description and analysis some adj
TRANSCRIPT
Erin Dinkel
ECO4935
November 6, 2016
Description and Analysis Paper
I INTRODUCTION
Healthcare has been a debated topic for some time, especially when it comes to the health
of children. Programs have been put in place in an attempt to provide children with healthcare,
such as the Children’s Health Insurance Program (CHIP), Medicaid, Obamacare, or private
health insurance.1 The assumption is that families that cannot afford health insurance for their
children would not be able to afford any surgeries as well, thus showing a positive relationship.
This study will attempt to find a correlation between the number of pediatric surgeries performed
and the percentage of children who are insured by Medicaid in comparison to those insured with
private insurance. The hypothesis is that in pediatric surgical areas, with a higher percentage of
children insured by Medicaid, there will be more pediatric surgeries performed. The study will
only be conducted through data collected from northern New England, thus the information
cannot be generalizable for all of the country. However, it will give a glimpse into relationships
between children’s healthcare and other variables.
II SAMPLE
The sample was taken from a study of pediatric surgical areas in the northern New
England region, by The Dartmouth Atlas of Health Care.2 The sample consists of thirty-one
pediatric surgical areas in the northern New England Region, including Maine, New Hampshire,
and Vermont. The sample contains information on geography, demographics, physician
1 KidsHealth from Nemours- How to Find Affordable Healthcare2 The Dartmouth Atlas of Children’s Health Care in Northern New England
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workforce, and surgeries. Additionally, there is data on whether or not Medicaid or private
insurance was used for surgery in each pediatric surgery area, as well as, Census data on the
number of people with a bachelor’s degree or higher3 and the percent of the black population.4
III DEPENDENT VARIABLE
Total Amount of Tympanostomy Surgeries
The dependent variable is the amount of tympanostomy surgeries that are done, per 1,000
children, in each of the hospitals studied. This surgery is the placement of a tube in the tympanic
membrane to equalize the pressure. This is done to treat ear fluid that builds up in the inner ear,
which can lead to “otitis media” as well as loss of hearing.5 This surgery is being considered as a
variable in the study because otitis media is the most common diagnosis among children and is
the second most common diagnosis in medicine in general.6 For this reason a proportionately
high or low number of these surgeries compared to the population could potentially show a
correlation between the two variables.
Typanostomy surgeries can become a necessity for children who experience frequent ear
infections. Ear infections can be either viral or bacterial. The infection causes swelling in the
middle ear, preventing air from the throat to reach the ear. This blockage can create a vacuum
which brings in fluid from the nose into the middle ear area, and is unable to be drained from the
swollen tube.7 Treatment for ear infections can be antibiotics, if it is bacterial, or simply waiting
until it passes, if it is viral. If frequent ear infections continue, tympanostomy surgery is
necessary. The tube placed in the ear during the surgery can be temporary, in which the tube will
3 U. S. Census Bureau, Bachelor's degree or higher, percent of persons age 25 years+, 2010-20144 U.S. Census Bureau, 2010 Census of Population Black or African American alone, percent, April 1, 20105 Medscape- Ear Tube Insertion6 A Report of the Dartmouth Atlas Project- Typanostomy Tube Placement7 Ear Infections Cause- WebMD
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fall out naturally within 6 months, or long-term, in which the tubes should be removed after a
longer period.8
IV INDEPENDENT VARIABLES
Percent of Children in Poverty (POV)
One independent variable is of the percentage of children living in poverty in the
specified pediatric surgical area. This variable will be an indicator if the children in this
neighborhood are insured with healthcare or not. Studying this variable in comparison to the
number in surgeries will give some indication if there is a relationship between the two. The
Affordable Care Act implemented an expansion of Medicaid in order to extend coverage to low-
income Americans. In a 2012 study, it was found that 63% of the people at the federal poverty
line (FPL) were eligible, and in eighteen states the thresholds for Medicaid were at or above the
FPL.9
Additionally, poverty can have an impact on the need for typanostomy surgery. Ear
infections can be caused by bacteria or a virus. Children living in poverty may be exposed to less
sanitary conditions, which could introduce them to more bacteria for potential ear infections.
