estimates for conversation while driving.
I thank Ken Rothman, Linda Angell, Richard Deering, Rich Hanowski, Barbara Wendling, and especially Joshua T. Cohen for comments on earlier drafts. I thank Sean Seaman for computational assistance with the GPS data, and Steve Tengler for artwork.
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8. Rothman K, Greenland S, Lash T. Modern Epidemiology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins; 2008.