The risk prediction for SPM and its impact on the survival in patients with head and neck squamous cell carcinoma

Head and Neck Squamous Cell Carcinoma (HNSCC) is the sixth common malignancy in the world, with high rates of developing second primary malignancy (SPM) and moderately low survival rates. This disease has become an enormous challenge in the cancer research and treatments. For HNSCC patients, a highly significant cause of post-treatment mortality and morbidity is the development of SPM. Hence, assessment of predicting the risk for the development of SPM would be very helpful for patients, clinicians and policy makers to estimate the survival of patients with HNSCC. In this study, we built a prognostic model to predict the risk of developing SPM in patients with newly diagnosed HNSCC. The dataset used in this research was obtained from The University of Texas MD Anderson Cancer Center. For the first aim, we used stepwise logistic regression to identify the prognostic factors for the development of SPM. Our final model contained cancer site and overall cancer stage as our risk factors for SPM. The Hosmer-Lemeshow test (p-value= 0.15>0.05) showed the final prognostic model fit the data well. The area under the ROC curve was 0.72 that suggested the discrimination ability of our model was acceptable. The internal validation confirmed the prognostic model was a good fit and the final prognostic model would not over optimistically predict the risk of SPM. This model needs external validation by using large data sample size before it can be generalized to predict SPM risk for other HNSCC patients. For the second aim, we utilized a multistate survival analysis approach to estimate the probability of death for HNSCC patients taking into consideration of the possibility of SPM. Patients without SPM were associated with longer survival. These findings suggest that the development of SPM could be a predictor of survival rates among the patients with HNSCC.^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^