Moreover, bacterial ear infections can only be treated with antibiotics. Meaning, children in
poverty may not have the means to afford antibiotics and will not be properly treated and
therefore be prone to more frequent ear infections.
Type of Insurance (INS)
8 Ear Tubes- American Academy of Otolaryngology9 Medicaid Expansions from 1997 to 2009 Increased Coverage and Improved Access and Mental Health Outcomes for Low-Income Parents.
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The type of insurance used will be another independent variable. It is intuitive that this
variable be measured in conjunction with the number of surgeries done to determine if there is a
strong correlation between the two. For children who are hospitalized, Medicaid is the largest
payer, and it can account for 40% of hospital discharges on a national scale.10 This will be
measured using a dummy variable. It is important to note that there is some data missing as to
the exact number of surgeries that use Medicaid or private insurance, however this is a small
amount of surgeries. If Medicaid is used in the pediatric surgery area, then it was assigned a
value of 1. If private insurance was used in the pediatric surgery area, then a value of 0 was
assigned.
Physician Workforce (PHY)
The physician’s work force in each area will be measured as an independent variable as
well. The data measures this variable as the number of Otolaryngologists (ear, nose, and throat
physicians) per 100,000 children and adults. This is important to consider because it could be a
factor in why there are a lot or little surgeries. For the purposes of this study we will assume that
the number of doctors in an area will have some affect as to the number of surgeries that are
performed as well.
Percent of Black Population (BLK)
This variable is being used to control for demographics differences. This variable will
show if the demographics have a strong correlation with the amount of surgeries. The hypothesis
is that it will not be significant as the amount of surgeries will be largely correlated with income
and type of insurance, rather than demographics.
Percent of Bachelor’s Degree or Higher (BA)
10 Medicaid, Hospital financial stress, and the Incidence of Adverse Medical Events for Children
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Similarly, this variable of percent of Bachelor’s Degrees of higher will be used to control
for demographic differences. The hypothesis for this variable is that people who receive a
Bachelor’s Degree or higher tend to earn higher wages, and can therefore afford other forms of
health insurance other than Medicaid, typically private insurance.
V RESULTS
With such a small sample size with the number of variables I wish to study, I intend to
run multiple regressions in order to test how certain variables will affect the results. For the first
regression I will include all of the variables and use the following model.
Tympanostomies=0+1(POV)+2(INS)+3(PHY)+4(BLK)+5(EDU)+E
This regression model resulted in the following relationship between the number of
tympanostomy surgeries per 1,000 and the variables.
Tympanostomies=10.056-.253(POV)+3.389(INS)+.467(PHY)-.063(BLK)-.060(EDU)
+E
For this regression, the adjusted R-Squared value demonstrates that 31% of the
tympanostomy surgeries per 1,000 are congruent with this model. Consequently, the presence of
Medicaid is expected to increase the amount of tympanostomy surgeries by 3.389 per 1,000 as
compared to private insurance.
In this study the null hypothesis is that 2=0, meaning that the presence of Medicaid as
compared with private insurance has no effect on the number of pediatric tympanostomy
surgeries performed. In this regression, the p-value for Insurance was .0002. This value is less
than .05, meaning I can reject the null hypothesis at the 95% confidence level. This value is also
less than .01, meaning that I can also reject the null hypothesis at the 99% confidence level.
