Causality and the Cox Regression Model

Author(s):  
Torben Martinussen

This article surveys results concerning the interpretation of the Cox hazard ratio in connection to causality in a randomized study with a time-to-event response. The Cox model is assumed to be correctly specified, and we investigate whether the typical end product of such an analysis, the estimated hazard ratio, has a causal interpretation as a hazard ratio. It has been pointed out that this is not possible due to selection. We provide more insight into the interpretation of hazard ratios and differences, investigating what can be learned about a treatment effect from the hazard ratio approaching unity after a certain period of time. The conclusion is that the Cox hazard ratio is not causally interpretable as a hazard ratio unless there is no treatment effect or an untestable and unrealistic assumption holds. We give a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

2018 ◽  
Vol 5 (02) ◽  
pp. 2022-2033
Author(s):  
Monireh Dehghani Arani ◽  
Alireza Abadi ◽  
Aarvin Yavari ◽  
Yousef Bashiri ◽  
Liley Mahmudi ◽  
...  

Introduction: The aim of this study is to fit Fine-Grey competing risk model and compare its results with stratified Cox model and to examine its application in breast cancer data. Methods: The study was conducted on 15830 women diagnosed with breast cancer in British Columbia, Canada. They were divided into four groups according to patients' stage of disease then for patients with stage III and IV breast cancer was fitted Cox's model and Fine-Grey competing risk flexible models to each group. Results: The data show that Out of 1888 patients, 578 lied in the age group of below 50 years old, while 1310 were above 50 years of age. The results obtained from fitting stratified Cox regression model indicate that the variables of age and surgery are significant. The patients in the age group of below 50 years old have 70% less hazard in comparison with people older than 50 years of age (HR=0.83). Further, the patients receiving surgery have 38% less hazard in comparison with the patients not receiving surgery (HR=0.62). Then we fit Fine-Grey competing risk models. the variable of chemotherapy is significant in both parametric and semi-parametric competing risk models, and its hazard ratio is HR=1.15 and HR=1.14 in the two models, respectively. On the other hand, the variable of age has not become significant in any of the models, and its hazard ratio is HR=0.92 and HR=0.93, respectively. The variable of surgery in the competing risk parametric model is significant with an HR of 0.67. In Cox model, the variable of surgery is also significant with HR=0.62. Moreover, the variable of age in the competing risk parametric model has not become significant (HR=0.92), and in contrast the variable of age in the Cox model is significant (HR=0.83). Conclusion: The results of this study show that Considering the comparison of the two models, it is observed that regardless of the properties of competing risk data, estimations of hazard ratio and the extent of significance resulting from Cox models are different from those of competing risk models.   


BMJ ◽  
2019 ◽  
pp. l1516 ◽  
Author(s):  
Jonas H Kristensen ◽  
Saima Basit ◽  
Jan Wohlfahrt ◽  
Mette Brimnes Damholt ◽  
Heather A Boyd

ABSTRACTObjectiveTo investigate associations between pre-eclampsia and later risk of kidney disease.DesignNationwide register based cohort study.SettingDenmark.PopulationAll women with at least one pregnancy lasting at least 20 weeks between 1978 and 2015.Main outcome measureHazard ratios comparing rates of kidney disease between women with and without a history of pre-eclampsia, stratified by gestational age at delivery and estimated using Cox regression.ResultsThe cohort consisted of 1 072 330 women followed for 19 994 470 person years (average 18.6 years/woman). Compared with women with no previous pre-eclampsia, those with a history of pre-eclampsia were more likely to develop chronic renal conditions: hazard ratio 3.93 (95% confidence interval 2.90 to 5.33, for early preterm pre-eclampsia (delivery <34 weeks); 2.81 (2.13 to 3.71) for late preterm pre-eclampsia (delivery 34-36 weeks); 2.27 (2.02 to 2.55) for term pre-eclampsia (delivery ≥37 weeks). In particular, strong associations were observed for chronic kidney disease, hypertensive kidney disease, and glomerular/proteinuric disease. Adjustment for cardiovascular disease and hypertension only partially attenuated the observed associations. Stratifying the analyses on time since pregnancy showed that associations between pre-eclampsia and chronic kidney disease and glomerular/proteinuric disease were much stronger within five years of the latest pregnancy (hazard ratio 6.11 (3.84 to 9.72) and 4.77 (3.88 to 5.86), respectively) than five years or longer after the latest pregnancy (2.06 (1.69 to 2.50) and 1.50 (1.19 to 1.88). By contrast, associations between pre-eclampsia and acute renal conditions were modest.Conclusions Pre-eclampsia, particularly early preterm pre-eclampsia, was strongly associated with several chronic renal disorders later in life. More research is needed to determine which women are most likely to develop kidney disease after pre-eclampsia, what mechanisms underlie the association, and what clinical follow-up and interventions (and in what timeframe post-pregnancy) would be most appropriate and effective.


