On Proportional Hazard Functions

The modeling of time to event data is an important topic with many applications in diverse areas. The collective of methods to analyze such data are called survival analysis, event history analysis or duration analysis. Survival analysis is widely applicable because the definition of an ’event’ can be manifold and examples include death, graduation, purchase or bankruptcy. Hence, application areas range from medicine and sociology to marketing and economics. In this paper, we review the theoretical basics of survival analysis including estimators for survival and hazard functions. We discuss the Cox Proportional Hazard Model in detail and also approaches for testing the proportional hazard (PH) assumption. Furthermore, we discuss stratified Cox models for cases when the PH assumption does not hold. Our discussion is complemented with a worked example using the statistical programming language R to enable the practical application of the methodology.

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Mortality hazard functions as related to neutropenia at different times after marrow transplantation

Blood ◽

10.1182/blood.v88.10.4058.bloodjournal88104058 ◽

1996 ◽

Vol 88 (10) ◽

pp. 4058-4062 ◽

Cited By ~ 22

Author(s):

F Offner ◽

G Schoch ◽

LD Fisher ◽

B Torok-Storb ◽

PJ Martin

Keyword(s):

Risk Ratio ◽

Marrow Transplantation ◽

Graft Function ◽

Severe Neutropenia ◽

Proportional Hazard ◽

Transplant Recipients ◽

Hazard Functions ◽

Risk Of Death ◽

Relative Risk Of Death ◽

The Relationship

We characterized the relationship between severe neutropenia and risk of death in 2,276 patients after marrow transplantation to define objective and clinically relevant criteria that could be used to judge the timing and potential value of interventions designed to improve survival in patients with delayed initial engraftment. Proportional hazard models were used to estimate the relative risk of death before day 100 among patients alive on any given day with an absolute neutrophil count (ANC) less than 100/microL compared with those alive on the same day with an ANC > or = 100/microL. Between day 10 and 14, the risk ratio remained close to 1.0, indicating that the risk of death before day 100 for patients with an ANC less than 100/microL was similar to that for patients with an ANC > or = 100/microL. Between day 15, when 38% of patients had an ANC less than 100/microL, and day 26, when 3.8% of patients had an ANC less than 100/microL, the risk ratio showed an overall upward trend, indicating that patients with an ANC less than 100/microL had a higher risk of death before day 100 than those with an ANC > or = 100/microL. Thereafter, the risk ratio fluctuated between 2.01 and 5.78, indicating consistently higher risks of mortality in patients with severe neutropenia. However, allogeneic and autologous transplant recipients each had distinctive risk ratio patterns. These results could be helpful in deciding the appropriate timing for treatment given to improve graft function after marrow transplantation.

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A Study of Factors Affecting the Length of Hospital Stay of COVID-19 Patients by Cox-Proportional Hazard Model in a South Indian Tertiary Care Hospital

Journal of Primary Care & Community Health ◽

10.1177/21501327211000231 ◽

2021 ◽

Vol 12 ◽

pp. 215013272110002

Author(s):

Gayathri Thiruvengadam ◽

Marappa Lakshmi ◽

Ravanan Ramanujam

Keyword(s):

Hospital Stay ◽

Tertiary Care ◽

Length Of Hospital Stay ◽

Hazard Model ◽

Cox Proportional Hazard Model ◽

Care Hospital ◽

Proportional Hazard ◽

Proportional Hazard Model ◽

Cox Proportional Hazard ◽

South Indian

Background: The objective of the study was to identify the factors that alter the length of hospital stay of COVID-19 patients so we have an estimate of the duration of hospitalization of patients. To achieve this, we used a time to event analysis to arrive at factors that could alter the length of hospital stay, aiding in planning additional beds for any future rise in cases. Methods: Information about COVID-19 patients was collected between June and August 2020. The response variable was the time from admission to discharge of patients. Cox proportional hazard model was used to identify the factors that were associated with the length of hospital stay. Results: A total of 730 COVID-19 patients were included, of which 675 (92.5%) recovered and 55 (7.5%) were considered to be right-censored, that is, the patient died or was discharged against medical advice. The median length of hospital stay of COVID-19 patients who were hospitalized was found to be 7 days by the Kaplan Meier curve. The covariates that prolonged the length of hospital stay were found to be abnormalities in oxygen saturation (HR = 0.446, P < .001), neutrophil-lymphocyte ratio (HR = 0.742, P = .003), levels of D-dimer (HR = 0.60, P = .002), lactate dehydrogenase (HR = 0.717, P = .002), and ferritin (HR = 0.763, P = .037). Also, patients who had more than 2 chronic diseases had a significantly longer length of stay (HR = 0.586, P = .008) compared to those with no comorbidities. Conclusion: Factors that are associated with prolonged length of hospital stay of patients need to be considered in planning bed strength on a contingency basis.

