Testing for bias in weighted estimating equations.

It is very common in regression analysis to encounter incompletely observed covariate information. A recent approach to analyse such data is weighted estimating equations (Robins, J. M., Rotnitzky, A. and Zhao, L. P. (1994), JASA, 89, 846-866, and Zhao, L. P., Lipsitz, S. R. and Lew, D. (1996), Biometrics, 52, 1165-1182). With weighted estimating equations, the contribution to the estimating equation from a complete observation is weighted by the inverse of the probability of being observed. We propose a test statistic to assess if the weighted estimating equations produce biased estimates. Our test statistic is similar to the test statistic proposed by DuMouchel and Duncan (1983) for weighted least squares estimates for sample survey data. The method is illustrated using data from a randomized clinical trial on chemotherapy for multiple myeloma.

A global goodness-of-fit statistic for Cox regression models.

In this paper, a global goodness-of-fit test statistic for a Cox regression model, which has an approximate chi-squared distribution when the model has been correctly specified, is proposed. Our goodness-of-fit statistic is global and has power to detect if interactions or higher order powers of covariates in the model are needed. The proposed statistic is similar to the Hosmer and Lemeshow (1980, Communications in Statistics A10, 1043-1069) goodness-of-fit statistic for binary data as well as Schoenfeld's (1980, Biometrika 67, 145-153) statistic for the Cox model. The methods are illustrated using data from a Mayo Clinic trial in primary billiary cirrhosis of the liver (Fleming and Harrington, 1991, Counting Processes and Survival Analysis), in which the outcome is the time until liver transplantation or death. The are 17 possible covariates. Two Cox proportional hazards models are fit to the data, and the proposed goodness-of-fit statistic is applied to the fitted models.

Inference using conditional logistic regression with missing covariates.

When there are many nuisance parameters in a logistic regression model, a popular method for eliminating these nuisance parameters is conditional logistic regression. Unfortunately, another common problem in a logistic regression analysis is missing covariate data. With many nuisance parameters to eliminate and missing covariates, many investigators exclude any subject with missing covariates and then use conditional logistic regression, often called a complete-case analysis. In this article, we derive a modified conditional logistic regression that is appropriate with covariates that are missing at random. Performing a conditional logistic regression with only the complete cases is convenient with existing statistical packages, but it may give bias if missingness is not completely at random.

Accurate confidence limits for quantiles under random censoring.

In survival analysis, estimates of median survival times in homogeneous samples are often based on the Kaplan-Meier estimator of the survivor function. Confidence intervals for quantiles, such as median survival, are typically constructed via large sample theory or the bootstrap. The former has suspect accuracy for small sample sizes under moderate censoring and the latter is computationally intensive. In this paper, improvements on so-called test-based intervals and reflected intervals (cf., Slud, Byar, and Green, 1984, Biometrics 40, 587-600) are sought. Using the Edgeworth expansion for the distribution of the studentized Nelson-Aalen estimator derived in Strawderman and Wells (1997, Journal of the American Statistical Association 92), we propose a method for producing more accurate confidence intervals for quantiles with randomly censored data. The intervals are very simple to compute, and numerical results using simulated data show that our new test-based interval outperforms commonly used methods for computing confidence intervals for small sample sizes and/or heavy censoring, especially with regard to maintaining specified coverage.

Functional limitation pathways and transitions in community-dwelling older persons.

The focus of this article is to determine the probability of making transitions through various ADL limitation levels, controlling for gender, age, and baseline ADL level, and using death as a competing outcome. We use the four waves of the Longitudinal Study of Aging and categorical data techniques to model the probability of these transitions. We find much heterogeneity among the transitions, with significant age and functional limitation effects. We also find that death and functional limitations are not necessarily highly linked.

A jackknife estimator of variance for Cox regression for correlated survival data.

Studies in the health sciences often give rise to correlated survival data. Wei, Lin, and Weissfeld (1989, Journal of the American Statistical Association 84, 1065-1073) and Lee, Wei, and Amato (1992, in Survival Analysis: State of the Art) showed that, if the marginal distributions of the correlated survival times follow a proportional hazards model, then the estimates from Cox's partial likelihood (Cox, D.R., 1972, Journal of the Royal Statistical Society, Series B 24, 187-220), naively treating the correlated survival times as independent, give consistent estimates of the relative risk parameters. However, because of the correlation between survival times, the inverse of the information matrix may not be a consistent estimate of the asymptotic variance. Wei et al. (1989) and Lee et al. (1992) proposed a robust variance estimate that is consistent for the asymptotic variance. We show that a "one-step" jackknife estimator of variance is asymptotically equivalent to their variance estimator. The jackknife variance estimator may be preferred because an investigator needs only to write a simple loop in a computer package instead of a more involved program to compute Wei et al. (1989) and Lee et al.'s (1992) estimator.