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Although studies of the relationship between risk factors measured at baseline and a binary outcome are common problems occurring in statistical analyses of epidemiologic studies, little has been written about what constitutes a good measure of the true baseline value of a risk factor. This paper considers different schemes of providing for baseline risk factor data and proposes and compares methods for correcting estimates of relative risks for bias due to measurement error. Repeated measurements taken at baseline appear to allow for a correction in the estimate of risk that is comparable to the correction based on repeated measurements over a number of visits close to baseline. The procedures proposed are regression calibration/ imputation type methods that involve estimating the covariates with less error and using these estimates in the standard model for the risk factor analysis. Shrinkage estimates from a linear mixed-effects model for multiple measurements at baseline are proposed as a method for estimating the true level of a risk factor at baseline. A simulation study shows that these shrinkage estimates give estimates of the risk of the outcome which have a smaller mean square error and confidence interval coverage proportions much closer to the nominal level than would be obtained using the observed data. This new imputation method is compared to the measurement error correction method earlier proposed by Rosner et al. (Rosner, B., Spiegelman, D., Willett, W. C. (1992). Correction of logistic regression relative risk estimates and confidence intervals for random within-person measurement error. American Journal of Epidemiology 136:1400-1413). In addition, the standard errors from the new method are compared to a nonparametric bootstrap estimate of the standard errors as well as to the asymptotic standard errors obtained using a method proposed by Carroll and Stefanski (Carroll, R. J., Stefanski, L. A. (1990). Approximate Quasi-likelihood Estimation... [ABSTRACT FROM AUTHOR]

Examines the implications of the hierarchical formulation of variables in linear mixed-effects models. Effects of linear transformations of variables on the models; Variable selection strategy that leads to considering growth curve models.

It may be clinically useful to know when prostate-specific antigen (PSA) levels first begin to rise rapidly and to determine if the natural history of PSA progression is different in men with locally confined prostate cancers compared to men with metastatic tumors. This article uses a nonlinear mixed-effects model to describe longitudinal changes in PSA in men before their prostate cancers were detected clinically. Repeated measurements of PSA are available for 18 subjects with a diagnosis of prostate cancer based on prostate biopsy. PSA measurements were determined on repeated frozen serum samples collected from subjects with at least 10.0 years and up to 25.6 years of observation before the cancer was detected. A piecewise model is used to describe this data. The model is linear long before the cancer was detected and exponential nearer the time the cancer was detected. The time at which the PSA levels change from linear to exponential PSA progression is unknown but can be estimated by including random terms that allow each subject to have his own transition time. The model also accounts for two groups of patients--those with local or regional cancer and those with advanced cancer or whose cancer has metastasized. Various parameters are allowed to differ between these two groups. By backward elimination of statistically non-significant parameters, a model is found that adequately describes the data. The model represents a situation where local/regional and advanced/metastatic cancers have similar rates of PSA progression, but advanced/metastatic cancers are diagnosed later. Piecewise mixed-effects models may be useful in a variety of research settings where it is necessary to estimate the unknown time of an event. [ABSTRACT FROM AUTHOR]