Absolute co-supplement and absolute co-coclosed modules

A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.Scientific and Technical Research Council of Turke

Low Prognostic Nutritional Index (PNI) Predicts Unfavorable Distant Metastasis-Free Survival in Nasopharyngeal Carcinoma: A Propensity Score-Matched Analysis

<div><p>Background</p><p>Poor nutritional status is associated with progression and advanced disease in patients with cancer. The prognostic nutritional index (PNI) may represent a simple method of assessing host immunonutritional status. This study was designed to investigate the prognostic value of the PNI for distant metastasis-free survival (DMFS) in patients with nasopharyngeal carcinoma (NPC).</p><p>Methods</p><p>A training cohort of 1,168 patients with non-metastatic NPC from two institutions was retrospectively analyzed. The optimal PNI cutoff value for DMFS was identified using the online tool “Cutoff Finder”. DMFS was analyzed using stratified and adjusted analysis. Propensity score-matched analysis was performed to balance baseline characteristics between the high and low PNI groups. Subsequently, the prognostic value of the PNI for DMFS was validated in an external validation cohort of 756 patients with NPC. The area under the receiver operating characteristics curve (AUC) was calculated to compare the discriminatory ability of different prognostic scores.</p><p>Results</p><p>The optimal PNI cutoff value was determined to be 51. Low PNI was significantly associated with poorer DMFS than high PNI in univariate analysis (P<0.001) as well as multivariate analysis (P<0.001) before propensity score matching. In subgroup analyses, PNI could also stratify different risks of distant metastases. Propensity score-matched analyses confirmed the prognostic value of PNI, excluding other interpretations and selection bias. In the external validation cohort, patients with high PNI also had significantly lower risk of distant metastases than those with low PNI (Hazards Ratios, 0.487; P<0.001). The PNI consistently showed a higher AUC value at 1-year (0.780), 3-year (0.793) and 5-year (0.812) in comparison with other prognostic scores.</p><p>Conclusion</p><p>PNI, an inexpensive and easily assessable inflammatory index, could aid clinicians in developing individualized treatment and follow-up strategies for patients with non-metastatic NPC.</p></div

Associations between PNI and clinicopathological features before and after propensity score matching.

<p>Associations between PNI and clinicopathological features before and after propensity score matching.</p

Univariable and multivariate analysis of associations with DMFS after 1:2 ratio propensity score matching.

<p>Univariable and multivariate analysis of associations with DMFS after 1:2 ratio propensity score matching.</p

Forest plot of subgroup effects for distant metastasis-free survival (DMFS) in 1,168 patients with nasopharyngeal carcinoma who underwent definitive radiotherapy.

<p>Subgroups are defined by factors showing significant associations between the PNI and DMFS. Univariate hazard ratios and 95% CI (bars) are presented. WBC, white blood cell count; HGB, hemoglobin; ALT, <a href="http://dict.cnki.net/dict_result.aspx?searchword=%e8%b0%b7%e4%b8%99%e8%bd%ac%e6%b0%a8%e9%85%b6(alt)&tjType=sentence&style=&t=alanine+transaminase+(alt)" target="_blank">alanine transaminase; AST, aspartate transaminase; ALP, alkaline phosphatase; LDH, lactate dehydrogenase; CRP, C-reactive protein; ALB, albumin; EBV, Epstein-Barr virus DNA;</a> CRT, conventional radiotherapy: IMRT, intensity-modulated radiation therapy; 3D-CRT, three-dimensional conformal radiation therapy; RT, radiotherapy; chemo-radiotherapy, chemotherapy plus radiotherapy.</p

Prognostic value of the prognostic nutritional index (PNI) for distant metastasis-free survival (DMFS).

<p>(A) In the training cohort before matching, (B) the validation cohort and (C) the training cohort after 2:1 ratio matching.</p

Hazard ratio (HR) for distant metastasis-free survival (DMFS) independent of the cutoff point for prognostic nutritional index (PNI) in patients with nasopharyngeal carcinoma.

<p>The vertical line designates the optimal cutoff points with the most significant split (log-rank test). The plots were generated using Cutoff Finder.</p

Comparisons of the area under the receiver operating curve (AUC) for predicting distant metastasis free survival (DMFS) by PNI, mGPS, PLR and NLR.

<p>(A) At 1-year (AUC = 0.780, 0.705, 0.673 and 0.572, respectively), (B) 3-year (AUC = 0.793, 0.711, 0.653 and 0.542, respectively) and (C) 5-year (AUC = 0.812, 0.715, 0.642 and 0.530, respectively).NLR, neutrophil to lymphocyte ratio; PLR, the platelet to lymphocyte ratio; mGPS, the modified Glasgow Prognostic Score; PNI, prognostic nutritional index.</p

Clinical and laboratory characteristics of the patients in the training set and validation set.

<p>Clinical and laboratory characteristics of the patients in the training set and validation set.</p