总体思路是使用数据挖掘中的挖掘频繁项原理来挖掘毒品之间的关系、人口普查数据与毒品之间的关系。
以下是论文第二部分的主干。
Glossary & Symbols
Glossary
数据立方体 data cube
维 dimension
分层 hierarchy hierarchy is a mapping sequence that maps the underlying conceptual set to a higher level
频繁模式 frequent pattern
关联规则 association rule
支持度 support
置信度 confidence
提升度 lift
出现频度 instances
频繁项集 frequent itemset
Symbols
公式
confidence(A => B) = P(A|B) = support_count(AUB)/support_count(A)
Model 1
1 Data Analysis
The data in MCM_NFLIS_Data.xlsx can be abstracted as data cut with 4 dimension, the 4 demension are time, position, substance name and substance report number. In time dimension we have one hierarchy —— year, in position dimension we have two hierarchy —— state and county, in substance name dimension we have one hierarchy with 69 kinds of substances and each substance has its report number in drug report number dimension.
1.1 The Intuitive Concept of States
In order to have an intuitive concept of states, we improve position dimension to state level, and statistic on the total number of drug report. 
The figure above shows the number of drugs found in five states in the past seven years. In terms of the number and proportion of drug detection, both OH and PA are on the rise, so we should focus on the data of these two states.
1.2 The Intuitive Concept of Substance
In order to have an intuitive concept of substance, we slice to substance level, and statistic on the total number of each substance in the past seven years. 
The figure above shows the top 13 substances number found in the past seven years. In terms of the number and proportion of these substance, Fentanyl, Carfentanil, Furanyl fentanyl, U-47700, Acryl fentanyl and Tramadol are on the rise, Heroin is always in a high level.
2 Data Mining
2.1 Data Preparation
We dice this data in two dimension time and position to get a list of substance name and report number in each county, then we roll-up report number dimension to get if a county has selected substance with true or false flag.
2.2 Data Mining
At first, we calculate support for each substance, if the instances of substance is higher than MIN_SUPPORT, this substance is a one item frequent itemset.
Then we use the frequent itemset at first step to generate the two item set. And calculate support for each set, if the instances of set is higher than MIN_SUPPORT, this set is a two item frequent itemset. Repeat this step until there is no support degree lager than MIN_SUPPORT. 
The chart above shows the distribution of support degree for one item frequent itemset. We find that there is a clear demarcation at support from 0.1 to 0.2.
The chart above shows the distribution of support degree for two item frequent itemset. We find that there is a clear demarcation at support near 0.1.
The chart above shows the distribution of support degree for two item frequent itemset. We find that there is a clear demarcation at support near 0.1.
It can be seen that the support degree of one item frequent itemset is bounded at 0.2-0.1, and the support degree between two item and three item frequent itemset is bounded at 0.1. In order to improve the stability and accuracy of the model, we set the MIN_SUPPORT to 0.1 so that this model can more accurately analyze and pay attention to the relatively serious situation, and can warn as early as possible.
We get 11 one item frequent itemset, 55 two item frequent itemset and 165 three item frequent itemset.
看篇幅情况，放适量的下方数据
