Does the co-use of cannabis exacerbate the effect of alcohol on the risk of crashing? A systematic review and meta-analysis

This is the second of two closely related systematic literature reviews with meta-analyses by the same authors. The first concluded that there is no convincing epidemiological evidence that the prior use of cannabis (as indicated by the presence of THC in a body fluid) directly increases the risk of crashing. The purpose of this second review is to consider the possibility that the co-use of cannabis indirectly increases the risk of crashing by exacerbating the effect of alcohol on the risk of crashing. The starting point for both reviews is a systematic literature search that identifies seventeen epidemiological studies of the relationship between the prior use of cannabis and the risk of crashing. Twelve of those studies also investigated the joint effects of cannabis and alcohol on the risk of crashing. Although the authors of some studies claimed to have found an exacerbation (or equivalent) effect, the results of a meta-analysis of exacerbation odds ratios failed to support the claim. It is concluded that there is no credible evidence from the twelve epidemiological studies that the co-use of cannabis exacerbates the effect of alcohol on the risk of crashing.


Background
This is the second of two closely related systematic literature reviews.The first (White and Burns, 2021; as corrected in White and Burns, 2022a) concluded that there is no good epidemiological evidence that the prior use of cannabis (as indicated by the presence of THC in a body fluid) directly increases the risk of crashing.The purpose of this second review is to consider the possibility that the co-use of cannabis indirectly increases the risk of crashing by exacerbating the effect of alcohol on the risk of crashing.
From many of the studies included in our review (see Table 1), it is evident that effect of alcohol on the risk of crashing is worse than for any other psychoactive drug (Brubacher et al. 2019;Drummer and Yap, 2016;Gadegbeku et al., 2011;Hels et al., 2013;Lacey et al., 2016;Longo et al., 2000;Martin et al., 2017;Ogden et al., 2011;Poulsen et al., 2014).And, while all of these studies found strong dose-related effects of alcohol on the risk of crashing, many did not find an effect for cannabis (see Table 1).
There are extensive literatures on the prevalence in the U.S. of the separate and combined use of cannabis and alcohol: for the general population (e.g., Gunn et al., 2022); for drivers on the road (e.g., Goncalves et al., 2022); and for crashed drivers (e.g., Lira et al., 2021).While patterns of co-usage may differ between countries, let us consider the example of seriously and fatally injured drivers in the Australian state of Victoria.Drummer et al. (2012) investigated the prevalence of drugs in the bloods of 1714 hospitalised drivers.Of the 9.8% who tested positive to the active ingredient of cannabis, delta-9-tetrahydrocannabinol (THC), 49% also tested positive to alcohol.Schumann et al. (2021) investigated the prevalence of drugs in the bloods of 2287 traffic-accident fatalities, most of whom were drivers.Of the 13.1% who tested positive to THC, 45% also tested positive to alcohol.From these figures, it seems reasonable to assume that, for countries where alcohol is a widely used recreational drug, roughly half of THC-positive crashed drivers will also have positive BACs.To obtain a comprehensive understanding of the risks of driving after using cannabis, it is therefore necessary to also understand the risks of driving after the co-use of cannabis and alcohol.

Definition of an 'exacerbation effect'
This review investigates the possibility that the recent co-use of cannabis exacerbates the effect of alcohol on the risk of crashing.The statistical issues involved in the consideration of joint effects can be quite complex, with researchers who construct statistical models distinguishing between additive and multiplicative effects.That is not the approach adopted here, where the criterion for an 'exacerbation effect' is different than for an additive or multiplicative effect.The question addressed here is whether the co-use of cannabis makes any difference at all to the effect of alcohol on the risk of crashing.For example, if the drug-crash odds ratio (OR) for cannabis was 3.0 and the OR for all levels of alcohol combined was 7.0, then an OR of 8.0 for their combined effect could count as evidence for an exacerbation effect of cannabis on alcohol, even though this value is slightly lower than for an additive effect (9.0; from 3.0 + 7.0-1.0),and much lower than for a multiplicative effect (21.0).Perhaps the main way that an exacerbation effect differs from additive or multiplicative effects is that it can exist even where there is no effect at all of cannabis alone on the risk of crashing (OR = 1.0).