Variable Coefficients P-valueIntercept 10.05602108 0.000752641
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Insurance 3.389285714 0.00015289Otolaryngologists 0.467175077 0.045102065Black -0.063452297 0.233765409% with BA -0.060317864 0.305334699% children in poverty -0.253043096 0.030178483
As for the other variables, the number or pediatric surgeons available present a p-value of
.045, which is less than .05, meaning that I can reject the null hypothesis at the 95% confidence
level. However, .045 >.01, meaning I cannot reject the null hypothesis at the 99% level as with
the Insurance variable. As expected, more surgeons are associated with more surgeries, since
more doctors available can perform more surgeries. For percent black, .234 >.05, so I cannot
reject the null hypothesis. This is not surprising, as the hypothesis presumes that the surgeries
would have a higher correlation with income and insurance rather than demographics. For
percent with a bachelor’s degree, .305 >.05, so I cannot reject the null hypothesis. This is
expected because, the hypothesis is that people with bachelor’s degrees earn a higher income and
can therefore afford private insurance and not Medicaid. Finally, for percent of children in
poverty .03 < .05, so I can reject the null hypothesis with 95% confidence. This is also expected
having a higher percent of children in poverty is associated with a lower percent of surgeries.
This is expected if children who are poor have less access to medicine and surgeries.
This model suggests that, with the significant variables (Insurance and Poverty), the
amount of tympanostomy surgeries would increase by 3.4 per 1,000 for every percentage
increase for those with Medicaid compared to those with private insurance, and decrease by .25
per 1,000 for every percentage increase in poverty. Both are at least significant at the 95%
confidence level; the Insurance variable is also significant at the 99% confidence level.
A note should be made about this regression that there is a possibility of multicollinearity
between the Insurance variable and the percent of children in poverty. It is known that many of
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the families that receive Medicaid, do so because they live at or below the poverty line. This can
also affect the amount of pediatric surgeries that occur as well. For this reason, I tested the
correlation coefficient of all the variables.
Insurance% children in
poverty Black % with BA Otolaryngologists Insurance 1% children in poverty -2.40692E-17 1Black -6.66912E-18 0.050726965 1% with BA 0 -0.580147263 0.236587343 1Otolaryngologists 7.35437E-18 -0.282722946 0.136771418 0.535800828 1
The above chart demonstrates that variables are not correlated because their correlation
coefficient’s absolute value is less than 0.8. For this reason, I have decided not to run separate
regression with each of these variables. At first glance it may seem odd that there is such an
extremely small correlation coefficient between the insurance and children in poverty. This is
because the insurance variable is a dummy. This means that the variable is the presence of
Medicaid compared to private insurance, which is why the correlation coefficient seems much
lower than expected.
The next regression will omit the percent of the black population variable and will use the
following model.
Tympanostomies=0+1(POV)+2(INS)+3(PHY)+5(EDU)+E
Following this regression model resulted in the following relationship between the
number of tympanostomy surgeries per 1,000 and the variables, omitting the percent of the black
population.
Tympanostomies=10.648-.277(POV)+3.397(INS)+.471(PHY)-.077(EDU)+E
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For this regressions the adjusted R-Squared value demonstrates that 31% of the tympanostomy
surgeries per 1,000 are congruent with this model. Consequently, the presence of Insurance is
expected to increase the amount of tympanostomy surgeries by 3.397 per 1,000.
Similarly, as before, the null hypothesis is that 2=0. In this regression, the p-value for
Insurance was .00009. This value is less than .05, meaning I can reject the null hypothesis at the
95% confidence level. This value is also less than .01, meaning that I can also reject the null
hypothesis at the 99% confidence level. As expected this is due to the fact that the presence of
Medicaid compared to private insurance makes it more affordable to get surgery for families who
are of lower income.
Variable Coefficients P-valueIntercept 10.6475147 9.39713E-05Insurance 3.396551724 9.05792E-05Otolaryngologists 0.470723546 0.040140048% with BA -0.076738905 0.156567176% children in poverty -0.277370519 0.011031707
As for the other variables, the number or pediatric surgeons available present a p-value of
.040, which is less than .05, meaning that I can reject the null hypothesis at the 95% confidence
level. However, .04 >.01, meaning I cannot reject the null hypothesis at the 99% level as with the
Insurance variable. As expected, more surgeons are associated with more surgeries, since more
doctors available can perform more surgeries.
For percent with a bachelor’s degree, .157 >.05, so I cannot reject the null hypothesis.