Below are some of the frequent itemset.
==================================================
frequent 1-itemsets support
==================================================
['Oxycodone'] 0.85
['Hydrocodone'] 0.81
['Heroin'] 0.74
['Buprenorphine'] 0.68
['Morphine'] 0.57
['Methadone'] 0.49
['Fentanyl'] 0.40
['Tramadol'] 0.38
['Hydromorphone'] 0.32
['Oxymorphone'] 0.32
['Codeine'] 0.28
==================================================
frequent 2-itemsets support
==================================================
['Oxycodone', 'Hydrocodone'] 0.76
['Oxycodone', 'Heroin'] 0.68
['Oxycodone', 'Buprenorphine'] 0.65
['Hydrocodone', 'Heroin'] 0.64
['Hydrocodone', 'Buprenorphine'] 0.63
['Buprenorphine', 'Heroin'] 0.59
['Oxycodone', 'Morphine'] 0.55
['Hydrocodone', 'Morphine'] 0.54
['Morphine', 'Heroin'] 0.48
['Methadone', 'Oxycodone'] 0.48
['Morphine', 'Buprenorphine'] 0.48
['Methadone', 'Hydrocodone'] 0.47
['Methadone', 'Heroin'] 0.42
['Methadone', 'Buprenorphine'] 0.41
['Fentanyl', 'Heroin'] 0.38
['Methadone', 'Morphine'] 0.38
['Oxycodone', 'Fentanyl'] 0.38
['Oxycodone', 'Tramadol'] 0.36
['Fentanyl', 'Hydrocodone'] 0.36
['Tramadol', 'Hydrocodone'] 0.35
['Fentanyl', 'Buprenorphine'] 0.35
['Tramadol', 'Buprenorphine'] 0.33
['Tramadol', 'Heroin'] 0.33
['Oxycodone', 'Oxymorphone'] 0.32
['Oxycodone', 'Hydromorphone'] 0.32
['Hydrocodone', 'Hydromorphone'] 0.31
['Oxymorphone', 'Hydrocodone'] 0.31
['Tramadol', 'Morphine'] 0.30
['Oxymorphone', 'Buprenorphine'] 0.29
['Fentanyl', 'Morphine'] 0.29
['Hydromorphone', 'Heroin'] 0.29
['Oxymorphone', 'Heroin'] 0.28
['Hydromorphone', 'Buprenorphine'] 0.28
['Codeine', 'Oxycodone'] 0.27
['Codeine', 'Hydrocodone'] 0.27
['Hydromorphone', 'Morphine'] 0.27
['Oxymorphone', 'Morphine'] 0.27
['Methadone', 'Tramadol'] 0.27
['Codeine', 'Heroin'] 0.26
['Codeine', 'Buprenorphine'] 0.25
['Methadone', 'Hydromorphone'] 0.24
['Methadone', 'Fentanyl'] 0.24
['Methadone', 'Oxymorphone'] 0.24
['Fentanyl', 'Tramadol'] 0.24
['Codeine', 'Morphine'] 0.24
['Methadone', 'Codeine'] 0.21
['Tramadol', 'Hydromorphone'] 0.19
['Oxymorphone', 'Tramadol'] 0.18
['Oxymorphone', 'Hydromorphone'] 0.18
['Codeine', 'Tramadol'] 0.18
['Oxymorphone', 'Fentanyl'] 0.18
['Codeine', 'Fentanyl'] 0.18
['Fentanyl', 'Hydromorphone'] 0.17
['Codeine', 'Oxymorphone'] 0.16
['Codeine', 'Hydromorphone'] 0.16
==================================================
frequent 3-itemsets support
==================================================
['Oxycodone', 'Hydrocodone', 'Heroin'] 0.62
['Oxycodone', 'Hydrocodone', 'Buprenorphine'] 0.61
['Oxycodone', 'Buprenorphine', 'Heroin'] 0.57
['Hydrocodone', 'Buprenorphine', 'Heroin'] 0.54
['Oxycodone', 'Hydrocodone', 'Morphine'] 0.53
['Oxycodone', 'Morphine', 'Heroin'] 0.47
['Oxycodone', 'Morphine', 'Buprenorphine'] 0.47
['Methadone', 'Hydrocodone', 'Oxycodone'] 0.46
['Hydrocodone', 'Morphine', 'Buprenorphine'] 0.46
['Hydrocodone', 'Morphine', 'Heroin'] 0.46
['Morphine', 'Buprenorphine', 'Heroin'] 0.42
['Oxycodone', 'Methadone', 'Buprenorphine'] 0.41
['Oxycodone', 'Methadone', 'Heroin'] 0.41
['Methadone', 'Hydrocodone', 'Buprenorphine'] 0.40
['Methadone', 'Hydrocodone', 'Heroin'] 0.40
['Methadone', 'Oxycodone', 'Morphine'] 0.38
['Methadone', 'Hydrocodone', 'Morphine'] 0.37
['Methadone', 'Buprenorphine', 'Heroin'] 0.37
['Oxycodone', 'Fentanyl', 'Heroin'] 0.36
['Oxycodone', 'Fentanyl', 'Hydrocodone'] 0.35
['Oxycodone', 'Hydrocodone', 'Tramadol'] 0.35
['Fentanyl', 'Heroin', 'Hydrocodone'] 0.34
['Methadone', 'Morphine', 'Buprenorphine'] 0.34
