Copyright 1997 by The Geronlological Society of America
Journal of Gerontology: SOCIAL SCIENCES
1997. Vol. 52B. No. 1, S37-S48
Loss to Follow-up in a Sample of Americans 70 Years
of Age and Older: The LSOA 1984-1990
Adrienne H. Mihelic1 and Eileen M. Crimmins2
'Department of Population Dynamics, Johns Hopkins University.
2
Andrus Gerontology Center, University of Southern California.
A LTHOUGH the increasing availability of panel data has
•**• been a great boon to researchers studying characteristics that change with age and over time, analysis of panel
data is complicated by the loss of panel members at followup interviews. All studies using panel data must investigate
the extent to which loss to follow-up has occurred and
whether the loss is likely to bias analytic results. Bias can be
introduced when loss to follow-up is not random and is
related to outcomes of interest. Such selection of the sample
may result in confounded associations (Schaie, Labouvie,
and Barrett, 1973; Siegler and Botwinick, 1979) and distorted prevalence estimates and transition rates (Corder,
Woodbury, and Manton, 1992; Van den Berg, Lindeboom,
and Ridder, 1994). For example, an analysis of health
change in a panel of older persons would be selected with
respect to the characteristic of interest if persons in worse
health were more likely to become nonrespondents than
others; this could result in biased estimates of the level of
health of the sample and the correlates of health change.
Samples of older persons are generally believed to be more
susceptible to nonresponse selection because the proportion
lost to follow-up tends to increase with age (Rodgers and
Herzog, 1992). Studies of nonresponse have suggested that
the differences between participants and nonrespondents
may be greater among older persons than younger (Schaie,
Labouvie, and Barrett, 1973). It is the magnitude of the
difference between the respondents and nonrespondents that
ultimately determines whether the sample is compromised
by nonresponse.
In this study, we are concerned with nonresponse that
occurs at an interview after the baseline interview, often
referred to as wave nonresponse. This type of nonresponse
should be distinguished both from item nonresponse, which
occurs when a person does not respond to a single question,
and from initial nonresponse, which occurs when a person
does not respond to the entire first interview. We also
distinguish nonresponse among those alive from nonresponse due to mortality, which we view as a "legitimate
outcome."
The goal of this study is to evaluate whether there is
nonrandom nonresponse in a multiwave panel study of older
Americans (the Longitudinal Study of Aging) and whether
this nonresponse is likely to significantly bias analytic results
based on these data. To determine whether there is nonrandom nonresponse related to observed characteristics, a predictive model of wave-nonresponse is developed. Individual
probabilities of nonresponse estimated from this model are
used to construct weights for the remaining sample members
which compensate for the loss to follow-up. Substantive
univariate and bivariate results from data adjusted for nonresponse with these weights are compared with those from
unadjusted data. In a second approach appropriate for multivariate analyses, the probability of sample selection (or loss
to follow-up) is modeled simultaneously with a substantive
outcome. This approach allows us to examine the effect of
any unobserved characteristics jointly affecting nonresponse
and our substantive outcome, and to evaluate the extent of
sample selection bias in a multivariate context.
An Overview of the Problem of Nonresponse
As noted above, nonresponse is an issue in all panel
surveys. In the first household interview of the National
Medical Care Utilization and Expenditure Survey (NMCUES), 10 percent did not respond. By the fifth interview,
conducted 15 months later, 22.1 percent of the sample were
nonrespondents (Wright, 1983). About 5 percent of the
Survey of Income and Program Participation (SIPP) sample
did not respond to the first interview. By the ninth wave, 36
months later, this rate had accumulated to 22.3 percent
(Kasprzyk and McMillen, 1987). Nonresponse to the annual
interview of the Panel Study of Income Dynamics (PSID)
was high in the first wave (24%), then leveled off to about 2
S37
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Loss to follow-up is a problem in longitudinal samples, and the literature on response rates in panels of older persons
suggests that they may be more vulnerable to nonrandom attrition and its consequent biases. The event history
approach used in this study to determine the correlates of nonresponse addresses important shortcomings of previous
analyses by incorporating time-varying covariates. Nonresponse is not random; persons of older ages, lower
education, who live alone, rent (not own), have more functioning impairments, or have another sample person in the
household are more likely to become nonrespondents. However, correction accounting for the effect of these
correlates of nonresponse, as well as unobserved characteristics potentially affecting nonresponse, suggests that the
association between these characteristics and the probability of nonresponse is not large enough to introduce bias.
While these results are not portable to other analyses or panels, they do indicate that in this case, significant
nonrandom nonresponse does not bias all related analytic results.
S38
MIHELICAND CRMMINS
How Do Persons Become ' 'Lost to Follow-up'' ?
Nonresponse can occur because a person refuses to respond to the survey, because the person cannot respond to
the survey, or because the person cannot be located. Refusal
to respond may indicate distaste for responding to surveys in
general, lack of interest in the particular survey, or competing uses for the potential respondent's time. Refusal may be
related to gender. Women might be more wary of personal
contact with interviewers; men might find long telephone
surveys distasteful. This might be why men are more likely
to be nonrespondents in some studies (Jay et al., 1993;
Kalton et al., 1990; Streib, 1982), while in others they are
not (Adams etal., 1990).
In general, persons of lower socioeconomic status, those
who have fewer years of education or lower incomes, are
more likely to become nonrespondents (Chyba and Fitti,
1991; Streib, 1982). It is possible that persons with higher
education could be more interested in the survey itself, or
more aware of the importance of survey response to research, and thus less likely to refuse. Persons of lower
socioeconomic status may have a greater distrust of survey
organizations or less identification with the interviewers,
and this may lead to more refusal. The relationship between
socioeconomic status and refusal could explain the finding
that African Americans have been more likely to be nonrespondents (Foley et al., 1990).
Inability to complete a future interview is more likely
among persons who are in worse health. Many studies have
reported that nonrespondents are likely to be in poorer
physical health, have a greater number of functioning difficulties, have worse self-reported health (Chyba and Fitti,
1991; Manton, 1988; Rodgers and Herzog, 1992; Speare,
A very, andLawton, 1991; Streib, 1982) or have lower levels
of cognitive functioning (Kalton et al., 1990; Schaie, Labouvie, and Barrett, 1973; Siegler and Botwinick, 1979).