Claims in recently published literature reviews about the combined effects of cannabis and alcohol on the risk of crashing
It is widely asserted in the road-safety literature that the combined use of cannabis and alcohol is associated with a higher risk of crashing than the use of alcohol alone.When authors assert that fact, they typically cite a small number of carefully selected epidemiological studies, without attempting to integrate all of the relevant evidence.Three examples from recent reviews of the cannabis-crash literature are provided.Where the reviewers cite earlier reviews, the paths to the original epidemiological studies are not followed; but where they cite the original studies, those studies are briefly discussed.
In a broad review of the health risks from the use of cannabis, Bannigan et al. (2022: p. 5) say 'Unsurprisingly, concurrent consumption of both cannabis and alcohol increases the risk of car accidents substantially more than consumption of either substance alone'.The authors cite three reviews (Hall, 2015;Rogeberg and Elvik, 2016;Sewell et al., 2009), and one original report of an epidemiological study (Dubois et al., 2015).This study is not included in the current review, because it fails to meet our inclusion criteria: by having unsafe driving actions (UDAs) as its outcome measures rather than direct measures of crash risk; and by using inherently unreliable information on cannabis consumption from the U.S. Fatality Analysis Reporting System (FARS; as discussed later in the Methods sub-section on the Literature search strategy).The reported findings for UDAs (see their Table 3) were only marginally different for drivers with alcohol alone and for drivers with alcohol combined with cannabis.For example, at a BAC of 0.08, the risk (odds ratio; 95% confidence interval) of a driver committing a UDA was 2.17 (2.11-2.33)for alcohol alone, and 2.28 (2.13-2.44)for alcohol combined with cannabis.So, there is no satisfactory evidence from Dubois et al. for an exacerbation effect.
A factsheet on the risk of crashing after using cannabis was recently published by the Drugged Driving Work  (Brubacher et al., 2019;Drummer et al., 2020).The selection of those two studies by the ICADTS authors was flawed, because each clearly fails to support the claim that the combined effects of alcohol and cannabis are associated with a higher crash risk than for alcohol alone (as discussed later in our Results section).
In summarizing the results of some case-control studies of the cannabis-crash relationship, Wood and Dupont (2020, p. 499) say that 'The best evidence to date is that … the combination of THC and alcohol is synergistic [supra-additive]'.This conclusion is apparently based on the findings from three reviews (Asbridge et al., 2012;Li et al., 2012;Rogeberg and Elvik, 2016) and two reports of epidemiological studies (Li et al., 2013;Li et al., 2017).The paper by Li et al. (2013) is discussed in Appendix A. The study by Li et al. (2017) is not included in the current review because it is based on FARS information.The outcome measure was whether or not the driver in a two-vehicle fatal crash had initiated the crash.The reported ORs for crash initiation (see their Table 3) were only slightly different for drivers with alcohol alone (5.37; 4.88-5.92)and for drivers with alcohol combined with cannabis (6.39; 5.19-7.88).Li et al. (2017) concluded that 'Concurrent use of alcohol and marijuana appears to have a positive interaction effect on the risk of fatal crash initiation on the additive scale, but not on the multiplicative scale ' (p. 346).This conclusion overlooks the fact that the difference was small and not statistically significant.
In summary, these three reviews of the evidence for exacerbation cited either earlier reviews or original studies that failed to provide adequate supporting evidence.Scientific myths can prosper where there is indifference to the underlying evidence.
The indifference to evidence that is found in the research can also be found in the translation of research into policy.An example from the Australian state of New South Wales is provided in Appendix A.