This is expected because, the hypothesis is that people with bachelor’s degrees earn a higher
income and can therefore afford private insurance and not Medicaid. Finally, for percent of
children in poverty .011 < .05, so I can reject the null hypothesis with 95% confidence. This is
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also expected having a higher percent of children in poverty is associated with a lower percent of
surgeries. This is expected if children who are poor have less access to medicine and surgeries.
This model suggests that, with the significant variables (Insurance, Poverty, and
Surgeons), the amount of tympanostomy surgeries would increase by 3.4 per 1,000 for every
percentage increase for those with Medicaid compared to those with private insurance, decrease
by .27 per 1,000 for every percentage increase in poverty, and increase by .47 per 1,000 for every
percentage increase in pediatric surgeons. Each of these are at least significant at the 95%
confidence level, the Insurance variable is also significant at the 99% confidence level.
I will then run the regression including the black population variable and excluding the
percent of bachelor degrees or higher, and will use the following model.
Typanostomies=0+1(POV)+2(INS)+3(PHY)+4(BLK)+E
Following this regression model resulted in the following relationship between the
number of tympanostomy surgeries per 1,000 and the variables, omitting the percent of people
with bachelor degrees or higher.
Tympanostomies=7.762-.187(POV)+3.389(INS)+.360(PHY)-.079(BLK)+E
For this regressions the adjusted R-Squared value demonstrates that 31% of the
tympanostomy surgeries per 1,000 are congruent with this model. Consequently, the presence of
Medicaid as compared to private insurance is expected to increase the amount of tympanostomy
surgeries by 3.389 per 1,000.
The null hypothesis is that 2=0. In this regression, the p-value for Insurance was .0002.
This value is less than .05, meaning I can reject the null hypothesis at the 95% confidence level.
This value is also less than .01, meaning that I can also reject the null hypothesis at the 99%
confidence level. This is expected for the same reasons stated earlier.
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Variable Coefficients P-valueIntercept 7.761585728 3.64449E-05Insurance 3.389285714 0.000151109Otolaryngologists 0.360139158 0.081442565Black -0.079269423 0.122069654% children in poverty -0.187164196 0.051735945
As for the other variables, the number or pediatric surgeons available present a p-value of
.081, which is greater than .05, meaning that I cannot reject the null hypothesis. This is different
from the other regressions which showed it as significant, and is not expected. This may be
because the bachelor’s degree variable has been taken out and therefore doesn’t account for the
surgeons who do have a bachelor’s degree. For the percent of black population variable, the p-
value is .122, which is greater than .05, meaning I cannot reject the null hypothesis. This is not
surprising, as the hypothesis presumes that the surgeries would have a higher correlation with
income and insurance rather than demographics.
Finally, for percent of children in poverty .051 > .05, so I cannot reject the null
hypothesis with 95% confidence, however I can reject it with 90% confidence. This is expected
for the same intuition that was stated earlier. Only Insurance was significant in this regression at
the 95%, although the percent of children in poverty was also significant with 90% confidence.
This model suggests that, with the significant variable (Insurance), the amount of
tympanostomy surgeries would increase by 3.4 per 1,000 for every percentage increase for those
with Medicaid compared to those with private insurance. This is the only variable that was
significant with 95% confidence.
Finally, I will run the regression using neither the percent black population variable nor
the percent of bachelor’s degrees of higher variable, using the following model.
Tympanostomies=0+1(POV)+2(INS)+3(PHY)+E
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Following this regression model resulted in the following relationship between the
number of tympanostomy surgeries per 1,000 and the variables, omitting the percent of people
with bachelor degrees or higher and the percent of the black population.
Tympanostomies=7.897-.202(POV)+3.397(INS)+.308(PHY)+E
For this regressions the adjusted R-Squared value demonstrates that 30% of the
tympanostomy surgeries per 1,000 are congruent with this model. Consequently, the presence of
Medicaid is expected to increase the amount of tympanostomy surgeries by 3.397 per 1,000
compared to private insurance.
