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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Indemnity Benefit Duration and Obesity
Presented by:
Chris Laws
Ratemaking and Product Management (RPM) SeminarMarch 11-13, 2013Huntington Beach, CA
© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Overview
Objective
Modeling Duration
Previous Research
The Data
Findings
Conclusion
Appendix2013, eForum, forthcoming, http://www.casact.org/pubs/forum/The paper is available at https://www.ncci.com/nccimain/IndustryInformation/ResearchOutlook/Pages/IndemnityBenefitDuration-Obesity.aspx
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Objective
Measure the indemnity benefit duration of claims with
obesity diagnoses relative to otherwise similar claims
Research design
Use a matched-pairs methodology that compares
“obese” claims to “non-obese” claims
Descriptive approach (Kaplan-Meier estimator)
Statistical approach (Bayesian semi-parametric Weibull
proportional hazard model)
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Findings
The application of a statistical framework for the
measurement of indemnity duration was pioneered
The indemnity duration for a claim categorized as “obese” is
5 times as long as an otherwise comparable claim
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Statistical Modeling of Duration
The duration of claims may be censored
Censoring occurs when the duration is only partially
known
Interval-Censored
The duration falls into a given interval
Example: Claims that did not breach the waiting period
Right-Censored
The duration is only known to be greater than a certain value
Example: Claims with ongoing indemnity payments
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Statistical Modeling of Duration
Any given set of claim durations may exhibit two mutually
exclusive types of censored claims, alongside uncensored
claims
Statistical models have been developed that are capable of
handling both interval-censored and right-censored data (*)
Advantages of statistical modeling
The effect of covariates (such as obesity) on the average (mean)
duration can be quantified
The model accounts for the possibility that a lengthening of duration
causes more claims to breach the waiting period
* See the appendix for computer code that handles both interval-censoring and right-censoring
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Previous Research
Studies by Duke University (2007), Johns Hopkins University
(2007/2008), and NCCI (2010) show that obesity contributes to
the cost of workers compensation
On the other hand, a recent study by the Liberty Mutual Research
Institute for Safety (2012) finds no effect of obesity on recovery
and return to work following onset of work-related low back
pain (*)
* Shaw, William S., Torill H. Tveito, Mary Jane Woiszwillo, and Glenn Pransky, “The Effect of Body Mass Index on Recovery and Return to Work Following Onset of Work-Related Low Back Pain,” Journal of Occupational and Environmental Medicine, 2012, forthcoming
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Previous ResearchDuke University
Duke University studied a cohort of 11,728 own health care and university employees over the period 1/1/1997 through 12/31/2004
Claimants in the highest obesity category (category III) lost 13 times more days from work injury or work-related illness as employees within the ideal body mass index (BMI 18.5-24.9); in part, this is due to the obese workers being twice as likely to sustain a workplace injury
Source: Østbye, Truls, John M. Dement, and Katrina M. Krause (2007) “Obesity and Workers’ Compensation: Results from the Duke Health and Safety Surveillance System,” Archives of Internal Medicine 167, 766-773
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Previous ResearchJohns Hopkins University
Johns Hopkins University studied a cohort of 7,690 hourly employees of a large, multi-site U.S. aluminum manufacturing company over the period 1/1/2002 through 12/31/2004—approximately 85 percent of injured workers were classified as overweight or obese
The odds of injury in the highest obesity category (category III) as compared with the ideal BMI category (18.5-24.9) were 2.21:1 (after adjusting for confounders, such as sex, age, education, physical demands of the job, time since hire, time in the job, and so on)
Injuries to the leg or knee were especially prevalent among members in obesity category III
Source: Pollack, Keshia M., Gary S. Sorock, Martin D. Slade, Linda Cantley, Kanta Sircar, Oyebode Taiwo, and Mark R. Cullen (2007/2008) “Association between Body Mass Index and Acute Traumatic Workplace Injury in Hourly Manufacturing Employees” (with discussion), American Journal of Epidemiology 166, 204-211 & 167, 123-124
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Previous ResearchNCCI
In 2010, NCCI studied medical claims
provided by carriers over injury years 1997
through 2006 in 36 states
Matching obese to non-obese claims with
maturities of 12, 36, and 60 months
The study shows that, in the aggregate,
obese claims are 2.8 times more expensive
than non-obese claims at the 12-month
maturity; this cost difference climbs to a
factor of 4.5 at the three-year maturity
and to 5.3 at the five-year maturity,
possibly due to differences in duration
between obese and non-obese claims
Source: http://www.ncci.com/documents/research-age-of-obesity.pdf
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Obese vs. Non-Obese Medical Claim Cost Development Over Time
NCCI research shows that cumulative medial payments for obese claims continued to grow at a faster pace than non-obese claims, with significantly increased costs at 12, 36, and 60 months
12 Months 36 Months 60 Months
3.0
3.5
4.0
4.5
5.0
5.5
Maturity
Rat
io o
f Tot
al D
olla
rs
© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Related ResearchNCCI
In 2012, NCCI expanded its 2010 study to
look at additional indicators of comorbidity and
provide additional information related to these diagnoses
This study found that
Claims with a comorbidity diagnosis have about twice the
medical costs of otherwise comparable claims
The share of workers compensation claims with a comorbidity
diagnosis nearly tripled from Accident Year 2000 to
Accident Year 2009, growing from a share of 2.4% to 6.6%Source: https://www.ncci.com/Documents/AIS-2012-Barry-Lipton_Comorbidities.pdf
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
The Data
We use a claims data set provided by insurance carriers
The data set covers injury years 1998-2008
Payment transaction dates are through 12/31/2009
The data is evaluated as of 6/30/2010, thus allowing for a reporting lag of six months
The data set comprises 40 U.S. states
AK, AL, AR, AZ, CO, CT, DC, FL, GA, HI, IA, ID, IL, IN, KS, KY, LA, MD, ME, MI, MO, MS, MT, NC, NE, NH, NM, NV, OK, OR, RI, SC, SD, TN, TX, UT, VA, VT, WI, WV
Claimants that are 15 years of age or younger are excluded
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Obese Flag
A claim is categorized as “obese” if (and only if)
for any diagnostic field (other than the primary
one) on any medical transaction that occurs
within 12 months after injury, the first three
digits of the ICD9 code equal 278
ICD9 278: Overweight, obesity, and other
hyperalimentation
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Indemnity Benefit Duration
We calculate indemnity benefit duration (duration, for short) based on recorded indemnity payment transactions
For the purpose of this study, we count the waiting period toward the indemnity benefit duration even where the retroactive period has not been reached
The transactions cover payment categories Temporary Total and Permanent Total
Any claims with transactions in the Fatal category are excluded
In a sensitivity analysis, we count transactions in the Permanent Partial category toward duration
If the claim has no indemnity transaction data, it is assumed that this claim has not breached the waiting period
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Indemnity Benefit Duration
For claims with indemnity payment transactions, benefit
duration is established by means of the concept of dormancy
Only transactions prior to the date of dormancy are considered
The date of dormancy is the first (*) transaction date that is
not followed by another transaction within 180 days
The latest date for which such a transaction-free time interval can
be established is 180 days prior to 12/31/2009 (which is the latest
transaction date considered in this study)
When no 180-day transaction-free interval can be established, the
claim is considered right-censored
* Re-opening are not accounted for
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Indemnity Benefit Duration
Duration is implemented as a calendar-time concept
Duration Concept I
Aggregation of disability days for which indemnity payment transactions indicate the claimant was compensated
If more than 20 percent of the payment transactions associated with a given claim are missing “from-date” and “through-date” (*)
information, then the claim is categorized as right-censored at the waiting period
Duration Concept II
Time interval between injury date and most recent “through-date” (*)
Payment transaction dates substitute for missing “through-dates” (*)
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* Most indemnity payment transactions record several dates. Two such dates are the “from-date” and the “through-date.” These dates record the period of time for which the claimant is being compensated.
© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Matched Pairs
We form matched pairs
An “obese” claim is paired with a “non-obese” claim, using
the claim characteristics itemized below
Injury year
State
Gender
NCCI industry group (*)
Primary ICD9 code (at the three-digit level)
Age (proximity matching)
* NCCI industry groups consist of Manufacturing, Contracting, Office and Clerical, Goods and Services, and Miscellaneous
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Immortal Time Bias
As mentioned, a claim is categorized as “obese” if this claim acquires the ICD9
code 278 within the first 12 months of inception
Allowing for a 12-month time period for acquiring the obesity flag favors long-duration
claims for inclusion in the obese category, thus introducing a survivor selection bias
that is known as immortal time bias
In order to correct for the immortal time bias, it is stipulated that a non-obese
claim be a potential match for a given obese claim only if this non-obese claim
had at least one medical transaction past the time span it took the obese claim
to acquire the ICD9 code 278
See the appendix for a simulation of the immortal time bias correction
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Descriptive StatisticsMatched Pairs
AK AL AR AZ CO CT DC FL GA HI IA ID IL IN KS KY LA MD ME MI MO MS MT NC NE NH NM NV OK OR RI SC SD TN TX UT VA VT WI WV
State
Pro
porti
on0.
000.
050.
100.
150.
200.
25
19
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Descriptive StatisticsClaims Included in Matched Pairs
16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 77 79 81
Age at Injury
Pro
porti
on0.
000
0.00
50.
010
0.01
50.
020
0.02
50.
030
0.03
5
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Kaplan-Meier Estimator
A survival curve is a graph that depicts the survival
experience of individuals
The Kaplan-Meier estimator is a simple way of
computing such a survival curve
The percentage of individuals surviving is displayed on the
time line (calendar time since injury)
The Kaplan-Meier estimator, as implemented, handles
interval-censored and right-censored data
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Kaplan-Meier EstimatorDuration Concept I
1 5 10 50 100 500 1000 5000
Duration Concept I
Days
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lllll lll ll llll ll ll llll lllll ll ll ll lll ll ll l llll lllllll l llll l lll lll ll llll llll l ll ll ll lll llllll ll lll lll lllll lll lllllll lll llll l l lll l lll lll lll ll l lllll ll lll llll ll l lll l lll lll l ll ll l lllll l lllllll lllllllll ll ll ll lll l lllll llll lll lll ll llllllllll llll lllll llll llllllll ll ll ll ll ll lll ll ll l llll l ll ll lll l ll llll l llll lll llllllll ll lll lll lll lll lllllllllll lllll llll llll lll ll l ll lll lll llll l lllll l lll lll lll l ll lll l llll lll ll ll ll llll llll ll l lll l ll llllll lll ll lll lllll ll lllllll l lllll llll ll ll llll lll llllllll lllll ll ll lll ll ll llll ll l ll lllllllllll llll lllll lll llll l lll lll ll llllll l ll lll ll lll llllllllllll llll ll ll ll llll lll ll lllll lllll lll lll l lllll ll llll l lllllll lll ll l l l lll lll lllllll lll llll llll ll lll ll ll llll ll ll ll ll ll llll llllll lll lllll ll lllll l ll lllll ll ll lll l lllll llllll l ll ll ll l l ll lll lll llll l l l lll l ll l ll ll ll llll l llll l ll llll l ll ll lllll ll l lll l ll l lll ll l l lll lll lll ll l llll l llll ll lll l ll ll ll ll ll l ll ll l ll l ll llll lll lll ll llll lllll ll lllll lll lll llllll ll ll lllllll l lll ll lll lll ll l ll ll l l llll ll ll l l ll ll ll lll lll llll lll ll ll ll ll ll lll ll l ll lll ll llll ll l ll l lll llll ll ll lll lll ll ll llll l lll lllll lll ll ll llll llll lllllllllll llll ll llll llll ll ll ll lll lllll lllll ll ll llll llllll llll ll lllllllllllll lll l llll l ll ll ll ll ll lllll lll ll lllll ll l ll ll llll lll lll lll ll lllll llll l ll l llll llllll llllllllllll lllll l llll ll l lll llll ll l llll llll ll llllllllllllll lll llll lllll lllll l lll llll lll lll llllll l lll ll llllll ll lll lll l llllll l lll llll l ll llll llll ll ll lllll l llll ll llll l l lll ll llllllllll ll llll lll llll llll llll l llllll lllll ll lllllll lll ll llll llll llllllllll lllll lll lll lllll lll lll ll ll lllllll ll l lll llll lll lll lllllllllll lllllll llll llll lll llll lll lll llll ll llllll lll llllllll lllllll llllllll lll lll lll lllll lll llll ll ll llllll ll ll llll llll lll lll llll lllllll llll llllllll lllll lllll lll llllllll ll ll llll lll lllllll l ll lll ll llll ll llllllll llll lllll ll l ll lll llllll ll lllll llll llll ll lll l lll l llll ll llll lll l ll llll ll ll l llllll llllll ll l ll llll ll llll l ll ll ll lll ll l ll lll ll lll llllll ll l lll lll ll llllll ll lll llll llllllll ll llll llll ll lllll ll llll llllll lll llll lll ll lllllllll ll lll llll ll llll llll llll lll ll lll l l ll lllllll lll ll lll lll lllllll ll ll lll lll l lll lll lllll ll ll llll llll l lll ll lll l llllll ll l lll ll lllll l lllll ll lll ll lll lll lll lll lll lll lll lll lll ll ll ll lll ll llll llll ll lllll llll lll llll llll l lllll llllll llllll l lll lll ll lll lll lllll ll lllll lll llll lllllll lll lll llll lll lll lllll llll lll