No abstract

The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to +/- infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation. It produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald tests and confidence intervals are available but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. The clear advantage of the procedure over previous options of analysis is impressively demonstrated by the statistical analysis of two cancer studies.

In asymptomatic patients with aortic stenosis, it appears to be relatively safe to delay surgery until symptoms develop. However, outcomes vary widely. The presence of moderate or severe valvular calcification, together with a rapid increase in aortic-jet velocity, identifies patients with a very poor prognosis. These patients should be considered for early valve replacement rather than have surgery delayed until symptoms develop.

The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to +/- infinity. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika 80, 27-38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.

Background-The management of asymptomatic severe mitral regurgitation remains controversial. The aim of this study was to evaluate the outcome of a watchful waiting strategy in which patients are referred to surgery when symptoms occur or when asymptomatic patients develop left ventricular (LV) enlargement, LV dysfunction, pulmonary hypertension, or recurrent atrial fibrillation. Methods and Results-A total of 132 consecutive asymptomatic patients (age 55Ϯ15 years, 49 female) with severe degenerative mitral regurgitation (flail leaflet or valve prolapse) were prospectively followed up for 62Ϯ26 months.Patients underwent serial clinical and echocardiographic examinations and were referred for surgery when the criteria mentioned above were fulfilled. Overall survival was not statistically different from expected survival either in the total group or in the subgroup of patients with flail leaflet. Eight deaths were observed. Thirty-eight patients developed criteria for surgery (symptoms, 24; LV criteria, 9; pulmonary hypertension or atrial fibrillation, 5). Survival free of any indication for surgery was 92Ϯ2% at 2 years, 78Ϯ4% at 4 years, 65Ϯ5% at 6 years, and 55Ϯ6% at 8 years. Patients with flail leaflet tended to develop criteria for surgery slightly but not significantly earlier.