The null hypothesis is that 2=0. In this regression, the p-value for Insurance was .0001.
This value is less than .05, meaning I can reject the null hypothesis at the 95% confidence level.
This value is also less than .01, meaning that I can also reject the null hypothesis at the 99%
confidence level. Again, this result is expected as in the other regressions.
Variables Coefficients P-valueIntercept 7.896801126 1.41572E-05Insurance 3.396551724 0.000101701Otolaryngologists 0.308004382 0.119790791% children in poverty -0.201692627 0.032828091
As for the other variables, the number or pediatric surgeons available present a p-value of
.120, which is greater than .05, meaning that I cannot reject the null hypothesis. This is not an
expected result and could be due to the limited number of variables in this regression. For the
percent of children in poverty .033 < .05, so I can reject the null hypothesis with 95%
confidence. This is expected as in the other regressions. So, Insurance and the percent of children
in poverty were significant in this regression.
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This model suggests that, with the significant variable (Insurance and Poverty), the
amount of tympanostomy surgeries would increase by 3.4 per 1,000 for every percentage
increase for those with Medicaid compared to those with private insurance and increase by 0.2
per 1,000 for every percentage decrease in poverty. Both variables were significant with 95%
confidence, and Insurance was also significant with 99% confidence.
With each of the variations of regressions, it was found to be consistent that the Insurance
variable was significant and we can reject the null hypothesis with 99% confidence. This
supports my hypothesis that the presence of Medicaid is highly correlated with the number of
pediatric surgeries as compared to the presence of private insurance. Presumably this is due to
the fact that the presence of Medicaid makes it more affordable to get surgery for families who
are of lower income. Although it is a possibility that there is some multicollinearity between the
presence of Medicaid and the percent of children in poverty, through the correlation coefficient it
was shown that it was not correlated enough to be of concern for this study. However, it is also
important to recognize that this study was conducted with a small sample, meaning the results
are not completely generalizable. Nonetheless the results still demonstrate a strong correlation, at
the 99% confidence level, between Medicaid as compared with private insurance and pediatric
surgery, as well as a correlation with the percent of children living in poverty, which rejected the
null hypothesis at the 95% confidence level.
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Typanostomy Insurance Otolaryngologists Mean 8.151785714 Mean 0.5 Mean 3.835714286Standard Error 0.498868792 Standard Error 0.067419986 Standard Error 0.290794127Median 7.7 Median 0.5 MedianMode 7.5 Mode 0 ModeStandard Deviation 3.733192203 Standard Deviation 0.504524979 Standard Deviation 2.176103989Sample Variance 13.93672403 Sample Variance 0.254545455 Sample Variance 4.735428571Kurtosis 4.953731858 Kurtosis -2.075471698 Kurtosis 7.07892278Skewness 1.575803011 Skewness 2.93069E-17 Skewness 2.125859571Range 21.7 Range 1 RangeMinimum 2.5 Minimum 0 MinimumMaximum 24.2 Maximum 1 MaximumSum 456.5 Sum 28 SumCount 56 Count 56 Count
Black % with BA % children in poverty Mean 3.196428571 Mean 31.48928571 Mean 12.99636786Standard Error 1.122355374 Standard Error 1.396662717 Standard Error 0.621965694Median 1.1 Median 29.55 Median 12.83515Mode 0.6 Mode 45.6 ModeStandard Deviation 8.398938554 Standard Deviation 10.45166674 Standard Deviation 4.654365066Sample Variance 70.54216883 Sample Variance 109.2373377 Sample Variance 21.66311417Kurtosis 23.19114773 Kurtosis -0.946948239 Kurtosis -0.630265979Skewness 4.847194847 Skewness 0.05316005 Skewness 0.187193226Range 45.2 Range 38.3 RangeMinimum 0.4 Minimum 10.8 MinimumMaximum 45.6 Maximum 49.1 MaximumSum 179 Sum 1763.4 Sum 727.7966Count 56 Count 56 Count
