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Recent developments in modern multivariate methods provide applied researchers with the means to address many important research questions that arise in studies with repeated measures data collected on individuals over time. One such area of applied research is focused on studying change associated with some event or critical period in human development. This tutorial deals with the use of the general linear mixed model for regression analysis of correlated data with a two-piece linear function of time corresponding to the pre- and post-event trends. The model assumes a continuous outcome is linearly related to a set of explanatory variables, but allows for the trend after the event to be different from the trend before it. This task can be accomplished using a piecewise linear random effects model for longitudinal data where the response depends upon time of the event. A detailed example that examines the influence of menarche on changes in body fat accretion will be presented using data from a prospective study of 162 girls measured annually from approximately age 10 until 4 years post menarche.

This paper presents a method for analysing longitudinal data when there are dropouts. In particular, we develop a simple method based on generalized linear mixture models for handling nonignorable dropouts for a variety of discrete and continuous outcomes. Statistical inference for the model parameters is based on a generalized estimating equations (GEE) approach (Liang and Zeger, 1986). The proposed method yields estimates of the model parameters that are valid when nonresponse is nonignorable under a variety of assumptions concerning the dropout process. Furthermore, the proposed method can be implemented using widely available statistical software. Finally, an example using data from a clinical trial of contracepting women is used to illustrate the methodology.

An approach is illustrated for the analysis of longitudinal variables collected during adolescence. Since the method requires complete data, three techniques are compared for application when some individuals have missing values. These methods are implemented in a study of systolic blood pressures and dietary fat intakes collected longitudinally in adolescent girls. The value of adolescent systolic and fat variables in predicting systolic pressure in adult women is investigated.

During autumn 1968 an oceanographic investigation was conducted in the region of the Subarctic boundary between 155°E and 180°. The geostrophic flow of the upper 500 m was remarkably similar in direction; hence the salinity-minimum, Intermediate water must have the same path of flow as water at the surface. A water mass analysis revealed a decrease in the percentage of Subarctic water to the south and east, plus an increase in the homogeneity of water to the east, which supports Reid's conclusions that the salinity minimum results mainly from lateral mixing in the pycnocline in this region. Salinity at the minimum increases toward the south and east, and the density at this level also increases slightly from the western to the central Pacific, perhaps as a result of unequal vertical mixing above and below the minimum.

The role of the pituitary gonadotrophins in controlling luteal function in the stumptailed macaque has been investigated by examining profiles of serum concentrations of LH, FSH, progesterone and oestradiol in daily blood samples from 13 monkeys during the menstrual cycle, and in blood samples taken at hourly intervals between 09.00 and 21.00 h on different days of the luteal phase in 13 cycles. The effects of acute withdrawal of gonadotrophins was investigated by administering a single injection of 300 μg LHRH antagonist/kg body weight at different stages of the luteal phase during 28 cycles.Although there were high basal values and marked fluctuations of bioactive LH during the first 4 days after the LH peak, progesterone profiles showed no corresponding short-term changes, there being a slow and steady rise in progesterone concentrations during the sampling periods. After day 5, basal LH secretion decreased, but high amplitude LH pulses were identified which were associated with episodes of progesterone secretion.Administration of the LHRH antagonist caused a suppression of bioactive LH and progesterone concentrations at all stages of the luteal phase, although some basal secretion of progesterone was maintained through the 24-h period of effective antagonist gonadotroph blockade. Luteal function recovered apparently normally in all monkeys treated in the early–mid-luteal phase.Serum concentrations of FSH and oestradiol fluctuated comparatively less during the 12-h sampling periods, and the antagonist had less suppressive effects on the concentrations of these hormones. The LHRH antagonist had no apparent effect on prolactin release.It appears that the corpus luteum is relatively unresponsive to the high serum LH concentrations during the early luteal phase, but that responsiveness increases as the corpus luteum develops. The corpus luteum is, however, susceptible to withdrawal of LH not only in the mid–late luteal phase when the relationship with LH is apparent, but also during the early luteal phase.J. Endocr.(1986) 111,83–90