['Fentanyl', 'Buprenorphine', 'Heroin'] 0.34
['Oxycodone', 'Fentanyl', 'Buprenorphine'] 0.34
['Methadone', 'Morphine', 'Heroin'] 0.34
['Oxycodone', 'Tramadol', 'Buprenorphine'] 0.33
['Fentanyl', 'Buprenorphine', 'Hydrocodone'] 0.32
['Oxycodone', 'Tramadol', 'Heroin'] 0.32
['Tramadol', 'Buprenorphine', 'Hydrocodone'] 0.32
['Tramadol', 'Hydrocodone', 'Heroin'] 0.31
['Oxycodone', 'Hydrocodone', 'Hydromorphone'] 0.31
['Oxycodone', 'Oxymorphone', 'Hydrocodone'] 0.31
['Tramadol', 'Buprenorphine', 'Heroin'] 0.30
['Oxycodone', 'Tramadol', 'Morphine'] 0.29
['Hydrocodone', 'Morphine', 'Tramadol'] 0.29
['Oxycodone', 'Oxymorphone', 'Buprenorphine'] 0.29
['Oxycodone', 'Hydromorphone', 'Heroin'] 0.28
['Oxymorphone', 'Buprenorphine', 'Hydrocodone'] 0.28
['Oxycodone', 'Fentanyl', 'Morphine'] 0.28
['Oxycodone', 'Oxymorphone', 'Heroin'] 0.28
['Fentanyl', 'Morphine', 'Hydrocodone'] 0.28
['Hydrocodone', 'Hydromorphone', 'Heroin'] 0.28
['Oxycodone', 'Hydromorphone', 'Buprenorphine'] 0.27
['Oxymorphone', 'Hydrocodone', 'Heroin'] 0.27
['Fentanyl', 'Morphine', 'Heroin'] 0.27
['Tramadol', 'Morphine', 'Buprenorphine'] 0.27
['Hydrocodone', 'Hydromorphone', 'Buprenorphine'] 0.27
['Oxycodone', 'Hydromorphone', 'Morphine'] 0.27
['Codeine', 'Hydrocodone', 'Oxycodone'] 0.27
['Hydrocodone', 'Hydromorphone', 'Morphine'] 0.27
['Fentanyl', 'Buprenorphine', 'Morphine'] 0.27
['Methadone', 'Tramadol', 'Oxycodone'] 0.27
['Oxycodone', 'Oxymorphone', 'Morphine'] 0.27
['Tramadol', 'Morphine', 'Heroin'] 0.26
['Oxymorphone', 'Morphine', 'Hydrocodone'] 0.26
['Methadone', 'Hydrocodone', 'Tramadol'] 0.26
['Oxymorphone', 'Buprenorphine', 'Heroin'] 0.26
['Codeine', 'Oxycodone', 'Heroin'] 0.26
['Hydromorphone', 'Buprenorphine', 'Heroin'] 0.25
['Codeine', 'Hydrocodone', 'Heroin'] 0.25
['Codeine', 'Oxycodone', 'Buprenorphine'] 0.25
['Methadone', 'Tramadol', 'Buprenorphine'] 0.25
['Oxymorphone', 'Buprenorphine', 'Morphine'] 0.25
['Codeine', 'Hydrocodone', 'Buprenorphine'] 0.25
['Hydromorphone', 'Morphine', 'Heroin'] 0.25
['Hydromorphone', 'Morphine', 'Buprenorphine'] 0.24
['Oxymorphone', 'Morphine', 'Heroin'] 0.24
['Methadone', 'Tramadol', 'Heroin'] 0.24
['Oxycodone', 'Hydromorphone', 'Methadone'] 0.24
['Codeine', 'Buprenorphine', 'Heroin'] 0.24
['Oxycodone', 'Fentanyl', 'Methadone'] 0.24
['Methadone', 'Hydrocodone', 'Hydromorphone'] 0.24
['Methadone', 'Oxymorphone', 'Oxycodone'] 0.24
['Codeine', 'Oxycodone', 'Morphine'] 0.23
['Methadone', 'Oxymorphone', 'Hydrocodone'] 0.23
['Codeine', 'Hydrocodone', 'Morphine'] 0.23
['Oxycodone', 'Fentanyl', 'Tramadol'] 0.23
['Methadone', 'Fentanyl', 'Hydrocodone'] 0.23
['Methadone', 'Tramadol', 'Morphine'] 0.23
['Methadone', 'Fentanyl', 'Heroin'] 0.23
['Fentanyl', 'Heroin', 'Tramadol'] 0.23
['Fentanyl', 'Hydrocodone', 'Tramadol'] 0.22
['Methadone', 'Fentanyl', 'Buprenorphine'] 0.22
['Fentanyl', 'Buprenorphine', 'Tramadol'] 0.22
['Methadone', 'Oxymorphone', 'Buprenorphine'] 0.22
['Codeine', 'Morphine', 'Heroin'] 0.22
['Codeine', 'Morphine', 'Buprenorphine'] 0.22
['Methadone', 'Hydromorphone', 'Heroin'] 0.22
['Methadone', 'Hydromorphone', 'Morphine'] 0.22
['Methadone', 'Hydromorphone', 'Buprenorphine'] 0.22
['Methadone', 'Oxymorphone', 'Heroin'] 0.21
['Methadone', 'Oxymorphone', 'Morphine'] 0.21
['Methadone', 'Codeine', 'Oxycodone'] 0.21
['Methadone', 'Codeine', 'Hydrocodone'] 0.21
['Methadone', 'Fentanyl', 'Morphine'] 0.21
['Codeine', 'Methadone', 'Buprenorphine'] 0.20
['Methadone', 'Codeine', 'Heroin'] 0.20
