time dependent relative risks in life insurance medical underwriting

Title:

Time dependent relative risks in life insurance medical underwriting

Author:

Robert F. Kneepkens, MD MScEBP

Affiliation:

Chief medical officer Achmea division Pension & Life

Financial support:

Achmea division Pension & Life

Address for correspondence:

Achmea division Pension & Life; Postbus 90106, 5000 LA, Tilburg, The Netherlands,

TSA06/054; phone: 0031-6-5145-1528; e-mail: robert.kneepkens@achmea.nl.

Correspondent:

Robert Kneepkens, MD MScEBP

Time dependent relative risks in life

insurance medical underwriting

Abstract

Introduction: Life insurance medicine focuses on mortality hazards in specified periods.

People are free to insure their lifes for shorter or longer terms. Because the chosen terms

range from one year to a life time, life insurers have to take into account the fact that the

predictive value of risk indicators can and will change over time. The time a risk indicator

keeps its predictive value, will be dependent on its biological effects, volatility, and

treatability. For a given applicant this implies that the RH calculated for his medical condition

should be dependent on the term of the insurance.

The main objective of this study is to determine if some commonly used risk indicators –

previously used to study age dependency of relative risks – have a predictive value that

increases with the observation period (1)

Methods: This population-based cohort study uses NHANES-datafiles from the Third

National Health and Nutrition Examination Survey (NHANES III) and the NHANES Linked

Mortality Files 2010. Only participants aged 20 to 69 that were examined in mobile

examination centers, without a history of some prevalent high risk diseases were included.

The observed mortality was compared to the expected mortality in a Generalized Linear

Model (GLM) with Poisson error structure with two reference populations, which both can

serve as preferred reference for life insurers: The United States Life Tables 2008 (USLT) and

the 2008 Valuation Basic Tables (VBT) based on the insured population of 35 US Life

insurers. The Time dependency of the RH’s of the systolic blood pressure (SBP), aspartate

aminotranseferase (ASAT), lactate dehydrogenase (LDH), serum albumen and albuminuria,

was assessed, with correction for ethnicity, household income, history of diabetes mellitus,

BMI and serum cholesterol. To be able to compare the results with the results of the Age

Dependency Study (ADS), we used the same data, the same risk indicators, and the same

statistical analysis method, the Generalized Linear Model (GLM).

Results: Contrary to the results in the univariate analyses, the multivariate analyses show

no difference between the USLT and VBT models. In both models the RH’s of SBP and

albuminuria increase over time, while the RH of LDH decreases over time. Only the slopes

are different, reflecting the rate of mortality increase between USLT and VBT. The RH’s of

ASAT and serum albumen are independent of time in both models.

Discussion: Time dependency of RH’s can be assumed to exist with many risk indicators.

Time dependency may take two forms: decreasing the RH and increasing the RH of a variable

as time passes. Medical underwriting guidelines should therefor differentiate between short

term and long term life insurances. Medical directors should realize that the presence of time

dependency diminishes the value of short term clinical studies for life insurance medical

underwriting. Life insurance mortality studies should always contain a discussion of the time

dependency of the predictive value of the variables under study.

Key Words: Time dependency, generalized linear model, life insurance, mortality,

relative hazard.

Time dependent relative risks in life

insurance medical underwriting

Introduction

Life insurance medicine focuses on mortality hazards in specified periods. People are free

to insure their lifes for shorter or longer terms. Because the chosen terms range from one year

to a life time, life insurers have to take into account the fact that the predictive value of risk

indicators can and will change over time. Some risk indicators are indicative of imminent

death, while others do only predict a raised relative risk in a more distant future.

Medical underwriting guidelines seldom include time-dependency of risk indicators. Time

is primarily used in two ways. The first years after assessment the risk may be deemed too

high and the insurance is postponed or only possible with temporary flat extra premiums. The

risk may also be deemed too high at the end of the requested insurance term, in which case a

shorter term will be offered. In most cases, these attenuations of the insurance proposal are

not based on specific risk indicators, but on the presence of certain diseases, like a

malignancy.