This paper proposes the use of two-factor models (age-period and age-cohort models) to estimate age, period, and cohort effects on pulmonary function by using the data collected in a 24-year longitudinal study in the Netherlands from 1965 to 1990. The analysis included 18,363 pulmonary function measurements on 6,148 subjects aged 20-54 years at the initial visit. The subjects were grouped into four birth cohorts (before 1923, 1923-1934, 1935-1946, and after 1946) and four survey periods (1965-1972, 1973-1978, 1979-1984, and 1985-1990). In the age-cohort model, the decrement in forced expiratory volume in 1 second (FEV1) associated with a yearly increase in age was 28.3 +/- 3.7 ml/year for a man 176 cm tall and 16.0 +/- 1.9 ml/year for a woman 163 cm tall. The estimated acceleration of decline with aging was significant for both men (beta = -0.212; standard error = 0.079 ml) and women (beta = -0.346; standard error = 0.058 ml). Compared with that of the cohort born before 1923, the average level of FEV1 was estimated to increase by 156, 277, and 379 ml, respectively, for the three younger cohorts in men (p = 0.01) and by 133, 213, and 328 ml for the three younger cohorts in women (p < 0.01). In the age-period model, the estimated linear age effect on FEV1 was 36.2 +/- 4.2 ml/year for a man and 30.5 +/- 2.3 ml/year for a woman. The age quadratic term was significant for women, but not for men. Average FEV1 was estimated to be increased by 141, 169, and 250 ml, respectively, for the periods 1973-1978, 1979-1984, and 1985-1990 in men and by 131, 138, and 219 ml in women. These period effects were significant for both men and women. In summary, this study applied the two-factor models to estimate cross-sectional and longitudinal effects of aging on FEV1 and demonstrated significant period and cohort effects, which could be attributed in part to changes in air pollutants, respiratory infections, vaccinations, types of cigarettes, diet, and lifestyles over time.

A central issue in studies of risk factors for childhood psychopathology is utilization of the information obtained about the child's mental health status from multiple informants. In this paper, the authors propose a new approach to the analysis of risk factor data when the outcomes are binary ratings (presence/absence of symptoms). This new approach has several attractive features in this setting. The strategy taken is to perform a single analysis using multivariate modeling, in which simultaneous logistic regressions are conducted for the outcomes given by each of several informants. The advantages of this approach include the following: 1) it retains the complete information about case status for each informant; 2) it permits assessment of informant-risk factor interactions as well as "overall" risk factor effects; 3) it provides measures of association between the multiple informants and adjusts for the association between responses in the analysis; and 4) missing data on a subset of respondents can be incorporated in a straightforward way, permitting all subjects with at least one informant to be used in the analysis. To illustrate the methods, the authors present findings on risk factors for measures of "Internalizing" and "Externalizing" behaviors from two surveys using parent and teacher ratings of 6- to 11-year-old children in Connecticut between 1986 and 1989.

The effectiveness of treatment for mild hypertension (diastolic pressures of 85 to 105 mm Hg) has not been conclusively demonstrated. Both the costs of a carefully designed clinical trial and the likelihood that it will produce definitive answers will depend importantly on the sample size. This paper presents sample-size estimates under a variety of assumptions regarding the characteristics of the population to be studied, the degree of blood pressure control to be achieved, and the health benefits to be expected. Under a central set of assumptions, the estimated sample size per group is 22,700 with death as an endpoint and 14,000 with morbid events (CHD and stroke) as endpoints. As individual assumptions are varied one at a time, required sample sizes range from 10,900 to 101,100 and from 6,800 to 63,100 for the respective endpoints. Results are most sensitive to the degree of blood pressure control actually achieved to the expected health benefits from blood pressure control. They are also highly sensitive to the sex composition of the population and to expected dropout rates. The choice of sample size will depend on the decision maker's assessment of the likelihood that each assumption will be fulfilled and on the degree of willingness to risk an inconclusive study result. By making explicit the effect of variation in each assumption, decision making is rendered more susceptible to critical examination by outside reviewers.

An empirical Bayes method for smoothing two-way tables is presented. It is based on the use of the log linear model and a normal prior distribution. Estimation of the variance component in the prior is discussed, and two approximations are considered, one which utilizes the EM algorithm.