RECURSIVE PARTITIONING METHODS TO …780 ever married individuals 50 years or older. ... Multifarious forces lead some people to outlive their ... of the many hypothesized factors

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RECURSIVE PARTITIONING METHODS TO UNDERSTAND FACTORS ASSOCIATED WITH

HUMAN LONGEVITY

Gilda Garibotti1, Heidi Hanson2,3, Mike Hollingshaus4, Ken Smith3,5

1Centro Regional Universitario Bariloche, Universidad Nacional del Comahue, Argentina

2Department of Family and Preventive Medicine, University of Utah

3Population Sciences, Huntsman Cancer Institute, University of Utah

4Ken C. Gardner Policy Institute, University of Utah

5Department of Family and Consumer Studies, University of Utah

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ABSTRACT

The number of forces affecting longevity are extensive and their interactions voluminous.

Biodemographers need to consider novel methodologies to identify how these numerous factors

alter the life chances of humans. We argue that recursive partitioning (RP) methods may offer a

useful approach to address this longstanding challenge. RP methods allow us to identify complex

combinations of family and individual circumstances present in early and mid-life that explain

the variability in longevity later in life. We apply this methodology to data from the Utah

Population Database (UPDB), a large biodemographic and genealogy resource. We identified

59,780 ever married individuals 50 years or older. We find that combinations of later birth

cohort, stronger family history of longevity, lower birth order, and later age at last birth are

associated with better survival. We also demonstrate the importance of ancillary methods needed

to apply RP methods to complex and large data sets.

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INTRODUCTION

The length of life among humans is variable and the roots of this variation are complex.

Multifarious forces lead some people to outlive their expected life span, while limiting that of

others. Not only are these factors extensive but the volume of their combinations is staggeringly

large. What strategies and methodologies are available to gerontologists and biodemographers

that can aid in advancing our understanding of the many hypothesized factors affecting longevity

differentials, studied separately or in combination? In this paper, we suggest that recursive

partitioning methods have much to offer to address this challenge.

Opinions differ on the main sources of variation and the intervening mechanisms that

affect health and longevity differentials, a state of affairs that argues for the inclusion of many

indicators so that their relative influence (and their interactions) can be assessed simultaneously.

Recursive partitioning methods allow investigators to identify combinations of risk and

protective factors related to lifespan, and to quantify the relative importance of life conditions

that contribute to health and longevity differentials.

What factors and mechanisms are potentially important for inclusion? We give special

attention to circumstances that are observable and represent conditions in utero and during

infancy, childhood and mid-life (Smith et al. 2009; Yi and Vaupel 2004; Smith et al. 2014). At

the earliest, prenatal conditions such as fetal nutrition and placental characteristics are known to

influence health outcomes in adult life (Eriksson et al. 2013; Barker and Thornburg 2013;

Godfrey and Barker 2000; Doblhammer 2004; Gluckman et al. 2008). The role of malnutrition,

infections and poor health during childhood on survival and late onset disease risk has been well

documented (Hanson and Smith 2013; Huang and Elo 2009; Crimmins and Finch 2006; Case,

Fertig and Paxson 2005; Blackwell, Hayward and Crimmins 2001; Yi, Gu and Land 2007).

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A range of family circumstances in early-life has also been studied in relation to mortality

risks later in life. Parental age at conception, sibship size, birth order, family’s socioeconomic

status, and early parental death influence offsprings’ life chances in a number of ways that have

been found to affect mortality risks of exposed children (Smith et al. 2009; Smith et al. 2014;

Huang and Elo 2009; Yi, Gu and Land 2007; Hubbard, Andrew and Rockwood 2009; Crimmins,

Kim and Seeman 2009; Kauhanen et al. 2006).