2017 ◽  
Vol 17 (2) ◽  
pp. 411-422 ◽  
Author(s):  
Yi-Ting Kuo ◽  
Hou-Hsun Liao ◽  
Jen-Huai Chiang ◽  
Mei-Yao Wu ◽  
Bor-Chyuan Chen ◽  
...  

Background: Pancreatic cancer is a difficult-to-treat cancer with a late presentation and poor prognosis. Some patients seek traditional Chinese medicine (TCM) consultation. We aimed to investigate the benefits of complementary Chinese herbal medicine (CHM) among patients with pancreatic cancer in Taiwan. Methods: We included all patients with pancreatic cancer who were registered in the Taiwanese Registry for Catastrophic Illness Patients Database between 1997 and 2010. We used 1:1 frequency matching by age, sex, the initial diagnostic year of pancreatic cancer, and index year to enroll 386 CHM users and 386 non-CHM users. A Cox regression model was used to compare the hazard ratios (HRs) of the risk of mortality. The Kaplan-Meier curve was used to compare the difference in survival time. Results: According to the Cox hazard ratio model mutually adjusted for CHM use, age, sex, urbanization level, comorbidity, and treatments, we found that CHM users had a lower hazard ratio of mortality risk (adjusted HR = 0.67, 95% CI = 0.56-0.79). Those who received CHM therapy for more than 90 days had significantly lower hazard ratios of mortality risk than non-CHM users (90- to 180-day group: adjusted HR = 0.56, 95% CI = 0.42-0.75; >180-day group: HR = 0.33, 95% CI = 0.24-0.45). The survival probability was higher for patients in the CHM group. Bai-hua-she-she-cao (Herba Oldenlandiae; Hedyotis diffusa Spreng) and Xiang-sha-liu-jun-zi-tang (Costus and Chinese Amomum Combination) were the most commonly used single herb and Chinese herbal formula, respectively. Conclusions: Complementary Chinese herbal therapy might be associated with reduced mortality among patients with pancreatic cancer. Further prospective clinical trial is warranted.


Author(s):  
Sella A Provan ◽  
Siri Lillegraven ◽  
Joe Sexton ◽  
Kristin Angel ◽  
Cathrine Austad ◽  
...  