Literature search strategy
The search strategy that identified the 17 epidemiological studies potentially included in this systematic review was described in some detail in the Methods section of the companion paper (White and Burns, 2021).Although the search was restricted to papers published up to 27 February 2020, one of us (MW) closely monitors the relevant literature, and is confident that no eligible papers have been published between the search date and 1 January 2023.The reader is referred to the companion paper for the details of the literature search strategy.The two main points to note are that: the included epidemiological studies were all either culpability (13) or case-control (4) studies; and that the identification of a driver as cannabis-positive was based on toxicological evidence for the presence of delta-9tetrahydrocannabinol (THC) in a body fluid (such that studies were rejected if they were based on the self-reported use of cannabis or on toxicological evidence for only THC-metabolites in the absence of THC).The literature search did not involve terms such as 'co-use', 'interaction effect' or 'joint effect', because it was important to identify all of the potentially relevant studies, whether or not they included special analyses of joint drug-alcohol effects.
We should make some observations here about the FARS database, which is administered by the U.S. National Highway Traffic Safety Administration (NHTSA).It is important to note that the NHTSA administrators themselves believe that FARS database is too unreliable to be used for rigorous drug-crash analyses.For example, in considering the validity of Li et al.'s (2013) findings (as discussed above), Compton and Berning (2015, p. 1) warn that 'Current limitations in the FARS dataset do not allow calculation of unbiased, reliable and valid estimates of crash involvement that results from drug use'.In a similar vein, Berning and Smither (2014, p. 3) warn that: 'Currently, the data in FARS is insufficient to allow comparisons of drug use across years, or across States.In addition, … it is also not possible to make inferences about impairment, crash causation, or comparisons to alcohol from this limited data'.And, according to a recent report by Berning et al. (2022), the quality of the FARS information on drugs other than alcohol is still inadequate for most purposes.White and Burns (2021) did not include any FARS-based studies in the companion review, because the toxicological identification of the prior use cannabis use, when done, was not necessarily based on the presence of THC.We should note that our concerns with the FARS database are limited to the information on drugs other than alcohol.We do not question the integrity of any other information, including that relating to the presence of alcohol (which we understand to be very strong).
For the purpose of the earlier review (White and Burns, 2021), we considered it appropriate to separately examine the results of the culpability and case-control studies.However, given that we are now interested only in exacerbation effects, and have no reason to expect that they will be different for the two research methodologies, we consider that the separate treatment of the two methodologies is not warranted.To accommodate this broadening of focus, we will normally use the general term 'risk of crashing' instead of the more specific terms 'risk of involvement in a crash' (for a case-control study) and 'risk of being culpable for the crash' (for a culpability study).

White and Burns
Some information on the 17 studies potentially included in the current review is given in date order in Table 1, under the name of the first author.Further information on the studies can be found in White and Burns (2021) and in its supplemental material.The meta-analytic summary cannabis-crash OR for the 4 case-control studies is 1.5 (0.9-2.3).A revised OR for the culpability study by Brubacher et al. (2019) comes from a Corrigendum (White and Burns, 2022a), where a corrected meta-analytic summary OR of 1.4 (1.1-1.7) for the 13 culpability studies is also provided.
An OR for the effect of cannabis on the risk of crashing or on the risk of being culpable for a crash is statistically significant if the 95% confidence interval (CI) does not include the value 1.00.Of the 17 cannabis effects in Table 1, only 7 were statistically significant.But, as noted above, the lack of main-effect significance does not necessarily exclude the possibility of a significant exacerbation effect.

Studies excluded from the current review
Studies from Table 1 are excluded from the current review if they fail to provide the information required to quantify the strength of a joint cannabis-alcohol effect on the risk of crashing.The five excluded studies are: Lowenstein

Two ways of demonstrating an exacerbation effect
There are two alternative statistical procedures for investigating the possibility that the use of cannabis with alcohol exacerbates the effect of alcohol on the risk of crashing.The first (two-step) procedure involves the comparison of the separate drug-crash ORs for alcohol alone and for alcohol combined with cannabis.Finding a combined OR that is significantly greater than the OR for alcohol alone would be evidence of an exacerbation effect.The second (single-step) procedure involves the calculation of a single 'exacerbation OR', which is simply the ratio of the combined OR and the OR for alcohol alone.Finding an exacerbation OR that is significantly greater than 1.0 would be evidence of an exacerbation effect.A worked example of these calculations is provided in Appendix B.

