The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

Cerebellar cortex contributions to the expression and timing of conditioned eyelid responses.

We used micro-infusions during eyelid conditioning in rabbits to investigate the relative contributions of cerebellar cortex and the underlying deep nuclei (DCN) to the expression of cerebellar learning. These tests were conducted using two forms of cerebellum-dependent eyelid conditioning for which the relative roles of cerebellar cortex and DCN are controversial: delay conditioning, which is largely unaffected by forebrain lesions, and trace conditioning, which involves interactions between forebrain and cerebellum. For rabbits trained with delay conditioning, silencing cerebellar cortex by micro-infusions of the local anesthetic lidocaine unmasked stereotyped short-latency responses. This was also the case after extinction as observed previously with reversible blockade of cerebellar cortex output. Conversely, increasing cerebellar cortex activity by micro-infusions of the GABA(A) antagonist picrotoxin reversibly abolished conditioned responses. Effective cannula placements were clustered around the primary fissure and deeper in lobules hemispheric lobule IV (HIV) and hemispheric lobule V (HV) of anterior lobe. In well-trained trace conditioned rabbits, silencing this same area of cerebellar cortex or reversibly blocking cerebellar cortex output also unmasked short-latency responses. Because Purkinje cells are the sole output of cerebellar cortex, these results provide evidence that the expression of well-timed conditioned responses requires a well-timed decrease in the activity of Purkinje cells in anterior lobe. The parallels between results from delay and trace conditioning suggest similar contributions of plasticity in cerebellar cortex and DCN in both instances.

Effect of patient accrual patterns on power and size of log-rank test for time-to-event outcome in clinical trials

The determination of size as well as power of a test is a vital part of a Clinical Trial Design. This research focuses on the simulation of clinical trial data with time-to-event as the primary outcome. It investigates the impact of different recruitment patterns, and time dependent hazard structures on size and power of the log-rank test. A non-homogeneous Poisson process is used to simulate entry times according to the different accrual patterns. A Weibull distribution is employed to simulate survival times according to the different hazard structures. The current study utilizes simulation methods to evaluate the effect of different recruitment patterns on size and power estimates of the log-rank test. The size of the log-rank test is estimated by simulating survival times with identical hazard rates between the treatment and the control arm of the study resulting in a hazard ratio of one. Powers of the log-rank test at specific values of hazard ratio (≠1) are estimated by simulating survival times with different, but proportional hazard rates for the two arms of the study. Different shapes (constant, decreasing, or increasing) of the hazard function of the Weibull distribution are also considered to assess the effect of hazard structure on the size and power of the log-rank test. ^