Abstract Objectives To examine all-cause and cardiovascular disease (CVD) mortality in consecutive cohorts of patients with incident RA, compared with population comparators. Methods The Oslo RA register inclusion criteria were diagnosis of RA (1987 ACR criteria) and residency in Oslo. Patients with disease onset 1994–2008 and 10 matched comparators for each case were linked to the Norwegian Cause of Death Registry. Hazard ratios for all-cause and CVD mortality were calculated for 5, 10, 15 and 20 years of observation using stratified cox-regression models. Mortality trends were estimated by multivariate cox-regression. Results 443, 479 and 469 cases with disease incidence in the periods 94–98, 99–03 and 04–08 were matched to 4430, 4790 and 4690 comparators, respectively. For cases diagnosed between 1994 and 2003, the all-cause mortality of cases diverged significantly from comparators after 10 years of disease duration [hazard ratio (95% CI) 94–98 cohort 1.42 (1.15–1.75): 99–03 cohort 1.37 (1.08–1.73)]. CVD related mortality was significantly increased after 5 years for the 94–98 cohort [hazard ratio (95% CI) 1.86 (1.16–2.98) and after 10 years for the 99–03 cohort 1.80 (1.20–2.70)]. Increased mortality was not observed in the 04–08 cohort where cases had significantly lower 10-year all-cause and CVD mortality compared with earlier cohorts. Conclusion All-cause and CVD mortality were significantly increased in RA patients diagnosed from 1994 to 2003, compared with matched comparators, but not in patients diagnosed after 2004. This may indicate that modern treatment strategies have a positive impact on mortality in patients with RA.


Blood ◽  
2012 ◽  
Vol 120 (21) ◽  
pp. 3973-3973
Author(s):  
Annemiek Broyl ◽  
Rowan Kuiper ◽  
Mark van Duin ◽  
Bronno van der Holt ◽  
Laila el Jarari ◽  
...  

Abstract Abstract 3973 Introduction: Cereblon (CRBN) expression has been described to be essential for the activity of Thalidomide and Lenalidomide. This suggests that presence and possibly increased level of CRBN expression would be associated with better outcome in Thalidomide/Lenalidomide treated patients. The aim of this study was to evaluate CRBN expression in relation to outcome in patients receiving Thalidomide maintenance. Patients and methods: The HOVON-65/GMMG-HD4 trial is a multi-center, phase III trial, comparing Bortezomib in induction and post-intensification vs. conventional chemotherapy and daily Thalidomide 50 mg for 2 years post-intensification in newly diagnosed MM patients. This trial demonstrated that Bortezomib during induction and maintenance improved CR and achieved superior PFS and OS (Sonneveld et al., JCO, July 16, 2012). Gene expression profiling was performed at the start of the trial by Affymetrix U133 Plus 2.0 GeneChip, and was available for 96 patients which started Thalidomide maintenance. CRBN expression levels were based on a combined value of probe sets 218142_s_at and 222533_at. CRBN expression was validated using real-time PCR. All survival analyses were performed in SPSS, with survival time taken from the start of maintenance. Results: In patients receiving Thalidomide maintenance, increased CRBN expression was significantly associated with longer progression free survival (p=0.005, hazard ratio = 0.7) and longer overall survival (p=0.04, hazard ratio= 0.7). Using Kaplan-Meier analysis for visualization and using the median expression to define high and low expression, a significant separation was found for PFS (Log rank p=0.009) but not for OS (Log rank p=0.13). No association was observed between CRBN expression and PFS/OS after Bortezomib maintenance (PFS, p=0.4, hazard ratio=1.1; OS, p=0.7, hazard ratio=1.1). Multivariate Cox regression analysis was performed using the covariates ISS, CRBN and high-risk cytogenetics, defined as having del(17p) and/or 1q gain and/or t(4;14). Higher CRBN levels remained significantly related to longer PFS (hazard ratio 0.7, p=0.03), but not OS (hazard ratio of 0.8, p=0.3). High-risk cytogenetics and ISS were both significant in both PFS and OS multivariate models, with hazard ratios of 2.8 and 3.6, for high-risk cytogenetics and 2.5 and 5.5, for ISS stage 3, respectively (p=0.0004, p=0.003, high-risk cytogenetics and p=0.01 and p=0.005, ISS stage 3, respectively). Conclusion: These data suggest use of CRBN as a biomarker for thalidomide outcome, but further analysis in other Thalidomide trials is required to validate this finding. Disclosures: Lokhorst: Genmab: Consultancy. Sonneveld:Onyx: Honoraria, Research Funding; Janssen: Honoraria, Research Funding; celgene: Honoraria, Research Funding.