Genetic and shared familial influences on life span have received considerable attention

in biodemography and gerontology. Several investigators found that a heritable component is

present in later-life survival (Smith et al. 2009; Garibotti et al. 2006; H. Hanson 2013, Gavrilov

et al. 2002; Coumil, Legay and Schachter 2000). Smith et al. found that a summary measure of

the longevity patterns of all known blood relatives for a given individual is an important

predictor of adult mortality (Smith et al. 2009).

For early adulthood, childbearing and child rearing affect the lives and the longevity of

parents (Hurt, Ronsmans and Thomas 2006; Smith, Mineau and Bean 2002). Measures of

fertility including parity, age at first birth, age at last birth, and interbirth intervals have been

studied in relationship to longevity. There remains, however, some disagreement on the direction

of these effects (Smith et al. 2009; Yi and Vaupel 2004; Hurt, Ronsmans and Thomas 2006;

Smith et al. 2002; Penn and Smith 2007; Smith et al. 2009; Dribe 2003).

How have these important predictors of human life span been commonly studied in the

literature? The Cox proportional hazards model and its extensions are clearly the most widely

used statistical tools in studies on human aging and the method of choice for linking early and

mid-life risk factors to later health outcomes. Although these models are useful they have

limitations. In particular, even though interactions between covariates can be incorporated, they

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have to be specified a priori, a challenge given the potentially large number of candidates

involved. Moreover, sample size often constrains the number of interactions that can be

reasonably included. As a consequence, interactions involving multiple variables are often

ignored thereby limiting hypothesis generation. However, life circumstances are intrinsically

related, with adverse events rarely arising in isolation. Individuals who lose a parent at a young

age may experience harder socioeconomic situations; premature parental death might indicate

adverse environmental conditions that also influence offspring risk of death; poor childhood

health may adversely affect health and social status in adulthood (Smith et al. 2014; Case, Fertig

and Paxson 2005).

In this study, we employ recursive partitioning (RP) methods for survival data to gain

new insights regarding circumstances present in early and mid-life that may arise in

combinations in their joint effects on mortality risk later in life. Unlike the classic application of

the Cox model, RP methods can automatically identify the main factors associated with

longevity while also detecting interactions between them without specifying them a priori. RP

methods have been extensively used in medicine, primarily for prognostic grouping of patients

based on the course of a disease (Zhang and Singer 2010). This analytical approach, though, is

relatively novel to research on aging and in studies of life course epidemiology (Kuh et al. 2003).

In gerontology, biodemography, and life course epidemiology, the challenge is to

determine the relative importance of combinations or sequences of early and mid-life conditions

that contribute to health and longevity differentials. We discuss a variable importance measure

based on random forests, an extension of the RP approach, which quantifies the relative

importance of covariates (Ishwaran et al. 2010). Identification of the most important variables

that are associated with survival differentials is necessary to expand our understanding of aging

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but it also helps to guide development of interventions or public policies aimed at improving

long term survival and healthy lifespan (Smith et al. 2014).

The purpose of this study is to first present the logic and procedures of RP methods and

secondly to argue that these methods are valuable analytic tools for identifying complex

combinations of family and individual circumstances present in early and mid-life that explain

the variability in longevity later in life. We apply this methodology to identify factors that

characterize subjects with differing survival experience based on conditions starting early in life

and spanning through the reproductive years, and to assess the relative importance of these

factors in expanding our understanding of late life survival differentials.

DATA

The study is based on data from the Utah Population Database (UPDB). The UPDB

comprises extensive genealogical data and is linked to numerous sources of data including Utah

birth and death certificates. Nearly 9 million individuals are now represented in the database;

new data and new members are added annually as they become available. The UPDB represents

a unique and rich resource of population-based information for demographic, genetic and

epidemiological studies.

