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: Ordinal Regression Statistical Associates Blue Book Series Book 9

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Delivery of cascade screening for hereditary conditions: A scoping review of the literature. Health Aff ; 37 —8. Integration of genomics, high throughput drug screening, and personalized xenograft models as a novel precision medicine paradigm for high risk pediatric cancer.

Cancer Biol Ther ; 19 — Breast cancer risk factors, survival and recurrence, and tumor molecular subtype: analysis of women from an indigenous Asian population. Breast Cancer Res ; 20 J Clin Oncol ; 31 A comparison between accelerated failure-time and Cox proportional hazard models in analyzing the survival of gastric cancer patients.

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Dose-escalated irradiation and overall survival in men with nonmetastatic prostate cancer. JAMA Oncol ; 1 — Koenker R, Bassett G Jr. Regression quantiles. Econometrica ;33— Role of Epigenetics in Cancer Initiation and Progression. Advances in Experimental Medicine and Biology , vol Springer, New York, NY, Esteller M. Epigenetics in cancer. N Engl J Med ; — Filipp FV. Crosstalk between epigenetics and metabolism- Yin and Yang of histone demethylases and methyltransferases in cancer. Brief Funct Genomics ; 16 —5. Carcinogenesis ; 31 — DNA methylation biomarkers in lung cancer diagnosis: closer to practical use?

Transl Cancer Res ; 6 :S—6. Genome Res ; 22 — Aberrant DNA methylation in non-small cell lung cancer-associated fibroblasts.

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Carcinogenesis ; 36 — Obesity, metabolic factors and risk of different histological types of lung cancer: A Mendelian randomization study. PLoS One ; 12 :e The heterogeneity in risk factors of lung cancer and the difference of histologic distribution between genders in Taiwan. Cancer Causes Control ; 12 — Application of censored quantile regression to determine overall survival related factors in breast cancer. J Res Health Sci ; 16 — Robust identification of gene-environment interactions for prognosis using a quantile partial correlation approach.

Genomics Hong HG, He X. Prediction of functional status for the elderly based on a new ordinal regression model. J Am Stat Assoc ; — Koenker R. Quantile regression for longitudinal data. J Multivariate Anal ; 91 — Yu K, Moyeed RA. Bayesian quantile regression. Stat Probab Lett ; 54 — Quantile regression: 40 years on.

Annu Rev Econ ; 9 — Waldmann E. Quantile regression: a short story on how and why. Stat Model ; 18 — A gentle introduction to quantile regression for ecologists. Front Ecol Environ ; 1 — Thinking beyond the mean: a practical guide for using quantile regression methods for health services research.

Shanghai Arch Psychiatry ; 25 Fitzenberger B, Wilke RA. Quantile regression methods. Lindgren A. Quantile regression with censored data using generalized L1 minimization. Comput Stat Data Anal ; 23 — Portnoy S. Censored regression quantiles. J Am Stat Assoc ; 98 — Efron B. The two sample problem with censored data. Peng L, Huang Y. Survival analysis with quantile regression models. Koenker R, Geling O. Reappraising medfly longevity: a quantile regression survival analysis. J Am Stat Assoc ; 96 — Hong HG, Li Y.

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Feature selection of ultrahigh-dimensional covariates with survival outcomes: a selective review. Appl Math ; 32 — Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data. Ann Stat ; 41 — A CpG-methylation-based assay to predict survival in clear cell renal cell carcinoma.

Nat Commun ; 6 For more than one explanatory variable, the process is called multiple linear regression. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Like all forms of regression analysis , linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.

Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. Linear regression has many practical uses. Most applications fall into one of the following two broad categories:. Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the "lack of fit" in some other norm as with least absolute deviations regression , or by minimizing a penalized version of the least squares cost function as in ridge regression L 2 -norm penalty and lasso L 1 -norm penalty.

Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms "least squares" and "linear model" are closely linked, they are not synonymous. Thus the model takes the form. Often these n equations are stacked together and written in matrix notation as.