The relationship between average and peak personal exposure to nitrogen dioxide and urinary excretion of hydroxyproline and desmosine was investigated in a population of preschool children and their mothers. Weekly average personal nitrogen dioxide exposures for subjects who resided in homes with one or more potential nitrogen dioxide source (e.g., a kerosene space heater, gas stove, or tobacco smoke) ranged between 16.3 and 50.6 ppb (30.6 and 95.1 micrograms/m3) for children and between 16.9 and 44.1 ppb (12.8 and 82.9 micrograms/m3) for mothers. In these individuals, the hydroxyproline-to-creatinine and desmosine-to-creatinine ratios were unrelated to personal nitrogen dioxide exposure--even though continuous monitoring documented home nitrogen dioxide concentration peaks of 100-475 ppb lasting up to 100 h in duration. Significantly higher hydroxyproline-to-creatinine and desmosine-to-creatinine ratios were observed in children, compared with mothers (p < .001 and .003, respectively).

We examined the extent of correlation between home air nicotine levels and urine cotinine/creatinine ratios (CCR) in 27 children who attended a research day care program where they were not exposed to environmental tobacco smoke (ETS) during the daytime hours. Average concentrations of nicotine in home air were determined by active air sampling during the evening and night hours on 2 consecutive days. Urine samples for cotinine and creatinine determinations were collected before, during, and after the two sampling periods. In addition, four sequential weekly urine samples for CCR were obtained from study children to determine the extent to which single determinations of CCR were representative for individual children. Fifteen children resided in homes with smokers, and 12 did not. Urine CCR consistently distinguished most exposed and unexposed children. However, three exposed children had urine CCRs that clustered routinely around the criterion CCR (30 ng/mg cotinine-creatinine) that best distinguished exposed and unexposed children. In children exposed to ETS in the home, there was a significant correlation between average home air nicotine levels and the average logarithm of urine CCR the two mornings after the home air monitoring periods (r = 0.68; p = 0.006). In study children, urine CCRs were remarkably stable over the 1-month observation period. Rank correlation coefficients for sequential weekly determinations of CCR were consistently greater than r = 0.88; p less than 0.0001.

Incomplete and mistimed longitudinal data are common problems in longitudinal studies of free living populations. One possible approach to the analysis of longitudinal data with randomly missing or mistimed data uses a mixed effects model. While the theory underlying this approach is not new (Harville, 1977), very little has been published about its actual application. The objective of this paper is to examine the behavior of the maximum likelihood estimates of mixed effects model parameters when the distribution of the parameters underlying the data is known. Specifically, the effects of different values of the error covariance parameters and missing and mistimed data are considered. Two iterative methods, the Method of Scoring and the EM algorithm, were utilized to solve the maximum likelihood equations. In the setting considered here, the Method of Scoring and the EM algorithm worked well for the analysis of longitudinal data with missing and/or mistimed data. The variance of the parameter estimates increased when the data were mistimed and/or missing. The Method of Scoring was computationally more efficient than the EM algorithm. Both methods converged to the same set of parameter estimates except when the covariance matrix of the random effects, D, was nearly singular. When this occurred the Method of Scoring sometimes produced non-positive definite estimates of D, The EM algorithm, while constraining [Dcirc] to be positive definite, often failed to meet the convergence criteria in the allotted number of iterations. Possible “solutions” to this problem are discussed.

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