lll llll llll ll llll lllll llllllllll ll ll lll lll llll llll ll l lllll llllllll lllllll ll llll l lll ll l lllll lllll llll lll lllll ll lllll llll ll lll lllll l lll ll ll lllllllllll ll llllllllll llllll l l lllll lll ll lll lll l llll ll ll ll ll ll l llllll ll llll l ll llll lll ll ll llll ll llllll l lll lllll lll lll llll ll ll lll ll l ll lll llll llllll ll ll llllll l ll l ll ll llllllll lll ll lllll lllllll lll lll l l lll lll llllll l llllll lll llllllll lllll l lll l llll ll llll ll ll ll ll ll lllll ll llll l lll l lll lll lllllll lll lll llll ll lll llll lll lll ll lllll lll ll lllll l llll llllll lll lll l llll lll l ll ll ll llll l lll ll llllll lllll lll ll ll ll llllll lllll l llll lll lll ll lll ll ll lll ll ll lll ll llll ll ll l ll l ll ll ll l ll lll lll lllll lll ll llll llll llll llll lllll lll llll l llllllll lll llllllllll lllllllll ll l lll l lllll llllll lll llll ll lll ll ll l ll l llll ll lll lllll lll lll ll l l ll lll ll lll ll ll llll l llll lll ll lllllll ll l lll ll llllll lllll l lll ll lll ll ll lll ll llll lllllll lll llllll l lll llll lll lll llll l llll llll ll l ll ll llll ll l ll lllll llllll l lll lll ll ll ll l ll lll lll llll l l lllll ll ll llll ll llll ll lll ll l lll lll lll ll lllllll llllll l lllll ll lll lll llll lll l ll llll lll ll llllllll llll ll lllll llll l llll lllll l ll ll lll lllll l ll llll lllll ll ll lll lll ll l llll ll ll ll lll ll ll lllll lll llllll lll ll llll ll ll ll lllllll l ll l lll lll llll llll ll llll llll lll llll lllll l lll llll llll lllll llll lllll ll l ll ll ll lll lll l lll ll l lllll ll lllll llll ll ll ll llll ll lll lll lll lllllllllll lllll lll llll ll lllllll llllllll llll lll lll lllllll lllllll lllll ll llll ll llllll lllll lllll llll ll ll llll ll lllllll lll ll lll llllll lllll ll lllllllll llll l lllll ll l ll llll lllll ll llll ll llll ll l ll ll ll lllll ll ll llllllll ll llllllllllllll llllll l lll ll ll ll lllll lllll ll ll l ll ll llll ll lll l ll lllll lllll l ll lll llll lllll llll ll llll lllll llll l llllllll lll lll l l lll llllll ll ll llllllll llllll ll llll lll llllll lll llll llll l ll lll lll ll lll ll ll ll l ll ll lllllll ll l llll ll l llll l llll lllll ll lll lll l ll ll lll ll ll lll l ll ll lll lllll l lll l lllll l lllll lll ll ll l llllllll lll llll lllll lll lll ll lllll lllll lllll l lllll lll llll l ll ll ll lllll ll lll llllllllll lll l lll lll lll llllll lllll llll lll lll ll lllll lllll lll ll ll lll lll ll l lll llll l llll ll ll lllll llllllll ll ll lllllll lll lll llll l llllll lll llll lll lll lll ll ll lll llll ll l ll ll lll lll ll lll llllllll llllll l ll ll lll ll llllllll l ll lllll llll lll llll l ll ll llll ll llllll lllllllllllll lllllll ll lllllllllll lll ll lll ll lll lllllllll lllllll lllllll lllll lllll lll ll llll ll ll lll ll l llll lllll l ll llll ll ll ll llllll llllllll lll lll llll llllllllll llll ll l lll lllllll lll ll llllll ll l ll lll ll llll l lll llllllll llllll lll llll lllll l llll l lll ll lllll ll llll ll llllll lll l ll l llllll l l ll l llll ll l llll lll ll ll ll l ll l ll llllll l ll ll l lllll lllll ll ll lll l lll llll ll lll llllll lll ll lllllll llll l lll llll ll lll ll lll lll ll ll ll ll llll ll ll ll ll lll l lll ll ll lllll l llllll llll l ll ll ll ll ll lll ll ll ll l lll l llll lll ll lll ll lll ll lll llll llll lll lll lll l ll ll llll lll ll ll llllllll ll l ll llllllll l llllll llll l l ll lllllll ll llllll l ll llll llll lllllll llllll llllllll lll lllll lll lll lllll lllllllll l llllll lllll lllllll llllllll lllll lll ll ll l llll llll ll llll llllll llll lll llllllllllll lll ll lllll l lll llll ll lll lll ll lll lll ll llll l llll l ll ll lll l ll l ll lll lll llll l ll llll lll llll lll llll ll l lll lll ll ll lll lll llllllll l llll lllllll l ll ll lll ll llll ll ll lllll lllll l l llll ll ll lll ll l ll ll lll lll ll ll llllll llll ll l ll llll llll ll lll lll llll ll lllllll l llll lll l lll ll l llll l ll llll ll lll l llll ll lll llllll lll llll ll lll lll ll ll ll llll lll llll lll lll lll ll llllll ll lllll ll ll lllllllll l ll l ll ll l ll lll lllllll llll ll l lll llll ll lll lllll lll ll l ll ll ll lll llll ll ll llll llll llll ll llllll ll ll llllllll lll lll lllllll ll ll lll ll l lll lll lll lll ll lllll lll l llll ll l lll l ll ll ll lll llllll ll lll lllll l lll ll lllll ll ll lllll lll l lllll l llll llll ll ll ll llll lllllll l lll lllll ll ll llll ll ll l lll ll ll lll ll lll l ll llll ll llll ll lll l l ll ll ll lll ll ll lll l ll l lll l lll lllll l l l llll lll ll lllll l l ll l ll ll ll llll llll l ll ll lll lllllll ll ll lll ll l ll l ll ll ll llll ll l llll lll ll llll ll lllll lll ll ll l lllllll l lllll lllllllll lll ll l lllllll ll llll ll ll l ll lll lllllll lllllll ll lllllllll llll ll llll lll lllllll lll lllll ll llllll lll lll lll lll llll ll
0
0.5
1
CensoredObserved
Non-ObeseObese
Sur
viva
l
“Observed”: non-censored; “censored”: interval-censored (whisker at right bound) or right-censored
22
© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Kaplan-Meier EstimatorDuration Concept II
1 5 10 50 100 500 1000 5000
Duration Concept II
Days