2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Manige Konig ◽  
Matthew C. Riddle ◽  
Helen M. Colhoun ◽  
Kelley R. Branch ◽  
Charles M. Atisso ◽  
...  

Abstract Background The REWIND trial demonstrated cardiovascular (CV) benefits to patients with type 2 diabetes and multiple CV risk factors or established CV disease. This exploratory analysis evaluated the degree to which the effect of dulaglutide on CV risk factors could statistically account for its effects on major adverse cardiovascular events (MACE) in the REWIND trial. Methods Potential mediators of established CV risk factors that were significantly reduced by dulaglutide were assessed in a post hoc analysis using repeated measures mixed models and included glycated hemoglobin (HbA1c), body weight, waist-to-hip ratio, systolic blood pressure, low-density lipoprotein (LDL), and urine albumin/creatinine ratio (UACR). These factors, for which the change in level during follow-up was significantly associated with incident MACE, were identified using Cox regression modeling. Each identified variable was then included as a covariate in the Cox model assessing the effect of dulaglutide on MACE to estimate the degree to which the hazard ratio of dulaglutide vs placebo was attenuated. The combined effect of the variables associated with attenuation was assessed by including all variables in an additional Cox model. Results Although all evaluated variables were significantly improved by treatment, only changes in HbA1c and UACR were associated with MACE and a reduction in the effect of dulaglutide on this outcome was observed. The observed hazard ratio for MACE for dulaglutide vs placebo reduced by 36.1% by the updated mean HbA1c, and by 28.5% by the updated mean UACR. A similar pattern was observed for change from baseline in HbA1c and UACR and a reduction of 16.7% and 25.4%, respectively in the hazard ratio for MACE with dulaglutide vs placebo was observed. When HbA1c and UACR were both included, the observed hazard ratio reduced by 65.4% for the updated mean and 41.7% for the change from baseline with no HbA1c-UACR interaction (P interaction = 0.75 and 0.15, respectively). Conclusions Treatment-induced improvement in HbA1c and UACR, but not changes in weight, systolic blood pressure, or LDL cholesterol, appear to partly mediate the beneficial effects of dulaglutide on MACE outcomes. These observations suggest that the proven effects of dulaglutide on cardiovascular disease benefit are partially related to changes in glycemic control and albuminuria, with residual unexplained benefit. Clinicaltrials.gov; Trial registration number: NCT01394952. URL: https://clinicaltrials.gov/ct2/show/NCT01394952


Blood ◽  
2016 ◽  
Vol 128 (22) ◽  
pp. 4321-4321
Author(s):  
Rami S. Komrokji ◽  
John Barnard ◽  
David P Steensma ◽  
Amy E. DeZern ◽  
Gail J. Roboz ◽  
...  