['Fentanyl', 'Morphine', 'Tramadol'] 0.20
['Methadone', 'Codeine', 'Morphine'] 0.19
['Oxycodone', 'Tramadol', 'Hydromorphone'] 0.19
['Hydrocodone', 'Hydromorphone', 'Tramadol'] 0.18
['Oxycodone', 'Tramadol', 'Oxymorphone'] 0.18
['Oxycodone', 'Oxymorphone', 'Hydromorphone'] 0.18
['Codeine', 'Tramadol', 'Oxycodone'] 0.18
['Oxymorphone', 'Tramadol', 'Hydrocodone'] 0.18
['Hydrocodone', 'Hydromorphone', 'Oxymorphone'] 0.18
['Oxycodone', 'Fentanyl', 'Oxymorphone'] 0.18
['Codeine', 'Hydrocodone', 'Tramadol'] 0.18
['Codeine', 'Fentanyl', 'Oxycodone'] 0.18
['Methadone', 'Fentanyl', 'Tramadol'] 0.17
['Tramadol', 'Hydromorphone', 'Buprenorphine'] 0.17
['Tramadol', 'Hydromorphone', 'Heroin'] 0.17
['Codeine', 'Fentanyl', 'Heroin'] 0.17
['Fentanyl', 'Oxymorphone', 'Hydrocodone'] 0.17
['Oxymorphone', 'Buprenorphine', 'Tramadol'] 0.17
['Codeine', 'Hydrocodone', 'Fentanyl'] 0.17
['Oxymorphone', 'Fentanyl', 'Heroin'] 0.17
['Codeine', 'Tramadol', 'Buprenorphine'] 0.17
['Tramadol', 'Hydromorphone', 'Morphine'] 0.17
['Oxycodone', 'Fentanyl', 'Hydromorphone'] 0.17
['Oxymorphone', 'Buprenorphine', 'Fentanyl'] 0.17
['Codeine', 'Tramadol', 'Heroin'] 0.17
['Oxymorphone', 'Hydromorphone', 'Buprenorphine'] 0.17
['Codeine', 'Fentanyl', 'Buprenorphine'] 0.17
['Oxymorphone', 'Hydromorphone', 'Heroin'] 0.17
['Fentanyl', 'Hydromorphone', 'Hydrocodone'] 0.17
['Oxymorphone', 'Hydromorphone', 'Morphine'] 0.17
['Fentanyl', 'Hydromorphone', 'Heroin'] 0.17
['Tramadol', 'Oxymorphone', 'Heroin'] 0.17
['Oxymorphone', 'Morphine', 'Tramadol'] 0.16
['Fentanyl', 'Hydromorphone', 'Buprenorphine'] 0.16
['Codeine', 'Tramadol', 'Morphine'] 0.16
['Methadone', 'Tramadol', 'Hydromorphone'] 0.16
['Codeine', 'Oxymorphone', 'Oxycodone'] 0.16
['Codeine', 'Oxymorphone', 'Hydrocodone'] 0.16
['Codeine', 'Fentanyl', 'Morphine'] 0.16
['Oxymorphone', 'Morphine', 'Fentanyl'] 0.16
['Codeine', 'Hydromorphone', 'Oxycodone'] 0.16
['Codeine', 'Hydrocodone', 'Hydromorphone'] 0.15
['Fentanyl', 'Hydromorphone', 'Morphine'] 0.15
['Codeine', 'Oxymorphone', 'Buprenorphine'] 0.15
['Methadone', 'Oxymorphone', 'Hydromorphone'] 0.15
['Methadone', 'Tramadol', 'Oxymorphone'] 0.15
['Codeine', 'Oxymorphone', 'Heroin'] 0.15
['Methadone', 'Codeine', 'Tramadol'] 0.15
['Codeine', 'Hydromorphone', 'Heroin'] 0.15
['Codeine', 'Hydromorphone', 'Buprenorphine'] 0.15
['Codeine', 'Hydromorphone', 'Morphine'] 0.15
['Codeine', 'Oxymorphone', 'Morphine'] 0.15
['Methadone', 'Codeine', 'Fentanyl'] 0.14
['Methadone', 'Codeine', 'Hydromorphone'] 0.14
['Methadone', 'Oxymorphone', 'Fentanyl'] 0.14
['Methadone', 'Fentanyl', 'Hydromorphone'] 0.14
['Methadone', 'Codeine', 'Oxymorphone'] 0.14
['Codeine', 'Fentanyl', 'Tramadol'] 0.13
['Fentanyl', 'Hydromorphone', 'Tramadol'] 0.13
['Fentanyl', 'Oxymorphone', 'Tramadol'] 0.13
['Oxymorphone', 'Hydromorphone', 'Tramadol'] 0.12
['Codeine', 'Tramadol', 'Hydromorphone'] 0.11
['Fentanyl', 'Hydromorphone', 'Oxymorphone'] 0.11
['Codeine', 'Oxymorphone', 'Tramadol'] 0.11
['Codeine', 'Oxymorphone', 'Hydromorphone'] 0.11
['Codeine', 'Oxymorphone', 'Fentanyl'] 0.11
['Codeine', 'Fentanyl', 'Hydromorphone'] 0.11Link two itemset to generate association rules. First we scan the data to statistic the quantity that both itemset appears in the same county, then we calculate the confidence of this rule using 公式confidence, if this confidence is larger than MIN_CONFIDENCE, this rule is a strong rule.
The chart above shows the distribution of confidence degree for rules.
