USING TRAJECTORIES FROM A BIVARIATEGROWTH CURVE OF COVARIATES IN A COXMODEL ANALYSIS

In many maintenance treatment trials, patients are first enrolled into an open treatmentbefore they are randomized into treatment groups. During this period, patients are followedover time with their responses measured longitudinally. This design is very common intoday's public health studies of the prevention of many diseases. Using mixed model theory, onecan characterize these data using a wide array of across subject models. A state-spacerepresentation of the mixed model and use of the Kalman filter allow more fexibility inchoosing the within error correlation structure even in the presence of missing and unequallyspaced observations. Furthermore, using the state-space approach, one can avoid invertinglarge matrices resulting in eficient computations. Estimated trajectories from these models can be used as predictors in a survival analysis in judging the efacacy of the maintenance treatments. The statistical problem lies in accounting for the estimation error in these predictors. We considered a bivariate growth curve where the longitudinal responses were unequally spaced and assumed that the within subject errors followed a continuous firstorder autoregressive (CAR (1)) structure. A simulation study was conducted to validatethe model. We developed a method where estimated random effects for each subject froma bivariate growth curve were used as predictors in the Cox proportional hazards model,using the full likelihood based on the conditional expectation of covariates to adjust for the estimation errors in the predictor variables. Simulation studies indicated that error corrected estimators for model parameters are mostly less biased when compared with thenave regression without accounting for estimation errors. These results hold true in Coxmodels with one or two predictors. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. A Visual Fortran 90 and a SAS IML program are developed

Controllable Electrodeposition Adjusts the Electrochromic Properties of Co and Mo Co-Modified WO₃ Films

Metal ion modification is considered to be an effective way to construct metal oxides with specific physical and chemical properties. In this paper, we prepare a tungsten oxide (WO3) film co-modified by Co-ion and Mo-ion to serve as the electrochromic material through a one-step electrodeposition method. The effect of electrodeposition time on film thickness, surface morphology and electrochromic properties is systematically studied as well. The results show that, compared with pure WO3 film, the surface morphology of the tungsten oxide film modified by Co-ion and Mo-ion (WO3: Co, Mo) is significantly different. The Co and Mo co-modified film possesses a higher transmission modulation (58.5% at 600 nm) and rapid switching speed (coloring and bleaching time are 2.7 s and 5.6 s, respectively), low impedance value and excellent cycle stability. The performance enhancement is mainly attributed to the coral-like structure of the membrane, which provides a larger specific surface area, more ion adsorption sites and faster ion diffusion. Therefore, this work provides a fast and low-cost method to prepare tungsten oxide electrochromic films co-modified with cobalt and molybdenum ions. At the same time, it also provides an idea to obtain films with different electrochromic properties by adjusting the film thickness