The focus of this study is on post-reproductive mortality risks. Accordingly, all survival

is based on individuals who lived to at least age 50. Individuals are sampled from sibships where

siblings are born between 1850 and 1900. This time period was selected for several reasons: (1)

family formation patterns from this period generally reflect natural fertility conditions which is

important for examining their effects prior to the advent of modern medicine and family planning

methods, (2) the first pioneers settled in Utah in 1847 and, therefore, people born after 1847 are

the first cohorts of this population with complete data in the UPDB, and (3) all individuals from

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this era are members of extinct cohorts where death dates are observed. All analyses are sex-

specific. One male from each sibship is selected where at least one male reached age 50 and

married (if there was more than one, one was chosen at random). The comparable process is

repeated for females. Finally, to assess early and mid-life factors that may affect later life

mortality, we utilize information from three generations: the individuals themselves, their parents

and their children.

The outcome for the study is time from age 50 to death from any cause. The early and

mid-life conditions considered are birth year, family excess longevity (FEL; vide infra), parental

age at subject’s birth, subject’s sibship size, subject’s birth order, father’s socioeconomic status,

and subject’s age at parental death, and several measures of subject’s fertility (parity, age at first

birth, and age at last birth) as suggested by the historical demographic studies of the early life

effects on longevity.

Familial excess longevity (FEL) is a measure of the familial or genetic propensity of an

individual for a long or short life based on the mortality patterns of blood relatives (Kerber et al.

2001). In order to calculate FEL for an individual, excess longevity is calculated for each blood

relative aged 65 or older. Excess longevity is obtained as the difference between the observed

age at death and the expected gender and birth year-specific age at death based on a lognormal

accelerated failure time model. Then FEL is obtained as the weighted average of these excess

longevities, with weights equal to the kinship coefficients, a measure of shared genes assuming a

Mendelian mode of transmission. Only relatives who reached age 65 are considered so that the

measure is less affected by deaths from external causes that dominate younger mortality patterns.

Childhood socioeconomic status is measured based on Nam and Powers (Nam and

Powers 1983) methods using the occupation of fathers, given that mothers during this era often

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do not have sufficient data on occupation. This index is based on the ‘usual occupation’ reported

on death certificates where higher scores are associated with higher socioeconomic status.

Subject’s age at maternal death was defined as a set of age variables. Actual age was used if the

mother died before the subject was 30. The specific value of 30 was used if the mother died after

the subject was age 30. Finally, the subject’s age at death was used if the mother outlived the

subject. A comparable approach was used for subject’s age at paternal death.

METHODS

RECURSIVE PARTITIONING (RP) METHODS

RP methods, also known as tree-based methods, were initially introduced in the context

of classification and regression (Morgan and Sonquist 1963; Breiman et al. 1984). The

development of RP methods for survival data started with work by Gordon and Olshen (1985)

and Ciampi et al. (1987). The rationale behind RP methods for survival data is to split the

covariate space to form groups of individuals which are similar according to their survival

probabilities. The first step of the RP process divides all subjects in two subgroups according to a

question posed to one of the explanatory variables. For example, “Is age at last birth 35 years or

more?” Allowable questions involve one covariate X: if X is ordered, the question has the form

“is X≥c?” for a given value c; if X is categorical the question has the form “is X in S?” where S is

any subset of categories of X. The question that defines the partition is automatically selected

among all allowable questions based on a rule that maximizes a measure of the improvement

associated to the new partition. We use the reduction in the deviance proposed by LeBlanc and

Crowley as the measure of improvement (LeBlanc and Crowley 1992). The process of splitting

the sample into two subsamples is repeated in each subgroup until the subgroups reach a

minimum size. Minimum subgroups size was set to 20, as it is usually considered. Each step

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results in subgroups that are more homogeneous in terms of survival experience than the groups

from the previous step. The resulting model can be represented as a binary tree whose leaves or

terminal nodes correspond to the final partition of the data and yield bins of individuals who all

share a common survival profile.

This first stage of the procedure yields a large tree with many terminal nodes which

might overfit the data and fail to generalize well to the population of interest. Two additional

stages are usually performed, as we do here, after the large tree is built: pruning and

amalgamation. These stages aim at readjusting the size of the tree by combining or

amalgamating nodes with similar survival experience to form the final groups (Breiman et al.