Risk indicators can fluctuate fast, specially if treated. The time a risk indicator keeps its

predictive value, will be dependent on its biological effects, volatility, and treatability.

Arythmias might be short lived, but so may be their bearers, despite the excellent possibilities

for treatment. On the other hand, smoking habits tend to lead to an accumulation of corporal

damage, while smokers sometimes seem to be incurable. In the former case the predicitve

value will be lost soon, while in the latter the predictive value will be increasing year after

In life insurance medicine the RH’s are calculated by comparing the observed mortality to

an expected mortality that is based on sex, smoking status, age at start, and time since medical

underwriting. This means that time dependency is integrated in the expected mortality and in

the standard premiums for life insurances, and therefor should be integrated in the

underwriting guidelines. For a given applicant this implies that the RH calculated for his

medical condition should be more dependent on the term of the insurance than is currently the

case. At least, the risk assessor should be more consciencious of the time dependency of a the

risk indicators present.

If time dependencies are used, acurate risk assessment will possible for every period of the

insurance term, making lower premiums possible without an accompanying higher risk of

profit loss due to excess policy loss or retention. Incorporating known time dependency in

underwriting guidelines could be profitable for both insurer and applicant.

Objectives

It stands without doubt that some commonly used risk indicators have a predictive value

for mortality that decreases with the observation time. However, life insurers need to be able

to predict long term mortality as acurate as short term mortality. The main objective of this

study is to determine if some commonly used risk indicators – previously used to study age

dependency of relative risks – have a predictive value that increases with the observation

period (1)

. To be able to compare the results with the results of the Age Dependency Study

(ADS), we used the same data, the same risk indicators, and the same statistical analysis

method, the Generalized Linear Model (GLM). GLM combines the advantages of life table

analysis – taking expected mortality into account – and Cox’ proportional hazards models –

allowing for many risk determinants in a proportional equation.

We expect that in a direct comparison of observed versus expected mortality the RH’s for

variables that signal any form of senescence, detoriation of organ damage – like serum and

urinary albumen – will be dependent on the time elapsed since the start of the insurance.

Other, more “volatile” variables are more apt to signal acute risk and will show decreasing

RH’s when time progresses. For the SBP, both outcomes are possible, as the result will

depend on the access to good health care and therapy adherence, and therefor on the

population under study.

Because time dependency of RH’s can differ according to the life tables used, this study

also looks at the effect of the life tables: the one-dimensional general population tables or the

two-dimensional insured lifes population. We expect the increase of RH’s to become more

prominent when one-dimensional tables are used, and the decrease to become more prominent

when two-dimensional tables are used.

Study design

The NHANES-datafiles from the Third National Health and Nutrition Examination

Survey (NHANES III) and the NHANES Linked Mortality Files 2010 were used for this This

population-based cohort study. The NHANES program from the National Center for Health

statistics (NCHS) has been designed to assess the health and nutritional status of non-

institutionalized adults and children in the United States. The anonymized datafiles are

publicly available for researchers (2)

To compare the observed mortality to the expected mortality we used a Generalized

Linear Model with Poisson error structure with two reference populations, which both can

serve as preferred reference for life insurers. The United States Life Tables 2008 (USLT)

served as unselected age and sex matched reference population (3)

. We used the insured

population of 35 US Life insurers as selected – medically underwritten – reference

population, which has been published as the 2008 Valuation Basic Tables (VBT) of the

American Academy of Actuaries and the Society of Actuaries (4)

Study and base population

Because insured populations will differ from state to state, company to company, and

product to product, we used the population-based study from the NCHS and the Centers for

Disease Control and Prevention (CDC), NHANES III, conducted from 1988 through 1994.

Population-based studies like NHANES tend to have results that are generalizible and contain

more and publicly accessible data. The NCHS searched death certificates, the National Death

Index (NDI), the Social Security Administration (SSA), and the Centers for Medicare and

Medicaid Services (CMMS) to retrieve the mortality status in 2010.

