Journal of Data Science

We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual's failure interval into nonoverlapping sub-intervals. Using the set of all interval endpoints in the data set, those that fall into the individual's interval are then used as the cut points for the sub-intervals. Each sub-interval has an accompanying weight calculated from a parametric Weibull model based on the current parameter estimates. A weighted PH model is then fit with multiple lines of observations corresponding to the sub-intervals for each individual, where the lower end of each sub-interval is used as the observed failure time with the accompanying weights incorporated. Right-censored observations are handled in the usual manner. We iterate between estimating the baseline Weibull distribution and fitting the weighted PH model until the regression parameters of interest converge. The regression parameter estimates are fixed as an offset when we update the estimates of the Weibull distribution and recalculate the weights. Our approach is similar to Satten et al.'s (1998) method for interval-censored survival analysis that used imputed failure times generated from a parametric model in a PH model. Simulation results demonstrate apparently unbiased parameter estimation for the correctly specified Weibull model and little to no bias for a mis-specified log-logistic model. Breast cosmetic deterioration data and ICU hyperlactemia data are analyzed.

Abstract: We present power calculations for zero-inflated Poisson (ZIP) and zero-inflated negative-binomial (ZINB) models. We detail direct computations for a ZIP model based on a two-sample Wald test using the expected information matrix. We also demonstrate how Lyles, Lin, and Williamson’s method (2006) of power approximation for categorical and count outcomes can be extended to both zero-inflated models. This method can be used for power calculations based on the Wald test (via the observed information matrix) and the likelihood ratio test, and can accommodate both categorical and continuous covariates. All the power calculations can be conducted when covariates are used in the modeling of both the count data and the “excess zero” data, or in either part separately. We present simulations to detail the performance of the power calculations. Analysis of a malaria study is used for illustration.

Abstract: Sample size and power calculations are often based on a two-group comparison. However, in some instances the group membership cannot be ascertained until after the sample has been collected. In this situation, the respective sizes of each group may not be the same as those prespecified due to binomial variability, which results in a difference in power from that expected. Here we suggest that investigators calculate an “expected power” taking into account the binomial variability of the group member ship, and adjust the sample size accordingly when planning such studies. We explore different scenarios where such an adjustment may or may not be necessary for both continuous and binary responses. In general, the number of additional subjects required depends only slightly on the values of the (standardized) difference in the two group means or proportions, but more importantly on the respective sizes of the group membership. We present tables with adjusted sample sizes for a variety of scenarios that can be readily used by investigators at the study design stage. The proposed approach is motivated by a genetic study of cerebral malaria and a sleep apnea study.