Estimation of the average hazard ratio

Biometrika ◽  
1981 ◽  
Vol 68 (1) ◽  
pp. 105-112 ◽  
Author(s):  
JOHN D. KALBFLEISCH ◽  
ROSS L. PRENTICE
Keyword(s):  
Hazard Ratio ◽  
Average Hazard Ratio

The Average Hazard Ratio – A Good Effect Measure for Time-to-event Endpoints when the Proportional Hazard Assumption is Violated?

2018 ◽  
Vol 57 (03) ◽  
pp. 089-100 ◽  
Author(s):  
Werner Brannath ◽  
Matthias Brückner ◽  
Meinhard Kieser ◽  
Geraldine Rauch
Keyword(s):  
Proportional Hazards ◽  
Weighting Function ◽  
Hazard Ratio ◽  
Group Differences ◽  
Proportional Hazard ◽  
Time To Event ◽  
Logrank Test ◽  
Proportional Hazard Assumption ◽  
Effect Measure ◽  
Average Hazard Ratio

Summary Background: In many clinical trial applications, the endpoint of interest corresponds to a time-to-event endpoint. In this case, group differences are usually expressed by the hazard ratio. Group differences are commonly assessed by the logrank test, which is optimal under the proportional hazard assumption. However, there are many situations in which this assumption is violated. Especially in applications were a full population and several subgroups or a composite time-to-first-event endpoint and several components are considered, the proportional hazard assumption usually does not simultaneously hold true for all test problems under investigation. As an alternative effect measure, Kalbfleisch and Prentice proposed the so-called ‘average hazard ratio’. The average hazard ratio is based on a flexible weighting function to modify the influence of time and has a meaningful interpretation even in the case of non-proportional hazards. Despite this favorable property, it is hardly ever used in practice, whereas the standard hazard ratio is commonly reported in clinical trials regardless of whether the proportional hazard assumption holds true or not. Objectives: There exist two main approaches to construct corresponding estimators and tests for the average hazard ratio where the first relies on weighted Cox regression and the second on a simple plug-in estimator. The aim of this work is to give a systematic comparison of these two approaches and the standard logrank test for different time-toevent settings with proportional and nonproportional hazards and to illustrate the pros and cons in application. Methods: We conduct a systematic comparative study based on Monte-Carlo simulations and by a real clinical trial example. Results: Our results suggest that the properties of the average hazard ratio depend on the underlying weighting function. The two approaches to construct estimators and related tests show very similar performance for adequately chosen weights. In general, the average hazard ratio defines a more valid effect measure than the standard hazard ratio under non-proportional hazards and the corresponding tests provide a power advantage over the common logrank test. Conclusions: As non-proportional hazards are often met in clinical practice and the average hazard ratio tests often outperform the common logrank test, this approach should be used more routinely in applications.

scholarly journals Associations of fat and carbohydrate intake with cardiovascular disease and mortality: prospective cohort study of UK Biobank participants

BMJ ◽  
2020 ◽  
pp. m688 ◽  
Author(s):  
Frederick K Ho ◽  
Stuart R Gray ◽  
Paul Welsh ◽  
Fanny Petermann-Rocha ◽  
Hamish Foster ◽  
...  
Keyword(s):  
Cardiovascular Disease ◽  
Energy Intake ◽  
Hazard Ratio ◽  
Dietary Advice ◽  
Macronutrient Intake ◽  
Uk Biobank ◽  
All Cause Mortality ◽  
Non Linear ◽  
Average Hazard Ratio

Abstract Objective To investigate the association of macronutrient intake with all cause mortality and cardiovascular disease (CVD), and the implications for dietary advice. Design Prospective population based study. Setting UK Biobank. Participants 195 658 of the 502 536 participants in UK Biobank completed at least one dietary questionnaire and were included in the analyses. Diet was assessed using Oxford WebQ, a web based 24 hour recall questionnaire, and nutrient intakes were estimated using standard methodology. Cox proportional models with penalised cubic splines were used to study non-linear associations. Main outcome measures All cause mortality and incidence of CVD. Results 4780 (2.4%) participants died over a mean 10.6 (range 9.4-13.9) years of follow-up, and 948 (0.5%) and 9776 (5.0%) experienced fatal and non-fatal CVD events, respectively, over a mean 9.7 (range 8.5-13.0) years of follow-up. Non-linear associations were found for many macronutrients. Carbohydrate intake showed a non-linear association with mortality; no association at 20-50% of total energy intake but a positive association at 50-70% of energy intake (3.14 v 2.75 per 1000 person years, average hazard ratio 1.14, 95% confidence interval 1.03 to 1.28 (60-70% v 50% of energy)). A similar pattern was observed for sugar but not for starch or fibre. A higher intake of monounsaturated fat (2.94 v 3.50 per 1000 person years, average hazard ratio 0.58, 0.51 to 0.66 (20-25% v 5% of energy)) and lower intake of polyunsaturated fat (2.66 v 3.04 per 1000 person years, 0.78, 0.75 to 0.81 (5-7% v 12% of energy)) and saturated fat (2.66 v 3.59 per 1000 person years, 0.67, 0.62 to 0.73 (5-10% v 20% of energy)) were associated with a lower risk of mortality. A dietary risk matrix was developed to illustrate how dietary advice can be given based on current intake. Conclusion Many associations between macronutrient intake and health outcomes are non-linear. Thus dietary advice could be tailored to current intake. Dietary guidelines on macronutrients (eg, carbohydrate) should also take account of differential associations of its components (eg, sugar and starch).

scholarly journals Competing Risks Models for the Assessment of Intelligent Transportation Systems Devices: A Case Study for Connected and Autonomous Vehicle Applications

2020 ◽  
Vol 5 (3) ◽  
pp. 30 ◽  
Author(s):  
Sylvester Inkoom ◽  
John Sobanjo ◽  
Eric Chicken
Keyword(s):  
Wireless Communication ◽  
Communication Networks ◽  
Competing Risks ◽  
Communication Systems ◽  
Intelligent Transportation ◽  
Transportation Systems ◽  
Hazard Ratio ◽  
Connected Vehicle ◽  
Average Hazard Ratio ◽  
The Impact

Intelligent transportation system (ITS) has become a crucial section of transportation and traffic management systems in the past decades. As a result, transportation agencies keep improving the quality of transportation infrastructure management information for accessibility and security of transportation networks. The goal of this paper is to evaluate the impact of two competing risks: “natural deterioration” of ITS devices and hurricane-induced failure of the same components. The major devices employed in the architecture of this paper include closed circuit television (CCTV) cameras, automatic vehicle identification (AVI) systems, dynamic message signals (DMS), wireless communication systems and DMS towers. From the findings, it was evident that as ITS infrastructure devices age, the contribution of Hurricane Category 3 as a competing failure risk is higher and significant compared to the natural deterioration of devices. Hurricane Category 3 failure vs. natural deterioration indicated an average hazard ratio of 1.5 for CCTV, AVI and wireless communications systems and an average hazard ratio of 2.3 for DMS, DMS towers and portable DMS. The proportional hazard ratios of the Hurricane Category 1 compared to the devices was estimated as <0.001 and that of Hurricane Category 2 < 0.5, demonstrating the lesser impact of the Hurricane Categories 1 and 2. It is expedient to envisage and forecast the impact of hurricanes on the failure of wireless communication networks, vehicle detection systems and other message signals, in order to prevent vehicle to infrastructure connection disruption, especially for autonomous and connected vehicle systems.

scholarly journals Using the Geometric Average Hazard Ratio in Sample Size Calculation for Time-to-event Data With Composite Endpoints

2021 ◽  
Author(s):  
Jordi Cortés Martínez ◽  
Ronald B Geskus ◽  
KyungMann Kim ◽  
Guadalupe Gómez Melis
Keyword(s):  
Sample Size ◽  
Proportional Hazards ◽  
Sample Size Calculation ◽  
Composite Endpoint ◽  
Hazard Ratio ◽  
Time To Event ◽  
Logrank Test ◽  
Geometric Average ◽  
Effect Measure ◽  
Average Hazard Ratio

Abstract Background: Sample size calculation is a key point in the design of a randomized controlled trial. With time-to-event outcomes, it’s often based on the logrank test. We provide a sample size calculation method for a composite endpoint (CE) based on the geometric average hazard ratio (gAHR) in case the proportional hazards assumption can be assumed to hold for the components, but not for the CE. Methods: The required number of events, sample size and power formulae are based on the non-centrality parameter of the logrank test under the alternative hypothesis which is a function of the gAHR. We use the web platform, CompARE, for the sample size computations. A simulation study evaluates the empirical power of the logrank test for the CE based on the sample size in terms of the gAHR. We consider different values of the component hazard ratios, the probabilities of observing the events in the control group and the degrees of association between the components. We illustrate the sample size computations using two published randomized controlled trials. Their primary CEs are, respectively, progression-free survival (time to progression of disease or death) and the composite of bacteriologically confirmed treatment failure or Staphilococcus aureus related death by 12 weeks. Results: For a target power of 0.80, the simulation study provided mean (± SE) empirical powers equal to 0.799 (±0.004) and 0.798 (±0.004) in the exponential and non-exponential settings, respectively. The power was attained in more than 95% of the simulated scenarios and was always above 0.78, regardless of compliance with the proportional-hazard assumption.Conclusions: The geometric average hazard ratio as an effect measure for a composite endpoint has a meaningful interpretation in the case of non-proportional hazards. Furthermore it is the natural effect measure when using the logrank test to compare the hazard rates of two groups and should be used instead of the standard hazard ratio.