Inclusion and exclusion criteria

The study is restricted to participants aged 20 to 69 that were examined in a mobile

examination center (MEC), to imitate as much as possible the underwriting practice of life

insurers.

We excluded participants with a history of a potentially life-threathening condition: heart

attack, congestive heart failure, stroke, emphysema, cancer, because the hazard of mortality

of these participants would be dictated too much by their medical history and could lead to

insurability. This exclusion should also ensure that the population resembles the insured

population more and will enable testing some often used risk determinants. We also excluded

MEC-examined participants that did not undergo the full blood and urine tests under study,

because life insurers would decline anyone who would refuse to undergo all tests that were

deemed necessary for the risk assessment. For a flow chart of participants, please see the ADS

Methods

The hazard of death relative to a life table of a large reference population, like the general

population or the insured population, can be analysed using GLM for RH’s, with fixed time-

periods of one year, the log of the observed total mortality as link, the log of the expected

total mortality according to the life tables as offset, and a Poisson error structure (5)

model is discussed in more detail in the ADS (1)

Data preparation

We linked the anonymized datafiles of the NHANES III Adult Household Interview,

Examination, Laboratory, and Mortality Linkage 2010 dataset, which are publicly available

for researchers at the website of the NCHS (2)

For each participant a separate case was created for each time period of one year he was in

observation, with only the last year being broken because of death or censoring. Expected

mortality was drawn from two sets of life tables, USLT and VBT, depending on sex, age at

the time of interview, time elapsed since this interview and his smoking status at the time of

interview. We used the life tables for non-smokers of the VBT for never-smokers and former

smokers who stopped smoking more than two years before the household interview. we used

the life tables for smokers for all others, including participants with unknown smoking habits.

For this study we used the SBP, ASAT, LDH, serum albumen and albuminuria as main

variables, and ethnicity, household income, history of diabetes mellitus or high blood sugar,

BMI and total cholesterol as additional variables. Detailed information on the data collection

in the NHANES III survey can be found in the ADS and at the website of the NCHS (1,2)

Parameters and endpoints

This study focuses on five continuous variables that are widely used in life insurance

underwriting: SBP, ASAT, LDH, serum albumen and albuminuria. These variables were

measured in most participants and have predictive value for all-cause mortality in a relatively

healthy population (6,7,8,9)

. They also account for many undocumented chronic diseases that

could otherwise render the model unstable. To enhance the stability, the model was corrected

for ethnicity (Non-Hispanic white, Non-Hispanic black, Mexican-American, Other),

household income (> or < 20,000 US$), history of diabetes mellitus, BMI (8 categories) and

serum cholesterol (5 categories). Age, sex, smoking status and time since the interview

determine the expected mortality and were therefore not added to the linear predictor with

explanatory variables.

Main outcomes

The main goal of this study is the assessment of the time dependency of the RH’s of the

SBP, ASAT, LDH, serum albumen and albuminuria for the ULST and VBT 2008 reference

populations. The variables are tested on time dependency in the generalized linear model, by

adding interaction terms between the variable and the year since the household interview, the

first year being year 1.

Other outcomes

Because it is probable that the strength and the direction of the time dependency depends

on the life tables used, all models were run with both sets of life tables (USLT, VBT). In VBT

the mortality increases faster during the observation period, which might lead to a negative

time dependency, while in USLT the slower increasing mortality may lead to a positive time

dependency, i.e. the RH of the variable increases over time.

Test procedures

In GLM the choice between models is made using the deviance of the log-likelihood from

the maximal possible log-likelihood, where there is an explanatory variable for every case.

The significance of explanatory variables was tested with a Type III test. The decision if

explanatory variables could stay in the model was made using the likelihood ratio test. As cut-

off point we used a P-value of 0.1.

We used standardized deviance residuals, leverages and Cook’s distances to verify that no

case contributed too much to the model compared to other cases.

All tests and analyses were performed with SPSS 22 (IBM SPSS Statistics for Windows,

Version 22.0. Armonk, NY: IBM Corp. Released 2013).