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Low serum parathyroid hormone is a risk factor for peritonitis episodes in incident peritoneal dialysis patients: a retrospective study

BMC Nephrology ◽

10.1186/s12882-021-02241-0 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Yuqi Yang ◽

Jingjing Da ◽

Yi Jiang ◽

Jing Yuan ◽

Yan Zha

Keyword(s):

Risk Factor ◽

Peritoneal Dialysis ◽

Parathyroid Hormone ◽

Proportional Hazard ◽

Serum Parathyroid Hormone ◽

Cox Proportional Hazard ◽

Cox Proportional Hazard Regression ◽

Gram Negative Organisms ◽

Serum Pth

Abstract Background Serum parathyroid hormone (PTH) levels have been reported to be associated with infectious mortality in peritoneal dialysis (PD) patients. Peritonitis is the most common and fatal infectious complication, resulting in technique failure, hospital admission and mortality. Whether PTH is associated with peritonitis episodes remains unclear. Methods We examined the association of PTH levels and peritonitis incidence in a 7-year cohort of 270 incident PD patients who were maintained on dialysis between January 2012 and December 2018 using Cox proportional hazard regression analyses. Patients were categorized into three groups by serum PTH levels as follows: low-PTH group, PTH < 150 pg/mL; middle-PTH group, PTH 150-300 pg/mL; high-PTH group, PTH > 300 pg/mL. Results During a median follow-up of 29.5 (interquartile range 16–49) months, the incidence rate of peritonitis was 0.10 episodes per patient-year. Gram-positive organisms were the most common causative microorganisms (36.2%), and higher percentage of Gram-negative organisms was noted in patients with low PTH levels. Low PTH levels were associated with older age, higher eGFR, higher hemoglobin, calcium levels and lower phosphate, alkaline phosphatase levels. After multivariate adjustment, lower PTH levels were identified as an independent risk factor for peritonitis episodes [hazard ratio 1.643, 95% confidence interval 1.014–2.663, P = 0.044]. Conclusions Low PTH levels are independently associated with peritonitis in incident PD patients.

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POS1329 A COHORT STUDY ON THE RISK OF DEVELOPING OBSTRUCTIVE SLEEP APNEA, TEMPOROMANDIBULAR JOINT DISORDERS AND CRANIOFACIAL DEFORMITIES IN PATIENTS WITH JUVENILE IDIOPATHIC ARTHRITIS

Annals of the Rheumatic Diseases ◽

10.1136/annrheumdis-2021-eular.3961 ◽

2021 ◽

Vol 80 (Suppl 1) ◽

pp. 947.1-947

Author(s):

K. S. K. MA ◽

L. T. Wang

Keyword(s):

