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

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.

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

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).

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

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.

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

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.

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

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.