DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Left, right and interval bivariate censored data: Evaluating screening mammography in the presence of lead -time bias, length bias and over-detection

Of the large clinical trials evaluating screening mammography efficacy, none included women ages 75 and older. Recommendations on an upper age limit at which to discontinue screening are based on indirect evidence and are not consistent. Screening mammography is evaluated using observational data from the SEER-Medicare linked database. Measuring the benefit of screening mammography is difficult due to the impact of lead-time bias, length bias and over-detection. The underlying conceptual model divides the disease into two stages: pre-clinical (T0) and symptomatic (T1) breast cancer. Treating the time in these phases as a pair of dependent bivariate observations, (t0,t1), estimates are derived to describe the distribution of this random vector. To quantify the effect of screening mammography, statistical inference is made about the mammography parameters that correspond to the marginal distribution of the symptomatic phase duration (T1). This shows the hazard ratio of death from breast cancer comparing women with screen-detected tumors to those detected at their symptom onset is 0.36 (0.30, 0.42), indicating a benefit among the screen-detected cases. ^