Obstructive Sleep Apnea ◽

Cohort Study ◽

Juvenile Idiopathic Arthritis ◽

Cox Proportional Hazard Model ◽

Proportional Hazard ◽

Proportional Hazard Model ◽

Cox Proportional Hazard ◽

Obstructive Sleep ◽

Subgroup Analyses ◽

Underlying Mechanisms

Background:Juvenile Idiopathic Arthritis (JIA), an autoimmune disease, has been proposed to be comorbid with obstructive sleep apnea (OSA).Objectives:We aimed at identifying the relationship between JIA and OSA.Methods:We performed a cohort study including JIA and OSA patients from 1999 to 2013. A total of 2791 patients diagnosed with OSA after JIA onset were recruited, which 11,164 eligible individuals without JIA history were selected as matched-controls. A Cox proportional hazard model was developed to estimate the risk of OSA in JIA patients. A cumulative probability model was adopted to assess the time-dependent effect of JIA on OSA development, implying the casual link of the association. To identify whether JIA patients have higher risks for developing temporomandibular joint (TMJ) disorders, craniofacial anomalies and deformities than non-JIA individuals, subgroup analyses was conducted. Finally, Ingenuity Systems Pathway Analysis (IPA) was conducted to identify underlying mechanisms of the above disease correlation among peripheral blood mononuclear cells (PBMCs) from rheumatic factor (RF)-positive and RF-negative JIA patients, and subcutaneous fat tissues from OSA patients, using p-value visualization for RNA-seq analyses.Results:The Cox proportional hazard model showed that JIA patients were more likely to have OSA than non-JIA individuals (adjusted hazard ratio =1.949, 95% CI =1.264–3.005). The incidence of developing OSA was particularly high among patients who developed JIA aged 18-30 years old (aHR= 2.034, 95% CI=1.305-3.169) and males (aHR=1.82, 95% CI=1.121-2.954). The risk of developing OSA increased within 0-36 months (aHR = 2.216, 95% CI = 1.001 – 4.907) and over 60 months (aHR = 2.558, 95% CI = 1.346 – 4.860) of follow-up duration after JIA onset. Subgroup analyses showed that JIA patients were more likely to have TMJ disorders (relative risk = 2.047, 95% CI = 1.446-2.898) and to receive treatment for craniofacial deformities (RR = 1.722, 95% CI = 1.38-2.148) than non-JIA controls. IPA analyses suggested that the underlying mechanisms involved activation of antigen presentation pathway followed by antigen presentation to CD4+ and CD8+ T lymphocytes, as well as B cell development.Conclusion:Our findings identified high risks of developing OSA, TMJ disorders, and craniofacial deformities following JIA onset, which the underlying mechanisms may involve both cellular and humoral immunity.Disclosure of Interests:None declared

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Association of Tooth Scaling with Acute Myocardial Infarction and Analysis of the Corresponding Medical Expenditure: A Nationwide Population-Based Study

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph18147613 ◽

2021 ◽

Vol 18 (14) ◽

pp. 7613

Author(s):

Yi-Wei Kao ◽

Ben-Chang Shia ◽

Huei-Chen Chiang ◽

Mingchih Chen ◽

Szu-Yuan Wu

Keyword(s):

Myocardial Infarction ◽

Acute Myocardial Infarction ◽

Periodontal Diseases ◽

Population Based ◽

Medical Expenditure ◽

Control Group ◽

Proportional Hazard ◽

Population Based Study ◽

Scaling Group

Accumulating evidence has shown a significant correlation between periodontal diseases and systemic diseases. In this study, we investigated the association between the frequency of tooth scaling and acute myocardial infarction (AMI). Here, a group of 7164 participants who underwent tooth scaling was compared with another group of 7164 participants without tooth scaling through propensity score matching to assess AMI risk by Cox’s proportional hazard regression. The results show that the hazard ratio of AMI from the tooth scaling group was 0.543 (0.441, 0.670) and the average expenses of AMI in the follow up period was USD 265.76, while the average expenses of AMI in follow up period for control group was USD 292.47. The tooth scaling group was further divided into two subgroups, namely A and B, to check the influence of tooth scaling frequency on AMI risk. We observed that (1) the incidence rate of AMI in the group without any tooth scaling was 3.5%, which is significantly higher than the incidence of 1.9% in the group with tooth scaling; (2) the tooth scaling group had lower total medical expenditures than those of the other group because of the high medical expenditure associated with AMI; and (3) participants who underwent tooth scaling had a lower AMI risk than those who never underwent tooth scaling had. Therefore, the results of this study demonstrate the importance of preventive medicine.

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LAMB1 Is Related to the T Stage and Indicates Poor Prognosis in Gastric Cancer

Technology in Cancer Research & Treatment ◽

10.1177/15330338211004944 ◽

2021 ◽

Vol 20 ◽

pp. 153303382110049

Author(s):

Tao Ran ◽

ZhiJi Chen ◽

LiWen Zhao ◽

Wei Ran ◽

JinYu Fan ◽

...