ll l lll lll ll l l ll ll l lll ll l l l ll ll lllll ll ll ll ll ll l l l ll l l ll ll ll l ll l ll ll l ll lll ll l ll l llll llll l ll lll lll ll ll lll l ll lll l ll l ll ll l lll l l ll ll lll ll llll l ll ll ll ll l ll ll l ll l ll ll l ll llll l lll l ll ll lll l lll ll l lll l ll l ll l l ll ll llll l ll lll ll ll lllll ll ll ll ll l l ll l ll lll l ll lll lll ll ll lll ll ll ll lll l ll lll l ll ll ll ll l ll ll ll ll ll ll lll llll ll lll ll ll ll l lll llll ll ll ll ll l ll lll ll l ll ll lll l lll ll lll ll ll ll l lll ll l l ll l lll l ll ll llll l lll ll ll ll ll lll l ll lll llll lll l ll l ll ll l lllll ll ll lllll l l ll l ll ll lll ll ll ll l ll ll ll ll llll ll ll ll ll lll l ll l l lll ll ll ll lll ll lll ll l lll l l ll l llll l ll ll ll l l lll ll l llll l ll ll l ll ll ll lll lll ll ll l l ll ll ll ll l l ll l ll lll l l ll lllll l ll l ll l ll lll l ll lll llll ll ll lll l ll l ll l l ll ll ll lll ll ll ll ll ll l ll ll l l lll l l ll l lll lll lll lll l lll ll l ll llll llll ll l l ll llll l ll l ll lll lll ll lll l ll lll l l l l l llll ll ll ll ll l lll ll l ll llll l lll ll l lll ll ll lll ll ll l lll ll l ll lll ll l l ll ll l lll ll ll ll l ll lll ll ll lll ll lll ll lll lll ll llll l lll ll ll lll l l ll ll ll l lll l l lll llll l l lll ll ll ll lll l lll ll l ll ll ll l ll l ll lll l ll ll l l ll ll l lll ll ll ll lll llll llll ll ll l ll l ll l l ll lll ll lll ll l ll ll l lll ll lll ll ll l ll ll ll l lllll l l ll lll ll l ll ll l llll l ll lll l lll ll ll lll l llll l l ll ll lll l lll lllll ll ll l lllll l ll ll lll l ll l ll l ll llll lll lll ll lll lll ll ll l l lll l ll l ll ll l ll lllll lll l l lll ll ll lll llll ll lll l lll l ll ll ll l llll ll lll lll l lll ll ll l ll l lll l lll llllll lll l llll lll ll l l ll ll l l lll l lll ll l ll l l ll ll ll l ll l ll l lll ll ll ll ll lll ll ll l ll ll ll ll ll lll ll ll llll l l l l llll l ll llll ll ll l ll ll llll l l ll ll lll ll ll ll ll l ll l ll ll l lll llll ll lll lll ll lll l l llll ll ll llll l ll ll l llll ll l ll l ll l lll ll l ll lll l l lll ll l llll l lll l lllll l lll lll lll lll ll l l l lll lll ll lll ll ll l l l lll lll ll ll lll l ll llll l ll ll l l llll lll ll l lll ll l ll l l l lll ll ll lllll l ll l ll l lll ll ll l l lll ll ll ll llll l ll l ll lll lll l llll lll l lll ll l ll ll l ll l ll l ll l l ll l llll ll lll ll lll lllll lll ll ll l ll lll l l lll lllll ll l lll ll ll ll l l ll lll ll l ll ll l l ll ll l ll llll l lll l ll l l ll l l lll l lll lll ll l l l lll l l llll ll llll l l lll ll lll ll l l ll ll ll lll llll l ll l ll ll l ll ll llll l lll ll lll ll ll l ll lll l lll ll l llll l lll l ll ll lll l l ll l ll lll ll l ll ll ll ll l ll ll lll l lll ll ll ll l ll l ll l lll ll l ll ll l l lll lll ll ll llll l lll l ll l lllll ll ll ll llll ll ll l lll ll ll ll ll l l ll lll l llll lll l lll ll l ll lll l ll lll ll l ll l l ll l llll lllll lll ll l ll l ll ll l l ll llll lll l ll ll l lll ll l ll l ll lll l l l lll llll l l l ll ll ll ll lll lll lll l ll llll lll ll l lll lll lll ll l ll llll lll ll l ll lllll l llllll l lll l ll lll lll ll l lll l l ll ll l l lll ll l ll ll ll ll lll ll lll lll llll l l ll ll ll ll lll lllll l ll l lll ll ll ll ll l ll l ll lll l l l lllll lll l l l lll l ll llll l ll l l lll lll lll lll l l l lll l ll l lll ll lll ll l l lll l ll l llll l ll lll ll ll l l lll ll lll ll ll ll l llll ll l ll ll ll l l lllll ll llll lll l lll llll ll lll ll llll ll l ll llll lllll llll ll l llll ll ll l l ll ll ll lll lll lll ll ll ll ll l ll l l lll ll llll l lll ll ll l l ll l ll l l l ll lll ll ll lll lll l l ll l lll l ll l l ll ll llll l l ll l l llll l ll l ll ll ll ll l ll l llll lll l ll l lll ll ll ll ll lllll l ll lll l llllll l ll l l l lll ll ll ll lll l llll l ll ll l l ll lll ll l ll llll l l ll l l ll ll l ll lll l ll ll lll lll ll lll l l lll l lll l ll ll l l ll ll lll ll lll l ll ll ll llll lll l ll l ll l ll l ll ll ll l lll l llll l ll ll ll ll l lll ll l lll l ll l ll l ll l l ll ll l ll lll lllll l ll ll lll l ll lll ll ll ll l ll ll ll lll l lll ll ll lll l l lll l llll l llll l l ll l ll l ll ll l l ll lll ll lll ll l ll l ll llll ll l ll lll lll lll ll l ll lll l l lll lll l ll ll ll llll ll l ll ll l ll llllll ll l ll l l lll l l l ll ll llll l ll l llll l lll l l ll lll l l lllll l lll ll lll l ll lll lll lll lll l llll l ll l lll l lll ll ll lll lll ll ll lll llll ll ll l ll l l lll l ll llll ll l ll ll ll ll ll llll ll ll l l lllll l lll l lll lll lll ll ll ll ll l lll lll ll ll ll ll lll ll ll l l l lll lll ll ll ll ll l ll lll l lll lll l lll lll ll lll l lllll lll llll ll ll ll l ll ll l lllll lll ll lll l ll ll ll ll l ll ll lll ll ll ll l ll ll l lll ll ll ll lll ll l ll l l lll ll ll lll lll l llll lll ll ll lll lll ll ll ll ll l ll l ll l ll ll l ll lll ll l ll l l ll l ll lll l l lll l l lll l lll ll ll llll ll ll llll l ll ll ll ll lll ll ll lll l l ll lll l lll l l ll l ll ll llll ll ll l ll lll l lll ll ll lll ll ll lll l l ll ll l ll l l llll llll ll lll llll lll l ll l l ll l l l lll llll ll l ll ll l ll l l lll lll l lll l ll ll l ll lll l l ll ll ll l ll ll ll l ll lll ll ll l lll l ll lll ll lll ll ll l lll ll ll l ll l llll ll l ll ll ll l ll lll ll llll l ll l ll lll ll l ll ll l l llll ll ll l llll ll ll llll l lll ll l ll ll ll l l