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 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.

scholarly journals A univariable and multivariable analysis of time-to-event data based on restricted mean survival time: A combination with traditional survival methods.

2019 ◽  
Author(s):  
Qiao Huang ◽  
Jun Lyv ◽  
Bing-hui Li ◽  
Lin-lu Ma ◽  
Tong Deng ◽  
...  
Keyword(s):  
Survival Time ◽  
Cox Regression ◽  
Multivariable Analysis ◽  
Hazard Ratio ◽  
Event Data ◽  
Time To Event ◽  
Mean Survival Time ◽  
Time To Event Data ◽  
Effect Measure ◽  
Restricted Mean Survival Time

Abstract Background Hazard ratio is considered as an appropriate effect measure of time-to-event data. However, hazard ratio is only valid when proportional hazards (PH) assumption is met. The use of the restricted mean survival time (RMST) is proposed and recommended without limitation of PH assumption. Method 4405 osteosarcomas were captured from Surveillance, Epidemiology and End Results Program Database. Traditional survival analyses and RMST-based analyses were integrated into a flowchart and applied for univariable and multivariable analyses, using hazard ratio (HR) and difference in RMST (survival time lost or gain, STL or STG) as effect measures. The relationship between difference in RMST and HR were explored when PH assumption was and was not met, respectively. Results In univariable analyses, using difference in RMST calculated by Kaplan-Meier methods as reference, pseudo-value regressions (R2=0.99) and inverse probability of censoring probability (IPCW) regressions with group-specific weights (R2=1.00) provided more consistent estimation on difference in RMST than IPCW with individual weights (R2=0.09). In multivariable analysis, age (HR:1.03, STL: 3.86 months), diagnosis in 1970~1980s (HR:1.39 STL:27.49 months), metastasis (HR:4.47, STL: 202 months), surgery (HR:0.58, SLG:35.55 months) and radiation (HR:1.46, SLT:44.65 months), met PH assumption and were main independent factors for overall survival. In both univariable and multivariable variables, a robust negative logarithmic linear relationship between HRs estimated by Cox regression and differences in RMST by pseudo-value regressions was only observed when PH assumption was hold (Difference in RMST = -109.3✕ln (HR) - 0.83, R² = 0.97, and Difference = -127.7✕ln (HR) – 9.49, R² = 0.93, respectively.) Conclusion The flowchart will be intuitive and helpful to instruct appropriate use of RMST based and traditional methods. RMST-based methods provided an absolute effect measure to inspect effects of covariates on survival time and promote evidence communication with HR. Difference in RMST should be reported with hazard ratio routinely.

scholarly journals A univariable and multivariable analysis of right censored time-to-event data based on restricted mean survival time: A combination with traditional survival methods.

2020 ◽  
Author(s):  
Qiao Huang ◽  
Jun Lyv ◽  
Bing-hui Li ◽  
Lin-lu Ma ◽  
Tong Deng ◽  
...  
Keyword(s):  
Survival Time ◽  
Cox Regression ◽  
Multivariable Analysis ◽  
Hazard Ratio ◽  
Event Data ◽  
Time To Event ◽  
Mean Survival Time ◽  
Time To Event Data ◽  
Effect Measure ◽  
Restricted Mean Survival Time

Abstract Background Hazard ratio is considered as an appropriate effect measure of time-to-event data. However, hazard ratio is only valid when proportional hazards (PH) assumption is met. The use of the restricted mean survival time (RMST) is proposed and recommended without limitation of PH assumption. Method 4405 osteosarcomas were captured from Surveillance, Epidemiology and End Results Program Database. Traditional survival analyses and RMST-based analyses were integrated into a flowchart and applied for univariable and multivariable analyses, using hazard ratio (HR) and difference in RMST (survival time lost or gain, STL or STG) as effect measures. The relationship between difference in RMST and HR were explored when PH assumption was and was not met, respectively. Results In group comparison and univariable regressions, using difference in RMST calculated by Kaplan-Meier methods as reference, pseudo-value regressions (R2=0.99) and inverse probability of censoring probability (IPCW) regressions with group-specific weights (R2=1.00) provided more consistent estimation on difference in RMST than IPCW with individual weights (R2=0.09). In multivariable analysis, age (HR:1.03, STL: 3.86 months), diagnosis in 1970~1980s (HR:1.39 STL:27.49 months), metastasis (HR:4.47, STL: 202 months), surgery (HR:0.58, SLG:35.55 months) and radiation (HR:1.46, SLT:44.65 months) met PH assumption and were main independent factors for overall survival. In both univariable and multivariable variables, a robust negative logarithmic linear relationship between HRs estimated by Cox regression and differences in RMST by pseudo-value regressions was only observed when PH assumption was hold. Conclusion The flowchart will be intuitive and helpful to instruct appropriate use of RMST based and traditional methods. RMST-based methods provided an absolute effect measure to inspect effects of covariates on survival time and promote evidence communication with HR. Difference in RMST should be reported with hazard ratio routinely.