Difficulty locating sample members may be a particularly
important problem among older respondents. Residential
relocation among the old may occur because a household
member dies or because an individual can no longer maintain
independent living. Persons identified by the survey organization as contact persons are also likely to be older and thus
more likely to die and dissolve their residences. Those who
do not own their homes are more likely to become nonrespondents because they have fewer barriers to moving and
thus are more likely to become unable to locate (Kalton,
1990; Speare, Avery, and Lawton, 1991).
Family composition and marital status both have been
linked to nonresponse (Speare, Avery, and Lawton, 1991).
Persons who are living alone may be more likely to become
lost to future interviews since they are less likely to leave
someone behind who would know their whereabouts. Lillard's (1989) finding that household response rates were
higher among those belonging to families with other households participating in the survey is consistent with this
hypothesis.
Age is almost always found to be a predictor of nonresponse (Adams et al., 1990; Rodgers and Herzog, 1992).
This may be due to the fact that the older one is, the more
likely one is to experience changes in residence that result in
household dissolution. The institutionalized population may
have even higher rates of nonresponse than the communitydwelling population because they are more difficult to locate
or because of resistance from the institution or caregivers
(Rodgers and Herzog, 1992).
In addition to individual characteristics that may influence
a person's propensity to continue responding to the survey,
there are also certain survey attributes that may enhance the
chances that a sample person will respond. The number of
interviews a person is requested to complete may be related
to respondent burden and thus to survey response (Kalton,
Kasprzyk, and McMillen, 1989); however, comparisons of
response rates among surveys with differences in the total
number of interviews conducted suggest that frequency of
interviews does not affect rates of nonresponse (Lillard,
1989). Nonresponse does accumulate over time; however,
with a pattern of decline in response rate at the first follow-up
interview, then a leveling off (e.g., Hill, 1992; Lillard,
1989; Streib, 1982). This initial flux might be caused by the
weeding out of "not-interesteds."
While we have used the literature to hypothesize the
mechanisms through which response is affected, it is not
clear from previous studies that these hypotheses are consistently supported by existing empirical work. Even in surveys
of similar populations, the literature in this area is replete
with conflicting findings which we would generally attribute
to the lack of multivariate analyses or the omission of
important variables. For instance, men are sometimes found
to be more likely to be nonrespondents (Jay et al., 1993;
Kalton et al., 1990; Streib, 1982), although sex has also
been found to be insignificant (Adams et al., 1990). It is
possible that whether or not a sex difference appears is
related to whether or not living arrangements, marital status,
and health are controlled. All of these characteristics are
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percent at each interview, accumulating at about 44 percent
in the twentieth wave (Hill, 1992).
In their comparison of the characteristics and methodologies of several surveys related to health among older persons, Corder and Manton (1991) report the relative level of
nonresponse in four longitudinal studies. Low nonresponse
rates of about 4 percent are reported for persons selected on
disability among those who had previously completed a
screening interview for the initial 1982 interview of the
National Long Term Care Survey (NLTCS). Among those
eligible for reinterview seven years later, only 6 percent
were lost to follow-up. On the other hand, in the NHANESI
follow-up, which required a physical exam, nonresponse
was a high 25 percent. According to Corder and Manton
(1991), among surveys of the older population on health
topics both the Longitudinal Study of Aging (LSOA) and the
National Nursing Home Survey fall within the moderate
range on nonresponse. While the new survey of Asset and
Health Dynamics Among the Oldest Old (AHEAD) does not
yet have a longitudinal component, 20 percent of the
screened sample was not interviewed on the first wave (Hurd
et al., 1994). These studies differ in their objectives, sampling strategies, observation plans, and methodologies, as
well as in their levels of follow-up nonresponse; the issue of
assessing the effect of panel nonresponse is, however, common to all of them.
AN ANALYSIS OF NON-RESPONSE
Correcting for Nonresponse
If loss to follow-up occurs nonrandomly, that is, differentially selecting persons with certain characteristics out of
the sample, attention must be given to correcting potential
bias. Weighting is perhaps the most often used approach to
unit nonresponse adjustment, although other techniques,
such as imputation, are also used. One of the more commonly used methods for constructing weights is the application of response probability weights (Lepkowski, Kalton,
and Kasprzyk, 1989; Rowland and Forthofer, 1993). Individual weights are constructed from the results of multivariate regressions predicting probability of nonresponse, and
these weights are as unique as the characteristics predicting
nonresponse (Iannacchione, Milne, and Folsom, 1991).
The weights can be applied to correct descriptive univariate
or bivariate statistics, including prevalence and transition
rates, for a sample with nonrandom nonresponse.
With a perfectly specified multivariate analysis in which
all characteristics contributing to nonresponse are controlled, bias would be eliminated. Since perfect specification
is not possible, one way to determine how much difference
an adjustment for nonresponse will make is by making the
adjustment using the best specified model possible and then
comparing corrected and uncorrected analyses.
While this is a common method for compensating for
nonresponse, it assumes that those who are lost to follow-up
are similar to continuing respondents on unobserved characteristics. If there are unobserved characteristics affecting
both nonresponse and outcomes of interest, correcting only
for observed characteristics will not eliminate the potential
bias. Jointly estimating the probability of nonresponse and
the substantive outcome of interest offers a way to correct for
unobserved characteristics (Hoem, 1985; Tin, 1995; Van
den Berg, Lindeboom, and Ridder, 1994).
While most studies of attrition in panel surveys find
nonrandom loss, several evaluations have found that correction has not altered the interpretation of the results (for
example, Goudy, 1985; Kalton, Kasprzyk, and McMillen,
1989; Norris, 1987; Rowland and Forthofer, 1993). On the
other hand, other studies have found that adjusting for
attrition significantly changes some substantive findings
(Hausman and Wise, 1979; Markides, Timbers, and Osberg,
1984). The reason for this is that whether or not nonrandom
nonresponse translates into a biased sample depends on the
relationship of the outcome of interest to nonresponse, how
well-specified the model of nonresponse is, the size of the
difference between respondents and nonrespondents, and the
extent of the loss (Braver and Bay, 1992). The importance of
sample attrition necessarily continues to be emphasized in
virtually all analyses of longitudinal data (Corder, Woodbury, and Manton, 1992; Hsiao, 1986) because it is not
possible to estimate whether or not a correction will matter
until it is applied (Berk, 1983).
