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Authors have observed that the distribution of medical expenditures has features that do not lend it to parametric modeling and can present significant challenges for least-squares-type estimators, even on a logarithmic scale. In this note, we discuss caveats and extensions of coefficient estimation in the bivariate accelerated lifetime model of medical cost and survival time on covariates. We consider the setting where medical cost is observed only when the event occurs and potential right-censoring of the event time induces a dependent censoring mechanism on cost. We adopt Huang's (2002) estimation framework using the weighted log-rank estimating equations and investigate his proposal for robust mark-scale coefficient estimation. Due to modeling restrictions on the joint distribution of survival time and cost, we conclude that his robust mark-scale coefficient estimator would benefit from a time-scale adjustment. We use basic principles from robust estimation to define a new weighted marked process that subsequently leads to a new time-corrected robust regression calibration estimator. Our simulation studies illustrate how the proposed estimator has desirable operating characteristics, including reduced sensitivity to extreme values in the cost distribution, smaller finite sample bias and variance than earlier proposals. We illustrate the method in an analysis of lifetime medical cost data from a lung cancer study conducted by the Southwest Oncology Group.

On Huberized Calibration Regression for Censored Medical Cost Data