1984; Therneau and Atkinson 2011). Summaries of the final groups are computed to interpret the

tree. When survival is the focus, Kaplan Meier curves are reported.

VARIABLE IMPORTANCE AND PARTIAL SURVIVAL FUNCTION BY RANDOM FORESTS

A random forest is an ensemble of survival trees obtained from random samples with

replacement (i.e., bootstrap samples) drawn from the original data set (Ishwaran et al. 2008).

Two estimates that we show are central to life course studies can be obtained from random

forests: variable importance measures (VIMP) and partial survival functions.

The relative importance of early and mid-life conditions that contribute to health and

longevity differentials can be quantified using VIMP. Variable importance measures based on

random forests have been proposed by several authors (Ishwaran et al. 2010; Breiman 1996;

Breiman 2001). In this article we use the VIMP offered by Ishwaran et al. (2010). The values of

this measure are associated with the depth at which a variable tends to appear in trees, with

higher values corresponding to variables that occur first in the recursive partitioning process (i.e.,

variables splitting higher in trees are more important). This measure can take both positive and

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negative values. Large positive VIMP values indicate that the associated variable is more

predictive.

In the context of random forests, an estimate of the survival function is obtained as the

average of the Nelson-Aalen survival function estimates for each tree of the forest (Ishwaran et

al. 2008). Further understanding of the effect of covariates on survival can be gained studying

the partial survival function (i.e., the survival at a fixed point in time considered as a function of

values of a covariate). More precisely, the partial predicted survival for a covariate X at time t is

�̂�(�) =��̂��, �, ��,0�,��=1

where �̂(�, �, ��,0) denotes the random forest predicted survival at X=x and at the observed values

for observation i, xi,0, for the other variables.

STATISTICAL ANALYSES

Gender-specific multivariate Cox proportional hazards models were estimated to evaluate

the simultaneous effect of early and mid-life conditions on survival past age 50. The RP

algorithm was then used to partition the sex-specific samples into groups of individuals with

similar survival experiences after age 50, and to identify the interrelated circumstances present in

early and mid-life that characterize these groups. For each group identified by the RP method,

we report Kaplan Meier curves, and the estimated median survival, and 95% confidence interval

(CI).

The VIMP of each factor studied was calculated to evaluate its relative importance for

understanding longevity. In addition, for each of the most important life conditions encountered

we study the pattern of the random forest partial survival function estimate at the median and

third quartile sample survival times. These times were chosen to assess how values of a covariate

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induce variations in survival with respect to the average longevity in the sample, and with respect

to one indicator of excess longevity (i.e., the third quartile). All analyses were performed with

the R 2.14.2 package. (R Core Team 2012) Recursive partitioning was done using rpart3.1-50

(Therneau 2011). Variable importance was implemented using the package

randomForestSRC1.4 (Ishwaran and Kogalur 2013).

RESULTS

In UPDB, 42,748 sibships born between 1850 and 1900 with at least one member who

reached age 50 and who was ever married were identified. Only one male and one female were

chosen from each sibship. We identified 59,780 individuals 50 years or older and ever married,

yielding the final samples comprising of 31,221 females and 28,559 males. The sample

descriptive characteristics are given in Table 1.

TABLE 1

Estimated Kaplan-Meier median survival for men and women surviving to age 50 was

74, and 78 years, respectively. Table 2 presents hazard rate ratios from single sex-specific

multivariate Cox proportional hazards models.