ll ll l l lll ll l ll ll ll lll ll ll lll ll l ll lll lll l ll lll l lll ll ll l ll ll l lll lll lll ll lll l l lll lll ll lll ll lll l l ll ll ll ll ll l lll ll ll ll l lll lllll lll l ll l lll l ll l ll ll l l lll ll ll ll ll l ll ll ll lll l ll ll ll l l ll l ll ll l ll llll l l lllll l ll l ll ll lll ll l ll ll l lll lll ll ll l l ll ll ll ll ll ll l ll llll lll lll l lll l lll llll l ll l ll ll ll llll lll ll lll l l l llll ll ll ll lll l l ll l lll llll ll lll l ll ll ll ll llll l ll ll llll l ll l llll lll l ll l lll lll ll l ll l l lll ll lll lll lll llll ll l ll l l llll ll l l llll ll ll l l ll l l llll llll ll l lll lllllll l lll ll ll ll lll l l ll lll ll ll ll ll ll l l lll lll ll l ll ll l ll l ll l lll l ll l llll lll ll l ll l ll ll ll ll l ll l ll ll l ll ll ll ll l ll ll ll l ll l ll l l ll l ll l ll llll ll ll lll llll l llll ll l l llll l ll ll l l ll l l ll lll ll lll l ll ll l llll ll l ll l l llll ll lll ll lll lll l ll l l l ll ll lll ll ll lll l ll l lll lll l lll l ll lll l ll llll ll lll l ll l lll lll lll l ll l ll lll ll l ll lll ll l lll ll ll ll l ll l lllll ll ll lll lll l ll l ll l lll l ll l l ll l l ll l lll ll lll ll lll l ll l lll ll l lll ll ll llll lll l ll l l ll ll lll ll ll ll l lll ll l l lll ll l ll l l ll l lll ll lll ll lll ll ll ll l ll l lll l lll l lll l ll l lll l lll ll ll l ll l lll llll l lll ll l l lll ll l lll ll ll ll ll ll lll lll l ll l lll l ll lllll ll ll l lllll lllll ll l lll ll l ll lll lll ll ll l lll l lll ll lll ll ll lll l lll llll ll l lllll lll ll lll lll l l llll ll lll l l lll l l ll ll ll l l lllll ll llll l ll lll lll l lll ll l lll ll l ll ll ll ll l l ll ll ll l lll l llll l ll l ll ll l lll lll lll l lll l ll l ll ll ll ll lll l lll llll llll ll lll l l l l ll ll l l llll l l llll ll ll lll llll ll llll l l lll lll ll ll lll ll l ll lll lllll ll llll lll ll ll ll llll llll lll l lll ll ll llll ll ll ll lll lll l ll ll ll lll l ll l ll l lll ll l ll l ll l l ll l ll ll ll ll lll l l ll l l lll ll lll ll ll ll ll ll l l ll lll llll lll ll lll l ll ll lll lll ll l lll lll lll l lll lll llll lll ll l lll l lll l l ll ll lll lll ll lll ll l ll lll ll l ll ll lll ll l ll l ll lll l ll l ll l ll lll ll l ll lll lll lll l l llll ll l l lll ll l ll lll lll l l ll lll ll l l ll ll l ll ll lll l lll ll l lll ll l llll ll l ll l ll lll lll l llll ll ll ll ll ll ll ll l lll lll lll lll lll lll l ll llll l lllll l ll lll ll l ll lll ll ll ll ll lll l llll l ll llll l l lll l l ll ll l ll llll l l ll ll lll l l lll ll ll ll l lll ll ll ll ll ll ll ll l ll lll l l llll l ll ll ll lll l ll l lll lll lll l ll l ll ll l ll lll l ll l ll llll l lll ll l lll ll l ll l l ll ll l ll lll l lll lll ll ll lll lll l ll lll lll ll llll l ll ll lll ll l l ll ll lll l ll l l ll ll ll l l lll l l ll ll l lll ll ll lll l ll l ll ll l ll llll l l lll ll ll l ll l lll ll ll ll l ll ll lllll l ll l ll ll ll ll ll ll l ll ll ll lll l ll ll ll lll l l lll l ll l ll lll lllll l lll ll ll l ll ll lll l lll ll ll lll lll ll lll l l l lll l lll ll ll l lll lllll l ll l llll ll ll ll ll ll l ll l ll ll l lll lll l ll lll lll l ll ll llll l l l ll ll l l llll ll l lll ll l ll ll ll ll ll ll ll lllll lll ll l ll ll lll ll ll ll ll ll lll ll ll ll ll ll lll ll ll lll l l ll ll lll l lll llll l lll lll l l llll l ll ll ll l l l ll lll l lll l ll lll ll ll l lll ll ll lll ll ll ll l ll l l ll ll lll ll ll l lll l ll ll l ll l ll ll ll l ll ll lll l l ll ll l l lllll l lll ll l lll l ll lll l ll lll l l ll lllll ll ll llll l l llll l ll l ll ll ll llll l l ll l l l l l lll lll l l ll l ll l ll ll l lll ll ll l ll ll lll l l ll ll lll ll ll lll ll l ll l l lll ll lll l ll ll l lll l ll ll l
l llll ll lllllll llllllllll lll lllll lll lllllll ll lllll lll ll lllllll l llll ll llll lll lll lll lll llll lllll lllll ll lllllll l lllll l ll lll lllll lll ll lll llllll lllll l lll lllll lll llllllllllllll lll lll llll llll llll l llll ll llllll llll ll llll lll llll lll llll l lllll lll llllll lllll lll ll lll lll lllllll lll lll lll lll lllll l lllllll lllllllll ll llllll lll lll llll l ll ll llll lll ll l l lll llll lll ll ll ll llllll ll ll lll ll ll ll l llllllllll ll ll llllllll lllllllll llllllll ll llllll ll lll llll ll llllll l l lll lll lll ll llll ll lll lllllllll llll lll l ll lllllll ll lllll ll l ll l ll ll llll ll l lllllll lllll l lll lllll lll llll lll lllll ll l lllll lll lll lll l lllll lll ll ll l ll ll lll llll ll l ll l ll lll llllll l l l llllllll l lll ll lllll l ll ll lll lll llllll l lllllll ll lllll l llllllllllllll ll lll ll ll llllll llll ll llll lll lllllll llll lllll ll ll llllll llll lll ll llll ll l l lll lllll l l lll l llllllllllll llll lllll lllll lllllllll llll ll ll llll l lll ll ll ll ll llllll lll lll ll ll ll llll llllll l lll ll l l ll llll l llll lll lllllll l lll ll l ll lll llll lll l ll lll lllll ll llll ll llllll ll lll l lll llll llll lll l llll llll llll ll lll llll l lllll ll llll l llll l llll lll l llll lll lll l llll l lll lll ll ll ll l lll ll l llll l ll ll l ll llll l ll ll llll ll ll lll ll lll llll l l ll lllll lll l llll lll llll lllllll lllllll ll lllllllllll ll llll lll lll ll ll ll llll lll lll ll llll llllll lllll l llll llll l ll lll llll lll lllllll