On the Bartlett Adjustment for the Partial Likelihood Ratio Test in the Cox Regression Model

The Bartlett adjustment for the partial likelihood ratio test in Cox regression model is established under one-dimensional parameter. If the baseline hazard is unspecified, the adjustment factor can be estimated from the data. The procedure give more accurate probability than the normal approximation to the log-rank test. Abbreviated Title. Bartlett's Adjustment for Partial Likelihood. AMS 1980 subject classification. Primary 62E20, 62G05; Secondary 62P10. Key Words and Phrases. Adjustment, Asymptotic Expansion, Partial likelihood, Cox regression model, Survival data. 1. Introduction and result. In parametric inference, the likelihood ratio test is one of the most popular statistics for inference. One reason for its popularity is the Bartlett (1937) adjustment to the likelihood ratio statistics. When the sample size is small, this adjustment may have a significant improvement over the ordinary asymptotic theory. For a detailed account and the proof, see Barndoff-Nielsen and Cox (1..

Aseptic loosening of tumor prostheses in distal femur after revision surgery: a retrospective study

Abstract Background Tumor prostheses of the distal femur after revision surgery is associated with high rates of aseptic loosening, which has introduced great challenges to the survival of patients, but only a few studies have evaluated their X-ray imaging. The purpose of this study was to analyze the risk factors for recurrence of aseptic loosening and make recommendations to reduce the incidence of aseptic loosening after revision surgery of tumor prostheses in the distal femur. Method A retrospective analysis was performed on 23 patients who had revision surgery for distal femur prostheses due to aseptic loosening between June 2002 and June 2021. They were divided into two groups based on the condition of the prostheses after revision surgery: loosening group (9 patients) and control group (14 patients). Following the initial replacement, the length and diameter of the prosthetic intramedullary stem were measured through the standard full-length anteroposterior X-ray imaging of both lower limbs. The osteotomy length, femoral length and diameter, femoral intramedullary stem diameter, hip-knee-ankle angle (HKAA), mechanical lateral distal femoral angle (mLDFA), mechanical medial proximal tibial angle (mMPTA), and so on were measured as well. Following that, statistical analysis was performed. Results Patients in the loosening group had statistically significant differences in the ratio of prostheses length to femur length (71.89 ± 6.62) and the ratio of intramedullary stem diameter to femoral diameter (25.50 ± 6.90) (P < 0.05), when compared to the control group. The HKAA (175.58 ± 2.78), mLDFA (94.42 ± 2.57), and the deviation angle between the lower limb alignment and the tibial prostheses force line (2.23 ± 1.09) in the loosening group were significantly different from those in the control group (P < 0.05) on postoperative radiographs of the entire length of the lower limbs. The lowest score in intramedullary manubrium I indicated less osteolysis, while the highest score in intramedullary manubrium III indicated the most serious osteolysis, and the difference was statistically significant (P < 0.05). Conclusions Our study suggests that the use of longer and thicker intramedullary stems can effectively decrease the occurrence of aseptic loosening. Additionally, it is important to avoid using the original prostheses and reconstruct the standard line of lower limb force to further reduce the incidence of aseptic loosening. It is crucial to closely monitor the distal segment of the intramedullary stem for osteolysis after surgery