Some terminology
The mathematical statistics of measuring joint outcomes can be complex, and the terminology used in the discussion of those outcomes can be confusing.As mentioned previously, joint effects can be additive or multiplicative.However, joint effects can also be 'interactive' and/or 'synergistic'.Conventionally, the term 'interactive' refers to a joint effect that differs from the type of joint effect predicted by the statistical model employed.For an additive model, an interactive effect can therefore be either supra-additive or infra-additive.A supra-additive effect can be described as 'synergistic'.And for a multiplicative model an interaction effect can be either supra-multiplicative or inframultiplicative.Confusingly, additive and multiplicative effects themselves can sometimes be described as 'interaction' effects.When considering the individual studies in our Results section, we will assume that a real additive or multiplicative effect would necessarily also be an exacerbation effect.So, a researcher who claims to have demonstrated an additive or multiplicative effect is thereby also implicitly claiming to have demonstrated an exacerbation effect.

Unadjusted vs adjusted drug-crash ORs
Drug-crash ORs that are not adjusted for the distorting effects of confounders through MLR analyses can give inaccurate (usually over-) estimates of the strength of drugcrash relationships.However, four of the early included studies (Terhune, 1982;Terhune et al., 1992;Longo et al., 2000;and Mura et al., 2003) provided only unadjusted cannabis-crash ORs.Interestingly, two early systematic reviews of cannabis-crash studies, by Asbridge et al. (2012) and Li et al. (2012), also restricted their meta-analyses to unadjusted cannabis-crash ORs.The findings of those reviews were justly criticized by Rogeberg and Elvik (2016) for providing over-estimates of cannabiscrash risks.
Nevertheless, the consideration of unadjusted ORs can provide some indication of the presence and strength of the cannabis-crash effect, the alcohol-crash effect and the exacerbation effect.While the failure to adjust for confounders would be expected to exaggerate the strength of firstorder drug-crash effects, it is not obvious that second-order effects, such as an exacerbation effect, would also be exaggerated.

