Improving the fit of bivariate smoothing splines when estimating longitudinal immunological and virological markers in HIV patients with individual antiretroviral treatment strategies

CD4+ lymphocyte count and HIV RNA plasma viral load are longitudinally moni tored in patients with HIV infection. Because data collection intervals may be unequally spaced and these markers experience high within-patient varia bility, they may be smoothed before use in subsequent models. Estimation st rategies must be able to accommodate the drastic changes in viral load whic h may occur when an individual's treatment strategy is updated. Because the se treatment changes are not regimented, these dynamics cannot be modelled using standard methods. We propose univariate and bivariate cubic smoothing splines to fit CD4+ count and viral load over time. The method is develope d using state space equations, and the Kalman filter is used to calculate t he log-likelihood. Non-linear optimization is used to obtain the maximum li kelihood estimates. A modification of the Kalman filter allows noninformati ve or diffuse priors at the initial observation. Since treatment changes ar e expected to alter the shape of the curve, we further extend the Kalman fi lter to permit greater flexibility in the smoothing spline at these time po ints. The method produces smoothed estimates of the viral load and CD4+ cou nt curves over time. Copyright (C) 2001 John Wiley & Sons, Ltd.