What type of research study repeatedly tests an age group over many years?

National Longitudinal Studies: NLS-72, HS and B, NELS: 88, and ELS: 2002

Four longitudinal studies have been carried out in the US so far, including the national longitudinal study of the high school class of 1972 (NLS-72), high school and beyond (HS&B), the national education longitudinal study of 1988 (NELS:88), and the educational longitudinal study of 2002 (ELS:2002).

The first of them, the NLS-72, surveyed 21 000 high school seniors (i.e., twelfth graders) in 1972. This data collection effort not only gathered background information on students and their schools, but also carried out cognitive tests during the base year. This cohort was resurveyed again in 1973, 1974, 1979, and 1986, as it entered higher education and the workforce. The first follow-up survey of 1973 also added 4500 new individuals to the sample. The second longitudinal study, HS&B, besides surveying and testing high school seniors, also collected information on sophomores (i.e., tenth graders). That is, it started collecting information of individuals earlier on in their life cycle. The younger cohort of HS&B was followed through 1992, and surveyed in 1982, 1984, 1986, and 1992. The high school senior cohort of 1980 was only followed through 1986 and surveyed every 2 years.

The third longitudinal study was initiated in 1988. The NELS of 1988 continued the trend of following individuals earlier on in their life cycle. The base year included a sample of about 25 000 eighth graders attending 1000 schools throughout the country. As the previous longitudinal studies, this sample was nationally representative of that particular cohort of students. Two years later the sample was expanded to allow national representativeness of estimates of tenth graders in 1990. The students were resurveyed in 1990, 1992, 1994, and 2000. The fourth and last longitudinal data collection effort, ELS: 2002, followed the cohort of tenth graders in 2002 over time. Again, student academic achievement was measured during the base year, as well as during the first follow-up in 2004. The last data point available (2006) followed this cohort into postsecondary education and the labor market.

The research agenda involving NLS-72 has focused extensively on the effect of college attendance on earnings. Frazis (1993) estimated the college premium trying to correct for selection bias, while Kane et al. (1999) proposed a methodology to identify measurement errors when schooling is self-reported (as it is in NLS-72 and HS&B), and analyzed its impact on the estimates of returns to schooling. Kane and Rouse (1995) studied the economic return of 2- and 4-year colleges. Altonji (1995) used NLS-72 to estimate the effect of high school curriculum on education and labor market outcomes. Finally, Acemoglu and Pischke (2001) used NLS-72, as well as HS&B, to analyze the link between family income and college education (Note that other research has been conducted using these data. This list is by no means exhaustive.).

The other longitudinal studies have provided invaluable information for analyzing other topics in the field. HS&B has been used by researchers to estimate the effect of Catholic schools on student test scores (see Coleman et al., 1982; Coleman and Hoffer, 1987) and educational attainment (see Evans and Schwab, 1995). Other examples of studies involving HS&B are Murnane et al. (2000), which studied the impact of cognitive abilities on earnings, and Dee (2004), which addressed the question of civic returns to education.

The research using NELS: 88 has been somewhat more focused on teachers. Ehrenberg et al. (1995) used NELS: 88 data to evaluate the relationship between teacher and student ethnic and gender match and student learning. Goldhaber and Brewer (1995) studied the impact of teacher certification on student achievement using NELS: 88. Other researched topics with NELS: 88 have been high school size and academic achievement (see Lee and Smith, 1997), and the effect of unobserved school, teacher, and class characteristics on student achievement (see Goldhaber and Brewer, 1997). Given the more recent availability of ELS: 2002, its literature is very limited. Dee et al. (2006) used this data source to study the effect of school size on parental involvement in education.

1 Introduction

Why should longitudinal studies in biomedical research be conducted? The answer to this question depends on the study objectives in biomedical research. There is a fundamental difference between a longitudinal study and a cross-sectional study. Cross-sectional studies are those in which individuals are observed only once. Most surveys are cross-sectional, as are studies to construct reference ranges. Longitudinal studies, however, are those that investigate changes over time, possibly in relation to an intervention. Therefore, the primary characteristic of a longitudinal study is that study subjects are measured repeatedly through time. The major advantage of a longitudinal study is its capacity to separate what in the context of population studies are called cohort and age effects (Diggle et al., 2002). Outcome variables in the longitudinal studies may be continuous measurements, counts, dichotomous, or categorical indicators, and in many cases, outcomes may even be multivariate as well. Covariates in the longitudinal studies may also be continuous measurements, counts, dichotomous, or categorical indicators, and in many cases, covariate may be time varying as well. As an example, in the study of healthy ageing and Alzheimer's disease (AD), the understanding of natural history of AD requires a longitudinal design and the corresponding appropriate analysis. One of the primary objectives in these studies is to model the cognitive function as a function of baseline age, the time lapse from the baseline, the disease status, and other possible risk factors. For the purpose of demonstration, we consider a simple case and let Y(a,t) be the cognitive function at time lapse t from the baseline (i.e., t = 0 at baseline) for a subject whose baseline age is a. Assume that the expected value of Y(a,t) is a linear function of both baseline age a and the time lapse t from the baseline, i.e.,

EY(a,t)=β0+β1a+β2t.