Results

20,050 adults participated in the household interview in the NHANES III Survey, but

6,470 participants were excluded because of age or not being examined in the mobile

examination center. From 10 participants the mortality status could not be retrieved in 2010.

From the 13,570 remaining participants 1,261 were excluded from this study because they had

an history of one or more potentially life threathening diseases that were documented in the

household interview: heart attack, congestive heart failure, stroke, emphysema, cancer. 1,140

participants were excluded because of incomplete laboratory testing. This study is performed

with the data of 11,169 participants aged 20 to 69 that completed the household interview, the

medical examination and the laboratory testing. 1,150 died during the observation period. The

participants were observed for a median of 14.8 years (IQR 13.3 – 16.5). The total number of

completed and incompleted observation years was 168,047. Detailed information on the

baseline characteristics of the participants can be found in table 1 of the Age Dependency

Study (1)

Univariate analysis

The continuous variables SBP, ASAT, LDH, serum albumen and albuminuria were all

significant with P<0.001 in univaratiate analyses in GLM with expected mortalities

calculated from USLT and VBT. This changed when their interaction term over time since the

interview was introduced. The results are shown in tables 2a–e.

Table 2a – GLM, univariate analysis, systolic blood pressure

US general population (US Life Tables 2008) US Insured Lifes (2008 Valuation Basic Tables)

Value Df Value Df

Deviance 12,222 168,044 v/df=0,073 12,054 168,044 v/df=0,072

Akaike’s Information criterion 14,528 14,360

Likelihood Ratio Chi-square 88.6 2 P<0.001 85.3 2 P<0.001

RH=exp(B) CI 95% LR Chi-sq. RH=exp(B) CI 95% LR Chi-sq.

Intercept 0.186 0.126 – 0. 275 P=0.004 0.386 0.261 – 0.572 P<0.001

Systolic blood pressure 1.012 1.009 – 1.015 P<0.001 1.014 1.011 – 1.017 P<0.001

Time * systolic blood pressure 1.00017 1.00007 – 1.00026 P=0.001 0.99980 0.99970 – 0.99990 P<0.001

Table 2b – GLM, univariate analysis, aspartate aminotransferase

Value Df Value Df

Deviance 12,250 168,044 v/df=0,073 12,060 168,044 v/df=0,072

Intercept 0.87 0.81 – 0.94 P=0.029 1.65 1.53 – 1.79 P<0.001

Aspartate aminotransferase 1.0079 1.0045 – 1.0112 P<0.001 1.014 1.012 – 1.016 P<0.001

Time * aspartate aminotransf. 1.00015 0.99983 – 1.00046 P=0.353 0.99939 0.99906 – 0.99971 P<0.001

Table 2c – GLM, univariate analysis, lactate dehydrogenase

Value Df Value Df

Deviance 12,236 168,044 v/df=0,073 12,033 168,044 v/df=0,072

Intercept 0.44 0.36 – 0.53 P=0.649 0.75 0.62 – 0.90 P<0.001

Lactate dehydrogenase 1.0044 1.0032 – 1.0057 P<0.001 1.0076 1.0065 – 1.0088 P<0.001

Time * lactate dehydrogenase 1.00011 1.00004 – 1.00019 P=0.003 0.99983 0.99976 – 0.99991 P<0.001

Table 2d – GLM, univariate analysis, serum albumen

Value Df Value Df

Deviance 12,179 168,044 v/df=0,072 12,027 168,044 v/df=0,072

Intercept 53.7 27.1 – 106.3 P=0.322 64.3 32.2 – 128.3 P<0.001

Serum albumen 0.36 0.30 – 0.53 P<0.001 0.45 0.38 – 0.54 P<0.001

Time * serum albumen 1.0073 1.0040 – 1.0106 P<0.001 0.9947 0.9914 – 0.9981 P=0.002