Abstract Introduction Recurrent somatic mutations in SF3B1, a gene encoding a spliceosome component, have been identified in patients (pts) with myelodysplastic syndromes (MDS). SF3B1 mutations (MT) are more commonly detected in pts with ring sideroblast (RS) morphology and are associated with favorable outcome. The proposed 2016 World Health Organization (WHO) MDS classification categorizes pts with >5% RS and SF3B1 MT as MDS with RS, in contrast to prior WHO classifications which required ≥15% RS regardless of genotype. In this study, we explored the prognostic value of RS and SF3B1 MT and assessed the validity of the new proposal. Methods We identified 471 pts with MDS and known SF3B1 mutational status from MDS CRC institutions. RS were assessed as present or absent (RS +/-) based on bone marrow aspirate reports (n=157); in cases where quantitative data on RS% were available (n=41), pts were grouped in the 5-15% RS group or > 15% RS group. Survival was calculated from time of diagnosis. Cox regression analysis was used to estimate hazard ratios for overall survival (OS) and AML free survival (AFS), which was defined as time to death or AML transformation, respectively. Chi-squared and Wilcoxon tests were used to test for differences in categorical and continuous distributions, respectively. Results: Among 471 pts with known SF3B1 mutational status, 76 (16%) had MT. Pts with MT had lower-risk International Prognostic Scoring System (IPSS) scores compared to SF3B1 wild-type (WT; 79% vs 57%, p < .001). Among pts with MT, 50% had RS + compared to 19% RS + in the WT group (p < .001). MT were independently associated with better OS (HR 0.48, p= .001) and longer AFS (HR 0.5, p <.005) after adjusting for age and IPSS. We compared outcomes of four groups: WT/RS-, MT/RS-, WT/RS+, and MT/ RS +. Adjusting for age and IPSS, pts with MT/RS + had the best outcome, with hazard ratios for AFS of 4.2 for WT/RS- vs. MT/RS+ (p =.018), 4.1 for MT/RS- vs. MT/RS+ (p =.045), and 5.1 for WT/RS+ vs. MT/RS+ (p= .01). We compared 7 pts with 5-15% RS to 22 pts with >15% RS. Among patients with RS 5-15%, 4/7 pts (57%) were classified as MDS with excess blasts compared to 24% for those RS >15% (p=.09). Pts with 5-15% RS were more likely to be thrombocytopenic (5/7, 71%) compared to >15% RS (29%, p=.04). One patient (14%) with 5-15% RS had MT compared to 12 (55%) pts with > 15% RS, p= .06. In Cox regression analysis using the RS 5-15% group as the reference, the hazard ratio for RS > 15% for AFS was 0.26 (p = .034) and the hazard ratio for MT for AFS was 0.08 (p= .002). Conclusions SF3B1 somatic mutations in MDS are commonly associated with RS, better OS and longer AML-free survival. Patients with RS and MT had a significantly better outcome than those with either isolated RS or MT, or neither. These data support incorporation of SF3B1 mutation status into the WHO classification regardless of RS percent, though with differentiation for those with RS and MT. Disclosures Komrokji: Novartis: Consultancy, Speakers Bureau; Celgene: Membership on an entity's Board of Directors or advisory committees, Research Funding; Incyte: Consultancy; Boehringer-Ingelheim: Research Funding. Roboz:Cellectis: Research Funding; Agios, Amgen, Amphivena, Astex, AstraZeneca, Boehringer Ingelheim, Celator, Celgene, Genoptix, Janssen, Juno, MEI Pharma, MedImmune, Novartis, Onconova, Pfizer, Roche/Genentech, Sunesis, Teva: Consultancy.


BMJ ◽  
2018 ◽  
pp. k4109 ◽  
Author(s):  
Saima Basit ◽  
Jan Wohlfahrt ◽  
Heather A Boyd

AbstractObjectiveTo explore associations between pre-eclampsia and later dementia, overall and by dementia subtype and timing of onset.DesignNationwide register based cohort study.SettingDenmark.PopulationAll women with at least one live birth or stillbirth between 1978 and 2015.Main outcome measureHazard ratios comparing dementia rates among women with and without a history of pre-eclampsia, estimated using Cox regression.ResultsThe cohort consisted of 1 178 005 women with 20 352 695 person years of follow-up. Women with a history of pre-eclampsia had more than three times the risk of vascular dementia (hazard ratio 3.46, 95% confidence interval 1.97 to 6.10) later in life, compared with women with no history of pre-eclampsia. The association with vascular dementia seemed to be stronger for late onset disease (hazard ratio 6.53, 2.82 to 15.1) than for early onset disease (2.32, 1.06 to 5.06) (P=0.08). Adjustment for diabetes, hypertension, and cardiovascular disease attenuated the hazard ratios only moderately; sensitivity analyses suggested that body mass index was unlikely to explain the association with vascular dementia. In contrast, only modest associations were observed for Alzheimer’s disease (hazard ratio 1.45, 1.05 to 1.99) and other/unspecified dementia (1.40, 1.08 to 1.83).ConclusionsPre-eclampsia was associated with an increased risk of dementia, particularly vascular dementia. Cardiovascular disease, hypertension, and diabetes were unlikely to mediate the associations substantially, suggesting that pre-eclampsia and vascular dementia may share underlying mechanisms or susceptibility pathways. Asking about a history of pre-eclampsia could help physicians to identify women who might benefit from screening for early signs of disease, allowing for early clinical intervention.