For both genders, mortality hazards had a negative association with birth year, and low

FEL was positively associated with mortality past age 50. Men and women in the top quartile of

the FEL distribution experienced a mortality hazard 20% lower than individuals with FEL in the

middle 50%; being in the bottom quartile of FEL was associated with a survival penalty. Men

and women whose fathers died when they were young adults (18-29 years old) had an increased

risk of mortality compared to those whose fathers died when they were 30 or older. There was

also a negative effect on female survival associated with experiencing father death during

childhood (0-4, 5-17 years) as well as experiencing mother death when they were young adults

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(18-29 years). In general these results point to the importance of parental death when subjects

are still dependent or they are at the age where they are making the transition to adulthood (i.e.,

under age 30). Men and women who had their first child before age 20 had excess mortality

hazard rates than those starting parenthood in middle age (20-39 years); in the case of men there

was also an adverse effect regarding late initiation of parenthood (≥40 years). Late age at last

birth conferred a survival benefit for both genders.

TABLE 2

The multivariate Cox proportional hazards models assumes the same relationships for all

people in the sample and generates separate estimates for each covariate without regard to their

combined influences. However, our interest is on the diversity of combinations that might

influence later life survival. Identifying interactions, especially those involving sets of variables

is problematic within the traditional Cox proportional hazards framework, as it involves

considering all two-way and higher level interactions. Instead, we used the RP methods outlined

above that allow different predictors, different cut points, and multiple variables considered

collectively.

RECURSIVE PARTITIONING

Figure 1 shows a summary of the RP analysis for males, the tree and the estimated

survival curves for the nine terminal nodes, as well as the overall survival curve. The tree is

organized so that at each partition, individuals in the left branch have better survival past age 50

than those in the right branch. There is a six year gap in median survival among the most long-

lived group (G1) and the least long-lived one (G9).

The tree shows that the first split was based on FEL (≥54% percentile vs. <54%

percentile). This threshold partitions the sample into two groups with a three year difference in

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median survival, 76 vs. 73 years (not shown in Figure 1). Among men with FEL that exceeds the

54% percentile, the method identified four groups with estimated median survival times ranging

from 74 to 78 years. Group G1 comprises men born during or after 1890 (top 18% percentile of

birth year), and group G4 includes men born before 1890 and whose last child was born before

they were 36 years old. The male group with the lowest median survival, G9, had individuals

with FEL<54% percentile, born before 1890, and whose last child was born before they were 36

years old.

FIGURE 1

The groups shown in Figure 1 are amalgamated (i.e., groups with similar survival

experience are combined) resulting in four groups with distinct all-cause survival past age 50.

Men in G1 and G2 have the best survival experiences and are grouped together with median

survival age of 77 years (95% CI: 76, 77). G3 has a distinct survival experience and was not

combined with any other group. A group with intermediate longevity is formed combining G4,

G5, G6 and G7, resulting in a median survival of 74 years (95% CI: 73, 74). The two groups

with the worse survival, G8 and G9, are joined into a group with median survival of 72 years

(95% CI: 71, 72). The Kaplan-Meier estimates of the four amalgamated groups are shown in

Figure 2.

FIGURE 2

Although twelve early and mid-life conditions were included in the recursive partitioning

analysis, only four conditions appeared in the final tree presented in Figure 1: FEL, age at last

birth, birth year, and birth order. Larger values of the first three factors were associated with a

more favorable outcome, while for birth order having been born first or second represented a

survival advantage.

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The summary of the RP analysis for females is presented in Figure 3. Female median

survival ranged from 74 years (G9) to 83 years (G1). FEL, birth year, age at first birth and birth

order are the early and mid-life conditions that determined these groupings. Unlike in the male

case, being the first child represented a liability regarding later life survival. Among women with

the worst outcome, being teenage mothers (age at first birth<20 years) played an important role

in later life survival; 74 years median survival for women starting maternity as teenagers

compared to 76 years for those starting maternity later in life.

FIGURE 3

The amalgamation process merged the groups with intermediate survival experience in

two groups, one joining G2, G3 and G4 and another one combining G5, G6 and G7 (Figure 4).

The median survival was 80 years (95% CI: 80, 81) for the former and 78 years (95% CI: 78, 78)

for the latter. G1, G8 and G9 have distinct survival experiences and are not combined with other

groups.