Table 2e – GLM, univariate analysis, albuminuria

Value Df Value Df

Deviance 12,253 168,044 v/df=0,073 12,080 168,044 v/df=0,072

Intercept 1.067 1.006 – 1.131 P=0.015 1.93 1.82 – 2.05 P<0.001

Albuminuria 1.00012 0.99993 – 1.00031 P=0.257 1.00026 1.00007 – 1.00044 P=0.022

Time * albuminuria 1.000024 1.000002 – 1.000045 P=0.016 1.000011 0.999990 – 1.000032 P=0.293

In univariate analyses most variables have a lower RH in the last year of the observation

period than in the first year of the observation period, when expected mortality is derived

from VBT. However, the RH’s of most variables are increasing during the observation period

when the USLT are used. The overall mortality is rising faster in VBT than in USLT and

apparently the RH’s of these variables show a rate of increase in univariate analysis that falls

in between the rates of the VBT and USLT.

There are two exceptions to this general observation. The RH of ASAT is not time

dependent compared with USLT, making ASAT a relatively short term predictor. The RH of

albuminuria has little predictive value in the first years when used with USLT and is not time

dependent compared with VBT, suggesting albuminuria is more suitable as a long term

predictor than as short term predictor.

Multivariate analysis

All variables were significant in mulitvariate analysis with GLM with expected mortalities

calculated from USLT and VBT (results shown in the ADS (1)

). If a variable predicts relative

mortality better in the short term than in the long term – or vice versa –, the RH of the

variable will be time dependent. This means that an added interaction term “time * variable” –

with “time” representing the year of observation – should be significant in the multivariate

analysis, as is the case for most variables in the univariate analysis.

The RH’s of the interaction terms with time for the SBP, LDH and albuminuria are

significant in mulitvariate analysis when a limit of P=0.1 is used, both in the USLT and the

VBT model. The RH’s of the continuous variables themselves stay significant after

introduction of the interaction terms, except for albuminuria. This indicates that albuminuria

has a relatively low predictive value for mortality in the first years of the insurance.

Contrary to the results in the univariate analyses, the multivariate analyses show no

difference between the USLT and VBT models. In both models the RH’s of SBP and

albuminuria increase over time, while the RH of LDH decreases over time. Only the slopes

are different, reflecting the rate of mortality increase between USLT and VBT. The RH’s of

ASAT and serum albumen are independent of time in both models.

The final models can be found in Table 3. The order in which the interaction terms had to

be removed differed depending on the life tables used.

Table 3 – Generalized Linear Model, with all explanatory variables, and interaction terms for

age dependency

All ages US general population (US Life Tables 2008) US Insured Lifes (2008 Valuation Basic Tables)

Value Df Value Df

Deviance 11,732 168,024 v/df=0,070 11,561 168,024 v/df=0,069

Akaike’s Information crit. 14,078 13,907

Intercept 4.55 1.92 – 10.81 P<0.001 4.59 1.91 – 10.99 P<0.001

Low or no income, <20,000

US$ 1.74 1.54 – 1.97

P<0.001

1.53 1.35 – 1.73

P<0.001

History of DM 1.63 1.39 – 1.91 P<0.001 1.71 1.46 – 2.01 P<0.001

SBP, mmHg 1.0050 1.0009 – 1.0092 P=0.016 1.0060 1.0019 – 1.0101 P=0.004

Time * SBP 1.00059 1.00028 – 1.00089 P<0.001 1.00034 1.00004 – 1.00064 P=0.033

ASAT, U/L 1.0076 1.0057 – 1.0094 P<0.001 1.0075 1.0056 – 1.0094 P<0.001

Time * ASAT removed (P=0.302) removed (P=0.296)

LDH, U/L 1.0050 1.0027 – 1.0074 P<0.001 1.0066 1.0044 – 1.0088 P=0.005

Time * LDH 0.99974 0.99951 – 0.99998 P=0.041 0.99964 0.99941 – 0.99988 P<0.001

Serum albumen, mg/dL 0.50 0.42 – 0.58 P<0.001 0.57 0.48 – 0.68 P<0.001

Time * serum albumen removed (P=0.613) removed (P=0.816)