Evidence of exacerbation from unadjusted ORs
For each of the twelve included studies, Table 3 provides three types of unadjusted drug-crash OR: for alcohol alone; for alcohol and cannabis combined; and for the exacerbating effect of cannabis on the effect of alcohol.The calculation of those ORs is based on the counts data provided in Table 2 for six categories of driver, as defined by: (1) three types of drug use: no alcohol or other drugs, alcohol only, and the combined use of alcohol and cannabis; (2) in conjunction with two types driver: case and control.
For the 10 culpability studies in Table 2, the term 'cases' should be taken to mean culpable drivers, and the term 'controls' to mean non-culpable drivers.Data extraction was undertaken by MW and checked by NB.Counts data for Gadegbeku et al. (2011) were provided in a personal communication of 8 December 2022 from Bernard Laumon to MW. Counts data for Drummer et al. (2004) was supplemented by information from the same dataset, as reported three years earlier by Drummer et al. (2001).More information on the sources of the counts data provided in Table 2 can be found in Appendix C.
We were able to calculate unadjusted exacerbation ORs for all twelve studies.Five of the studies have an exacerbation OR of 1.0 or less.An OR that is significantly lower than 1.0 (as indicated by its 95% CI lying below the value 1.0) would imply an ameliorating effect of cannabis on the crash risk from alcohol.However, only one of the five ORs, from Terhune (1982), is significantly lower than 1.0.The seven other exacerbation ORs are all greater than 1.0.Only one of the twelve studies had a statistically significant exacerbation OR (as indicated by its 95% CI lying above the value 1.0): Gadegbeku et al. (2011) had an exacerbation OR is 2.1 (1.1-3.8).
By comparing the unadjusted summary OR for alcohol alone (7.3: 5.5-9.6) with the summary ORs for cannabis alone, as relating to the information here in Table 1, for
both the thirteen culpability studies (1.4: 1.1-1.7;from White and Burns, 2022a, Corrected Figure 2) and for the four case-control studies (1.5: 0.9-2.3;from White and Burns, 2021, Figure 4), it can be seen that alcohol alone has a much greater effect on the risk of crashing than cannabis alone.In terms of incremental risks (above OR = 1.0), the incremental risk for alcohol alone is about 15-times greater than for cannabis alone.
In the two-step procedure for examining the possibility of an exacerbation effect, the summary OR for alcohol and cannabis combined (8.6: 5.1-14.1) is compared with the summary OR for alcohol alone (7.3: 5.5-9.6).It can be seen that, although the difference between the two ORs has the correct sign for an exacerbation effect, the size of the difference is relatively small (15.1%), and there is considerable overlap between the two 95% CIs.So, the null-hypothesis cannot be rejected, although the results are also compatible with a weak or moderate exacerbation effect.The single-step procedure involves the calculation of an exacerbation OR (1.3: 0.9-1.8).It can be seen that, although the OR is above 1.0, the 95% CI includes the value 1.0.So, again, there is no convincing evidence here for an exacerbation effect.

Evidence of exacerbation from adjusted ORs
From Table 4 it can be seen that only four of the twelve studies (Drummer et al., 2004;Gadegbeku et al., 2011;Brubacher et al., 2019;Drummer et al., 2020) employed MLR analyses to provide adjusted drug-crash ORs that are relevant to the demonstration of an exacerbation effect through either the two-step or single-step procedures.
Three of the four studies in Table 4 fail to provide statistically significant evidence of an exacerbation effect.For Gadegbeku et al. (2011) the adjusted combined OR of 14 (8.0-27.4) is greater than the adjusted OR for alcohol alone of 8.5 (7.2-10.1),but the 95% CI for the combined effect includes the mean value for the alcohol effect.For Brubacher et al. (2019), although the adjusted exacerbation OR of 1.6 is above the null value of 1.0, the 95% CI of 0.3 to 15.7 is very wide, and comfortably incorporates the value 1.0.For Drummer et al. (2020) the possibility of an exacerbation effect is denied by the fact that the adjusted combined OR of 14 (4.4-46.0) is less than the adjusted OR for alcohol alone of 16 (9.4-26.0).
Only one of the four studies in Table 4 provides a statistically-significant result in favour of an exacerbation effect.Drummer et al. (2004) reported a significant adjusted exacerbation OR of 2.9 (1.1-7.7).
Our discussion of the information in Tables 3 and 4 reveals that there are two studies for which the evidence for an exacerbation effect is somewhat inconsistent (i.e., where the adjusted ORs do not lead to the same conclusion as the unadjusted ORs).For the study reported by Gadegbeku et al. (2011), the adjusted OR for cannabis and alcohol combined (14: 8.0-27.4) was not significantly greater than for alcohol alone (8.5: 7.2-10.1),thus questioning the reliability of the statistically-significant unadjusted exacerbation OR 2.1 (1.1-3.8).There was also an inconsistency in relation to the study by Drummer et al. (2004), where the significant adjusted exacerbation OR of 2.9 (1.1-7.7) is slightly larger than the clearly non-significant unadjusted OR of 2.3 (0.3-17.0).This is not a typical finding: in most instances the adjusted OR is smaller than the corresponding unadjusted OR.In summary, there was no study for which the unadjusted and adjusted analyses fully agree that an exacerbation effect had been demonstrated.
The overall evidence for an exacerbation effect from a consideration of the individual studies is weak and inconsistent.The conclusion that an exacerbation effect is not evident is supported by the non-significance of the meta-analytic summary unadjusted exacerbation OR of 1.3 (0.9-1.8).
Detailed information about exacerbation from the twelve studies, as considered individually, is provided in Appendix D.

