Supplementary Online Content

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Supplementary Online Content

Cerdá M, Wall M, Feng T, et al. Association of state recreational marijuana laws with adolescent marijuana use. JAMA Pediatr. Published online December 27, 2016. doi:10.1001/jamapediatrics.2016.3624.

eAppendix. SUDAAN code for estimated prevalence of marijuana use and perceived harmfulness in states before and after recreational marijuana legislation and difference-in-difference tests

eTable 1. Past-month frequency of marijuana use for Colorado (CO) and Washington (WA) vs states without recreational marijuana laws (RML) before and after passage of RML by grade

eTable 2. Past-month prevalence of marijuana use for Colorado (CO) and Washington (WA) vs states with medical marijuana laws (MML) only before and after passage of recreational marijuana laws (RML) by grade

eTable 3. Parallel assumption test: difference-in-difference tests of marijuana use 12 years prior to passage of recreational marijuana laws (RML), comparing 2010-2012 with 2001-2003 in states that legalized recreational marijuana use in 2012 compared with those that did not legalize marijuana by that time

This supplementary material has been provided by the authors to give readers additional information about their work.

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eAppendix. SUDAAN code for estimated prevalence of marijuana use and perceived harmfulness in states before and after recreational marijuana legislation and difference-in-difference tests

Below we provide the SUDAAN code used to obtain Tables 2 and 3.

Variables:

time is a dummy variable = 0 for 2010, 2011, 2012 and =1 for 2013, 2014, 2015 RML is a 3-category variable = 1, 2, 3 where 1=Colorado, 2=Washington, 3 = Other

Data:

The data, trim8, trim10, trim12, include individual level data from students (8^th, 10^th, and 12^th grade respectively) from years 2010-2015 except for Oregon (dropped from all analysis)

Here is the SUDAAN program:

%macro RMLtrends(inputdat, title,outcome,link);

title2 bold color=green &title;

proc &link data = &inputdat;

nest _ONE_ school;

weight _ONE_;

class time RML gender race grade par_ed class_size public pop_dens;

reflevel time=0 RML=3 ; ***this command makes pre-passage time (0) and the non- RML (3) the reference groups;

model &outcome = time RML time*RML /*individual covariates*/ age gender race par_ed /*school level covariates*/class_size public pop_dens

/*state level covariates*/ pct_nohs male_pct white_pct pct10_24;

predMARG time*RML; *****Provides estimated means of CO, WA, and non-RML by time;

pred_eff time=(-1 1)*RML=(1 0 0)/name ="year effect in CO(1)";

pred_eff time=(-1 1)*RML=(0 1 0)/name ="year effect in WA(2)";

pred_eff time=(-1 1)*RML=(0 0 1)/name ="year effect in Other(3)";

pred_eff time=(-1 1)*RML=(1 0 -1)/name ="Diff-in-Diff CO vs Other";

pred_eff time=(-1 1)*RML=(0 1 -1)/name ="Diff-in-Diff WA vs Other";

setenv linesize=132 decwidth=10 colwidth=14 pagesize=58 labwidth=12;

OUTPUT / FILENAME=predmarg_comb_&inputdat._&outcome FILETYPE=SAS pred_mrg = default REPLACE ;

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OUTPUT / FILENAME=predcont_comb_&inputdat._&outcome FILETYPE=SAS PRMGCONS=default REPLACE;

run;

%mend;

*by grade;

%RMLtrends (trim8, "MJ_M 8th graders" ,mj_m, rlogist);

Explanation of the model specification:

The software creates dummy variables with (k-1) categories for every variable in the class statement. Since RML has 3 categories, two dummy variables are created. Denote CO=1 if the RML state is Colorado (and 0 otherwise) and WA = 1 if the RML state is WA (and 0 otherwise), then the regression equation being fit to the individual data is:

logit (pr Y) = intercept + time + CO + WA + CO*time + WA*time +

age gender race educ + class_size + public + pop_dens + pct_nohs + male_pct + white_pct + pct10_24

The model expected values for pre and post passage in the 3 groups (CO, WA, and non- RML) after fixing the covariates is then (on the logit scale):

intercept Pre passage mean in the non-RML states, intercept + time Post passage mean in the non-RML states, intercept + CO Pre-passage mean in CO

intercept + time + CO + CO*time Post-passage mean in CO intercept + WA Pre-passage mean in WA

intercept + time + WA + WA*time Post-passage mean in WA

The test for Diff-in-Diff on the logit scale is simply the test of CO*time and WA*time terms. We are performing tests of Diff-in-Diff on the prevalence (i.e. additive) scale and not on the logit scale, hence the PREDMARG command (and associated PRED_EFF) are used to back transform each of the above expected logits to the prevalence scale

marginalizing over the covariates. Then a test for trends within WA and CO and non- RML as well as the Diff-in-Diffs for WA and CO are obtained directly by forming the appropriate contrasts using the PRED_EFF command. For example, the Diff-in-Diff for WA is tested with the command:

pred_eff time=(-1 1)*RML=(0 1 -1)/name ="Diff-in-Diff WA vs Other";

which translates into:

[PM(intercept + time + WA + WA*time) – PM(intercept + WA)] – [PM(intercept + time)

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– PM(intercept)]

where PM denotes predicted marginal (after back-transformation from logit scale and marginalizing over covariates).

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eTable 1. Past-month frequency of marijuana use for Colorado (CO) and Washington (WA) vs states without recreational marijuana laws (RML) before and after passage of RML by grade

Pre RML (2010-2012) Post RML (2013-2015)

Grade

level Frequency State % 95% CI % 95% CI Difference Pre

to Post RML SE P-value

8

0 occasion

CO 91.2% (82.4% 95.9%) 91.3% (89.2% 93.1%) 0.1% 3.3% 0.98

WA 93.7% (91.2% 95.5%) 91.7% (89.2% 93.7%) -2.0% 1.5% 0.18

Non-

RML 92.4% (91.9% 92.9%) 93.7% (93.2% 94.1%) 1.2% 0.3% 0.00

Diff-in-Diff CO vs Non-RML -1.1% 3.3% 0.73

Diff-in-Diff WA vs Non-RML -3.2% 1.5% 0.03

1-2 occasions

CO 2.8% (1.2% 6.2%) 3.2% (2.3% 4.3%) 0.4% 1.2% 0.73

WA 3.6% (2.3% 5.6%) 4.1% (2.7% 6.1%) 0.5% 1.1% 0.66

Non-

RML 3.4% (3.1% 3.6%) 2.7% (2.5% 3.0%) -0.6% 0.2% 0.00

Diff-in-Diff CO vs Non-RML 1.0% 1.2% 0.40

Diff-in-Diff WA vs Non-RML 1.1% 1.1% 0.33

>= 3 occasions

CO 6.0% (2.7% 12.6%) 5.5% (4.2% 7.3%) -0.5% 2.4% 0.84

WA 2.7% (1.9% 3.9%) 4.2% (3.2% 5.4%) 1.5% 0.7% 0.03

Non-

RML 4.2% (3.9% 4.6%) 3.6% (3.3% 4.0%) -0.6% 0.2% 0.01

10

0 occasion

CO 83.0% (80.6% 85.1%) 86.5% (81.0% 90.5%) 3.5% 2.4% 0.15

WA 83.8% (81.4% 86.0%) 80.0% (76.1% 83.4%) -3.8% 1.8% 0.03

Non-

RML 82.7% (82.0% 83.5%) 83.6% (82.8% 84.4%) 0.9% 0.5% 0.07

1-2 occasions

CO 7.2% (6.1% 8.4%) 5.9% (3.6% 9.3%) -1.3% 1.4% 0.35

WA 6.0% (4.8% 7.6%) 6.0% (4.0% 8.9%) 0.0% 1.3% 0.98

Non-

RML 6.7% (6.3% 7.0%) 6.3% (6.0% 6.7%) -0.3% 0.2% 0.13

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Pre RML (2010-2012) Post RML (2013-2015) Grade