In this paper we use MIN_CONFIDENCE=0.9 to get more credible information. And some strong rules list below.
此处适当列出部分强关联规则
['Codeine', 'Oxymorphone'] => ['Oxycodone'] conf:1.00
['Methadone', 'Hydromorphone'] => ['Oxycodone'] conf:1.00
['Methadone', 'Codeine'] => ['Oxycodone'] conf:1.00
['Oxymorphone', 'Hydromorphone'] => ['Oxycodone'] conf:1.00
['Codeine', 'Tramadol'] => ['Oxycodone'] conf:1.00
['Methadone', 'Oxymorphone'] => ['Oxycodone'] conf:1.00
['Codeine', 'Hydromorphone'] => ['Oxycodone'] conf:1.00
['Methadone', 'Tramadol'] => ['Oxycodone'] conf:1.00
['Codeine', 'Buprenorphine'] => ['Oxycodone'] conf:1.00
['Tramadol', 'Oxymorphone'] => ['Oxycodone'] conf:1.00
['Methadone', 'Morphine'] => ['Oxycodone'] conf:1.00
['Codeine', 'Oxymorphone'] => ['Hydrocodone'] conf:0.99
['Codeine', 'Fentanyl'] => ['Oxycodone'] conf:0.99
['Methadone', 'Fentanyl'] => ['Oxycodone'] conf:0.99
['Codeine', 'Morphine'] => ['Oxycodone'] conf:0.99
['Codeine', 'Hydromorphone'] => ['Hydrocodone'] conf:0.99
['Oxymorphone', 'Morphine'] => ['Oxycodone'] conf:0.99
['Tramadol', 'Hydromorphone'] => ['Oxycodone'] conf:0.99
['Oxymorphone', 'Buprenorphine'] => ['Oxycodone'] conf:0.99
['Fentanyl', 'Oxymorphone'] => ['Oxycodone'] conf:0.99
['Fentanyl', 'Hydromorphone'] => ['Oxycodone'] conf:0.99
['Methadone', 'Buprenorphine'] => ['Oxycodone'] conf:0.99
['Hydromorphone', 'Buprenorphine'] => ['Oxycodone'] conf:0.99
['Oxymorphone', 'Hydromorphone'] => ['Hydrocodone'] conf:0.99
['Oxymorphone', 'Heroin'] => ['Oxycodone'] conf:0.99
['Oxymorphone', 'Hydrocodone'] => ['Oxycodone'] conf:0.99
['Hydromorphone', 'Morphine'] => ['Oxycodone'] conf:0.99
['Tramadol', 'Morphine'] => ['Oxycodone'] conf:0.99
['Codeine', 'Morphine'] => ['Hydrocodone'] conf:0.99
['Hydrocodone', 'Hydromorphone'] => ['Oxycodone'] conf:0.99
['Hydromorphone', 'Heroin'] => ['Oxycodone'] conf:0.99
['Methadone', 'Codeine'] => ['Hydrocodone'] conf:0.99
['Codeine', 'Hydrocodone'] => ['Oxycodone'] conf:0.99
['Methadone', 'Hydrocodone'] => ['Oxycodone'] conf:0.99
['Hydrocodone', 'Tramadol'] => ['Oxycodone'] conf:0.99
['Methadone', 'Heroin'] => ['Oxycodone'] conf:0.99
['Methadone', 'Hydromorphone'] => ['Hydrocodone'] conf:0.99
['Tramadol', 'Buprenorphine'] => ['Oxycodone'] conf:0.99
['Oxymorphone'] => ['Oxycodone'] conf:0.99
['Codeine', 'Tramadol'] => ['Hydrocodone'] conf:0.99
['Methadone', 'Oxymorphone'] => ['Hydrocodone'] conf:0.99
['Morphine', 'Buprenorphine'] => ['Oxycodone'] conf:0.99
['Codeine', 'Heroin'] => ['Oxycodone'] conf:0.99
['Hydromorphone', 'Buprenorphine'] => ['Hydrocodone'] conf:0.99
['Oxymorphone', 'Tramadol'] => ['Hydrocodone'] conf:0.98
['Oxymorphone', 'Morphine'] => ['Hydrocodone'] conf:0.98
['Methadone', 'Tramadol'] => ['Hydrocodone'] conf:0.98
['Fentanyl', 'Tramadol'] => ['Oxycodone'] conf:0.98
['Tramadol', 'Hydromorphone'] => ['Hydrocodone'] conf:0.98
['Hydromorphone', 'Morphine'] => ['Hydrocodone'] conf:0.98
['Methadone', 'Morphine'] => ['Hydrocodone'] conf:0.98
['Methadone'] => ['Oxycodone'] conf:0.98
['Codeine', 'Fentanyl'] => ['Heroin'] conf:0.98
['Codeine'] => ['Oxycodone'] conf:0.98
['Codeine', 'Buprenorphine'] => ['Hydrocodone'] conf:0.98