FIGURE 4

VARIABLE IMPORTANCE AND PARTIAL SURVIVAL FUNCTION BY RANDOM FORESTS

Figure 5 provides information on the relative contribution of each early and mid-life

condition in predicting later life survival. Familial excess longevity (FEL) is clearly the strongest

predictor for males and females. The next most important predictor for males is age at last birth,

while for females both birth year and age at first birth contribute considerably to predicting later

life survival.

FIGURE 5

The random forest estimate of the partial survival function of FEL for males assessed at

the median survival time (i.e., the survival at age 74 considered as a function of FEL) increases

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sharply for those at the absolute bottom to those at the 10% of FEL. That is, men with the

minimum value of FEL have an estimated 35% survival at age 74 while those at the 10%

percentile of FEL have a 45% estimated chance of survival at the same age (i.e., the initial abrupt

rise in the curve). The partial survival function then shows a plateau for men between the 10%

and the 40% percentile of FEL and above that it continues to increase at an approximately

constant rate (Figure S1a). A similar pattern was found for survival at age 82 (third quartile of

survival age); survival past age 82 rises from 15% for men with the minimum value of FEL to

above 30% for people at the 60th percentile of FEL (Figure S1b). The estimated survival at 74

and 82 years increases steadily with increasing ages at last birth (Figures S2a-b). At age 74, men

whose last birth was at age 30 have a below average predicted survival of 43%, compared to a

predicted survival above 52% for those whose last child was born after age 40.

For women, the estimated partial survival of FEL at the median follow up time, 78 years,

increases sharply for people in the bottom 10% of FEL, rising from about 28% for people with

the lowest values of FEL to 40% for people in the top 10% percentile of FEL. After that, the

predicted survival stabilizes up to the 25% percentile of FEL and then it continues to show an

upward trend (Figure S3a). Survival at 85 years (third quartile of follow up time) also increases

as FEL increases, from approximately 13% for women with the lowest values of FEL to above

30% for people in the top 20% of FEL (Figure S3b). Survival both at age 78 and 85 increases

steadily with birth year (Figures S4a-b). Regarding age at first birth, survival at age 78 and 85

increases rapidly from age 15 to age 22, then it shows a decreasing trend (Figure S5a-b).

We should emphasize that the partial survival function is derived from survival trees.

Accordingly, all the curves shown in Figures S1-S5 account for all the interactions with the other

variables.

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DISCUSSION

This study examined a diverse and well-documented set of early and mid-life conditions

and, using a novel approach via RP methods, identified combinations among these predictors

that relate to longevity differentials past age 50. In addition, using VIMP measures we assessed

the relative contribution of early and mid-life conditions in their effects on longevity

discrepancies.

Beyond the well demonstrated main effects of FEL on later life survival (Smith et al.

2009; Smith et al. 2014), we identified interactions of FEL with other life circumstances. For

males in the top half of the FEL distribution (FEL≥54%), interactions with birth year, and age at

last birth were encountered, resulting in median over-all survival probabilities ranging from an

exceptionally high of 78 years to an average median of 74 years. Among women in the top 45%

of FEL, mortality risks differed depending on birth year, and birth order; RP identified a group of

women with an exceptionally high median all-cause survival past age 50 of 83 years (G1).

Interestingly, women with FEL in the bottom 45%, born in or after 1884 (G7) have a similar

mortality risk to groups of female with FEL in the top 45% percentile born before 1884 (G5 and

G6), suggesting an interesting interplay between the overall effects of history (as reflected by

birth year) separate from family history. It is worth noting that while the Cox regression analyses

also showed that FEL was significantly associated with survival, the RP analysis allows for a

more precise identification of the subpopulations whose longevity is enhanced or penalized.