level Frequency State % 95% CI % 95% CI Difference Pre

to Post RML SE P-value

10

>= 3 occasions

CO 9.8% (8.4% 11.5%) 7.7% (5.8% 10.1%) -2.2% 1.1% 0.05

WA 10.1% (8.3% 12.3%) 14.0% (11.1% 17.5%) 3.9% 1.7% 0.02

Non-

RML 10.6% (10.1% 11.2%) 10.0% (9.5% 10.6%) -0.6% 0.4% 0.11

12

0 occasion

CO 72.6% (66.8% 77.8%) 74.6% (70.9% 77.9%) 2.0% 2.9% 0.51

WA 78.8% (74.4% 82.5%) 78.1% (73.9% 81.8%) -0.7% 2.6% 0.80

Non-

RML 77.7% (76.8% 78.6%) 77.9% (77.0% 78.8%) 0.2% 0.6% 0.78

1-2 occasions

CO 9.3% (7.8% 11.0%) 10.5% (9.1% 12.1%) 1.2% 0.8% 0.14

WA 7.8% (5.9% 10.2%) 10.0% (8.0% 12.5%) 2.2% 1.4% 0.12

Non-

RML 7.7% (7.3% 8.1%) 7.5% (7.2% 7.9%) -0.2% 0.3% 0.50

>= 3 occasions

CO 18.1% (13.6% 23.8%) 14.9% (12.1% 18.2%) -3.2% 2.8% 0.26

WA 13.4% (10.3% 17.3%) 11.9% (8.3% 16.7%) -1.6% 2.6% 0.56

Non-

RML 14.6% (13.9% 15.2%) 14.6% (13.9% 15.3%) 0.0% 0.5% 0.99

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eTable 2. Past-month prevalence of marijuana use for Colorado (CO) and Washington (WA) vs states with medical marijuana laws (MML) only before and after passage of recreational marijuana laws (RML) by grade

Pre RML (2010-2012) Post RML (2013-2015) Grade level

% used in past month

95% CI % used in

past month 95% CI Difference Pre to

Post RML S.E. P-value

8

CO 8.9% (4.2% 17.7%) 8.8% (7.0% 11.1%) -0.01% 3.3% 0.9971

WA 6.2% (4.4% 8.7%) 8.2% (6.3% 10.7%) 2.0% 1.4% 0.1607

Other

MML 7.8% (7.0% 8.7%) 6.2% (5.5% 6.9%) -1.6% 0.5% 0.0007

Diff-in-Diff CO vs Other MML 1.6% 3.3% 0.6206

Diff-in-Diff WA vs Other MML 3.6% 1.5% 0.0154

10

CO 17.4% (15.1% 20.0%) 13.8% (9.6% 19.3%) -3.6% 2.5% 0.1360

WA 16.5% (14.3% 19.0%) 20.6% (17.2% 24.5%) 4.1% 1.8% 0.0221

Other

MML 18.2% (17.1% 19.4%) 16.5% (15.2% 17.8%) -1.7% 0.8% 0.0346

Diff-in-Diff CO vs Other MML -1.9% 2.6% 0.4643

Diff-in-Diff WA vs Other MML

5.8% 2.0% 0.0030

12

CO 27.6% (22.3% 33.6%) 25.6% (22.3% 29.2%) -2.0% 3.0% 0.4998

WA 21.3% (17.5% 25.7%) 21.8% (18.1% 26.1%) 0.5% 2.7% 0.8436

Other

MML 25.1% (23.7% 26.6%) 24.5% (23.1% 26.0%) -0.6% 0.9% 0.4940

Diff-in-Diff CO vs Other MML -1.4% 3.1% 0.6598

Diff-in-Diff WA vs Other MML 1.1% 2.9% 0.6815

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eTable 3. Parallel assumption test: difference-in-difference tests of marijuana use 12 years prior to passage of

recreational marijuana laws (RML), comparing 2010-2012 with 2001-2003 in states that legalized recreational marijuana use in 2012 compared with those that did not legalize marijuana by that time

Grade Effect Difference

estimate SE T value P value

8

2010-2012 vs. 2001-2003 in CO 0.01 0.03 0.41 0.68

2010-2012 vs. 2001-2003 in WA 0.00 0.03 -0.13 0.89

2010-2012 vs. 2001-2003 in Non-RML States -0.01 0.00 -1.37 0.17

Diff-in-Diff 2010-2012 vs. 2001-2003, CO vs Non-RML States 0.02 0.03 0.58 0.56 Diff-in-Diff 2010-2012 vs. 2001-2003, WA vs Non-RML States 0.00 0.03 0.08 0.94

10

2010-2012 vs. 2001-2003 in CO 0.03 0.08 0.41 0.68

2010-2012 vs. 2001-2003 in WA -0.06 0.03 -2.35 0.02

2010-2012 vs. 2001-2003 in Non-RML States 0.00 0.01 -0.41 0.68

Diff-in-Diff 2010-2012 vs. 2001-2003, CO vs Non-RML States 0.03 0.08 0.44 0.66 Diff-in-Diff 2010-2012 vs. 2001-2003, WA vs Non-RML States -0.06 0.03 -2.23 0.03

12

2010-2012 vs. 2001-2003 in CO -0.05 0.04 -1.14 0.26

2010-2012 vs. 2001-2003 in WA -0.05 0.04 -1.21 0.23

2010-2012 vs. 2001-2003 in Non-RML States 0.00 0.01 -0.10 0.92

Diff-in-Diff 2010-2012 vs. 2001-2003, CO vs Non-RML States -0.05 0.04 -1.11 0.27 Diff-in-Diff 2010-2012 vs. 2001-2003, WA vs Non-RML States -0.05 0.04 -1.17 0.24