METHODS
Sample. — The Longitudinal Study of Aging (LSOA) is a
four-wave panel survey that was designed to represent the
community-dwelling population 70 years of age and older in
the United States at the initial interview in 1984. The
original LSOA interview took place among those eligible
who responded to the 1984 National Health Interview Survey (NHIS). Among surveyed households, 96.4 percent
responded to the NHIS (Ries, 1986), and 96.7 percent of
these responded to the Supplement on Aging, the baseline
interview for the LSOA (Kovar, Fitti, and Chyba, 1992).
Three follow-up LSOA interviews are conducted at twoyear intervals, with the last interview occurring in 1990.
When a sample member is unable to respond because of a
physical or mental health problem, proxy responses are
accepted. While the original interview was face-to-face, the
follow-up interviews were done primarily by phone, using a
mail interview where a phone interview could not be completed. Additional details of the survey design and interview
protocol are available in Kovar, Fitti, and Chyba (1992).
Data from the National Death Index (NDI) appended to
the LSOA survey files provide confirmation and date of
death. A sample person is assumed to be dead if a contact
person reported that person as deceased or if that person has
a "good match" with the National Death Index (Kovar, Fitti,
and Chyba, 1992) and did not respond to any surveys
subsequent to the date of death; sample persons are otherwise assumed to be alive. We make this assumption because
evaluations of the accuracy of the National Death Index
using match strategies comparable to that used by the LSOA
indicate its sensitivity (correctly identifying persons known
to be deceased) is approximately 97 percent and its specificity (not identifying those known to be alive as dead) is about
99 percent (Rich-Edwards, Corsano, and Stampfer, 1994;
Williams, Demitrack, and Fries, 1992). Nevertheless, it is
possible that a few persons we assume to be alive and
nonrespondent could have died. This is especially true in the
final year because of a considerable lag-time recording
deaths in the NDI (Rich-Edwards, Corsano, and Stampfer,
1994), though this error is further minimized because we do
not rely solely on the NDI data, but have contact persons'
reports as well.
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known to be quite different among older men and women.
The literature is also ambiguous about the effect of household and family composition on nonresponse. Not being
married is sometimes associated with nonresponse (Speare,
Avery, and Lawton, 1991) and sometimes not (Streib,
1982). Living arrangements and marital status have both
been linked to health. Streib (1982) controlled for health,
whereas Speare, Avery, and Lawton (1991) did not. The
response rate among African Americans is sometimes lower
than that among others (Foley et al., 1990), but sometimes
not (Streib, 1982). Perhaps race is confounded with socioeconomic status and health. Streib controls for these characteristics; Foley apparently does not.
Analyses of nonresponse in panels of older persons have
often unnecessarily focused on a limited range of characteristics, neglected to account for the possibility that individuals' characteristics may change over time, or ignored the
contribution of unobserved characteristics. The consequences of these shortcomings are the presentation of spurious relationships, time-inappropriate linking of characteristics and outcomes, and a failure to fully account for
nonresponse bias.
S39
MIHEL1C AND CRIMMINS
S40
Analysis. — This section begins with a description of how
nonresponse and death contribute to the decrement of the
sample over time. Both aggregate outcomes for the entire
sample and individual patterns of response for the four
waves are presented. Next, we turn to a multivariate analysis
relating nonresponse to observed characteristics. Based on
this analysis, we proceed with an application of a weighting
approach to compensate for this loss and examine the effect
on distributions and bivariate relationships. We conclude
with an approach to multivariate analysis that allows correction for both observed and unobserved characteristics affecting nonresponse.
RESULTS
Multivariate Analysis of Loss to Follow-up
To determine whether there are differences between the
20 percent of the sample that does eventually become lost to
follow-up and continuing respondents, we use a multivariate
analysis predicting nonresponse over the four waves of the
LSOA. The outcome variable of interest is the first instance
of nonresponse recorded for a panel member for any reason
other than death. Persons who do not respond because they
died are removed from the analysis for that and subsequent
interviews. If the dead are retained and death is modeled as a
competing risk, the estimated coefficients and standard errors for the relative risk of nonresponse are virtually identical
to those presented here. We do not explicitly model death in
this analysis, however, because this source of sample decrement is not an' 'error'' to be corrected for. Loss to death is an
important part of the sample dynamic, however, and it
should be taken into account in any substantive analysis.
Nonresponse after the first occurrence is not considered in
the equation because persons' characteristics at the beginning of those intervals are missing. In our analysis the event
Table 1. Sample Nonresponse in Four Waves of the LSOA
Wave 1
1984
n
Wave 3
1988
Wave 2
1986
%
n
%
n
Wave 4
1990
%
n
%
2,676
1,857
618
5,151
52.0
36.1
12.0
100.0
1 A. Frequency and Percentages of Persons by Interview Status at Each Wave
Interviewed
Lost to death
Nonresponse
Total
5,151
—
—
5,151
100.0
—
—
100.0
4,114
645
392
5,151
79.9
12.5
7.7
100.0
3,314
1,291
546
5,151
64.3
25.0
10.5
100.0
IB. Percent of Those Alive on Previous Wave Not Interviewed on Next Wave Because of Death or Nonresponse
Lost to death
Nonresponse
12.5
7.6
14.3
12.1
14.7
16.0
14.1
18.8
1C. Percent of Those Alivf : Who Are Nonrespondents
8.7
ID. Percent of Those Alive Who Become Nonrespondents for the First Time Among Those Who Were Not Previously Nonrespondents
8.7
9.7
11.1
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Description of Sample Dynamics
The number of respondents diminished at each successive
wave (Table 1A). Of the original 5,151 respondents, 80
percent were interviewed in 1986, 64 percent in 1988, and
just over half of the sample was interviewed at the last wave
in 1990. Three-quarters of this loss is due to death. By the
second wave 12 percent of the original sample had died; by
the fourth wave more than one-third was dead. Interestingly,
even in this older sample, the percentage who died between
interviews among those known to be alive at the preceding
interview was fairly constant across the three intervals (Table IB). Between the first and second interviews 12 percent
of the sample had died; between the third and fourth interviews about 15 percent had died.