scholarly journals A new modeling and inference approach for the Systolic Blood Pressure Intervention Trial outcomes

2018 ◽  
Vol 15 (3) ◽  
pp. 305-312 ◽  
Author(s):  
Song Yang ◽  
Walter T Ambrosius ◽  
Lawrence J Fine ◽  
Adam P Bress ◽  
William C Cushman ◽  
...  
Keyword(s):  
Treatment Effect ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Rank Test ◽  
Time To Event ◽  
New Approach ◽  
New Methods ◽  
Log Rank Test ◽  
Hazards Model ◽  
Average Hazard Ratio

Background/aims In clinical trials with time-to-event outcomes, usually the significance tests and confidence intervals are based on a proportional hazards model. Thus, the temporal pattern of the treatment effect is not directly considered. This could be problematic if the proportional hazards assumption is violated, as such violation could impact both interim and final estimates of the treatment effect. Methods We describe the application of inference procedures developed recently in the literature for time-to-event outcomes when the treatment effect may or may not be time-dependent. The inference procedures are based on a new model which contains the proportional hazards model as a sub-model. The temporal pattern of the treatment effect can then be expressed and displayed. The average hazard ratio is used as the summary measure of the treatment effect. The test of the null hypothesis uses adaptive weights that often lead to improvement in power over the log-rank test. Results Without needing to assume proportional hazards, the new approach yields results consistent with previously published findings in the Systolic Blood Pressure Intervention Trial. It provides a visual display of the time course of the treatment effect. At four of the five scheduled interim looks, the new approach yields smaller p values than the log-rank test. The average hazard ratio and its confidence interval indicates a treatment effect nearly a year earlier than a restricted mean survival time–based approach. Conclusion When the hazards are proportional between the comparison groups, the new methods yield results very close to the traditional approaches. When the proportional hazards assumption is violated, the new methods continue to be applicable and can potentially be more sensitive to departure from the null hypothesis.

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.

scholarly journals Association of Brain Natriuretic Peptide With Mortality in Exceptionally Long-Lived Families

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 211-211
Author(s):  
Allison Kuipers ◽  
Robert Boudreau ◽  
Mary Feitosa ◽  
Angeline Galvin ◽  
Bharat Thygarajan ◽  
...  
Keyword(s):  
Older Adults ◽  
Brain Natriuretic Peptide ◽  
Natriuretic Peptide ◽  
Sex Education ◽  
Proportional Hazards ◽  
Cox Proportional Hazards ◽  
Time To Event ◽  
Healthy Older Adults ◽  
Secondary Analyses