The standard interpretation of β1 is the expected change of cognitive function at the baseline (or at the same time t during the longitudinal course) for two subjects whose baseline age is 1 year apart. The standard interpretation of β2 is the expected change of cognitive function per time unit for the same subject during the longitudinal course of the study. The crucial difference between β1 and β2 is that β1 measures a between-subject or a cross-sectional change, whereas β2 measures a within-subject or a longitudinal change. If only cross-sectional cognitive measures are available, i.e., the study is measured only at baseline, then t = 0 and EY(a,t) = β0 + β1a. Therefore, any statistical inferences from the cross-sectional data can only be made on β1, i.e., the cross-sectional rate of change. On the other hand, if longitudinal cognitive measures are available, then statistical inferences can be made on both β1 and β2. Therefore, longitudinal studies enable not only the estimation of cross-sectional rate of change based on baseline age, but also the estimation of the rate of intra-individual change based on the time lapse in the study.

Another main study objective for a longitudinal study is to relate intra-subject rate of change over time to individual characteristics (e.g., exposure, age, etc.), or to an experimental condition. In the above example, studying the healthy ageing and AD, many potential risk factors in addition to baseline age could affect not only the cognitive status of subjects at baseline but also the rate of cognitive decline after the baseline. These risk factors range from demographics such as gender and education to genetic status (i.e., Apolipoprotein E genotypes) and to relevant biomarkers and imaging markers. In addition, the stage or the severity of AD could also be an important factor affecting the rate of further cognitive decline. In general, therapeutic trials of AD are longitudinal, and the most crucial scientific question to be addressed in these trials is whether the therapeutic treatment is efficacious in slowing the cognitive and functional decline of AD patients. Therefore, the rate of cognitive decline in AD clinical trials is modeled as a function of treatment received. More specifically, let β2tbe the expected rate of cognitive decline over time for subjects randomly assigned to receive a therapeutic treatment, and let β2cbe the expected rate of cognitive decline over time for control subjects. The longitudinal nature of the study allows the statistical test on whether β2tis the same as β2cand the statistical estimation on the difference between these two rates of cognitive decline.

As in all biomedical studies, there are two major statistical components in longitudinal studies: statistical design and statistical analysis. This chapter will review some of the most used statistical models for the analyses of longitudinal data and relevant design issues based on these models. Throughout this chapter, we will focus on the conceptualization of basic longitudinal statistical models, the basic assumptions these models are based on, and the interpretations of model parameters. It is not our intention to present the detailed theory on statistical estimations and inferences based on these models. Instead, we will present the implementations for some of these basic longitudinal models in SAS through real-world applications. For detailed statistical theory on the parameter estimation and inferences from these models, readers are referred to some of the excellent references in longitudinal statistical methods such as Diggle et al. (2002), Fitzmaurice et al. (2004), Verbeke and Molenberghs (2000), and Singer and Willett (2003).

Attrition and Missing Data

The value of longitudinal study must be judged against the problems of collecting longitudinal data and the implications these have for data quality. Magnusson and Bergman, in 1990, set these out in the third of 10 books resulting from the work of the European Science Foundation's network on longitudinal research referred to earlier. The most serious of these data quality problems is “attrition”—the loss of sample members over time. Subjects may disappear from the study because they have died, moved house, changed their names (through marriage), or are simply no longer interested in taking part; others move in and out of the study depending on their availability at the time a particular survey is to be carried out.

