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PubMed1998

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.

Bias↗

PubMed1996

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.

Acquired Immunodeficiency Syndrome↗