The percentage of the original sample not responding to
the survey increased with each wave. Among those not
known to be dead at each wave (Table 1C), the likelihood of
nonresponse increased from almost 9 percent at the second
wave to 19 percent at the fourth wave. The percentage
becoming new nonrespondents (Table ID) does not increase
nearly as dramatically, indicating that the likelihood of not
responding to future waves is much higher for those who are
earlier nonrespondents. This pattern of relatively low rates
of increase in new nonresponse over time that accumulate to
overall larger rates of total nonresponse has been observed
by others (Kalton, Kasprzyk, and McMillen, 1989).
The frequency of the observed three-interval pattern of
response for individuals presented in Table 2 gives a fuller
picture of how sample nonresponse affects our ability to
trace changes in individuals' characteristics across interviews. For instance, "III" or an interview at each of the
three follow-up waves, is the most common pattern of
response. Eighty percent of the original respondents are
interviewed at every wave before death. Another 10 percent
of the sample is only missing at one interview and assumed
to be still alive. Only 4 percent of the sample are never
interviewed again after the initial interview, and one-third of
these are dead before the fourth wave. Thus, even with this
level of sample attrition, the changes in individual characteristics can be traced for most living members of the sample.
S41
AN ANALYSIS OF NON-RESPONSE
Table 2. Response Patterns for Three Waves of Follow-up
Pattern
Frequency
Percent
Description
2,431
47.2
IID
ID.
D..
442
597
645
8.6
11.6
12.5
UN
INI
Nil
302
134
70
5.9
2.6
1.4
INN
NIN
NNI
128
47
41
2.5
0.9
0.8
IND
NID
80
22
1.6
0.4
2.0% One more interview, dead
ND.
NND
50
21
1.0
0.4
1.4% Never interviewed again, dead
141
2.7
2.7% Never interviewed again, presumed alive
5,151
100.1
III
32.7% Interviewed until death
9.9% Two more interviews, still alive
4.2% One more interview, still alive
100.1
Note: I = Interviewed; N = Nonresponse; D = Dead. Period (ID.) = Previously deceased.
of first nonresponse can occur at any one of the three
interviews after the initial interview. A person-interval logistic regression is modeled; the log odds for the conditional
probabilities of the event of first-time nonresponse occurring
are estimated using SAS PROC LOGISTIC (SAS Institute,
1989).
To enable us to take advantage of fresh information collected at each interview, a pooled data set is created in which
each observation gets a unique record for each interval (n =
10,756) and characteristics at the beginning of the interval are
related to response status at the end of the interval. This
approach assumes that the error terms for each observation (in
this case each person-interval) are not correlated. To evaluate
the sensitivity of the results to this assumption, regression
results from a generalized estimating equation (GEE), which
treats the correlation across an individual's observations as a
nuisance parameter, were compared with the results presented here (Groemping, 1994; Liang and Zeger, 1986;
Lipsitz, Kim, and Zhao, 1994). There were no differences in
patterns of significance or size of coefficients with and without the autocorrelation controlled.
Our model of loss to follow-up includes characteristics
that should be related to refusal to participate in the survey,
inability to participate, and inability to be located. We
hypothesize that being older, male, Black, having fewer
years of education, not owning a home, currently residing in
an institution, and reporting a greater number of functioning
limitations will be associated with higher odds of nonresponse. An indicator for having another sample person in the
household indicates family involvement in the survey. Our
expectation is that having another family member in the
survey will increase participation. An indicator of whether
the follow-up where loss occurs is the first, second, or third
wave after baseline is also included. This allows us to
evaluate whether the rate of first-time nonresponse increases
at successive interviews independent of changes in other
characteristics.
The record for each person-interval contains two kinds of
independent variables. The first are those variables which
typically remain constant over adult life: sex, race, and years
of education. The second type of variable was collected or
can be inferred at each interview: age, living arrangement,
whether the respondent lives in an institution, home ownership, the presence of another sample member, and functioning ability. The operational definitions of most of the
variables are straightforward. Functioning ability is operationalized as the number of 13 ADL and IADL functions
a respondent reports having difficulty with (bathing, dressing, eating, transferring, walking, getting outside, toileting, shopping, preparing meals, using the telephone,
managing money, doing light housework, and doing heavy
housework). While this approach makes the best use of the
repeated measures that are available, a kind of measurement
error may still arise because the interview at which these
characteristics are measured occurs at least two years prior to
the nonresponse, and the characteristics could change in that
interval.
Results. — Table 3 compares the full sample at baseline,
those who respond to each interview, those who live but
become nonrespondents, and those who die. The bivariate
data in this table suggest that those lost to nonresponse are
more likely to be female, Black, older, have lower education, live alone, not own a home, or have more functioning
problems than those who are interviewed at each opportunity. Death selects those who are male as well as those who
have more functioning problems.
While Table 3 gives a picture of the bivariate relationships, the effect of these variables when other characteristics
are controlled is shown in a series of logistic regression
models (Table 4). Four nested models were estimated so that
the effects of successively including groups of predictor
variables covering different types of hypothesized effects
could be compared. Model 1 includes demographic charac-
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NNN
47.2% Completed all interviews
M1HELIC AND CRMM1NS
S42
Table 3. Comparison of Characteristics at Baseline for the Total Original Sample, for Those Actually Interviewed
at Each Wave, for Those Who Become Nonrespondents at One or More Waves But Are Eligible To Be Interviewed,
and for Those Who Become Deceased During the Course of the Survey
Full
Respondents
n = 2,431
64%
11%
37%
76%
67%
11%
37%
80%
72%
13%
44%
67%
56%
9%
35%
75%
60%
13%
2%
1%
36%
78.21
9.76
1.62
71%
12%
1%
0%
37%
76.56
10.27
0.90
62%
14%
2%
0%
35%
77.88
9.16
1.20
44%
13%
4%
2%
36%
80.52
9.35
2.76
teristics which are hypothesized to be related to the likelihood of refusal. Model 2 adds characteristics of living
arrangements which we expect to relate to loss of contact.