ll ll llll ll lll lll lllll lll lll lllll lll l lll llllll l ll l llllllll ll l lll llllll llllllll ll lll llllllllllll lll lllllllll llllll ll lll l ll lll ll l llll llllll lllll ll llll lllllll lll ll llllllllll ll lllll ll ll lllll ll llll llll lllllll ll llllllllllll lll ll ll l ll llll ll lll llll lllll l llll l lll lll llllllll l ll ll lllll lll ll llll ll ll llll llll ll ll ll lll ll ll l llll lllllll l llll l lll lll ll llll llll l ll ll ll lll llllll ll lll lll lllll lll lllllll ll llll l l lll l lll lll lll ll l lllll ll lll llll ll l lll l lll lll l lll l lllll l lllllll lllllllll ll ll ll lll l lllll llll lll lll ll llllllllll llll lllll llll llllllll ll ll ll ll ll lll ll ll l llll l ll ll lll l ll llll l llll lll llllllll ll lll lll lll lll lllllllllll lllll llll llll lll ll l ll lll lll llll l lllll l lll lll lll l ll lll l llll lll ll ll ll llll llll ll l lll l ll llllll lll ll lll lllll ll lllllll l lllll llll ll ll llll lll llllllll lllll ll ll lll ll ll llll ll l ll lllllllllll llll lllll lll llll l lll lll ll llllll l ll lll ll lll llllllllllll llll ll ll ll llll lll ll lllll lllll lll lll l lllll ll llll l lllllll lll ll l l l lll lll lllllll lll llll llll ll lll ll ll llll ll ll ll ll ll llll llllll lll lllll ll lllll l ll lllll ll ll lll l lllll llllll l ll ll ll l l ll lll lll llll l l l lll l ll l ll ll ll llll l llll l ll llll l ll ll lllll ll l lll l ll l lll ll l l lll lll lll ll l llll l llll ll l ll l ll l lll ll ll l ll ll l ll l ll llll lll lll ll llll lllll ll lllll lll lll llllll ll ll lllllll l lll ll lll lll ll l ll ll l l llll ll ll l l ll ll ll lll lll llll lll ll ll ll llll l ll ll l ll lll ll llll ll l ll l lll llll ll ll lll lll ll ll llll l lllllll lll ll ll llll llll lllllllllll llll ll llll llll ll ll ll lll lllll lllll ll ll lllllllll lllll lllllllllll lll l llll l ll lll ll ll lllll ll ll lllll ll l lll llll l lll lll l lllll llll ll l llll llllll llllllllllllll lll l ll l l lllll lll llll ll llllllllllll lll llll lllll lllll l lll ll ll lll llllll ll l llllll ll lll lll l llll l ll lll l ll lll llll ll ll lllll llll ll llll l lll ll lllllllll l llll lll lllllll llll llllll lllll ll llllll ll ll llll llll llllllllll lllll lll lllll ll lll ll ll lllllll ll l ll llll lll lll lllllllllll lllllll llll llll lll llll ll lll llll llllll llllllllll llllllllllllll lll lll lll lllll ll llll ll lllll ll ll llll llll llll llll lllllll lll llllllll llll lllll ll llllllll ll ll llll lll llllll ll ll lll ll llllllllll llll llll ll l ll lll lllll ll lllll llll llll ll lll l lll l llll ll llllll l ll llll l ll llllll llllll ll l ll llll ll lll l ll ll l ll ll l ll lll ll lll llllll ll l lll lll ll lllll llll lll llllllll llll llll ll lllll l llll llllll lllll lll ll lllllll ll lll llll ll llll llll llll lll l ll l llllllll lll ll ll lll lllllll ll ll lll ll l lll lll lllll ll ll lll llll l ll ll lll l llllll ll l lll ll lllll l llll lll ll lll lll lll l ll lll lll lll lll lll ll ll ll lll lll llll ll llll llll lll llll llll l lllll llllll llllll l lll lll llll lll lllll ll lllll lll lll l llllllll lll llll ll ll lllll llll lll lll lll llll ll llll lllll llllllllll ll ll lll lll l lll llll ll l lll lllllll llllll ll llll l lll ll l lllll llll llll ll llll lllll llll ll ll lllll l lll ll lllllllll llllll lllllll l l lllll lll ll lll lll llll ll ll lll ll l llllll ll lll l ll lll ll lll llll ll llllll lll lllll lll ll llll ll ll lll ll l ll lll ll lllllll ll llllll l ll ll ll lllllll lll ll llll lllllll lll ll l l lll lll lllll l l lllll lll lllllll lllll l lll l llll ll ll lll ll ll ll l lllll ll ll lll l lll lll llllll ll lll lllll lll llll ll lll ll llll ll ll llll lll lllll lll lll l llll ll l ll ll ll llll l lll ll llllllllll ll ll ll ll llll llll l llll llll ll ll lll lll l lll llll lll lll l ll l ll l ll ll lll lll lllll lll l llll llll llll lll lllll lll llll l lllllll lll lllllllll lllllll lll l lllll llllll llllll lll ll ll l ll l lll ll lll llll lll lll ll l l ll ll ll lll ll ll llll llll lll l llllll ll l lll llllllllll l lll llll ll ll lll ll ll llllll llllllll l lll llll lll lll lll ll llll llll ll l lll llll ll l ll llll llll l ll ll ll ll ll l ll ll lll llll l llll ll ll lllll llll lll ll l llll lll ll lllllll lllll l llllll lll lll llll lll l ll llll lll llllllll ll ll lllll llll llllllll l ll ll ll llll l ll llll ll lll ll ll lll lll ll llll ll ll ll ll ll ll llllll llllll lll ll l lll ll ll ll llllll l ll l lll ll lll llll ll llll llll lll llll lllll lll llll llll lllll llllllll ll ll ll ll lll lll l lll ll l lllll ll lllll llll ll ll ll lll lll lll lll llllllllll llll lll lll ll llllll llllll llll lll lll llllll lllll ll lllll l llll ll lllll lllll lllll lllll ll llll ll lllllll ll llll llllll llll ll llllllll llll l lllll ll l ll lll lllll lll ll llll l ll llllll ll ll llllllll ll llllllllllllll llllll l lll ll ll ll lllll lllll ll ll l ll ll llll ll lll l ll lllll lllll l ll lllll lllll lll ll llll lllllll l lllllll ll lll l lll llllll ll ll llllll ll lllllll lllll llllllll lll llll l ll lll lll ll lll l lll l lll lllllll ll l llll ll l llll l llll lllll ll lll lll l ll ll lll ll lllll l ll ll lll llll l lll l lllll lllll lll ll l llllllll lll lll lllll lll lll ll lllll lllll lllll