Gamma Knife surgery as sole treatment for multiple brain metastases: 2-center retrospective review of 1508 cases meeting the inclusion criteria of the JLGK0901 multi-institutional prospective study

2010 ◽  
Vol 113 (Special_Supplement) ◽  
pp. 48-52 ◽  
Author(s):  
Toru Serizawa ◽  
Masaaki Yamamoto ◽  
Yasunori Sato ◽  
Yoshinori Higuchi ◽  
Osamu Nagano ◽  
...  
Keyword(s):  
Brain Metastases ◽  
Gamma Knife ◽  
Class Ii ◽  
Hazard Ratio ◽  
Gamma Knife Surgery ◽  
Inclusion Criteria ◽  
Primary Tumors ◽  
Poor Prognostic Factor ◽  
Group A ◽  
Group B

Object The authors retrospectively reviewed the results of Gamma Knife surgery (GKS) used as the sole treatment for brain metastases in patients who met the eligibility criteria for the ongoing JLGK0901 multi-institutional prospective trial. They also discuss the anticipated results of the JLGK0901 study. Methods Data from 1508 consecutive cases were analyzed. All of the patients were treated at the Gamma Knife House of Chiba Cardiovascular Center or the Mito Gamma House of Katsuta Hospital between 1998 and 2007 and met the following JLGK0901 inclusion criteria: 1) newly diagnosed brain metastases, 2) 1–10 brain lesions, 3) less than 10 cm3 volume of the largest tumor, 4) no more than 15 cm3 total tumor volume, 5) no findings of CSF dissemination, and 6) no impairment of activities of daily living (Karnofsky Performance Scale score < 70) due to extracranial disease. At the initial treatment, all visible lesions were irradiated with GKS without upfront whole-brain radiation therapy. Thereafter, gadolinium-enhanced MR imaging was performed every 2–3 months, and new distant lesions were appropriately retreated with GKS. Patients were divided into groups according to numbers of tumors: Group A, single lesions (565 cases); Group B, 2–4 tumors (577 cases); and Group C, 5–10 tumors (366 cases). The differences in overall survival (OS) were compared between groups. Results The median age of the patients was 66 years (range 19–96 years). There were 963 men and 545 women. The primary tumors were in the lung in 1114 patients, gastrointestinal tract in 179, breast in 105, urinary tract in 66, and other sites in 44. The overall mean survival time was 0.78 years (0.99 years for Group A, 0.68 years for Group B, and 0.62 years for Group C). The differences between Groups A and B (p < 0.0001) and between Groups B and C (p = 0.0312) were statistically significant. Multivariate analysis revealed significant prognostic factors for OS to be sex (poor prognostic factor: male, p < 0.0001), recursive partitioning analysis class (Class I vs Class II and Class II vs III, both p < 0.0001), primary site (lung vs breast, p = 0.0047), and number of tumors (Group A vs Group B, p < 0.0001). However, no statistically difference was detected between Groups B and C (p = 0.1027, hazard ratio 1.124, 95% CI 0.999–1.265). Conclusions The results of this retrospective analysis revealed an upper CI of 1.265 for the hazard ratio, which was lower than the 1.3 initially set by the JLGK0901 study. The JLGK0901 study is anticipated to show noninferiority of GKS as sole treatment for patients with 5–10 brain metastases compared with those with 2–4 in terms of OS.

Does Perioperative Hemoglobin A1c Level Affect the Incidence, Pattern and Mortality of Lower Extremity Amputation?

