Dear All,

I have individual level data on poisonings in the 50 US states and I want to study the impact of state regulations on drug dispensing on incidence of poisonings. My raw data of individual poisoning incidences includes a dummy for whether the state adopted drug dispensing regulations (treatMA), a dummy for whether the poisoning episode included multiple substances (poly) and an interaction dummy post that takes a value of 1 if the episode occurred in a state that adopted regulation (treatMA=1) and it is the period after the new regulation. My raw data looks as follows:

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input double caseid str3 state float(qtr poly) byte treatMA float post
   53202011 "CT"  1 1 1 .
  123362017 "NY" 25 1 1 1
  573202012 "CT"  5 1 1 .
  803362014 "NY" 13 1 1 1
  893362014 "NY" 13 1 1 1
 1503362017 "NY" 25 1 1 1
 2353362011 "NY"  1 1 1 .
 2433362011 "NY"  1 1 1 .
 3813202012 "CT"  5 1 1 .
 4273202012 "CT"  5 1 1 .
 4523362011 "NY"  1 1 1 .
 4913362014 "NY" 13 1 1 1
 4973202012 "CT"  5 1 1 .
 5043622011 "NY"  1 1 1 .
 5113202012 "CT"  5 1 1 .
 5143202012 "CT"  5 1 1 .
 5143622011 "NY"  1 1 1 .
 5743362013 "NY"  9 1 1 .
 6233622011 "NY"  1 1 1 .
 6713622011 "NY"  1 1 1 .
 6753202012 "CT"  5 . 1 .
 6753622011 "NY"  1 1 1 .
 6793622011 "NY"  1 1 1 .
 6863622011 "NY"  1 1 1 .
 6923202012 "CT"  5 1 1 .
 6973362011 "NY"  1 1 1 .
 6993362017 "NY" 25 1 1 1
 7103202012 "CT"  5 1 1 .
 7513202011 "CT"  1 1 1 .
 7543202012 "CT"  5 1 1 .
 7573362013 "NY"  9 1 1 .
 7613202011 "CT"  1 1 1 .
 7623362013 "NY"  9 1 1 .
 7643362011 "NY"  1 1 1 .
 8233202012 "CT"  5 1 1 .
 8273362014 "NY" 13 1 1 1
 8363362017 "NY" 25 1 1 1
 8683362017 "NY" 25 1 1 1
 8973362014 "NY" 13 1 1 1
 8973622011 "NY"  1 1 1 .
 9013202012 "CT"  5 . 1 .
 9223362014 "NY" 13 1 1 1
 9613362014 "NY" 13 1 1 1
 9673362013 "NY"  9 1 1 .
 9683362013 "NY"  9 1 1 .
 9753362017 "NY" 25 1 1 1
 9853362017 "NY" 25 1 1 1
 9873202012 "CT"  5 1 1 .
 9903362017 "NY" 25 1 1 1
10003622011 "NY"  1 1 1 .
10143362017 "NY" 25 1 1 1
10303362011 "NY"  1 . 1 .
10773622011 "NY"  1 1 1 .
12103362011 "NY"  1 1 1 .
12103622011 "NY"  1 1 1 .
12473622011 "NY"  1 1 1 .
12543362017 "NY" 25 1 1 1
12893202012 "CT"  5 . 1 .
13143362011 "NY"  1 1 1 .
13393362011 "NY"  1 1 1 .
13683202011 "CT"  1 1 1 .
13763362017 "NY" 25 1 1 1
14163202011 "CT"  1 1 1 .
14343622011 "NY"  1 . 1 .
14753362017 "NY" 25 . 1 1
15183202012 "CT"  5 1 1 .
15263202011 "CT"  1 1 1 .
15883362013 "NY"  9 1 1 .
15913622011 "NY"  1 1 1 .
16143202011 "CT"  1 1 1 .
16413362013 "NY"  9 1 1 .
16743622011 "NY"  1 1 1 .
16923622011 "NY"  1 1 1 .
17003202011 "CT"  1 1 1 .
17343362013 "NY"  9 1 1 .
17483362017 "NY" 25 1 1 1
17663202011 "CT"  1 1 1 .
18133202011 "CT"  1 1 1 .
18213362011 "NY"  1 1 1 .
18263202011 "CT"  1 . 1 .
18343622011 "NY"  1 . 1 .
18423202012 "CT"  5 1 1 .
18793202012 "CT"  5 . 1 .
19103622011 "NY"  1 1 1 .
19153362014 "NY" 13 1 1 1
19653362014 "NY" 13 1 1 1
19793622011 "NY"  1 1 1 .
20043202012 "CT"  5 1 1 .
20243202011 "CT"  1 1 1 .
21003362017 "NY" 25 1 1 1
21623202012 "CT"  5 1 1 .
21703622011 "NY"  1 1 1 .
21763202012 "CT"  5 1 1 .
22013362013 "NY"  9 1 1 .
22063362013 "NY"  9 1 1 .
22083362017 "NY" 25 1 1 1
22093622011 "NY"  1 1 1 .
22113362013 "NY"  9 . 1 .
22223362013 "NY"  9 1 1 .
22823362011 "NY"  1 1 1 .
end
To evaluate the impact of the state regulations on the 'rates of poisonings' I collapse the data at the state-quarter level :