Albuminuria, ug/mL removed (P=0.939) removed (P=0.798)

Time * albuminuria 1.000024 1.000016 – 1.000031 P<0.001 1.000023 1.000015 – 1.000032 P<0.001

Ethnicity: P<0.001 P=0.052

- Non-Hispanic white (ref.) 1 1

- Non-Hispanic black 1.16 1.00 – 1.35 1.08 0.93 – 1.26

- Mexican-American 0.87 0.74 – 1.02 0.91 0.77 – 1.06

- Other 0.71 0.49 – 1.02 0.75 0.52 – 1.09

BMI, kg/m2 P<0.001 P=0.002

- Lower than 20.0 (ref.) 1 1

- 20.0 – 22.4 0.64 0.48 – 0.86 0.74 0.55 – 0.98

- 22.5 – 24.9 0.50 0.38 – 0.66 0.60 0.46 – 0.79

- 25.0 – 27.4 0.48 0.37 – 0.63 0.60 0.46 – 0.79

- 27.5 – 29.9 0.46 0.35 – 0.60 0.61 0.47 – 0.80

- 30.0 – 32.4 0.42 0.32 – 0.56 0.56 0.42 – 0.75

- 32.5 – 34.9 0.51 0.37 – 0.69 0.67 0.49 – 0.91

- 35.0 and over 0.54 0.40 – 0.72 0.78 0.59 – 1.04

Cholesterol (mg/dl) P<0.001 P<0.001

- Lower than 175 (ref.) 1 1

- 175 – 199 0.75 0.62 – 0.89 0.74 0.62 – 0.89

- 200 – 224 0.65 0.54 – 0.78 0.65 0.54 – 0.78

- 225 – 249 0.69 0.57 – 0.84 0.67 0.55 – 0.81

- 250 and over 0.65 0.54 – 0.79 0.64 0.53 – 0.77

DM = diabetes mellitus, SBP = systolic blood pressure, ASAT = aspartate aminotransferase, LDH = lactate dehydrogenase, BMI = body

mass index. Decision about inclusion of explanatory variables were made on the basis of a Type III test, using the P-value of the Likelihood

Ratio Chi-square (LR Chi-sq.) given in this table. In case of removal of a variable or interaction term, the last recorded P-value is given

between brackets.

A few cases with exceptional high ASAT, LDH and albuminuria had larger Cook’s

Distances than the rest of the cases, although none of the Cook’s Distances were larger than 1.

Sensitivity analysis consisted of removing these cases. Removal did not change the results of

the base models, but in both models with time dependency the RH’s of ASAT and “time *

albuminuria” were increased, without affecting the models themselves.

Discussion

Life insurance underwriting guidelines help underwriters and medical directors to

calculate a best estimate of the mortality ratio. This study shows that the duration of the life

insurance should be taken into account when the applicant’s data are assessed.

Most risk indicators, like SBP, ASAT, LDH, serum albumen and albuminuria, predict

mortality over a longer period. In the multivariate analysis of this study, the RH’s of two of

them – ASAT and serum albumen – were independent of the time elapsed since the household

interview and medical examination. Only one of them – LDH – had RH’s that decreased over

time. The RH of LDH decreases to 1.00 within 20 years, making LDH less suitable for

prediciting mortality in the more distant future. The RH’s of the remaining two variables –

SBP and albuminuria – increased over time. The RH of the SBP squared in 9 to 18 years,

depending on the life tables used. The RH of albuminuria even started at virtually 1.00 at the

start of the observation, rendering the variable unsuitable for short term mortality predictions.

Important implications of these results are, that life insurance underwriting is rightfully

claimed to focus more on long term prognosis than curative medicine does, and that most

clinical studies have a too short observation period to be of much use to life insurance medical

underwriting.

This study failed to show important differences between the models with the USLT as

reference and the models with the VBT as reference. In both sets of models the results of

mulitvariate analyses concerning the time dependency were comparable. Only in univariate

analyses differences could be noted.