Descriptive Statistics
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Regression for All Variables: Typanostomies=0+1(POV)+2(INS)+3(PHY)+4(BLK)
+5(EDU)+E
Regression StatisticsMultiple R 0.612549269R Square 0.375216606Adjusted R Square 0.312738267Standard Error 3.094863019Observations 56
ANOVA df SS MS F Significance F
Regression 5 287.6109662 57.52219323 6.005547047 0.000199823Residual 50 478.9088553 9.578177105Total 55 766.5198214
Variables Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 10.05602108 2.801156852 3.589952869 0.000752641 4.429731957 15.6823102Insurance 3.389285714 0.827136934 4.097611381 0.00015289 1.727932289 5.05063914Otolaryngologists 0.467175077 0.227313689 2.05519993 0.045102065 0.010602096 0.923748059Black -0.063452297 0.052644906 -1.205288458 0.233765409 -0.169192702 0.042288108% with BA -0.060317864 0.058239873 -1.035679865 0.305334699 -0.177296091 0.056660364% children in poverty -0.253043096 0.113408641 -2.231250576 0.030178483 -0.480831056 -0.025255136
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Regression without black population
Typanostomies=0+1(POV)+2(INS)+3(PHY)+5(EDU)+E
Regression StatisticsMultiple R 0.601104236R Square 0.361326302Adjusted R Square 0.313124514Standard Error 3.052057647Observations 58
ANOVA df SS MS F Significance F
Regression 4 279.3070384 69.82675961 7.496118169 7.31443E-05Residual 53 493.6979616 9.315055878Total 57 773.005
Variables Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 10.6475147 2.519157917 4.226616613 9.39713E-05 5.594723798 15.7003056Insurance 3.396551724 0.801509605 4.237693102 9.05792E-05 1.788927044 5.004176404Otolaryngologists 0.470723546 0.223728626 2.10399337 0.040140048 0.02198075 0.919466341% with BA -0.076738905 0.053398436 -1.437100251 0.156567176 -0.183842604 0.030364793% children in poverty -0.277370519 0.105296712 -2.634180245 0.011031707 -0.488568978 -0.06617206
Regression without bachelor’s degrees
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Typanostomies=0+1(POV)+2(INS)+3(PHY)+4(BLK)+E
Regression StatisticsMultiple R 0.601509221R Square 0.361813343Adjusted R Square 0.311759488Standard Error 3.097066044Observations 56
ANOVA df SS MS F Significance F
Regression 4 277.3370994 69.33427485 7.228481011 0.000108613Residual 51 489.182722 9.591818079Total 55 766.5198214
Variables Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 7.761585728 1.715432758 4.524564249 3.64449E-05 4.317710764 11.20546069Insurance 3.389285714 0.827725717 4.094696642 0.000151109 1.727556998 5.05101443Otolaryngologists 0.360139158 0.202605495 1.777538946 0.081442565 -0.046608346 0.766886662Black -0.079269423 0.050416867 -1.572279842 0.122069654 -0.180485506 0.02194666% children in poverty -0.187164196 0.093957053 -1.992018575 0.051735945 -0.375790851 0.00146246
Regression without black population or bachelor’s degrees
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Typanostomies=0+1(POV)+2(INS)+3(PHY)+E
Regression StatisticsMultiple R 0.580033646R Square 0.336439031Adjusted R Square 0.299574532Standard Error 3.082014574Observations 58
ANOVA df SS MS F Significance F
Regression 3 260.0690529 86.68968429 9.126369438 5.53228E-05Residual 54 512.9359471 9.498813836Total 57 773.005
Variables Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 7.896801126 1.653904991 4.774640121 1.41572E-05 4.580921265 11.21268099Insurance 3.396551724 0.80937668 4.196503075 0.000101701 1.773849183 5.019254265Otolaryngologists 0.308004382 0.194855237 1.580683112 0.119790791 -0.082656846 0.698665611% children in poverty -0.201692627 0.092077815 -2.190458432 0.032828091 -0.386297532 -0.017087722
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