### A New Method of Odds Ratio and Hazard Analysis of Head and Neck Cancer

#### Abstract

The main topic of this paper is to focus on a new method for calculating odds ratios and hazard ratios through probabilities and effect modification. This probability is derived through an odds ratio proof for the common conditional odds ratio of Cochran Mantel Hansel showing theta equals one. Subsequently, the probability formula is obtained and the hazard ratio expression derived. However, the new relation of this proof is to show that logits equals itself through probability. From this derivation, an expression of risk is obtained which is an odds ratio. Parameters are obtained through a novel method of Survreg and its proportional hazard assumption. The odds ratio obtained is given as per strata as well as hazard ratio method demonstrated which is curvilinear to probability in comparison for the interaction model to represent percent change. The odds ratios from PROC GLIMMIX for interaction model has odds ratio of 1.76 vs 1.73 and 1.83 vs 1.76 for white and black males of a logit expression another expression of a logit. A parametric analysis shows correlation to the odds ratios for strata and probability Pr(z) that can work from a new derivation for an odds ratio with for the exposure shown to have power with the RANTBL function of about 83 % with effect modification included at 100% power. The comparison of effect modification P values to hazard ratio is then made for differences across strata.

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ISSN: 1929-6029