2019 ◽  
Vol 17 (4) ◽  
pp. 354-364
Author(s):  
Hassan Al-Thani ◽  
Moamena El-Matbouly ◽  
Maryam Al-Sulaiti ◽  
Noora Al-Thani ◽  
Mohammad Asim ◽  
...  
Keyword(s):  
Glycemic Control ◽  
Lower Extremity ◽  
Hazard Ratio ◽  
Lower Extremity Amputation ◽  
Group 4 ◽  
Group 3 ◽  
Group 5 ◽  
Group 2 ◽  
Extremity Amputation ◽  
Group 1

Background: We hypothesized that perioperative HbA1c influenced the pattern and outcomes of Lower Extremity Amputation (LEA). Methods: A retrospective analysis was conducted for all patients who underwent LEA between 2000 and 2013. Patients were categorized into 5 groups according to their perioperative HbA1c values [Group 1 (<6.5%), Group 2 (6.5-7.4%), Group 3 (7.5-8.4%), Group 4 (8.5-9.4%) and Group 5 (≥9.5%)]. We identified 848 patients with LEA; perioperative HbA1c levels were available in 547 cases (Group 1: 18.8%, Group 2: 17.7%, Group 3: 15.0%, Group 4: 13.5% and Group 5: 34.9%). Major amputation was performed in 35%, 32%, 22%, 10.8% and 13.6%, respectively. Results: The overall mortality was 36.5%; of that one quarter occurred during the index hospitalization. Mortality was higher in Group 1 (57.4%) compared with Groups 2-5 (46.9%, 38.3%, 36.1% and 31.2%, respectively, p=0.001). Cox regression analysis showed that poor glycemic control (Group 4 and 5) had lower risk of mortality post-LEA [hazard ratio 0.57 (95% CI 0.35-0.93) and hazard ratio 0.46 (95% CI 0.31-0.69)]; this mortality risk persisted even after adjustment for age and sex but was statistically insignificant. The rate of LEA was greater among poor glycemic control patients; however, the mortality was higher among patients with tight control. Conclusion: The effects of HbA1c on the immediate and long-term LEA outcomes and its therapeutic implications need further investigation.

scholarly journals The risk factors of local recurrence and distant metastasis on pT1/T2N0 mid-low rectal cancer after total mesorectal excision

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
I-Li Lai ◽  
Jeng-Fu You ◽  
Yih-Jong Chern ◽  
Wen-Sy Tsai ◽  
Jy-Ming Chiang ◽  
...  
Keyword(s):  
Risk Factors ◽  
Rectal Cancer ◽  
Local Recurrence ◽  
Distant Metastasis ◽  
Resection Margin ◽  
Radical Resection ◽  
Hazard Ratio ◽  
Low Rectal Cancer ◽  
Distal Resection Margin ◽  
Lymph Node Yield

Abstract Background Radical resection is associated with good prognosis among patients with cT1/T2Nx rectal cancer. However, still some of the patients experienced cancer recurrence following radical resection. This study tried to identify the postoperative risk factors of local recurrence and distant metastasis separately. Methods This retrospective, single-center study comprised of 279 consecutive patients from Linkou branch of Chang Gung Memorial Hospital in 2005–2016 with rectal adenocarcinoma, pT1/T2N0M0 at distance from anal verge ≤ 8cm, who received curative radical resection. Results The study included 279 patients with pT1/pT2N0 mid-low rectal cancer with median follow-up of 73.5 months. Nineteen (6.8%) patients had disease recurrence in total. Nine (3.2%) of them had local recurrence, and fourteen (5.0%) of them had distant metastasis. Distal resection margin < 0.9 (cm) (hazard ratio = 4.9, p = 0.050) was the risk factor of local recurrence. Preoperative carcinoembryonic antigen (CEA) ≥ 5 ng/mL (hazard ratio = 9.3, p = 0.0003), lymph node yield (LNY) < 14 (hazard ratio = 5.0, p = 0.006), and distal resection margin < 1.4cm (hazard ratio = 4.0, p = 0.035) were the risk factors of distant metastasis. Conclusion For patients with pT1/pT2N0 mid-low rectal cancer, current multidisciplinary treatment brings acceptable survival outcome. Insufficient distal resection margin attracted the awareness of risk factors for local recurrence and distant metastasis as a foundation for future research.

