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Indemnity Benefit Duration and Obesity

Presented by:

Chris Laws

Ratemaking and Product Management (RPM) SeminarMarch 11-13, 2013Huntington Beach, CA


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

2


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)

3


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

4


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

5


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

6


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

7


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

8


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

9


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

10

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


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

11


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

12


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

13


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

14



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

15



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” (*)

16

* 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.


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

17


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

18


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


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

20


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

21


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


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

23


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

24


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

25


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


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


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

28


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


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

30



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

31



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

32


AppendixJAGS Code (Proportional Hazard Model)

33