A better understanding of factors affecting human longevity requires analytical tools that

take into account the interrelation between events occurring throughout life. This study has

shown how the RP method represents a valuable methodology to uncover interactions between

life circumstances in relation to mortality risks in later life. Figures 1 and 3 allow us to visualize

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the complicated ways in which early and mid-life conditions co-occur to produce longevity

patterns in males and females. Within the Cox regression methodology, only interactions

specified a priori in the model by the analyst can be evaluated, the RP approach builds a model

in a more flexible way. Another advantage of the RP method over the traditional Cox approach is

that it automatically categorizes numerical predictors guaranteeing that the survival pattern for a

final group of individuals is homogeneous within that group; while in the traditional Cox

approach the categorization has to be decided a priori by the investigator with no guarantee of

homogeneity within the group. Also, the recursive nature of the RP method allows the

identification of prognostic factors that exert their influence in subsets of subjects rather than

across all subjects as with the Cox regression model. A limitation of the approach is due to the

known sensitivity of trees to the characteristics of the sample. Also, control parameters provided

to the algorithm such as the minimum terminal node size are arbitrarily chosen and may

influence the final description. The R program used for building the tree, rpart, produces a

number of trees that are within one standard deviation from the optimal tree. The researcher is

tasked to choose among these trees based on the context of the problem (Breiman et al. 1984).

The variable importance measure, based on an ensemble of survival trees, is a useful

technique for answering questions regarding early and mid-life conditions that are most

important for understanding variation in mortality risk later in life. For men, the main factors

associated with later life survival were FEL, and age at last birth. For women, the strongest

predictors were FEL, birth year, and age at first birth.

As in our previous work, FEL was found to be an important predictor of mortality risk

after the reproductive years both for males and females (Smith et al. 2009; Smith et al. 2014;

Garibotti et al. 2006). Higher values of FEL confer a protection on survival after the reproductive

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years; the average probability of survival at the sample median age at death, 74 years for males

and 78 years for females increases continuously as FEL increases (Figures S1, and S3).

Association between fertility patterns and post-reproductive longevity had been reported (Smith,

Mineau and Bean 2002).

This study contributes to understanding the complexity of the interrelations between early

and mid-life conditions that account for survival decades later. The study also shows that the

recursive partitioning, and random forest methodologies are valuable tools to study determinants

of longevity.

AKNOWLEDGMENTS

This work was supported by the National Institutes of Health – National Institute of

Aging [Grant Numbers 1R21AG036938-01, 2R01 AG022095] and the Universidad Nacional del

Comahue, grant from the Research Secretary B188. The authors wish to thank the Huntsman

Cancer Foundation for database support provided to the Pedigree and Population Resource of the

HCI, University of Utah. Partial support for all datasets within the UPDB was provided by the

HCI Cancer Center Support Grant, P30 CA42014 from National Cancer Institute. We also thank

Alison Fraser and Diana Lane Reed for valuable assistance in managing the data.

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TABLE 1. Descriptive statistics of early and mid-life conditions by gender.

Variable

Males Females

Mean Standard

deviation Mean

Standard

deviation

Age at death 73.71 11.03 76.65 11.55

Birth year 1876.63 12.50 1876.16 12.33

Father<20 yrs old at subject birth 0.004 0.060 0.003 0.058

Father≥50 yrs old at subject birth 0.094 0.292 0.093 0.290

Mother<20 yrs old at subject birth 0.061 0.239 0.065 0.246

Mother≥40 yrs old at subject birth 0.085 0.278 0.084 0.278

Sibship size 7.29 3.39 7.34 3.37

Birth order 3.22 2.75 3.35 2.77

Father’s Nam Power 43.20 15.01 43.14 15.00

Subject 0-4 yrs old at father death 0.034 0.181 0.036 0.186



Subject 0-4 yrs old at mother death 0.046 0.209 0.046 0.209



Parity 5.84 3.38 6.12 3.35

Age at first birth<20 yrs old 0.016 0.126 0.194 0.395

Age at first birth≥40 yrs old 0.050 0.219 0.009 0.094

Age at last birth 35-44 yrs old 0.463 0.499 0.633 0.482

Age at last birth≥45 yrs old 0.336 0.472 0.069 0.253

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TABLE 2. Hazard rate ratios from multivariate Cox proportional hazards models.

Variable Males Females

Hazard rate P Hazard rate P

Birth year 0.993 <0.001 0.989 <0.001

Top 25th percentile of FEL 0.802 <0.001 0.805 <0.001

Bottom 25th percentile of FEL 1.280 <0.001 1.248 <0.001

Father<20 yrs old at subject birth 1.107 0.439 0.895 0.417

Father≥50 yrs old at subject birth 0.988 0.678 0.956 0.115

Mother<20 yrs old at subject birth 1.022 0.529 1.065 0.059

Mother≥40 at subject birth 0.978 0.470 0.990 0.751

Sibship size 1.006 0.068 1.004 0.183

Birth order 1.000 0.978 0.995 0.250

Father’s Nam Power 1.000 0.605 0.999 0.075







Parity 0.999 0.822 1.004 0.229

Age at first birth<20 yrs old 1.158 0.016 1.104 <0.001

Age at first birth≥40 yrs old 1.109 0.016 1.040 0.654

Age at last birth 35-44 yrs old 0.898 <0.001 0.975 0.229

Age at last birth≥45 yrs old 0.827 <0.001 0.877 0.001

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FIGURE 1. Recursive partitioning (RP) analysis for male sample. a) RP tree: In each terminal node the following information is given: group identification (G1-G9), n: sample size, p50: Kaplan-Meier median survival estimate, and 95% confidence intervals. alb: age at last birth, brthord: birth order, byr: birth year, FEL: familial excess longevity (given as percentile with respect total data set), b) Kaplan-Meier survival past age 50 curves for groups defined by terminal nodes of RP algorithm (a).

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FIGURE 2. Kaplan-Meier survival past age 50 curves for the final groups of men obtained after

applying the amalgamation algorithm. Overall: overall male survival past age 50, G1-G9 group

identification as in Figure 1 a.

26

FIGURE 3. Recursive partitioning tree for female sample. In each terminal node the following

information is given: group identification (G1-G9), n: sample size, p50: Kaplan-Meier median

survival estimate, and 95% confidence intervals. afb: age at first birth, brthord: birth order, byr:

birth year, FEL: family excess longevity (given as percentile with respect to total data set).

27

FIGURE 4. Kaplan-Meier survival past age 50 curves for the final groups of women obtained after

applying the amalgamation algorithm. Overall: overall female survival past age 50, G1-G9 group

identification as in Figure 3.

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FIGURE 5. Variable importance by random forest results of early and mid-life conditions in

predicting survival past age 50. a. Male, b. Female.

byr: birth year, FEL: family excess longevity, ma.age.bth: maternal age at subject birth,

pa.age.bth: paternal age at subject birth, sibsize: sibship size, brthord: birth order, SES: father’s

socioeconomic status, age.ma.dth: age at maternal death, age.pa.dth: age at paternal death, ceb:

parity, afb: age at first birth, alb: age at last birth.

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APENDIX A. Supplementary figures

FIGURE S1. Male random forest estimated partial survival functions for FEL. a. at 74 years of

age, b. at 82 years of age.

30

FIGURE S2. Male random forest estimated partial survival functions for age at maternal death. a.

at 74 years of age, b. at 82 years of age.

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FIGURE S3. Female random forest estimated partial survival functions for FEL. a. at 78 years of

age, b. at 85 years of age.

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FIGURE S4. Female random forest estimated partial survival functions for birth year. a. at 78

years of age, b. at 85 years of age.

33

FIGURE S5. Female random forest estimated partial survival functions for age at maternal death.

a. at 78 years of age, b. at 85 years of age.

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