Such changes in the cohort's composition can seriously weaken the research potential of the data. Sample loss reduces the numbers available for data analysis—a particular problem in longitudinal analysis that strictly requires complete records across the time span of the research. Attrition can also bias the data if those who leave the study are not typical of those who started it. On the other hand, unlike the cross-sectional survey, with any longitudinal data set there is full information about the characteristics of the sample when the study began. Accordingly, if reduction in the size of the cohort through attrition occurs differentially across groups, e.g., groups defined by socioeconomic status of parents, then the sample can be reweighted to restore the distributions of such key variables to the form they were earlier. This is only a partial solution, however, as the variables of central interest, on which the missing cohort members differ from those still participating, may not have been measured at the start of the study. The most effective cohort studies, therefore, place a large amount of investment in minimizing attrition by maintaining contact with the cohort in between surveys and tracing the present whereabouts of sample members through administrative records, and even national and local media publicity campaigns, when leading up to a new one.

Missing data are not restricted to loss of cohort members from the study. Nonresponse at the variable level due to respondent failure or refusal to answer a particular question, or accept a particular measurement, can occur across the data set. Much of this nonresponse is unlikely to be occurring at random and thus constitutes another source of potential bias in the data. Again, the problem multiplies across follow-ups, both reducing the numbers available for longitudinal analysis and increasing the bias. The solution must be an analytic one. There have been major developments in the statistical methodology for “imputing” missing data, which are increasingly applied in the analysis of cohort study. But again prevention is better than cure. Comprehensive development work involving much piloting and prepiloting of all survey procedures is an essential prerequisite for any new follow-up. They need to be minimally burdensome and maximally sensitive to the cohort member's situation.

3.3 Real example: the renal data

The data set in relation to this longitudinal study is obtained from 131 patients with IgA nephropathy. The resulting variable is the patients' serum levels of creatinine (creat) which best reflect the renal kidney function. The covariates include cortex (co), glomerular grade (gg), tubulointerstitial grade (tig), sex (= 0 for ‘male’, and = 1 for ‘female’), total protein in 24-hour urine (24utp), and serum calcium (ca). Let yij = log creatij be the jth observation for the ith patient. For this data set, we consider the following normal random effects model:

yij=β0+β1coi+β2ggi+β3tigi+β4sexi+β524utpij+β6caij+bi+ɛij,i=1,…,131,

where bi ~ N(0, σb2) and εij ~ N(0, σf2). To cope with the missing responses in this data set, we use the following logistic regression to model the missing mechanism:

(19)logit Pr(rij=1|yi,γ)=γ0+γ1yi,j−1+γ2yi,j+γ3coi+γ4ggi+γ5tigi+γ6sexi+γ724utpij+γ8caij.

The ML estimates of the model parameters obtained via the MCEM algorithm (Ibrahim et al., 2001) are reported in Table 2. To estimate the local influence measures, we used the Gibbs sampler to collect 52 000 random observations from the joint conditional distribution [Ym, Ω|Yo, R, ψˆ] based on the ML estimates were derived. After discarding the first 2000 observations as burn-in phase, the last 50 000 random observations were used to calculate Δω0 and Q¨Ψ(ψˆ) via the formulae (A.3) and (A.4) given in Appendix A.

Table 2. Results for the renal data

Para.MLESEPara.MLESEβ03.7990.037γ01.1360.341β1−0.0170.003γ1−0.1880.031β20.1340.012γ2−0.1420.072β30.3440.012γ3−0.0910.023β40.2420.016γ40.4010.026β5−0.0320.009γ5−0.6010.036β60.0340.015γ6−0.6430.039γ7−1.4380.313σf20.1220.005σb20.1240.012

The four perturbation schemes given in Section 3.1 are considered. Plots of M(0)j for case weights perturbation within patients (perturbation scheme 1) are shown in Figure 6. From this figure, we know that 14 observations stand out as the influential or potential outliers, and they are (2, 7), (9, 8), (49, 9), (62, 5), (66, 3), (88, 2), (88, 3), (88, 4), (99, 2), (108, 9), (112, 2), (112, 3), (113, 2), and (127, 9), in which the first entry in the bracket represents the patient's number, and the second entry denotes the observation's servation's number. We find out that these data points are significantly larger or smaller than the other observations in the data set. For example, the seventh observation of the second patient (2, 7) is 146, but the other observations of this patient are from 998 to 1358. Therefore, we should pay more attention to this patient; specifically, why the patient's serum levels of creatinine change so sharply should be studied.

To identify the influential clusters, we considered the case weights perturbation among clusters (perturbation scheme 2). Plots of M(0)j associated with this perturbation scheme are presented in Figure 7. There are three patients who were detected as influential. They are the 9th, 88th, and 112th patients. From the above results, we can see that some patients with influential observations can also be detected as influential clusters by the perturbation scheme 2. The 9th patient has the most influential observation (9, 8) which has the largest M(0)j in the perturbation scheme 1. Meanwhile, the 88th and 112th patients who have more than one influential observations.