Abstract Natriuretic peptides are produced within the heart and released in response to increased chamber wall tension and heart failure (HF). N-Terminal prohormone Brain Natriuretic Peptide (NT-proBNP) is a specific natriuretic peptide commonly assayed in persons at risk for HF. In these individuals, NT-proBNP is associated with future disease prognosis and mortality. However, its association with mortality among healthy older adults remains unknown. Therefore, we determined the association of NT-proBNP with all-cause mortality over a median follow-up of 10 years in 3253 individuals free from HF at baseline in the Long Life Family Study, a study of families recruited for exceptional longevity. We performed cox proportional hazards analysis (coxme in R) for time-to event (mortality), adjusted for field center, familial relatedness, age, sex, education, smoking, alcohol, physical activity, BMI, diabetes, hypertension, and cancer. In addition, we performed secondary analyses among individuals (N=2457) within the normal NT-proBNP limits at baseline (<125pg/ml aged <75 years; <450pg/ml aged ≥75 years). Overall, individuals were aged 32-110 years (median 67 years; 44% male), had mean NT-proBNP of 318.5 pg/ml (median 91.0 pg/ml) and 1066 individuals (33%) died over the follow-up period. After adjustment, each 1 SD greater baseline NT-proBNP was associated with a 1.30-times increased hazard of mortality (95% CI: 1.24-1.36; P<0.0001). Results were similar in individuals with normal baseline NT-proBNP (HR: 1.21; 95% CI: 1.11-1.32; P<0.0001). These results suggest that NT-proBNP is a strong and specific biomarker for mortality in older adults independent of current health status, even in those with clinically-defined normal NT-proBNP.

Abstract P098: Slower Gait Speed is Associated with Increased Mortality Risk in Chronic Kidney Disease.

Circulation ◽  
2012 ◽  
Vol 125 (suppl_10) ◽  
Author(s):  
Baback Roshanravan ◽  
Cassiane Robinson-Cohen ◽  
Kushang V Patel ◽  
Greg Levin ◽  
Ian H de Boer ◽  
...  
Keyword(s):  
Chronic Kidney Disease ◽  
Kidney Disease ◽  
Gait Speed ◽  
Proportional Hazards ◽  
Prognostic Significance ◽  
Continuous Variable ◽  
Hazard Ratio ◽  
Risk Of Death ◽  
Social Security Death Index

Objective: Skeletal muscle dysfunction (sarcopenia) is an under-recognized complication of chronic kidney disease (CKD) that may have important clinical consequences. Gait speed is associated with sarcopenia and comorbid disease burden among older adults; however, little is known about the prognostic significance of gait speed in CKD. We determined the association of gait speed with all-cause mortality in a prospective cohort of non-dialysis CKD patients. Methods: We measured usual gait speed over 4-meters in 309 participants from a prospective study of non-dialysis CKD. Included subjects had an estimated glomerular filtration rate (eGFR ckdepi ) <90mL/min/1.73m 2 , were stroke-free and did not require a wheelchair for ambulation. Study coordinators assessed mortality during follow-up by phone contacts, medical record review, and the social security death index. We evaluated gait speed continuously, and using a cut point of 0.8 m/s, consistent with previous studies. We used Cox's proportional hazards to estimate the association of gait speed with mortality after adjustment for age, sex, race, smoking, diabetes, pre-existing CAD, BMI, eGFR and hemoglobin. Results: Median follow-up time was 2.7 years; range 27 days to 4.8 years. The mean age was 58.9 ± 13 years and mean eGFR by cystatin C (eGFR cysc ) was 48.5 ± 23mL/min/1.73m 2 . There were a total of 31 deaths (10.4%) during follow-up. Unadjusted mortality rates were 23 and 80 deaths per 1,000 person-years among participants who had a gait speed of >0.8m/s versus ≤0.8m/s, respectively. After full adjustment, gait speed ≤0.8m/s was associated with a 2.8-fold greater risk of death compared to a gait speed >0.8 m/s. Gait speed was also strongly associated with mortality when analyzed as a continuous variable ( Table ) and a stronger predictor of death than age, history of CAD, or diabetes. No. Deaths (%) Model 1 + Model 2 # Hazard Ratio 95% CI Hazard Ratio 95% CI Gait speed * 32(10) 0.74 (0.64-0.86) 0.75 (0.64-0.87) >0.8m/s 13 (6) Reference Reference ≤0.8m/s 19(19) 3.49 (1.54-7.95) 2.84 (1.25-6.48) * Gait speed analyzed continuously per 10cm/s increase in speed. +Model 1: Adjusted for age, sex, race, study site #Model 2: adds smoking, BMI, eGFR cysc , diabetes, prevalent coronary disease. Conclusion: Gait speed is strongly associated with death in a cohort of middle-aged CKD patients.