Model 3 adds an indicator of functioning which should be
related to ability to respond, and Model 4 includes characteristics of the survey. This approach should clarify why some
studies in the literature find that certain variables are related
to nonresponse while others do not. The odds ratios and the
log-odds ratios indicating the probability of being a first-time
nonrespondent relative to being a continuing respondent are
reported in Table 4.
When only the demographic variables are included in the
model, we find that women are more likely to be nonrespondents than men, holding race, age, and education constant
(Model 1). When living arrangements are controlled,
women are no more likely than men to become nonrespondents (Model 2). Thus, women do not appear to be refusers
but to become lost because of gender differences in living
arrangements; persons who live alone are more likely to
become nonrespondents.
Blacks are no more likely than non-Blacks to become
nonrespondents when education is controlled. Years of education remains significant, and living alone becomes significant when level of functioning is controlled (Model 3).
Persons who are better educated may find themselves more
interested in the survey itself, or they may have more of an
understanding of the potential usefulness of the survey; it is
also possible that they are less intimidated by the interviewer.
As hypothesized earlier, persons who live alone may be
less likely to leave someone behind who knows their whereabouts when the interviewer is not able to locate the person;
and renters, being more likely to move, have a greater
chance of being lost to follow-up than those who own their
home (Models 3 and 4). Although it may be difficult to
follow people into nursing homes from the community,
those persons who have completed an interview in an institution are no more likely to become nonrespondents than those
living in the community.
Those Who
Become Deceased
Between 19841990 Interviews
n = 1,857
Both number of functioning problems and age are consistent predictors of nonresponse. Age could be reflecting unmeasured health dimensions that result in inability to respond. Or, in this sample of persons over 70 years of age, the
older cohort may be more averse to survey participation or
contact with strangers. The chance of institutionalization
increases with age, and persons moving into institutions may
be disproportionately lost to follow-up, either because they
cannot be located, because they are unable to respond, or
because a proxy or the institution refuses in their behalf.
Having another sample person in the household is strongly
related to nonresponse. This could mean that having another
sample person in the house increases the burden of response
so that both members do not feel a need to participate. They
may feel that one person telling the "family story" is
sufficient. However, in interpreting the effect of another
household member in the survey, the reference category
must be clarified. When living alone is included along with
having a sample person in the household, the omitted reference group becomes living with a nonsample person. Living
with another sample person and living alone are associated
with about the same increase in relative risk of nonresponse
compared with persons who are living with other nonsample
persons. Another sample person must be older because the
sample is limited to those 70 and over. Those living with
nonsample persons would generally be living with someone
younger, who was not eligible for the survey. Thus, the
effect of a sample member in the household could really be
the effect of an older household context versus a younger
household context. In that case, the relationship between
nonresponse and having another sample member in the
house could be caused by a greater inability to locate older
households.
The coefficients of the interval variables indicate whether
(and how) the odds of becoming a nonrespondent differ at
the second and third intervals with reference to the first
(Model 4). The significance of the dummy variable for the
third interval indicates that those persons responding at the
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Female
Black
Lives alone
Owns home
Functioning difficulties
None
One
Six
Thirteen
Other sample person
Mean age
Mean years of education
Mean number of functioning difficulties
Original
Sample
n = 5,151
Alive 1984-1990
but Nonrespondent
at One or More
Interviews
n = 863
S43
AN ANALYSIS OF NON-RESPONSE
Table 4. Regression Coefficients and Odds Ratios for Predictors of Nonresponse (standard errors in parentheses)
Model 2
Model 1
Intercept
Female
Black
Age
Years education
Log
Odds
Odds
Ratio
Log
Odds
Odds
Ratio
Log
Odds
Odds
Ratio
Log
Odds
Odds
Ratio
^t.186**
(0.495)
0.175*
(0.075)
0.058
(0.109)
0.029**
(0.006)
-0.056**
(0.009)
0.01
-3.648**
(0.503)
0.086
(0.079)
0.034
(0.110)
0.026**
(0.006)
-0.054**
(0.010)
0.122
(0.075)
0.290
(0.270)
-0.502**
(0.075)
0.03
-3.308**
(0.513)
0.056
(0.080)
0.007
(0.110)
0.021**
(0.006)
-0.050**
(0.010)
0.154*
(0.076)
0.202
(0.271)
-0.488**
(0.075)
0.039**
(0.012)
0.04
-3.375**
(0.525)
0.064
(0.080)
0.018
(0.110)
0.019*
(0.006)
-0.055**
(0.010)
0.321**
(0.092)
0.2376
(0.274)
-0.502**
(0.075)
0.041**
(0.012)
0.316**
(0.094)
0.026
(0.083)
0.220*
(0.087)
0.03
1.19
1.06
1.03
0.94
Lives in institution
Owns home
No. limitations
1.09
1.03
1.03
0.95
1.13
1.34
0.60
Other sample person in household
Interval 2
Interval 3
Chi-square
df
p-value
6191.64
covariates
76.626
4
.0001
6139.79
m2 v ml
51.853
3
.0001
6129.62
m3 v m2
10.175
1
.01
1.06
1.01
1.02
0.95
1.17
1.22
0.61
1.04
1.07
1.02
1.02
0.95
1.38
1.27
0.60
1.04
1.37
1.03
1.25
6112.06
m4 v m3
17.559
3
.001
Response Categories: 1 = 935 (nonresponse), 0 = 9,360 (response)
*p< .05;**p< .001.
third interview after baseline were more likely to be lost than
respondents to the first interview after baseline. There was
no significant difference in the likelihood of loss between the
first and second interviews after baseline.
As noted earlier, the LSOA has a complex sample design.
To examine the sensitivity of these results to the violation of
the independence of observations assumption, we again
employ GEE (Groemping, 1994), now correcting the standard errors for correlation within the sampling clusters. We
find our results unchanged.
