Overdose Statistics

The mean rate of overdose is 30.69 per 100,000.

The mean rate of unemployment is 4.06%

The data is likely skewed to the right since the max is 22 times larger than the mean.

Overdose Statistics
Overall (N=2160)
Overdose Rate
   Mean (SD) 30.691 (32.076)
   Range 1.535 - 686.813
Unemployment Rate
   Mean (SD) 4.059 (1.375)
   Range 1.600 - 21.100
Located in Rural Community
   Mean (SD) 0.579 (0.494)
   Range 0.000 - 1.000

Unemployment is a valid proxy for economic stress since the vast majority of people depend on employment for economic stability while some people may have saving to cover lay offs burning these reserves is in and of itself a form of economic stress.

The relationship between drug overdose and unemployment appears to be linear with an positive relationship.

This model has temporal precedence concerns since it assumes that higher rates of unemployment proceeds higher overdose rates. However,the inverse is just as plausible e.g., a community experiences a wave of drug overdoses causing people with skills and jobs to leave in effect raising the overall unemployment rate.

If rural status was omitted it would confound the model and introduce OVB because rural and non-rural communities have different employment patterns and health out-comes.

I think this model suffers from OVB since it does not consider access to health care. Certain communities may have a large number of non fatal overdoses due to access to healthcare while other community’s may have a relatively low number of total overdoses with most being fatal due to poor access to health care. I think the rural portion of model trys to speak to this disparity but does not fully address it.

Exploring the Effect of Unemployement on Fatal Overdose Rates

I believe we will find a significant, but linear relationship between the unemployment rate and overdose rates.

H0, B1 = 0 ; unemployment has no effect on OD rates H1, B1 =/= 0 ; unemployment has an effect on OD rates H0, B2 = 0 ; the relationship between unemployment and OD rates is linear.
H1, B2 =/= 0; the relationship between unemployment and OD rates is non-linear.

I expect B1 to be positive and and B2 to be positive since the scatter plot did not show any U-like features.

Based on the scatter plot I expect a strong linear relationship, so I expect B1 to be >0 and B2 to be close to 0 or negative.

## # A tibble: 4 × 7
##   term              estimate std_error statistic p_value lower_ci upper_ci
##   <chr>                <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
## 1 intercept           22.9        3.55     6.45    0       15.9     29.8  
## 2 unemployment        -0.099      1.27    -0.078   0.938   -2.60     2.4  
## 3 I(unemployment^2)    0.06       0.1      0.596   0.551   -0.137    0.257
## 4 rural               12.3        1.41     8.74    0        9.54    15.1

A one unit increase in unemployment is associated with a 0.388 increase in ODs per 100k.

At an unemployment rate of 0.825 the fatal drug overdose rate is minimized.

We fail to reject both B1 and B2.

The range of plausible values for B1 are -2.60 to 2.40 The range of plausible values for B2 are -0,137 to 0.257

No the results do not have practical significance because the range of plausible values for both B1 and B2 are so wide and the estimate is small relative to the data set.

The estimate for rural status is 12.3 meaning rural areas have a fatal overdose rate 12.3 units higher than non-rural communities.

Altnative Testing

## # A tibble: 3 × 7
##   term         estimate std_error statistic p_value lower_ci upper_ci
##   <chr>           <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
## 1 intercept       2.78      0.048     58.0        0    2.69     2.88 
## 2 unemployment    0.042     0.011      3.75       0    0.02     0.064
## 3 rural           0.327     0.031     10.5        0    0.266    0.388

A one unit increase in the unemployment rate is associated with a 4.2% increase in the fatal overdose rate.

Yes, the unemployment rate estimate is statistically significant since the P-value = 0.

The unemployment rate is not practically significant since this is a small increase in absolute terms and there may be other variables that better explain the increase than economic distress.

Conclusion

I would prefer the log level model since it reports unemployment as significant and better matches the more linear relationship shown in the scatter plot. The quadratic model does not show a significant relationship between the unemployment rate and the fatal overdose rate. Moreover the quadratic model shows a positive B2 going against the inverted U-theory.

The 2 unit increase in the unemployment rate could lead to a 8.4% increase in the mortal overdoses. However, the this is moderate confidence assumption due to the risk of OVB, and since this is a larger suburban or urban community there may be more robust access to healthcare that would diminish the expected increase in fatal overdoses.

Currently, the county spends 1,000 USD per death with an increase of 8.4% we would expect 10.5 additional overdoses, so the County should allocate an additional 10,500 USD to the program. Overall,to maintain the same efficacy rate the county should put forward a budget of 135,500 USD.