The Louisiana Lung Cancer Dataset, consisting of 337 extended pedigrees, is analyzed to determine whether a major Mendelian gene interacts with cumulative tobacco smoking (pack-years). The proportional hazards model is utilized, as it is a natural framework for estimating relative risks while adjusting for variability in age of disease onset. Segregation analyses show evidence that a Mendelian gene is segregating in these families, with the most parsimonious model, including sex, pack-years, pack-years squared, and a dominant major gene. The estimated frequency of the high-risk allele is 2% and carriers are estimated to have relative risk of 17.3 for developing lung cancer, compared to noncarriers. The addition of a gene x pack-years interaction does not significantly improve the fit of the model, indicating that on a multiplicative scale, these two factors independently influence lung cancer risk. Smoking history is missing for 23% of the study subjects and degree of "missingness" depends on disease status, age, and birth-year. To account for the nonrandomness of the missing data, a Markov chain Monte Carlo method for covariate imputation is proposed and implemented. Results from this analysis also support a nonsignificant gene-smoking interaction and an allele frequency of 2%, but a lower genetic relative risk (9.0) compared to the "complete case" analysis.