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Related Concept Videos

Hazard Ratio01:12

Hazard Ratio

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The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups.
For example, in a clinical trial...
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Hazard Rate01:11

Hazard Rate

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The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
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Geometric Mean01:15

Geometric Mean

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The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...
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Comparing the Survival Analysis of Two or More Groups01:20

Comparing the Survival Analysis of Two or More Groups

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Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and...
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Actuarial Approach01:20

Actuarial Approach

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The actuarial approach, a statistical method originally developed for life insurance risk assessment, is widely used to calculate survival rates in clinical and population studies. This method accounts for participants lost to follow-up or those who die from causes unrelated to the study, ensuring a more accurate representation of survival probabilities.
Consider the example of a high-risk surgical procedure with significant early-stage mortality. A two-year clinical study is conducted,...
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Kaplan-Meier Approach01:24

Kaplan-Meier Approach

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The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
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Using the geometric average hazard ratio in sample size calculation for time-to-event data with composite endpoints.

Jordi Cortés Martínez1, Ronald B Geskus2,3, KyungMann Kim4

  • 1Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Jordi Girona, 31, Barcelona, 08034, Spain. jordi.cortes-martinez@upc.edu.

BMC Medical Research Methodology
|May 7, 2021
PubMed
Summary

Calculating sample size for composite endpoints in clinical trials is crucial. This study introduces a method using the geometric average hazard ratio (gAHR) for time-to-event data, ensuring reliable power calculations even with non-proportional hazards.

Keywords:
Composite endpointCopulaNon-Proportional HazardsProgression-Free SurvivalRandomized Controlled TrialSimulationTreatment Effect

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Area of Science:

  • Clinical Trials
  • Biostatistics
  • Epidemiology

Background:

  • Sample size calculation is critical for randomized controlled trial design.
  • Time-to-event outcomes often rely on the logrank test.
  • A new method is proposed for composite endpoints (CE) using the geometric average hazard ratio (gAHR) when proportional hazards assumptions do not hold for the CE.

Purpose of the Study:

  • To provide a sample size calculation method for composite endpoints (CE) in randomized controlled trials.
  • To evaluate the empirical power of the logrank test for CEs using the gAHR.
  • To demonstrate the application of the method with real-world clinical trial data.

Main Methods:

  • Sample size and power formulae are derived from the logrank test's non-centrality parameter under the alternative hypothesis, based on the gAHR.
  • The CompARE web platform is utilized for sample size computations.
  • A simulation study assessed the empirical power of the logrank test for CEs, considering various component hazard ratios, event probabilities, and degrees of association.

Main Results:

  • The simulation study achieved mean empirical powers of 0.799 (±0.004) and 0.798 (±0.004) in exponential and non-exponential settings, respectively, for a target power of 0.80.
  • Power was attained in over 95% of simulated scenarios, consistently exceeding 0.78.
  • The method proved robust regardless of proportional hazard assumption compliance.

Conclusions:

  • The geometric average hazard ratio (gAHR) offers a meaningful interpretation for composite endpoints, especially with non-proportional hazards.
  • gAHR is the natural effect measure for logrank tests comparing hazard rates and should replace the standard hazard ratio.
  • This approach enhances the reliability of sample size calculations for composite endpoints in clinical trials.