The probability of nonresponse. — Having identified
which characteristics are associated with the relative risk of
nonresponse in this sample, the next question is: How does
variation in these characteristics affect the absolute probability of becoming a nonrespondent? To explore this question,
in Table 5 the mean probability of becoming a nonrespondent is estimated for selected categories of each of the significant predictor variables using the results of Model 4 from
Table 4. These probabilities provide useful information on
the absolute size of the effect of certain characteristics in this
sample.
For example, if our entire sample were age 70 and each
individual retained all other observed characteristics, the
mean probability of becoming a first-time nonrespondent
would be 7.7 percent. If the whole sample were 90 years old,
the probability of becoming a nonrespondent would increase
approximately 3 percentage points to 10.8 percent. Similarly, having another sample person in the household, regardless of whether that person chose to respond or not,
results in an increase of 3 percent in the probability of
nonresponse to the subsequent interview. If our entire sample had difficulty with all 13 ADLs and IADLs, the mean
probability of nonresponse would increase from .0849 (having no difficulty with any functions) to . 1695. This is the
largest contrast among the characteristics listed.
Of course, any given person would have some combination of these characteristics. In this sample, the highest
probability of becoming a nonrespondent (.32428) occurred
in the final interval for a 95-year-old Black woman who
reported no formal education, was living alone at the time of
the third interview; she was not institutionalized, but neither
was she a homeowner. She reported having difficulty with 5
of 13 possible ADL and IADL tasks. The lowest observed
probability, .02867, occurred in the first interval for a 70year-old White man with 18 years of education, living with
his spouse at that first interview in 1984 in a home he owned,
and reporting no difficulty with any ADL or IADL. The
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Lives alone
-2 Log L
Model 4
Model 3
MIHELIC AND CRIMM1NS
S44
Table 5. Predicted Mean Probability of Becoming
a Nonrespondent for Specific Values of Significant
Independent Variables With All Other
Characteristics as Observed
Variable Value
Age
Age 70
Age 90
Mean
Probability
.0769
.1083
Standard
Error
.0003
.0004
Table 6. Comparison of Means, Standard Deviations,
and Sample Sizes for Number of ADLs with Difficulty
and Number of IADLs with Difficulty at Each Wave
of Follow-up with LSOA Sample Weights
and With Weights Constructed To Correct
for Probability of Nonresponse
Number of ADLs
with Difficulty
LSOA Weights
Nonresponse
Weights
Number of IADLs
with Difficulty
LSOA Weights
Nonresponse
Weights
.0982
.0660
.0003
.0002
Living Arrangement
Lives with others
Lives alone
Mean = 1.09 Mean = 1.10 Mean = 1.07 Mean = 1.08
= 1.86 SD
= 1.67 SD
= 1.93 SD
1986 SD
= 1.67
N
= 4146 N
= 4458 N
= 4054 N
= 4358
.0804
.1070
.0003
.0004
Tenure Type
Does not own home
Owns home
Mean = 1.19 Mean = 1.22 Mean = 1.04 Mean = 1.07
1988 SD
= 1.98 SD
= 1.66 SD
= 2.16 SD
= 1.81
N
= 3294 N
= 3812 N
= 3785
= 3271 N
.1242
.0795
.0004
.0002
Functioning Problems (ADL/IADL)
No difficulties
Difficulty with 6 functions
Difficulty with 13 functions
Mean = 1.29 Mean = 1.34 Mean = 1.09 Mean = 1.13
1990 SD
= 2.08 SD
= 1.74 SD
= 2.38 SD
= 1.99
N
= 2562 N
= 2542 N
= 3235 N
= 3208
.0845
.1051
.1667
.0003
.0004
.0007
Other Sample Person in Household
No
Yes
.0835
.1104
.0004
.0005
Respondent at 3rd Wave
No
Yes
.0860
.1046
.0003
.0004
median probability for the sample was .08220. Several
people had this precise probability of becoming a nonrespondent. They were 78-year-old non-Black women with eight
years of education, living alone in their own homes, and
reporting no difficulty in ADLs or IADLs. Each had responded to the first two interviews.
Compensating for Nonresponse
Actual probabilities of nonresponse are calculated for
each individual responding in 1984, 1986, and 1988 using
the significant coefficients from Model 4, Table 4. These
probabilities are then used to construct weight adjustment
factors to compensate for any bias in the remaining sample
due to nonrandom nonresponse over the three survey intervals in the LSOA. The effect of using the adjusted weights is
illustrated by comparing results using only the weights
provided with the survey to adjust for the sampling strategy
with the weights that compensate for sample loss as well as
the sample design.
Constructing weights. — Because the LSOA is a multistage cluster sample, the LSOA sample weight is provided to
adjust for baseline nonresponse to the SOA and the subsampling of certain populations. The weight adjusts the baseline
sample so that it is representative of the noninstitutionalized
population that is 70 years of age and over in 1984 by sex,
race, and age. We use this sample design weight for the
baseline data and then modify it cumulatively at each successive wave to compensate for loss to follow-up. The weights
for dates after 1984 are calculated by multiplying the weight
for the previous date by (1 + the probability of nonresponse). When these weights are applied, the contribution of
those persons who actually respond is inflated to also represent those who did not respond, based on characteristics
included in the computation of the probabilities. Thus, the
weights alter the distribution of the characteristics in the
sample to reflect the greater propensity of persons with
certain characteristics to become nonrespondents.
Effect of weighting for nonresponse. — Table 6 compares
the mean number of ADLs and IADLs in 1986, 1988, and
1990 calculated in two ways: weighting only with the normalized LSOA weight and weighting for loss to follow-up.
Using the LSOA weight, by 1990 the sample responding to
ADL questions had diminished to 2,562. However, the
nonresponse weights increase the weighted sample size of
those responding to this question by 673 persons, making the
weighted sample just 19 shy of what the total sample would
have been in 1990 if the only source of nonresponse had been
death. (The difference of 19 is due to item nonresponse to
this question.)