Effectiveness, Durability, and Safety of Dolutegravir and Lamivudine Versus Dolutegravir, Lamivudine, and Abacavir in a Real-Life Cohort of HIV-Infected Adults

2021 ◽  
pp. 106002802110341
Author(s):  
Inés Mendoza ◽  
Alicia Lázaro ◽  
Miguel Torralba
Keyword(s):  
Viral Load ◽  
Safety Profile ◽  
Real Life ◽  
Hazard Ratio ◽  
Treatment Discontinuation ◽  
Treatment Naïve ◽  
Tn 4 ◽  
Risk Of Treatment ◽  
Hiv 1 ◽  
All Treatment

Background: Dolutegravir (DTG) plus lamivudine (2-DR) is suggested as an initial and switch option in HIV-1 treatment. Objective: To analyze the effectiveness, durability, and safety of 2-DR compared with DTG plus abacavir/lamivudine (3-DR). Methods: This was an observational, ambispective study that included all treatment-naïve (TN) and treatment-experienced (TE) patients who started 2-DR or 3-DR between July 1, 2018, and November 30, 2020. The primary end point was noninferiority, at 24 and 48 weeks, of 2-DR versus 3-DR regarding the percentage of patients with viral load (VL)≥50 and 200 copies/mL in TN (4% margin) and VL<50 and 200 copies/mL in TE (margin 12%). Durability of response, and safety were also measured. Results: 242 patients were included (53 TN and 189 TE). Two TN patients on 2-DR had VL≥50 copies/mL and 1 had VL≥200 copies/mL at week 24. In TE patients on 2-DR, 90.2% achieved VL<200 copies/mL at week 24 (difference: 3.8%; 95% CI = −6.3% to 14%) and 91.8% at week 48 (difference: 0.06%; 95% CI = −9% to 10%), meeting noninferiority criteria. Among the 53 TN patients, only 1 VF was observed in 2-DR. In TN patients, the risk of treatment discontinuation was similar between groups (hazard ratio [HR] = 0.37; P = 0.15); similar rates were also found in TE patients (HR = 0.94; P = 0.85). TE patients on 2-DR showed a better safety profile compared with 3-DR patients ( P<0.001). Conclusion and Relevance: Our results did not show noninferiority in terms of virological effectiveness. Nevertheless, all effectiveness measures support the use of 2-DR in a real-life cohort of TN and TE. Additionally, durability and safety of 2-DR were confirmed to be similar to that of 3-DR.

Factors that contribute to urban–rural gradients in risk of schizophrenia: Comparing Danish and Western Australian registers

2021 ◽  
pp. 000486742110096
Author(s):  
Oleguer Plana-Ripoll ◽  
Patsy Di Prinzio ◽  
John J McGrath ◽  
Preben B Mortensen ◽  
Vera A Morgan
Keyword(s):  
Confidence Interval ◽  
Western Australia ◽  
Urban Areas ◽  
Proportional Hazards ◽  
Cox Proportional Hazards ◽  
Hazard Ratio ◽  
Indigenous Status ◽  
Increased Risk ◽  
The Relationship ◽  
Western Australian

Introduction: An association between schizophrenia and urbanicity has long been observed, with studies in many countries, including several from Denmark, reporting that individuals born/raised in densely populated urban settings have an increased risk of developing schizophrenia compared to those born/raised in rural settings. However, these findings have not been replicated in all studies. In particular, a Western Australian study showed a gradient in the opposite direction which disappeared after adjustment for covariates. Given the different findings for Denmark and Western Australia, our aim was to investigate the relationship between schizophrenia and urbanicity in these two regions to determine which factors may be influencing the relationship. Methods: We used population-based cohorts of children born alive between 1980 and 2001 in Western Australia ( N = 428,784) and Denmark ( N = 1,357,874). Children were categorised according to the level of urbanicity of their mother’s residence at time of birth and followed-up through to 30 June 2015. Linkage to State-based registers provided information on schizophrenia diagnosis and a range of covariates. Rates of being diagnosed with schizophrenia for each category of urbanicity were estimated using Cox proportional hazards models adjusted for covariates. Results: During follow-up, 1618 (0.4%) children in Western Australia and 11,875 (0.9%) children in Denmark were diagnosed with schizophrenia. In Western Australia, those born in the most remote areas did not experience lower rates of schizophrenia than those born in the most urban areas (hazard ratio = 1.02 [95% confidence interval: 0.81, 1.29]), unlike their Danish counterparts (hazard ratio = 0.62 [95% confidence interval: 0.58, 0.66]). However, when the Western Australian cohort was restricted to children of non-Aboriginal Indigenous status, results were consistent with Danish findings (hazard ratio = 0.46 [95% confidence interval: 0.29, 0.72]). Discussion: Our study highlights the potential for disadvantaged subgroups to mask the contribution of urban-related risk factors to risk of schizophrenia and the importance of stratified analysis in such cases.

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