To study the effects of departure from the assumption that bi ~ N(0, σb2), we considered the multiplicative perturbation on random effects (perturbation scheme 3). The diagnostic measures are presented in Figure 8 which also shows us that the 41st, 46th, 88th, and 100th patients are influential clusters. That is to say that about 3% of the observations (i.e., four among 131 patients) are more sensitive to the variance σb2. Therefore, it seems that the assumption of homogeneity of the random effects is reasonable.

To investigate the sensitivity of the missing mechanism, we also considered perturbation scheme 4 for this data set. The diagnostic measures of this perturbation scheme are plotted in Figure 9. From this figure, we see that there are only two responses which are more influential. They are the 9th observation of the 6th patient, and the 5th observation of the 88th patient. Therefore, almost all responses are robust to missing model (19).

1.8.2 Asset and health dynamics among the oldest old (AHEAD)

The second dataset comes from a large-scale longitudinal study on older Americans, the Survey of AHEAD. This survey, conducted by the Institute for Social Research (ISR), University of Michigan, is funded by the National Institute on Aging as a supplement to the Household and Retirement Survey (HRS). As a supplemental survey attached to HRS, Wave I of the AHEAD survey was conducted between October 1993 and April 1994. Specifically, a sample of individuals aged 70 years or older (born in 1923 or earlier) was identified throughout the HRS screening of an area probability sample of households in the nation. This procedure identified 9,473 households and 11,965 individuals in the target area range. The Wave I respondents have been followed by telephone every second or third year, with proxy interviews designed for those deceased between two successive waves. At present, AHEAD survey registers 10 waves of investigation in 1993, 1995, 1998, 2000, 2002, 2004, 2006, 2008, 2010, and 2012. As a longitudinal, multidisciplinary, and US population-based study, AHEAD provides a highly representative and reliable data base for longitudinal data analysis of older Americans aged 70 years or older.

AHEAD acquires detailed information on a number of domains, including demographic characteristics, health status, health care use, housing structure, disability, retirement plans, and health and life insurance. Survival information throughout the follow-up waves has been obtained by a link to the data of National Death Index (NDI). To provide empirical illustrations, this book uses AHEAD data of six waves from 1998 to 2008, viewing the 1998 panel as baseline. Given the illustrative nature of using this dataset, I randomly select 2000 persons from the baseline AHEAD sample to conduct empirical analyses in the book. Additionally, due to the same reason for providing examples, the weight factor, included in the AHEAD dataset for adjusting oversampling of certain subpopulations, is not considered in the empirical illustrations. Therefore, readers interested in following the examples of this book for an actual analysis should use the full AHAED sample and incorporate the weight variable for deriving unbiased analytic results.

Limitations of Studies

ECEC has, generally speaking, positive effects. Another positive conclusion is that longitudinal studies continue to find effects years after completion of a program; ECEC therefore continues to work long after the end of the program. How large an effect must be before it constitutes a meaningful result remains an open question. Guidelines from the research literature are not the only important considerations in this regard; other considerations include the importance of the variables themselves, the necessary investments in terms of time and money, and the availability of alternatives. As emphasized by various authors, the results that have been found in ECEC evaluations are encouraging, while also calling for realistic expectations on the part of policymakers and directly involved parties.

Despite a growing body of literature, the modest knowledge base remains an important limitation in discussions of the effectiveness in ECEC. First, the internal validity of studies has traditionally been a topic of discussion in this regard. In addition to randomized studies, the literature includes results from quasi-experimental designs, which suffer from methodological weaknesses. Other questions can be raised regarding external validity. One issue involves the extent to which findings from predominantly US studies can be generalized to other countries that differ from the USA in many respects. Projects conducted in other parts of the world should be systematically evaluated and should receive more attention in the research literature, which is currently dominated by Western (and largely USA) studies. Another issue involves the generalizability of results from the past to the present and near future. The demographic composition of populations is changing continually, ECEC programs are in transition, and there are shifts in the participation of various groups in home-based, center-based, and combined programs.

A related question involves the determination of which approach is more effective – which approach works the best? The steadily increasing database of ECEC evaluations makes it possible to use meta-analysis to identify characteristics that are associated with greater or lesser effects. This is also interesting because various program designs have been evaluated with differing results. These lines of research show that combined programs are more effective than center-based programs from the perspective of education, and that center-based programs in turn are more effective than home-based programs (Blok et al., 2005). Correlations have also been found with improved training for personnel, more favorable child-to-staff ratios, and greater program intensity (Karoly et al., 2005). For home-based programs, possible success factors have been shown to vary with regard to parent or child outcomes. When child outcomes are the focus, more intensive programs, working with professionals and single-site programs are more effective, although the associations that have been found are not strong (Sweet and Applebaum, 2004).