Since those in poor physical functioning are less likely to
respond, the use of nonresponse weights results in slight
increases in all the means. The size of the difference gets
larger in later years as there is more loss to follow-up and
because the loss has been accumulating. However, the
differences between the two estimates for any one year are
statistically and substantively insignificant. Examining sample change in functioning over the 1984 to 1990 period, the
increase in the average number of ADLs would be .24 with
adjusted weights and .20 without. For IADLs the increase
would be .05 versus .02. While greater, the difference is not
significant. Note that these tests of significance are performed using the actual, not the weighted, sample size.
Table 7 shows the differences resulting from the two sets
of weights in the estimated percentage making a two-year
transition from no difficulty performing an ADL or IADL to
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Education
8 years school
16 years school
AN ANALYSIS OF NON-RESPONSE
Table 7. Percent of Those Having No Difficulty
at a Given Wave But Having Difficulty With One
or More ADL or IADL at the Next Wave
Nonresponse
Weights
34.44%
1008
26.04%
451
28.22%
386
34.52%
1080
26.29%
520
28.15%
466
Persons 70-84 Years Old in 1984
1 9 8 4 ^ 1986
32.97%
908
1 9 8 6 ^ 1988
25.31%
424
1988-^ 1990
27.63%
368
33.02%
971
25.53%
488
27.54%
444
Persons 85 Years and Older in 1984
1 9 8 4 ^ 1986
57.86%
100
1986 -» 1988
47.78%
27
1988 ^ 1990
50.79%
18
57.8
110
47.94%
32
49.49%
23
Full Sample
1984 -» 1986
1986-> 1988
1 9 8 8 ^ 1990
Table 8. Parameter Estimates for Incident Disability,
With and Without Correcting for Selection Bias
From Loss to Follow-up (standard errors in parentheses)
Variable
difficulty with at least one function. Using these weights to
adjust for nonresponse makes little difference in either sample means or proportions making transitions even among the
oldest persons in the sample, who are presumably both more
frail and more likely to become lost to follow-up.
Correcting/or nonresponse with a bivariate probit model.
— Most researchers ultimately use multivariate analyses,
however, and the weighting method proposed above is not
typically used in that context. A bivariate probit with selection (Greene, 1992) allows us to simultaneously estimate the
probability of nonresponse and the probability of making a
transition of substantive interest, in this case, incident ADL
disability. Comparing the results of this simultaneously
estimated model with those from a univariate probit indicates the effect of not taking attrition into account. Furthermore, we are able to determine whether results are biased by
some characteristics we have not observed, such as distaste
for survey response, cognitive impairment, or circumstances
associated with moving into a nursing home. The correlation
between the error terms for the two equations (rho), representing the unobserved influences common to both the process of disability and attrition, is included in the estimation.
(For details of the method see Greene [1993] and for another
application see Defo [1992].)
The results of the bivariate probit are presented in Table 8
along with probit results for the two equations estimated
separately. Note that the dependent variable for the selection
equation is the same as the nonresponse outcome from Table
4, but the coding is inverted (1 = respondent) so the signs
are opposite. The data are again pooled for a person-interval
analysis. But, since the outcome of interest is the first report
Univariate
Probits
Dependent Variable: Disability
Constant
-3.835** (0.285)
Female
-0.009
(0.038)
Black
0.070 (0.062)
Years of age
0.039** (0.003)
Years of education
-0.020** (0.005)
Under poverty threshold
0.089
(0.056)
Missing poverty indicator
0.003
(0.051)
History of heart disease
0.256** (0.053)
History of cancer
0.016
(0.058)
History of stroke /
cardiovascular
0.385** (0.095)
Diabetes
0.353** (0.067)
Arthritis
0.378** (0.037)
Osteoporosis
0.221* (0.107)
Difficulty with hearing
0.089
(0.095)
Difficulty with vision
0.609** (0.092)
Very low weight
0.099
(0.068)
Very high weight
0.205* (0.063)
Rho
Log likelihood
N = 6,090
Dependent Variable: Response
Constant
Female
Black
Years of age
Years of education
Lives alone
Lives in institution
Owns home
Other sample person
in household
Interval 2
Interval 3
Log likelihood
N = 6,628
Bivariate
Probit With
Selection
-3.82**
-0.011
0.071
0.038**
-0.019*
0.087
0.004
0.255**
0.017
(0.288)
(0.039)
(0.060)
(0.004)
(0.007)
(0.055)
(0.052)
(0.053)
(0.059)
0.385**
0.352**
0.378**
0.220*
0.089
0.608**
0.098
0.205*
0.107
(0.091)
(0.067)
(0.037)
(0.109)
(0.094)
(0.091)
(0.068)
(0.062)
(0.484)
1.873**
-0.067
0.040
-0.012*
0.039**
-0.083
-0.990
0.309**
(0.349)
(0.049)
(0.079)
(0.004)
(0.007)
(Q.059)
(0.811)
(0.053)
-3213.7
Status
1.869**
-0.067
0.038
-0.012*
0.039**
-0.086
-0.960
0.308**
(0.355)
(0.050)
(0.078)
(0.004)
(0.006)
(0.061)
(0.760)
(0.052)
-0.101
(0.060)
0.017
(0.054)
-0.050
(0.058)
-1815.4
-0.099
(0.060)
0.022
(0.054)
-0.044
(0.059)
-5029.1
*p< .05;**p< .001.
of ADL disability, the sample is selected at the beginning of
each interval for those with no ADL disability. This reduces
the number of observations to 6,597 and accounts for the
now nonsignificant effect of living alone. Rho itself is not
significant, and there are only very small differences in the
estimates and levels of significance when rho is controlled,
suggesting minimal bias in these estimates due to loss to
follow-up.
DISCUSSION
Our analysis has demonstrated the dramatic sample loss in
a panel survey of older persons. Decrement to the sample
occurs through two distinct sources: loss to follow-up and
death. Clearly, when a sample of older persons is followed
for even a few years, there is tremendous loss to death. In
this sample, over a third of the original population was lost to
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LSOA Weights
S45
S46
MIHELICAND CRIMMINS
sample of older persons is not random. Characteristics associated with nonresponse may be used to develop targeting
criteria for those interested in the retention of sample persons. Loss to follow-up could be lowered if survey organizations made special efforts to maintain contact with renters
and those who live alone. In addition, extra effort might be
devoted to retaining those in worse health and the oldest old.