2020 ◽  
Author(s):  
Anders Husby ◽  
Anton Pottegaard ◽  
Anders Peter Hviid

Background Recent evidence has established a beneficial effect of systemic corticosteroids for treatment of moderate-to-severe COVID-19. However, it is unknown if inhaled corticosteroid use is associated with reduced morbidity of the disease. Methods In a nationwide cohort of hospitalized SARS-CoV-2 test-positive individuals in Denmark, we estimated the 30-day hazard ratio of intensive care unit (ICU) admission or death among users of inhaled corticosteroids (ICS) compared with users of non-ICS inhalers (β2-agonist/muscarinic-antagonists), or non-users of ICS, with Cox regression adjusted for age, sex, and other confounders. We repeated these analyses among influenza test-positive patients during 2010-2018. Results Among 2,180 hospitalized SARS-CoV-2 patients, 282 were admitted to ICU and 421 died within 30 days. ICS use was associated with a hazard ratio of 1.25 (95% CI [CI], 0.60 to 2.61) for ICU admission and 0.84 (95% CI, 0.54 to 1.31) for death compared with non-ICS inhaler use. Compared with no ICS use, the hazard ratio of ICU admission or death was 1.22 (95% CI, 0.77 to 1.94) and 1.05 (95% CI, 0.75 to 1.47), respectively. Among 10,279 hospitalized influenza patients, the hazard ratios were 1.43 (95% CI, 0.89 to 2.30) and 1.11 (95% CI, 0.85 to 1.46) for ICU admission, and 0.80 (95% CI, 0.63 to 1.01) and 1.03 (95% CI, 0.87 to 1.22) for death compared with non-ICS inhaler use and no ICS use, respectively. Conclusions Our results do not support an effect of inhaled corticosteroid use on COVID-19 morbidity, however we can only rule out moderate-to-large reduced or increased risks.


2020 ◽  
Author(s):  
Roshan Karunamuni ◽  
Minh-Phuong Huynh-Le ◽  
Chun C Fan ◽  
Wesley Thompson ◽  
Rosalind Eeles ◽  
...  

Background: Polygenic hazard scores (PHS) can identify individuals with increased risk of prostate cancer. We estimated the benefit of additional SNPs on performance of a previously validated PHS (PHS46). Materials and Method: 180 SNPs, shown to be previously associated with prostate cancer, were used to develop a PHS model in men with European ancestry. A machine-learning approach, LASSO-regularized Cox regression, was used to select SNPs and to estimate their coefficients in the training set (75,596 men). Performance of the resulting model was evaluated in the testing/validation set (6,411 men) with two metrics: (1) hazard ratios (HRs) and (2) positive predictive value (PPV) of prostate-specific antigen (PSA) testing. HRs were estimated between individuals with PHS in the top 5% to those in the middle 40% (HR95/50), top 20% to bottom 20% (HR80/20), and bottom 20% to middle 40% (HR20/50). PPV was calculated for the top 20% (PPV80) and top 5% (PPV95) of PHS as the fraction of individuals with elevated PSA that were diagnosed with clinically significant prostate cancer on biopsy. Results: 166 SNPs had non-zero coefficients in the Cox model (PHS166). All HR metrics showed significant improvements for PHS166 compared to PHS46: HR95/50 increased from 3.72 to 5.09, HR80/20 increased from 6.12 to 9.45, and HR20/50 decreased from 0.41 to 0.34. By contrast, no significant differences were observed in PPV of PSA testing for clinically significant prostate cancer. Conclusion: Incorporating 120 additional SNPs (PHS166 vs PHS46) significantly improved HRs for prostate cancer, while PPV of PSA testing remained the same.


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