Keyword(s):

Gastric Cancer ◽

Poor Prognosis ◽

Hazard Models ◽

Proportional Hazard ◽

Kegg Analysis ◽

Proportional Hazard Models ◽

Cox Proportional Hazard ◽

Kaplan Meier ◽

Cox Proportional Hazard Models ◽

Gastric Cancer Patients

Background and Objective: Gastric cancer (GC) is a common tumor malignancy with high incidence and poor prognosis. Laminin is an indispensable component of basement membrane and extracellular matrix, which is responsible for bridging the internal and external environment of cells and transmitting signals. This study mainly explored the association of the LAMB1 expression with clinicopathological characteristics and prognosis in gastric cancer. Methods: The expression data and clinical information of gastric cancer patients were downloaded from The Cancer Genome Atlas (TCGA) and Asian Cancer Research Group (ACRG). And we analyzed the relationship between LAMB1 expression and clinical characteristics through R. CIBERSORTx was used to calculate the absolute score of immune cells in gastric tumor tissues. Then COX proportional hazard models and Kaplan-Meier curves were performed to evaluate the role of LAMB1 and its influence on prognosis in gastric cancer patients. Finally, GO and KEGG analysis were applied for LAMB1-related genes in gastric cancer, and PPI network was constructed in Cytoscape software. Results: In the TCGA cohort, patients with gastric cancer frequently generated LAMB1 gene copy number variation, but had little effect on mRNA expression. Both in the TCGA and ACRG cohorts, the mRNA expression of LAMB1 in gastric cancer tissues was higher than it in normal tissues. All patients were divided into high expression group and low expression group according to the median expression level of LAMB1. The elevated expression group obviously had more advanced cases and higher infiltration levels of M2 macrophages. COX proportional hazard models and Kaplan-Meier curves revealed that patients with enhanced expression of LAMB1 have a worse prognosis. GO/KEGG analysis showed that LAMB1-related genes were enriched in PI3K-Akt signaling pathway, focal adhesion, ECM-receptor interaction, etc. Conclusions: The high expression of LAMB1 in gastric cancer is related to the poor prognosis of patients, and it may be related to microenvironmental changes in tumors.

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Lower Risk for Dementia Following Adult Tetanus, Diphtheria and Pertussis (Tdap) Vaccination

The Journals of Gerontology Series A ◽

10.1093/gerona/glab115 ◽

2021 ◽

Author(s):

Jeffrey F Scherrer ◽

Joanne Salas ◽

Timothy L Wiemken ◽

Christine Jacobs ◽

John E Morley ◽

...

Keyword(s):

Lower Risk ◽

Protective Effects ◽

Proportional Hazard ◽

Veterans Health ◽

Cox Proportional Hazard ◽

Dementia Risk ◽

Incident Dementia ◽

Nonspecific Effects ◽

Reduce Risk

Abstract Background Adult vaccinations may reduce risk for dementia. However it has not been established whether tetanus, diphtheria, pertussis (Tdap) vaccination is associated with incident dementia. Methods Hypotheses were tested in a Veterans Health Affairs (VHA) cohort and replicated in a MarketScan medical claims cohort. Patients were ≥65 years of age and free of dementia for 2 years prior to index date. Patients either had or did not have a Tdap vaccination by the start of either of two index periods (2011 or 2012). Follow-up continued through 2018. Controls had no Tdap vaccination for the duration of follow-up. Confounding was controlled using entropy balancing. Competing risk (VHA) and Cox proportional hazard (MarketScan) models estimated the association between Tdap vaccination and incident dementia in all patients and in age sub-groups (65-69, 70-74, ≥75 years of age). Results VHA patients were, on average, 75.6 (SD±7.5) years of age, 4% female, and 91.2% were white race. MarketScan patients were 69.8 (SD±5.6) years of age, on average and 65.4% were female. After controlling for confounding, patients with, compared to without Tdap vaccination, had a significantly lower risk for dementia in both cohorts (VHA: HR=0.58; 95%CI:0.54 - 0.63 and MarketScan: HR=0.58; 95%CI:0.48 - 0.70). Conclusions Tdap vaccination was associated with a 42% lower dementia risk in two cohorts with different clinical and sociodemographic characteristics. Several vaccine types are linked to decreased dementia risk, suggesting that these associations are due to nonspecific effects on inflammation rather than vaccine-induced pathogen-specific protective effects.

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