l llll lll llll l ll ll ll lllll ll lll llllllllll lll l lll ll lll lllll lllll llll ll llll lllll lllll lll ll llll ll l lll llll l llll ll l lllll llllllll ll ll llllll lll lll llll l lllll lll llll lll lll lll ll ll lll ll ll l ll llllll lll llllllll lllll l ll ll lll ll llllllll l ll lllll llll ll llll l lllll ll lllll lllllllllll lllllll ll llllllllll lll ll lll ll lll lllllllll llllll lllllll lllll lllll lll ll lll l ll lll ll llll lllll l ll llll ll ll ll llllll llllllll lll ll lll llllllllll llll ll l ll llllll ll ll llllllll l ll lll ll llll l lll llllllll llllll lll llll lllll l llll l lll ll lllll ll llll ll llllll ll l ll l llllll l l ll l llll ll l llll lll ll ll l ll ll llllll l ll ll l lllll lll lll lll l lll llll lll lll ll lll ll llllll llll l lll llll ll lll ll ll lll ll ll lll llll ll ll ll lll ll ll l lllll l lllll llll ll ll l ll ll ll ll ll l lll l ll ll lll lll ll ll llll llll llll lll lll lll l ll llll llll lllllllll ll l ll llllll l lll llll l l ll lllll ll lllll l ll lllll llllllllll llllllll lll lllllll lll llll lllllllll llllll lllll lllllll lllllll llll lll ll ll l llll llll ll llll llllll llllllllllllllll lll ll llll l llllll ll lll llll ll lll ll lll l llll l ll llll ll l ll lll ll llll l ll llll lll llll lll llll ll ll lll ll ll lll lll llllllll l llll llllll l lll lll ll llll ll ll llll lllll l llll ll ll ll ll l ll llll ll ll lllllll llll ll ll lll lll ll lll llll ll lllllll l lll ll l ll ll llll l ll llll ll lll llll ll llllll lllll ll lll lll ll ll lllll llllllll lll lll ll llllll ll lll l ll lllllll l ll l ll ll lll llllll llll ll l lll lll ll ll lllll lll ll ll ll llll llll ll ll llll llll lll ll lllll ll lllll ll lll lll llllll ll ll lll ll l lll ll lll lll ll lllll lll l llll ll l lll l ll ll lll llllll ll lll llll l lll ll llllll ll lllll ll llll l llll llll ll ll ll lll llllll l lll lllll ll ll llll ll l llll ll ll ll ll ll llll ll llll ll lll l l ll ll ll lll ll l lll l ll lll l lll lllll l l l llll lll ll lllll l l ll l ll ll ll llll llll l ll ll ll lllll ll ll ll l l ll lll ll ll lll ll l llll lll l llll ll lll lll lll l lllllll l llll lllllllll lll ll l llllll l lll ll ll l ll ll llllll llllllll lllllllll llll ll llll lll llllll lll llll ll llllll lll lll lll lll llll ll
0
0.5
1
CensoredObserved
Non-ObeseObese
Sur
viva
l
“Observed”: non-censored; “censored”: interval-censored (whisker at right bound) or right-censored
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Immortal Time BiasDuration Concept I
The displayed estimated survival curve for obese claims with immortal time bias correction (ITBC, for short) is indistinguishable from the one without this correction
1 5 10 50 100 500 1000 5000
Duration Concept I
Days
Surv
ival
0
0.5
1 Obese With ITBCNon-Obese With ITBCObese Without ITBCNon-Obese Without ITBC
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Weibull Proportional Hazard Model
The hazard manifests itself in the outcome “indemnity benefits ending”
A proportional hazard model implies that the hazard in one group (e.g., the obese) is, on the time line (calendar time since injury), a constant proportion of the hazard in the other group (e.g., the non-obese) (*)
The baseline hazard as a function of time follows a Weibull distribution (**)
As specified, the model accommodates interval-censoring and right-censoring
The Weibull proportional hazard model is semi-parametric
Obesity is the only covariate in the parametric component
Age is the only covariate in the non-parametric component, and serves the purpose of absorbing the influence of proximity matching
* This proportion is known as the hazard ratio** The Weibull distribution is the only distribution where the measured effect can be interpreted within a proportional hazard framework and, alternatively, within an accelerated failure time (AFT) framework
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© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Multiplicative Effect of Obesity on DurationM
ultip
licat
ive
Impa
ct5
67
Duration I Duration II
Excluding Permanent PartialDuration I Duration II
Including Permanent Partial
5.37 5.32
6.606.69
A multiplicative impact of x means that, for the set of obese claimants, the mean (and median) claim duration is x times as long as it is for the set of non-obese claimantsThe displayed credible intervals comprise 80 percent of the posterior probability
26
© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
Conclusion
Obesity contributes in important ways to indemnity benefit duration
The duration of a claim with an obesity diagnosis is more than five times as long as the
duration of a claim without such a diagnosis
The magnitude of the effect agrees with previous research at Duke University
The estimated effect of obesity may reflect an upper bound
The proportion of claimants categorized as obese in the data set is considerably
smaller than in the U.S. population, thus suggesting that (1) many of the claimants
categorized as obese are of the highest BMI category and (2) many of the claimants
categorized as non-obese are in fact obese—whereas the former causes an
overestimation of the effect of obesity, the latter causes an underestimation