The major weakness of this study is the fact that the population under study is not a

population of insured lifes or life insurance applicants. As explained in the study design

section the use of insurance populations lowers the generalizibility, suffers from the fact that

most data are only collected for specific subgroups, and may contain competition sensitive

information. The choice for NHANES III data implies that the reported RH’s cannot be

copied to medical underwriting guidelines for life insurances. Further research in subgroups

of insurance populations is needed when the goal is to update underwriting guidelines.

A second weakness of this study is that not all possible forms of time dependency are

studied. Some variables used in medical underwriting may be indicative of more than one

disease processes, with as a result a biphasic mortality curve. These forms of time dependency

are not studied.

The major strength of this study is that the observed mortality has been compared directly

to the expected mortality for every year of observation separately. Life insurers do not only

want to know who dies first, but also what an applicant’s mortality will be compared to his

peers. The GLM combines this direct comparison with a linear predictor containing many risk

determinants, which leads to more stable results.

By using two sets of life tables to provide the expected mortality, the effect of the choice

of the life tables can be studied. The fact that the results in both sets of models are comparable

lends power to the findings of this study.

Conclusion

Time dependency of RH’s can be assumed to exist with many risk indicators. Time

dependency may take two forms: decreasing the RH and increasing the RH of a variable as

time passes. Medical underwriting guidelines should therefor differentiate between short term

and long term life insurances.

Medical directors should realize that the presence of time dependency diminishes the

value of short term clinical studies for life insurance medical underwriting. Life insurance

mortality studies should always contain a discussion of the time dependency of the predictive

value of the variables under study.

References

1. Kneepkens RF, Lindeboom R. Age dependent decline of relative risks in life insurance

medical underwriting. J Insur Med 2014; 44: ... - ...

2. National Center for Health Statistics and Centers for Disease Control and Prevention:

Analytic and reporting guidelines: The third National Health and Nutrition Examination

Survey, NHANES III (1988–1994). http://www.cdc.gov/nchs/nhanes/nh3rrm.htm#ag.

Accessed May 5, 2013.

3. Arias E. United States life tables, 2008. National vital statistics reports; vol 61 no 3.

Hyattsville, MD: National Center for Health Statistics. 2012.

4. American Academy of Actuaries / Society of Actuaries, Joint Preferred Mortality Project

Oversight Group. 2008 Valuation Basic Table. Paper presented at the March 2008

meeting of the National Association of Insurance Commissioners’ Life and Health

Actuarial Task Force, Orlando, Florida, March, 2008: 49-50, 53-54, 57-58, 61-62.

Accessed: September, 2013 from http://www.actuary.org/pdf/life/tables_march08.pdf.

5. Jong P van, Heller GZ. Generalized Linear Models for insurance data. Melbourne.

Cambridge University Press 2008, 2012.

6. Perloff D, Grim C, Flack J, Frohlich ED, Hill M, McDonald M, Morgenstern BZ. Human

blood pressure determination by sphygmomanometers. Circulation 1993; 88: 2460-2470.

7. Fulks M, Stout RL, Dolan VF. Using liver enzymes as screening tests to predict mortality

risk. J Insur Med 2008; 40: 191-203.

8. Fulks M, Stout RL, Dolan VF. Albumin and all-cause mortality risk in insurance

applicants. J Insur Med 2010; 42: 11-17.

9. Ohsawa M, Fujioka T, Ogasawara K, Tanno K, Okamura T, Turin TC, Itai K, Ogawa A,

Yoshida Y, Omama S, Onoda T, Nakamura M, Makita S, Ishibashi Y, Tanaka F,

Kuribayashi T, Ohta M, Sakata K, Okayama A. High risks of all-cause and cardiovascular

deaths in apparently healthy middle-aged people with preserved glomerular filtration rate

and albuminuria: A prospective cohort study. Int J Cardiol 2013.

http://dx.doi.org/10.1016/j.ijcard.2013.10.076.

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accelerated underwriting

masters of underwriting smoothing out the home saver...

section - underwriting

164 underwriting