['Morphine', 'Heroin'] => ['Oxycodone'] conf:0.98
['Hydromorphone'] => ['Oxycodone'] conf:0.98
['Hydrocodone', 'Morphine'] => ['Oxycodone'] conf:0.98
['Oxymorphone', 'Buprenorphine'] => ['Hydrocodone'] conf:0.98
['Fentanyl', 'Morphine'] => ['Oxycodone'] conf:0.98
['Fentanyl', 'Hydromorphone'] => ['Hydrocodone'] conf:0.98
['Codeine', 'Oxycodone'] => ['Hydrocodone'] conf:0.98
['Hydrocodone', 'Buprenorphine'] => ['Oxycodone'] conf:0.98
['Tramadol', 'Heroin'] => ['Oxycodone'] conf:0.98
['Methadone', 'Buprenorphine'] => ['Hydrocodone'] conf:0.98
['Tramadol', 'Morphine'] => ['Hydrocodone'] conf:0.97
['Fentanyl', 'Oxymorphone'] => ['Hydrocodone'] conf:0.97
['Oxycodone', 'Hydromorphone'] => ['Hydrocodone'] conf:0.97
['Codeine', 'Fentanyl'] => ['Hydrocodone'] conf:0.97
['Tramadol'] => ['Oxycodone'] conf:0.97
['Oxycodone', 'Oxymorphone'] => ['Hydrocodone'] conf:0.97
['Fentanyl', 'Hydrocodone'] => ['Oxycodone'] conf:0.97
['Codeine', 'Heroin'] => ['Hydrocodone'] conf:0.97
['Fentanyl', 'Hydromorphone'] => ['Heroin'] conf:0.97
['Fentanyl', 'Buprenorphine'] => ['Heroin'] conf:0.97
['Morphine'] => ['Oxycodone'] conf:0.97
['Oxymorphone', 'Heroin'] => ['Hydrocodone'] conf:0.97
['Morphine', 'Buprenorphine'] => ['Hydrocodone'] conf:0.97
['Codeine'] => ['Hydrocodone'] conf:0.97
['Fentanyl', 'Buprenorphine'] => ['Oxycodone'] conf:0.97
['Oxymorphone'] => ['Hydrocodone'] conf:0.97
['Methadone', 'Oxycodone'] => ['Hydrocodone'] conf:0.97
['Hydrocodone', 'Heroin'] => ['Oxycodone'] conf:0.97
['Hydromorphone', 'Heroin'] => ['Hydrocodone'] conf:0.97
['Fentanyl', 'Tramadol'] => ['Heroin'] conf:0.97
['Fentanyl', 'Morphine'] => ['Hydrocodone'] conf:0.97
['Buprenorphine', 'Heroin'] => ['Oxycodone'] conf:0.97
['Oxymorphone', 'Fentanyl'] => ['Heroin'] conf:0.96
['Methadone', 'Fentanyl'] => ['Hydrocodone'] conf:0.96
['Methadone', 'Heroin'] => ['Hydrocodone'] conf:0.96
['Hydromorphone'] => ['Hydrocodone'] conf:0.96
['Tramadol', 'Buprenorphine'] => ['Hydrocodone'] conf:0.96
['Codeine', 'Oxymorphone'] => ['Buprenorphine'] conf:0.96
['Methadone'] => ['Hydrocodone'] conf:0.96
['Oxycodone', 'Morphine'] => ['Hydrocodone'] conf:0.96
['Oxymorphone', 'Tramadol'] => ['Buprenorphine'] conf:0.96
['Oxycodone', 'Tramadol'] => ['Hydrocodone'] conf:0.96
['Methadone', 'Fentanyl'] => ['Heroin'] conf:0.96
['Codeine', 'Tramadol'] => ['Buprenorphine'] conf:0.96
['Oxymorphone'] => ['Oxycodone', 'Hydrocodone'] conf:0.96
['Codeine'] => ['Oxycodone', 'Hydrocodone'] conf:0.96
['Oxycodone', 'Fentanyl'] => ['Heroin'] conf:0.96
['Fentanyl', 'Morphine'] => ['Heroin'] conf:0.95
['Buprenorphine'] => ['Oxycodone'] conf:0.95
['Morphine', 'Heroin'] => ['Hydrocodone'] conf:0.95
['Hydromorphone'] => ['Oxycodone', 'Hydrocodone'] conf:0.95
['Codeine', 'Hydromorphone'] => ['Heroin'] conf:0.95
['Morphine'] => ['Hydrocodone'] conf:0.95
['Fentanyl', 'Tramadol'] => ['Hydrocodone'] conf:0.95
['Fentanyl'] => ['Heroin'] conf:0.95
['Fentanyl', 'Hydrocodone'] => ['Heroin'] conf:0.95
['Fentanyl', 'Heroin'] => ['Oxycodone'] conf:0.95
['Codeine', 'Fentanyl'] => ['Buprenorphine'] conf:0.95
['Methadone'] => ['Oxycodone', 'Hydrocodone'] conf:0.95
['Codeine', 'Oxymorphone'] => ['Heroin'] conf:0.95