The meta-analytic line of research also involves a number of limitations. First, although the primary data from intervention studies are experimental or quasi-experimental (and thus aimed at identifying causal relationships), the study of these programs through meta-analysis is correlational. The classic adage “correlation is not causation” is applicable in this regard. In addition, characteristics of programs are usually confounded, thereby making it impossible to determine the unique contribution of a given program characteristic. For example, as could be expected, combined programs offer more services than do other types of programs, and they tend to be characterized by higher intensity and thus by a higher dose of the intervention than home-based programs are. The unique contribution of delivery model or intensity to effectiveness is therefore difficult to interpret unambiguously. An additional complicating factor is that there is sometimes too little variation in background characteristics. For example, many home-based programs pursue similar goals for similar populations, making it impossible to make a true comparison on these points (Karoly et al., 2005). An additional limitation is that associations between program characteristics and effects are usually investigated with regression models under the assumption of linearity. Whether this assumption is always valid remains an open question. For example, it is questionable whether the effects decrease constantly over time or whether each home visit in a home-based program always adds a constant effect, as assumed by a linear model. It could be that the relationships are not linear or that it is necessary to consider threshold values below which effects cannot be seen.

Briefly summarized, the empirical research that has been conducted provides answers (at least tentatively) to three important questions in the field: Does ECEC work? How long does it work? What works the best? Nonetheless, authors unanimously emphasize that the empirical basis for home-based, center-based, and combined programs continue to have limitations, despite the impressive efforts of various involved parties.

Identifying and Enhancing Intellectual Giftedness

To accomplish his meritocratic objectives and with financial support from the Commonwealth Fund of New York, Terman launched a longitudinal study of gifted children in 1921. This was the first follow-up study to use a large sample. Children with an IQ of at least 135 were categorized as gifted. Terman and his research team generated a sample of approximately 1500 gifted children, based on canvassing elementary and secondary schools in urban areas of California. In an effort to dispel the popular notion that gifted children were underdeveloped in nonintellectual areas, medical and physical assessments were included as well as measures of personality, character, and interests. The gifted sample was compared with a control group of California schoolchildren of comparable age.

In the first of a series of monographs on the gifted study, the major finding was that gifted children excelled in measures of academic achievement when matched for age with control children. The composite profiles of the gifted children also revealed that they were emotionally as well as intellectually mature. Based on these initial results, Terman strongly promoted a differentiated school curriculum that would place gifted children in special classrooms in which they could progress educationally according to their ability rather than their age. With additional research funding, Terman was able to follow up his sample for a period of 35 years. At midlife, the intellectual level of the gifted group continued to be within the upper 1% of the general population, and their vocational achievement was well above the average of college graduates. Moreover, as earlier reports had demonstrated, they showed few signs of such serious problems as insanity, delinquency, or alcoholism. The midlife report also included some marked gender differences. Whereas the men as a group had attained a high level of career success, few women had comparable levels of career achievement. As Terman observed in the 1959 monograph on the gifted sample at midlife, career opportunities for women were restricted by gender role conformity and job discrimination.

Terman's involvement with the gifted study entailed more than data collection and research reports. Especially after he retired in 1942, he devoted himself to the interests of gifted children by promoting gifted education and, through contacts with journalists, disseminated the results of the gifted study in newspapers and magazines. He also popularized his work by making a guest appearance on the radio show “The Quiz Kids.” His appearance in 1947 coincided with the publication of the 25-year follow-up. These forays into the popular media also served as a vehicle for Terman to change the public's negative stereotypes of gifted children as maladjusted. In his work with the gifted, Terman experienced particular satisfaction in his personal contact with the participants under study. He maintained correspondence with many of them over the years and in some instances received them as guests in his home. For a number of the gifted who “grew up” and came to be identified as “Termites,” he was a benevolent father figure and psychological counselor. By the early 1950s, with plans developing for the continuation of the gifted follow-up, Terman appointed Stanford colleague Robert Sears (who coincidentally was a member of the gifted sample) to succeed him as research director. The gifted sample was thus followed up through late adulthood.

What type of research design follows a group of people over many years repeatedly testing them?

What type of study follows and retests the same group of people over time?

Which type of study involves testing different age groups at the same time?