Brief summary of the epidemiological results
Our review of the evidence for an exacerbation effect was based on the most rigorous epidemiological studies as identified by White and Burns (2021).We conclude that the evidence is weak and inconsistent.We consider that the existence of an exacerbation effect is unlikely.However, we acknowledge that the evidence to date is insufficient Mura ( 2003) Drummer (2004) 2.9 (1.1-7.7)Gadegbeku (2011) 8.5 (7.2-10.1) 14 (8.0-27.4)Poulsen (2014) Lacey ( 2016) Martin ( 2017) Brubacher (2019) 1.6 (0.3-15.7)Drummer (2020) 16 (9.4-26.0) 14 (4.4-46.0) to rule out the possibility that such an effect could be firmly established in the future.

Caveat
The degree of impairment resulting from cannabis use is clearly related to the dosage administered (e.g., Schlienz et al., 2020).However, that relationship does not seem to translate into demonstrable dose-response relationship between the concentration of THC in the blood or oral fluid and either the level of impairment (Arkell et al., 2021;White and Burns, 2022b: 16-18;Wurz and DeGregorio, 2022) or the risk of crashing (Macdonald, 2018: 96;White and Burns, 2021: 12-13).Nevertheless, it is certainly possible to get so intoxicated on cannabis that one is incapable of safely driving a car.This point relates to the interpretation of our finding of no demonstrable exacerbation effect on crash risk: our finding should be interpreted in the sense that the 'normal' levels of cannabis intoxication among drivers, reflecting light to moderate cannabis use, cannot be shown to have an exacerbating effect.