['Oxymorphone', 'Fentanyl'] => ['Buprenorphine'] conf:0.95
['Codeine', 'Methadone'] => ['Buprenorphine'] conf:0.95
['Tramadol', 'Heroin'] => ['Hydrocodone'] conf:0.95
['Codeine', 'Hydromorphone'] => ['Buprenorphine'] conf:0.94
['Fentanyl'] => ['Oxycodone'] conf:0.94
['Tramadol'] => ['Hydrocodone'] conf:0.94
['Codeine', 'Tramadol'] => ['Heroin'] conf:0.94
['Methadone', 'Codeine'] => ['Heroin'] conf:0.94
['Codeine', 'Buprenorphine'] => ['Heroin'] conf:0.94
['Codeine', 'Hydromorphone'] => ['Morphine'] conf:0.94
['Fentanyl', 'Tramadol'] => ['Buprenorphine'] conf:0.94
['Codeine', 'Morphine'] => ['Heroin'] conf:0.94
['Hydrocodone'] => ['Oxycodone'] conf:0.94
['Oxymorphone', 'Hydromorphone'] => ['Buprenorphine'] conf:0.94
['Methadone', 'Fentanyl'] => ['Buprenorphine'] conf:0.94
['Fentanyl', 'Hydromorphone'] => ['Buprenorphine'] conf:0.94
['Oxycodone', 'Buprenorphine'] => ['Hydrocodone'] conf:0.94
['Methadone', 'Oxymorphone'] => ['Buprenorphine'] conf:0.94
['Oxymorphone', 'Hydromorphone'] => ['Heroin'] conf:0.93
['Methadone', 'Tramadol'] => ['Buprenorphine'] conf:0.93
['Codeine', 'Morphine'] => ['Buprenorphine'] conf:0.93
['Tramadol'] => ['Oxycodone', 'Hydrocodone'] conf:0.93
['Tramadol', 'Hydromorphone'] => ['Buprenorphine'] conf:0.93
['Tramadol', 'Hydromorphone'] => ['Heroin'] conf:0.93
['Codeine', 'Oxymorphone'] => ['Morphine'] conf:0.93
['Morphine'] => ['Oxycodone', 'Hydrocodone'] conf:0.93
['Codeine', 'Oxycodone'] => ['Heroin'] conf:0.93
['Oxymorphone', 'Hydromorphone'] => ['Morphine'] conf:0.93
['Codeine', 'Hydrocodone'] => ['Heroin'] conf:0.93
['Fentanyl', 'Buprenorphine'] => ['Hydrocodone'] conf:0.93
['Fentanyl', 'Morphine'] => ['Buprenorphine'] conf:0.93
['Oxymorphone', 'Morphine'] => ['Buprenorphine'] conf:0.92
['Codeine'] => ['Heroin'] conf:0.92
['Methadone', 'Codeine'] => ['Morphine'] conf:0.92
['Tramadol', 'Morphine'] => ['Buprenorphine'] conf:0.92
['Heroin'] => ['Oxycodone'] conf:0.92
['Oxycodone', 'Fentanyl'] => ['Hydrocodone'] conf:0.92
['Oxymorphone', 'Heroin'] => ['Buprenorphine'] conf:0.92
['Buprenorphine', 'Heroin'] => ['Hydrocodone'] conf:0.92
['Tramadol', 'Oxymorphone'] => ['Heroin'] conf:0.92
['Methadone', 'Hydromorphone'] => ['Heroin'] conf:0.92
['Hydromorphone', 'Buprenorphine'] => ['Heroin'] conf:0.92
['Codeine', 'Heroin'] => ['Buprenorphine'] conf:0.92
['Buprenorphine'] => ['Hydrocodone'] conf:0.91
['Tramadol', 'Heroin'] => ['Buprenorphine'] conf:0.91
['Codeine', 'Oxycodone'] => ['Buprenorphine'] conf:0.91
['Tramadol', 'Hydromorphone'] => ['Morphine'] conf:0.91
['Codeine'] => ['Oxycodone', 'Heroin'] conf:0.91
['Oxymorphone', 'Hydrocodone'] => ['Buprenorphine'] conf:0.91
['Codeine', 'Hydrocodone'] => ['Buprenorphine'] conf:0.91
['Oxycodone', 'Heroin'] => ['Hydrocodone'] conf:0.91
['Oxycodone', 'Oxymorphone'] => ['Buprenorphine'] conf:0.90
['Methadone', 'Hydromorphone'] => ['Morphine'] conf:0.90
['Hydromorphone', 'Morphine'] => ['Heroin'] conf:0.90
['Tramadol', 'Hydrocodone'] => ['Buprenorphine'] conf:0.90
['Methadone', 'Oxymorphone'] => ['Heroin'] conf:0.90
['Fentanyl'] => ['Oxycodone', 'Heroin'] conf:0.90
['Oxymorphone', 'Buprenorphine'] => ['Heroin'] conf:0.90
