Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.     

CYP1A1 and CYP2D6 polymorphism and risk of lung cancer in a North Indian population

This case–control study was conducted to examine the association between the CYP1A1 and CYP2D6 genotypes and lung cancer risk among North Indians. The estimated relative risk for lung cancer associated with the CYP1A1 Val/Val allele was 2.68, and was four-fold when cases with small cell lung cancer (SCLC) were considered alone. With regard to the metabolism of debrisoquine, no poor metabolizers were found amongst the subjects. The odds ratio of risk with the heterozygous extensive metabolizer (HEM) genotype was 1.5. However, in the presence of at least a single copy of the variant CYP1A1 MspI allele and the CYP2D6 HEM genotype, the risk was two-fold for squamous cell carcinoma (SQCC). When the CYP1A1 Val/Val and CYP2D6 HEM genotypes were taken together, the risk for SCLC was four-fold. Stratified analysis indicated an interaction between bidi smoking and variant CYP1A1 genotypes on the risk for SQCC and SCLC. Heavy smokers (Brinkman index>400) with Val/Val genotypes were at a very high risk of developing lung cancer (odds ratio 29.30, 95% confidence interval 2.42–355, p=0.008). Heavy smokers with CYP1A1 MspI (CYP1A1*1/2A or CYP1A1*2A/*2A) genotype had a seven-fold risk for SCLC compared with non-smokers. This study is the first to be carried out on a North Indian population, and, although small, suggests that CYP1A1 and CYP2D6 polymorphisms might have a role in determining the risk for lung cancer and should be investigated further.