Identifying joint effects: a can of worms
In discussing joint alcohol-cannabis effects on the risk of crashing from their U.S case-control study, Lacey et al. (2016: 62) commented: Tables 28 and 29 describe the unique contribution of each drug class to crash risk; however, they do not address the potential interaction effect between each drug class and alcohol.That is, they do not address whether the concurrent use of alcohol and any of these drug classes interact synergistically in a way that would increase or decrease crash risk beyond the additive risk of each substance separately.
Here, a joint effect is described as an 'interaction' effect, which, in turn, is described as a 'synergistic' effect, which is then defined as a supra-additive or infra-additive effect.As shown here in Table 3, Lacey et al. did not find any such effect.
Two similar responsibility studies involving fatal road accidents were conducted in France about 10 years apart.The first was reported by both Laumon et al. (2005) and Gadegbeku et al. (2011).The second was reported by Martin et al. (2017).As demonstrated in Tables 3 and 4, neither study was convincingly able to demonstrate an exacerbation effect.Nevertheless, the researchers involved in both studies claimed to have found multiplicative effects of cannabis and alcohol on the risk of crashing.Let us consider how they reached that conclusion.Laumon et al. (2005: 5) argued: 'We were not able to highlight any interaction: consumption of both cannabis and alcohol would only multiply the risks related to the consumption of either cannabis or alcohol alone, without specific potentiation of the effects of one by the other'.Much the same argument was proffered by Gadegbeku et al. (2011: 298): 'No interaction was detected among alcohol and cannabis.This implies that consumption of both cannabis and alcohol merely multiplies the risks related to the consumption of either cannabis or alcohol alone'.In a similar vein, in relation to the second French study, Martin et al. (2017: 2) concluded: 'There was no significant alcohol x cannabis interaction.This means that … the OR for a driver under the influence of both alcohol and cannabis can be estimated by the product of the OR relative to alcohol and the OR relative to cannabis'.In these arguments, the researchers have defined an 'interaction' as a supra-multiplicative effect (thereby setting the bar very high).Their definition was based on the fact that their statistical model incorporated the assumption that the joint effect of the two drugs would have to be at least multiplicative.So, when no 'interaction' effect was found, they adopted the model's fallback assumption that the relationship was multiplicative.We consider that they should have been more influenced by the actual evidence than by an arbitrary assumption built into a statistical model.Martin et al.'s concluding advice, based on their assumption, was: 'It is important to note that one in two drivers considered to be under the influence of cannabis were also under the influence of alcohol.With risks cumulating between the two, it is particularly important to point out the danger of consuming them together' (p.2).We are not convinced that the advice is warranted by the evidence from the two French studies.The absence of a statisticallysignificant supra-multiplicative effect should not be taken to imply the presence of a 'merely' multiplicative effect.
These French researchers have ignored the pragmatic approach that was first adopted in Australia by Drummer et al. (2004) to the definition of a joint effect.The Australian researchers acknowledged that the crash risk from the use of alcohol was far higher than from cannabis, such that a sensible question is: Does the co-use of cannabis exacerbate the effect of alcohol on the risk of crashing?The requirement to demonstrate an exacerbation effect sets the bar appropriately low: an exacerbation effect can be submultiplicative or even sub-additive.The answer to the question asked by Drummer et al. would be of practical benefit to a policy maker who wanted to know if the penalty for alcohol-driving offences should be increased for the co-use of cannabis.
In this review, we support the practical approach introduced by Drummer et al. (2004), and we lament the confusion created in the literature by statistical modellers who can provide only esoteric advice because of the constraints of their models.For example, how should a policy maker interpret this advice from Li et al. (2013: 208): 'Our results suggest that, when alcohol and drugs are used together, there is a modest negative interaction effect on White and Burns the risk of fatal crash involvement on the multiplicative scale'?
The limited contribution of the co-use of cannabis to crash causation at high BACs It seems likely that the incremental effect of the co-use of cannabis on the risk of crashing will be indiscernible at high BACs.Measured BACs are mostly very high in alcohol-positive drivers who are fatally or seriously injured in road crashes.For example, in a recent study of Victorian road-traffic fatalities (Schumann et al., 2021, Table 3), 88% of those with BACs over 0.05 had BACs greater than 0.10; and in a recent study of injured drivers in Victoria (DiRago et al., 2021, Table 1), 81% of those with BACs over 0.05 had BACs greater than 0.15.
The probability that it is the driver's use of alcohol, at a particular BAC, that causes the driver to crash ('probability of causation' -PC) can be calculated from the relative risk (RR) of crashing at that BAC, according to the formula (see e.g., Greenland & Robins, 2000): PC = 1.0 − (1.0/RR) Lacey et al.'s (2016) Table 27 gives alcohol-crash RRs of 5.9, 13.6 and 27.1 for BACs of 0.10, 0.15 and 2.0 and above, respectively.According to the formula above, these RRs correspond to PC%s of 83%, 93% and 96%, respectively.In other words, at the BACs typically found in crashed drivers, the use of alcohol alone is almost always a sufficient cause of the crash.The scope for the co-use of cannabis to contribute to crash causation is therefore limitedeven in the absence of other considerations, as discussed above.

Evidence for exacerbation from studies of impairment
We have not yet referred to any of the experimental literature on the deleterious effects of cannabis in combination with alcohol on driving performance or behaviour.While the focus of this paper is on the epidemiology of crash risk, it seems worth exploring the possibility that the experimental and epidemiological literatures are inconsistent.If the experimental evidence for exacerbation were strong, the conclusions reached here from the epidemiological evidence would have to be revisited.These matters are considered in Appendix E, where we conclude that the experimental evidence is consistent with the epidemiological evidence that exacerbation is either very weak or non-existent.

Table 2 .
Numbers of drivers involved in investigations of exacerbation effects.

Table 3 .
Evidence for exacerbation from unadjusted drug-crash ORs.

Table 4 .
Evidence for exacerbation effects from adjusted drug-crash ORs.