['Tramadol', 'Buprenorphine'] => ['Heroin'] conf:0.90
['Methadone', 'Hydromorphone'] => ['Buprenorphine'] conf:0.90
['Oxymorphone'] => ['Buprenorphine'] conf:0.90
['Methadone', 'Tramadol'] => ['Heroin'] conf:0.90
['Oxymorphone', 'Tramadol'] => ['Morphine'] conf:0.90
['Oxycodone', 'Tramadol'] => ['Buprenorphine'] conf:0.90
['Codeine'] => ['Buprenorphine'] conf:0.90
['Fentanyl', 'Hydromorphone'] => ['Morphine'] conf:0.90
['Codeine'] => ['Hydrocodone', 'Heroin'] conf:0.90
['Oxymorphone', 'Morphine'] => ['Heroin'] conf:0.90
['Hydromorphone', 'Morphine'] => ['Buprenorphine'] conf:0.90
['Methadone', 'Oxymorphone'] => ['Morphine'] conf:0.90
['Fentanyl'] => ['Hydrocodone'] conf:0.90
['Codeine', 'Tramadol'] => ['Morphine'] conf:0.90
['Fentanyl', 'Heroin'] => ['Hydrocodone'] conf:0.90
['Oxycodone'] => ['Hydrocodone'] conf:0.90Predict
We use these strong rules to identify if there is any possible locations where specific opioid use might have started in each of the five states using data in 2017. The result is about 20,000, so we filtered out the substances that had already appeared in history but didn’t find them in 2017. And below is our result.
The chart above is results number with its confidence.
FIPS_Combined already find substance [/latex]gt; predict conference has been appeared
54093 ['Hydrocodone', 'Buprenorphine'] [/latex]gt; ['Oxycodone'] conf:0.98 [False]
21165 ['Fentanyl', 'Buprenorphine'] [/latex]gt; ['Heroin'] conf:0.97 [False]
54093 ['Buprenorphine'] [/latex]gt; ['Oxycodone'] conf:0.95 [False]
21165 ['Fentanyl'] [/latex]gt; ['Heroin'] conf:0.95 [False]
51820 ['Codeine', 'Fentanyl'] [/latex]gt; ['Buprenorphine'] conf:0.95 [False]
21171 ['Codeine', 'Fentanyl'] [/latex]gt; ['Buprenorphine'] conf:0.95 [False]
54093 ['Hydrocodone'] [/latex]gt; ['Oxycodone'] conf:0.94 [False]
51580 ['Hydrocodone'] [/latex]gt; ['Oxycodone'] conf:0.94 [False]
51620 ['Hydrocodone'] [/latex]gt; ['Oxycodone'] conf:0.94 [False]
21171 ['Codeine', 'Morphine'] [/latex]gt; ['Buprenorphine'] conf:0.93 [False]
21171 ['Fentanyl', 'Morphine'] [/latex]gt; ['Buprenorphine'] conf:0.93 [False]
51520 ['Tramadol', 'Oxymorphone'] [/latex]gt; ['Heroin'] conf:0.92 [False]
21171 ['Codeine', 'Heroin'] [/latex]gt; ['Buprenorphine'] conf:0.92 [False]
51820 ['Codeine', 'Heroin'] [/latex]gt; ['Buprenorphine'] conf:0.92 [False]
51820 ['Codeine', 'Oxycodone'] [/latex]gt; ['Buprenorphine'] conf:0.91 [False]
21171 ['Codeine', 'Oxycodone'] [/latex]gt; ['Buprenorphine'] conf:0.91 [False]
21171 ['Codeine', 'Hydrocodone'] [/latex]gt; ['Buprenorphine'] conf:0.91 [False]
21165 ['Fentanyl'] [/latex]gt; ['Oxycodone', 'Heroin'] conf:0.90 [True, False]
51520 ['Oxymorphone', 'Buprenorphine'] [/latex]gt; ['Heroin'] conf:0.90 [False]
21053 ['Tramadol', 'Buprenorphine'] [/latex]gt; ['Heroin'] conf:0.90 [False]
51520 ['Tramadol', 'Buprenorphine'] [/latex]gt; ['Heroin'] conf:0.90 [False]Model 2
我们将各个county的统计数据与其毒品检出数量进行关联，然后使用神经网络进行拟合，得到统计数据中每个特征的权重，取前30个。通过多次神经网络的训练，我们获取出现频次最多的特征，将其按平均值分为两种类型LOW和HIGH，并将其添加到前文的模型，得到了新的关联规则。例如：
[Oxycodone HC01_VC186_LOW] [/latex]gt; [Hydrocodone] conf:94
[Hydrocodone HC01_VC186_LOW] [/latex]gt; [Oxycodone] conf:97.8
