In a prospective cohort study of 249 children from birth to two years of age, we assessed the relation between prenatal and postnatal lead exposure and early cognitive development. On the basis of lead levels in umbilical-cord blood, children were assigned to one of three prenatal-exposure groups: low (less than 3 micrograms per deciliter), medium (6 to 7 micrograms per deciliter), or high (greater than or equal to 10 micrograms per deciliter). Development was assessed semiannually, beginning at the age of six months, with use of the Mental Development Index of the Bayley Scales of Infant Development (mean +/- SD, 100 +/- 16). Capillary-blood samples obtained at the same times provided measures of postnatal lead exposure. Regression methods for longitudinal data were used to evaluate the association between infants' lead levels and their development scores after adjustment for potential confounders. At all ages, infants in the high-prenatal-exposure group scored lower than infants in the other two groups. The estimated difference between the overall performance of the low-exposure and high-exposure groups was 4.8 points (95 percent confidence interval, 2.3 to 7.3). Between the medium- and high-exposure groups, the estimated difference was 3.8 points (95 percent confidence interval, 1.3 to 6.3). Scores were not related to infants' postnatal blood lead levels. It appears that the fetus may be adversely affected at blood lead concentrations well below 25 micrograms per deciliter, the level currently defined by the Centers for Disease Control as the highest acceptable level for young children.

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Longitudinal studies have a prominent role in psychiatric research; however, statistical methods for analyzing these data are rarely commensurate with the effort involved in their acquisition. Frequently the majority of data are discarded and a simple end-point analysis is performed. In other cases, so called repeated-measures analysis of variance procedures are used with little regard to their restrictive and often unrealistic assumptions and the effect of missing data on the statistical properties of their estimates. We explored the unique features of longitudinal psychiatric data from both statistical and conceptual perspectives. We used a family of statistical models termed random regression models that provide a more realistic approach to analysis of longitudinal psychiatric data. Random regression models provide solutions to commonly observed problems of missing data, serial correlation, time-varying covariates, and irregular measurement occasions, and they accommodate systematic person-specific deviations from the average time trend. Properties of these models were compared with traditional approaches at a conceptual level. The approach was then illustrated in a new analysis of the National Institute of Mental Health Treatment of Depression Collaborative Research Program dataset, which investigated two forms of psychotherapy, pharmacotherapy with clinical management, and a placebo with clinical management control. Results indicated that both person-specific effects and serial correlation play major roles in the longitudinal psychiatric response process. Ignoring either of these effects produces misleading estimates of uncertainty that form the basis of statistical tests of hypotheses.

Formulas for estimating sample sizes are presented to provide specified levels of power for tests of significance from a longitudinal design allowing for subject attrition. These formulas are derived for a comparison of two groups in terms of single degree-of-freedom contrasts of population means across the study timepoints. Contrasts of this type can often capture the main and interaction effects in a two-group repeated measures design. For example, a two-group comparison of either an average across time or a specific trend across time (e.g., linear or quadratic) can be considered. Since longitudinal data with attrition are often analyzed using an unbalanced repeated measures model (with a structured variance-covariance matrix for the repeated measures) or a random-effects model for incomplete longitudinal data, the variance-covariance matrix of the repeated measures is allowed to assume a variety of forms. Tables are presented listing sample size determinations assuming compound symmetry, a first-order autoregressive structure, and a non-stationary random-effects structure. Examples are provided to illustrate use of the formulas, and a computer program implementing the procedure is available from the first author.