collapse (count) caseid (mean) treatMA post poly, by(state qtr)

and then calculate the rate of poisoning as the number of episodes per 100,000 persons in the state. This looks as follows:


Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input float rate_poisoning str5 state float qtr long poly byte treatMA float post
 .6743052 "AK" 23  10 1 0
1.6183325 "AK" 21  18 1 0
.40675375 "AK" 20   9 1 0
 .8135075 "AK" 19  12 1 0
.27135384 "AK"  9   7 1 0
 .8140616 "AK" 11  10 1 0
 1.506026 "AK"  5  14 1 0
 .9694781 "AK"  1  13 1 0
 .6790646 "AK" 13   7 1 0
1.1079749 "AK"  3  13 1 0
.54764587 "AK"  7   6 1 0
 .8214688 "AK"  6  10 1 0
1.3567692 "AK" 10  12 1 0
1.2137494 "AK" 24  12 1 0
 .8135075 "AK" 17  12 1 0
 .6845573 "AK"  8  12 1 0
1.2464718 "AK"  2  12 1 0
1.4869165 "AK" 26  15 1 0
1.2223163 "AK" 16  13 1 0
1.0865033 "AK" 14  11 1 0
1.3517423 "AK" 25  16 1 0
2.0337687 "AK" 18  16 1 0
 .8148775 "AK" 15  12 1 0
1.0788883 "AK" 22  15 1 0
 1.938956 "AK"  4  19 1 0
1.3567692 "AK" 12  15 1 0
 1.169202 "AL" 25  80 0 0
1.2919805 "AL"  3  91 0 0
1.0714668 "AL" 17  76 0 0
1.2835217 "AL" 11  93 0 0
1.3336573 "AL"  1  84 0 0
1.5694435 "AL" 14  97 0 0
 1.377256 "AL" 22  89 0 0
 1.312819 "AL"  2  91 0 0
1.0072471 "AL" 24  73 0 0
1.1100273 "AL" 23  69 0 0
1.0278031 "AL" 21  62 0 0
1.3249255 "AL" 10  94 0 0
  1.34979 "AL"  6  84 0 0
1.3456275 "AL"  9  86 0 0
1.5074917 "AL" 13  97 0 0
  1.55745 "AL"  7  98 0 0
 1.370556 "AL"  5  85 0 0
 1.236308 "AL" 19  81 0 0
1.3422872 "AL" 16  94 0 0
1.0835966 "AL"  4  72 0 0
 1.256913 "AL" 20  82 0 0
 .9684412 "AL" 18  61 0 0
 1.594051 "AL" 12 113 0 0
1.1897143 "AL" 26  72 0 0
 1.548793 "AL" 15 105 0 0
 1.515918 "AL"  8 101 0 0
1.3653027 "AR" 26  57 1 1
1.1704081 "AR" 22  53 1 0
  .986258 "AR"  2  35 1 0
 .9182402 "AR"  3  35 1 0
 .8447233 "AR" 11  35 1 0
 .5781513 "AR"  4  22 1 0
 .8468522 "AR"  6  31 1 0
 1.337609 "AR" 23  59 1 0
 .8423958 "AR" 16  36 1 0
 .6993014 "AR" 25  37 1 1
1.0072498 "AR" 18  45 1 0
1.0700874 "AR" 24  43 1 0
 .8760917 "AR" 13  38 1 0
 .8807263 "AR"  5  32 1 0
 .8447233 "AR" 10  33 1 0
  .779104 "AR"  8  32 1 0
 .8109344 "AR"  9  33 1 0
 .8468522 "AR"  7  33 1 0
 .5728292 "AR" 14  23 1 0
1.6115998 "AR" 19  64 1 0
 .8729499 "AR" 17  41 1 0
 .9460901 "AR" 12  33 1 0
1.2038482 "AR" 21  56 1 0
 .7076125 "AR" 15  33 1 0
 .7481958 "AR"  1  30 1 0
1.3429998 "AR" 20  54 1 0
1.5592886 "AZ" 14 151 1 0
1.3170226 "AZ" 19 142 1 0
1.4470392 "AZ" 25 142 1 0
1.4946705 "AZ"  7 141 1 0
1.5693723 "AZ" 23 148 1 0
1.5071592 "AZ"  9 140 1 0
 1.591103 "AZ"  1 150 1 0
1.2810854 "AZ" 12 116 1 0
 1.513865 "AZ"  4 138 1 0
1.8302088 "AZ"  6 176 1 0
 1.468587 "AZ" 22 141 1 0
1.4256353 "AZ" 16 127 1 0
  1.61869 "AZ" 15 169 1 0
1.4318013 "AZ" 10 130 1 0
 1.295812 "AZ" 21 119 1 0
 1.331656 "AZ" 20 129 1 0
 1.582517 "AZ" 11 134 1 0
  1.40316 "AZ"  5 144 1 0
1.6837885 "AZ"  3 159 1 0
1.4489152 "AZ"  8 130 1 0
1.3901905 "AZ" 17 132 1 0
 1.336533 "AZ" 13 122 1 0
end
So now I have a panel for the 50 US states for 26 quarters each. To estimate the impact of the new regulation on the rate of poisonings I regress:

reg
rate_poisoning treatMA post i.qtr i.state [aweight=population], vce(cluster state)

I find:

(Std. Err. adjusted for 47 clusters in state)
----------------------------------------------------------------------------------------
| Robust
narc_nocod2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
post | .0987154 .035155 2.81 0.007 .027952 .1694787
treatMA | 2.840195 4.95225 0.57 0.569 -7.128167 12.80856
-----------------------+----------------------------------------------------------------



Next, I want to see if the increase in the rate of poisonings is driven by the incidence of poly-drug poisonings. The poly variable is simple the count of the poly-drug poisoning episodes in the state and not a *rate* per 100,000 persons like the outcome variable. For this I estimate:

reg
rate_poisoning treatMA post##poly i.qtr i.state [aweight=population], vce(cluster state)

and get:

(Std. Err. adjusted for 47 clusters in state)
----------------------------------------------------------------------------------------
| Robust
narc_nocod2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
post | .0040671 .0660497 0.06 0.951 -.1288841 .1370183
poly | .0055046 .0011748 4.69 0.000 .0031399 .0078693
poly_post | .0004862 .0005581 0.87 0.388 -.0006371 .0016096
treatMA | 2.335998 2.621396 0.89 0.377 -2.9406 7.612595
-----------------------+----------------------------------------------------------------



However, I am not sure if the interaction term really captures that? I will appreciate any direction I may get to specify a model that helps me capture that the increase in the poisonings rate is driven by an increase in the poly drug poisonings following state regulation.

Sorry for the long post but I wanted to share the data and output.

Thank you in advance,
Sincerely,
Sumedha.