Abstract 13950: Predicted Heart Mass and BMI: Evaluating Undersized Heart Transplantation in Obese vs. Non-Obese Patients

Circulation ◽  
2020 ◽  
Vol 142 (Suppl_3) ◽  
Author(s):  
Samuel T Kim ◽  
Mark R Helmers ◽  
Peter Altshuler ◽  
Amit Iyengar ◽  
Jason Han ◽  
...  
Keyword(s):  
Propensity Score ◽  
Heart Transplantation ◽  
Propensity Score Matching ◽  
Proportional Hazards ◽  
Cox Proportional Hazards ◽  
Hazard Ratio ◽  
Obese Patients ◽  
Heart Transplants ◽  
Term Survival ◽  
Heart Mass

Introduction: Although guidelines for heart transplant currently recommend against donors weighing ≥ 30% less than the recipient, recent studies have shown that the detriment of under-sizing may not be as severe in obese recipients. Furthermore, predicted heart mass (PHM) has been shown to be more reliable for size matching compared to metrics such as weight and body surface area. In this study, we use PHM to characterize the effects of undersized heart transplantation (UHT) in obese vs. non-obese recipients. Methods: Retrospective analysis of the UNOS database was performed for heart transplants from Jan. 1995 to Sep. 2020. Recipients were stratified by obese (BMI ≥ 30) and non-obese (30 > BMI ≥ 18.5). Undersized donors were defined as PHM ≥ 20% less than recipient PHM. Obese and non-obese populations separately underwent propensity score matching, and Kaplan-Meier estimates were used to graph survival. Multivariable Cox proportional-hazards analyses were used to adjust for confounders and estimate the hazard ratio for death attributable to under-sizing. Results: Overall, 50,722 heart transplants were included in the analysis. Propensity-score matching resulted in 2,214, and 1,011 well-matched pairs, respectively, for non-obese and obese populations. UHT in non-obese recipients resulted in similar 30-day mortality (5.7% vs. 6.3%, p = 0.38), but worse 15-year survival (38% vs. 35%, P = 0.04). In contrast, obese recipients with UHT saw similar 30-day mortality (6.4% vs. 5.5%, p = 0.45) and slightly increased 15-year survival (31% vs. 35%, P = 0.04). Multivariate Cox analysis showed that UHT resulted in an adjusted hazard ratio of 1.08 (95% CI 1.01 - 1.16) in non-obese recipients, and 0.87 (95% CI 0.78 - 0.98) in obese recipients. Conclusions: Non-obese patients with UHT saw worse long-term survival, while obese patients with UHT saw slightly increased survival. These findings may warrant reevaluation of the current size criteria for obese patients awaiting a heart.

scholarly journals Prognostic implications of depression and inflammation in patients with metastatic lung cancer

2020 ◽  
Author(s):  
Daniel C McFarland ◽  
Rebecca M. Saracino ◽  
Andrew H. Miller ◽  
William Breitbart ◽  
Barry Rosenfeld ◽  
...  
Keyword(s):  
Lung Cancer ◽  
Hazard Ratio ◽  
Proportional Hazard ◽  
Metastatic Lung Cancer ◽  
Proportional Hazard Models ◽  
Cox Proportional Hazard ◽  
Kaplan Meier ◽  
Metastatic Lung ◽  
Cox Proportional Hazard Models ◽  
Prognostic Implications

Background: Lung cancer-related inflammation is associated with depression. Both elevated inflammation and depression are associated with worse survival. However, outcomes of patients with concomitant depression and elevated inflammation are not known. Materials & methods: Patients with metastatic lung cancer (n = 123) were evaluated for depression and inflammation. Kaplan–Meier plots and Cox proportional hazard models provided survival estimations. Results: Estimated survival was 515 days for the cohort and 323 days for patients with depression (hazard ratio: 1.12; 95% CI: 1.05–1.179), 356 days for patients with elevated inflammation (hazard ratio: 2.85, 95% CI: 1.856–4.388), and 307 days with both (χ2 = 12.546; p < 0.001]). Conclusion: Depression and inflammation are independently associated with inferior survival. Survival worsened by inflammation is mediated by depression-a treatable risk factor.

Sign in / Sign up

Export Citation Format

Share Document