For some claims, the arrival of medical complications may be causal to the claimant
being coded as obese—such cases pose a problem of “self-selection”
27
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AppendixPrimary ICD9 Code Logic
The primary ICD-9 code of a given claim is the first ICD-9 code associated with reported
medical transactions (using a valid service date) based on the following order of priority
1) Paid amount must be greater than zero
2) Provider Group must be one of the following four:
01 (Physician), 04 (Hospital, ASC, X-Ray, Lab), 05 (Clinic), 07 (Non Medical)
When no such transaction exists, transactions from all other providers are considered:
02 (Chiropractor), 03 (Therapist), 06 (Pharmacies and DME Center), 08 (Other)
3) Transactions are selected from the first service date, subject to data cleansing considerations
4) From the ICD-9 codes resulting from steps 1 through 3, the ICD-9 codes associated with the highest
paid amount over the (heretofore recorded) life of the claim are selected
The paid amount of a transaction is assigned in full to any ICD-9 code associated with the transaction
5) If there are ties after applying the mentioned criteria, an ICD-9 code is randomly selected from the set
of tied codes
ASC: Ambulatory Surgical CenterDME: Durable Medical Equipment
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AppendixDetermining the Median Duration
Assume that an obese claim has multiple matching non-obese claims
First, sort the matching claims by duration
In the event that the number of matching claims is odd
Identify all claims that have the same duration as the central value
If more than one such claim exists, choose among these claims based on the following
hierarchy, listed in descending order: right-censored, non-censored, interval-censored
In the event that the number of matching claims is even
Identify the two central values
Identify all claims with a duration that equals the longest duration of these two values
If more than one such claim exists, choose among these claims based on the following
hierarchy, listed in descending order: right-censored, non-censored, interval-censored
29
© Copyright 2013 National Council on Compensation Insurance, Inc. All Rights Reserved.
AppendixImmortal Time Bias Correction
A Monte-Carlo simulation was conducted to investigate the validity of the immortal time
bias correction described earlier
The simulation maintains the primary features of the underlying data generation process
under the assumptions that
The data generation process for benefit duration is the same for all claims
The probability of acquiring a 278 ICD9 code is governed solely by the duration of a claim
The simulation assumes that
Claims only generate ICD9 codes while they are open
Claims are only considered open over their indemnity benefit duration
There is a fixed probability, , that on any day that a claim is open it will produce a 278 ICD9 code
The acquiring of a 278 ICD9 on day is independent of the acquiring of a 278 on day , provided
In this simulation, the parameters were calibrated to reflect important characteristics of the
data and of the estimated statistical model
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AppendixImmortal Time Bias Correction
The algorithm generates pairs of obese and non-obese claims as follows
1. Draw the indemnity benefit duration and the time to the first 278 ICD9 code for a claim classified as
obese
a) Randomly generate an indemnity benefit duration from a Weibull distribution and round up to the next integer
b) Randomly draw the time to the first 278 ICD9 code from a geometric distribution with parameter
(Note: This step b is independent of step a)
c) If the time to the first 278 ICD9 code is greater than the minimum of the drawn indemnity benefit duration or 1 year,
then reject the draw and return to step 1
• Otherwise, accept the draw and proceed to step 2
2. Draw a suitable non-obese claim to pair with the obese claim generated in step 1)
a) Randomly generate an indemnity benefit duration from a Weibull distribution and round up to the next integer
b) Randomly draw the time to the first 278 ICD9 code from a geometric distribution with parameter
(Note: This step b is independent of step a)
c) If the time to the first 278 ICD9 code is less than the minimum of the drawn indemnity benefit duration or 1 year, then
reject the draw and return to step 2
• Otherwise, accept the draw and return the obese non-obese pair
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AppendixImmortal Time Bias Correction
Under the aforementioned simulation
The average duration for claims flagged as obese is 98.5 days
The average duration for claims flagged as non-obese is 98.2 days
Conducting the simulation without the immortal time bias correction is equivalent to all
generated claims passing step 2c
Without the immortal time bias correction
The average duration for claims flagged as obese is 98.5 days
The average duration for claims flagged as non-obese is 9.5 days
The result suggests that the proposed immortal time bias correction makes up most of the
difference between the two categories
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AppendixJAGS Code (Proportional Hazard Model)
33