Handling incomplete smoking history data in survival analysis

While data are unavoidably missing or incomplete in most observational studies, consequences of mishandling such incompleteness in analysis are often overlooked. When time-varying information is collected irregularly and infrequently over a long period, even precisely obtained data may implicitly involve substantial incompleteness. Motivated by an analysis to quantitatively evaluate the effects of smoking and radiation on lung cancer risks among Japanese atomic-bomb survivors, we provide a unique application of multiple imputation to incompletely observed smoking histories under the assumption of missing at random. Predicting missing values for the age of smoking initiation and, given initiation, smoking intensity and cessation age, analyses can be based on complete, though partially imputed, smoking histories. A simulation study shows that multiple imputation appropriately conditioned on the outcome and other relevant variables can produce consistent estimates when data are missing at random. Our approach is particularly appealing in large cohort studies where a considerable amount of time-varying information is incomplete under a mechanism depending in a complex manner on other variables. In application to the motivating example, this approach is expected to reduce estimation bias that might be unavoidable in naive analyses, while keeping efficiency by retaining known information.