Those with less education might be converted to continuing
response with extra educational effort.
Although our results are consistent with our general typology of nonrespondents as people who refuse, are unable to
respond, and who cannot be located, a useful elaboration of
this analysis would consider predictors of nonresponse by
reason for nonresponse. Indeed, if sufficient heterogeneity
between types of nonresponse exists, the salience of the
predictors considered here may have been obscured because
we have grouped all types of nonresponse. Unfortunately, in
this survey reasons for not-completed interviews were insufficiently differentiated for such an analysis. We cannot overemphasize the need to accurately record some detail about
why interviews are not completed. It will not be possible to
either improve response rates or more effectively evaluate the
extent of nonresponse bias without this information.
In order to evaluate whether this nonrandom nonresponse
biases analytic results, we constructed response probability
weights based on the characteristics observed to increase the
probability of nonresponse. The approach to developing
weights suggested here allows for optimal use of each
sample member's contribution to the survey by estimating
response probabilities within each interval and applying
these to form a cumulative weight. Weighting on these
characteristics restored the characteristics of this sample to
what they would have been without the loss, but did not significantly affect univariate and bivariate distributions. Ideally, initial nonresponse (nonresponse to the baseline interview) could be included in this phase; in practice, information on the characteristics of these persons is frequently
unavailable. In this study, partial compensation is made
because the LSOA weights on which the nonresponse
weights are based adjust the distributions of age, sex, and
race to account for initial nonresponse to the NHIS and
SOA, which comprise the baseline sample of the LSOA.
Ultimately, we need to assess the effect of nonrandom
nonresponse in a multivariate environment. We have presented a substantive analysis predicting incident disability
and evaluated it for nonresponse bias with correction for
selection by attrition. By including the correlation between
the error terms of the two equations, this procedure also
adjusts the coefficients for the unobserved characteristics
affecting both processes. Thus, we can observe whether our
original coefficients changed (i.e., whether they were biased), and also whether the unobserved characteristics themselves had a significant effect on incident disability. In this
survey, for our outcome of interest, unobservables did not
have a significant effect and did not bias our results.
We find, then, that nonresponse in this sample of older
persons is not random. Also, however, we find that this
nonrandom nonresponse does not produce bias of any consequence. Though significantly associated with the outcome,
our observed variables were not strongly enough correlated
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death in six years. We set out to determine whether loss to
follow-up in this sample is random; whether nonrandom loss
significantly biases analytic results when evaluated with
correction based on observed characteristics; and whether
there are unobserved differences between those who become
lost and continuing respondents, and whether those differences alter our conclusions.
The LSOA has a significant amount of nonresponse,
reaching almost 20 percent of those alive by the fourth wave.
Those who are older, have lower educational attainment,
live alone, have worse functioning, and rent their homes are
more likely to become nonrespondents. We had hypothesized that certain characteristics previously found to be
associated with nonresponse were acting as proxies for
characteristics that were not included in those analyses.
Among the variables previously identified as ambiguous in
their relationship to attrition, we find that sex becomes insignificant when measures of living arrangement are included.
And, once functioning ability is controlled, living alone
emerges as a significant predictor of becoming a nonrespondent. We do not find any effect of race, a characteristic that
several previous studies found to predict nonresponse.
We had expected persons living in an institution to be
more prone to loss to follow-up because they might be more
difficult to locate, because of the possibility of resistance
from the institution or caregivers, or because of increased
frailty beyond what has been included in the model. Among
persons who have been interviewed in an institution, nonresponse at subsequent interviews is not more likely than for
community-dwelling persons. Although previous analysis
finds that persons moving into institutions are disproportionately lost to follow-up (Crimmins, Hay ward, and Saito,
1994), we are not able to ascertain the extent to which this
loss contributes to sample selection. Underrepresentation of
the institutionalized population poses an important threat to
the representativeness of older samples. However, while it
may be especially difficult to follow people into an institution, once they have been successfully followed, they are not
more likely to be nonrespondents.
Frequently surveys collect information from multiple
members of a single household so that studies involving
household behavior may be completed. We find in this
survey that having another sample person in the household
increases the probability of nonresponse considerably, relative to living with other nonsample persons. Households
with two sample persons are older, and as such are less likely
to have job ties, and may more freely move for amenities, or
social or environmental support. Those living with older
respondents are also more likely to become widowed during
the course of the survey, and this may be the catalyst for a
move or a loss of interest in survey participation. Household
response behavior is clearly an area in which further research
would be useful. The lesson from this finding is not that
survey designs including multiple sample members from a
single household should be avoided, as this would result
in a loss of valuable information. Rather, awareness that
such sample persons may be more prone to loss to follow-up
might call for special attention to retaining these sample
members.
These findings suggest that wave nonresponse in this
AN ANALYSIS OF NON-RESPONSE
While our analyses showed both nonrandom nonresponse
and negligible nonresponse bias for the substantive outcome
considered, there is no rule of thumb to ascertain whether
bias exists for other outcomes or for other panel studies. The
evaluation of the effects of the nonrandom nonresponse in
this survey is a single case study, applicable for others
undertaking analysis with the LSOA, and hopefully a useful
demonstration of how to approach nonresponse evaluation
for those using other panel data.
ACKNOWLEDGMENTS
This project was supported by Grant RO3 HS08459 from the Agency for
Health Care Policy and Research, and T32 AG0O237 and R01 AG11235
from the National Institute on Aging.
Address correspondence to Dr. Adrienne Mihelic, Department of
Population Dynamics, School of Hygiene and Public Health, Johns
Hopkins University, 615 N. Wolfe St., Baltimore, MD 21205. E-mail:
amihelic(Sihpcsun01 .sph.jhu.edu
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with the probability of nonresponse for the resulting weights
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unobserved is presented by Whitehead, Groothuis, and
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significant differences between our respondents and nonrespondents exist on observed variables only, but these differences are apparently not so large that adjusting for them
alters our results. This is an important point, because it
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the result of compensating and the strength of the relationship between the predictive characteristics and the outcome
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