PubMed · 15420261
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A N BLACK. 1950. Weighted probits and their use.. https://pubmed.ncbi.nlm.nih.gov/15420261/
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In this paper we present a simple method for constructing (1- alpha)100 per cent confidence intervals for binomial proportions with near nominal coverage for all underlying proportion parameters on the unit interval. This new method uses, with a slight modification, the standard normal approximation technique taught in introductory statistics classes. Specifically, we first augment the observed binomial data with an imaginary failure to compute the lower bound and an imaginary success to compute the upper bound. By contrast, the Agresti-Coull method adds the same number of imaginary successes and failures to the observed data, yet it can still give somewhat subnominal coverage. As motivation, we discuss the relationship between this new method and the Clopper-Pearson exact method. We also present numerical calculations to illustrate the satisfactory performance of this new method compared with several common alternatives. Finally, we argue that for certain statistical applications, such as the design and analysis of clinical trials with adverse events, this new method represents a valuable complementary approach.
We consider efficient study designs to estimate sensitivity and specificity of a candidate diagnostic or screening test. Our focus is the setting in which the candidate test is inexpensive to administer compared to evaluation of disease status, and the test results, available in a large cohort, can be used as a basis for sampling subjects for verification of disease status. We examine designs in which disease status is verified in a sample chosen so as to optimize estimation of either sensitivity or specificity. We then propose a sequential design in which the first step of sampling is conducted to efficiently estimate specificity. If the candidate test is determined to be of sufficient specificity, then step two of sampling is conducted to estimate sensitivity. We propose estimators based on this sequential sampling scheme, and show that the performance of these estimators is excellent. We develop sample size calculations for the sequential design, and show that this design, in most situations, compares favourably in terms of expected sample size to a fixed size design.
We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations. To conduct the imputation, we use two working survival models to define a nearest neighbour imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two non-parametric multiple imputation methods are considered: risk set imputation, and Kaplan-Meier imputation. For both methods a future event or censoring time is imputed for each censored observation. With a categorical auxiliary variable, we show that with a large number of imputes the estimates from the Kaplan-Meier imputation method correspond to the weighted Kaplan-Meier estimator. We also show that the Kaplan-Meier imputation method is robust to mis-specification of either one of the two working models. In a simulation study with time independent and time-dependent auxiliary variables, we compare the multiple imputation approaches with an inverse probability of censoring weighted method. We show that all approaches can reduce bias due to dependent censoring and improve the efficiency. We apply the approaches to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable.