Sunday, December 10, 2017

Recurrent Events versus Composite Events: Statistical Analysis Methods for Recurrent Events

Recurrent events are repeated occurrences of the same type of event.
Composite endpoint is a combination of various clinical events that might happen, such as heart attack or death or stroke, where any one of those events would count as part of the composite endpoint.

While composite endpoint may also be discussed within the scope of the recurrent event endpoint, there are some distinctions between these two terms. The methods for statistical analysis are also different:
Recurrent Event Endpoint
Composite Endpoint
  • Relapses in multiple sclerosis
  • Exacerbations in pulmonary diseases such as chronic obstructive pulmonary disease
  • Bleeding episodes in hemophilia

  • MACE in cardiovascular trials where MACE (major adverse cardiac event) includes death, MI, and stroke.
  • Clinical worsening event in pulmonary arterial hypertension where clinical worsening includes all-cause death, PAH-related hospitalization, PAH-related deterioration of disease,…

Same type of event
Different type of event
Each event has the same contribution to the total number of events.
It is usually criticized that each component may contribute differently to the total counts (death is much severe event comparing with others)
The study design is usually with fixed duration. Events are collected over a fixed duration of time
The study design is usually an event-driven study. Different subjects may be followed up for different durations
Usually for events with relatively frequency
Usually for events that not frequently or rarely happen (so that we combine all these types to increase the power and minimize the sample size)
Can be analyzed as:
Frequency of events
Annualized rate of events
Time to first event
Duration of events
Duration of event free
Can be analyzed:
Time to the first event
Time to event for each component
Frequency of events
Competing risk is less an issue
Competing risk is an issue
Example of a trial with recurrent event endpoint:
Example of a trial with composite endpoint:

While the composite endpoint is usually analyzed as time to first event (whichever occurs the first for any of the components) using log rank test or Cox proportional hazard model, the recurrent event may be analyzed using different ways. Below are some examples of  

Emicizumab Prophylaxis in Hemophilia A with Inhibitors

The primary end point was the difference in the rate of treated bleeding events (hereafter referred to as the bleeding rate) over a period of at least 24 weeks between participants receiving emicizumab prophylaxis (group A) and those receiving no prophylaxis (group B) after the last randomly assigned participant had completed 24 weeks in the trial or had discontinued participation, whichever occurred first.
For all bleeding-related end points, comparisons of the bleeding rate in group A versus group B and the intraindividual comparisons were performed with the use of a negative binomial-regression model to determine the bleeding rate per day, which was converted to an annualized bleeding rate.
The primary efficacy end point was the annual rate of sickle cell–related pain crises, which was calculated as follows: total number of crises× 365 ÷ (end date − date of randomization + 1),with the end date defined as the date of the last dose plus 14 days. Annualized rates were used for the comparisons because they take into account the duration that a participant was in the trial. The crisis rate for every patient was annualized to 12 months. The annual crisis rate was imputed for patients who did not complete the trial. The difference in the annual crisis rate between the high-dose crizanlizumab group and the placebo group was analyzed with the use of the stratified Wilcoxon rank-sum test, with the use of categorized history of crises in the previous year (2 to 4 or 5 to 10 crises) and concomitant hydroxyurea use (yes or no) as strata. A hierarchical testing procedure was used (alpha level of 0.05 for high-dose crizanlizumab vs. placebo, and if significant, low-dose crizanlizumab vs. placebo).

A painful crisis was defined as a visit to a medical facility that lasted more than four hours for acute sickling-related pain (hereinafter referred to as a medical contact), which was treated with a parenterally administered narcotic (except for a few facilities in which only orally administered narcotics were used); the definition is similar to that used in a previous study. Annual rates were computed by dividing the number of crises by the number of years elapsed (e.g., 6 crises in 1.9 years - 3.16 crises per year). To test the effect of treatment on the crisis rate, the patients were ranked according to the number of crises they had had per year for observed periods of up to two years. Death was considered the worst outcome, followed by a stroke (defined as a documented new neurologic deficit lasting more than 24 hours, confirmed by a neurologist) or the institution of long-term transfusion therapy (more than four months); outcomes for all other patients were ranked according to the individual crisis rate. These ranks were used to compare the two treatment groups (Van der Waerden’s test). A rank statistic was planned for the primary analysis because it was expected to have more power to detect differences and to be less influenced by extreme values than a t-test of the means.

The primary efficacy endpoint was mean change from baseline in frequency of headache days for the 28-day period ending with week 24. A headache day was defined as a calendar day (00:00 to 23:59) when the patient reported four or more continuous hours of a headache, per the patient diary. Subsequent to study initiation, but prior to study completion and treatment unmasking, the protocol and statistical analysis plan for PREEMPT 2 was amended to change the primary and secondary endpoints, making frequency of headache days the PREEMPT 2 primary endpoint. This change was made based on several factors: availability of PREEMPT 1 data, guidance provided in newly issued International Headache Society clinical trial guidelines for evaluating headache prophylaxis in CM (34) and the earlier expressed preference of the US Food and Drug Administration (FDA), all of which supported using headache day frequency as a primary outcome measure for CM. For each primary and secondary variable, prespecified comparisons between treatment groups were done by analysis of covariance of the change from baseline, with the same variable’s baseline value as a covariate, with main effects of treatment group and medication overuse strata. The baseline covariate adjustment was prespecified as the primary analysis; sensitivity analyses (e.g., rank-sum test on changes from baseline without a baseline covariate) were also performed.

The primary outcome was the time to the first acute exacerbation of COPD, with acute exacerbation of COPD defined as “a complex of respiratory symptoms (increased or new onset) of more than one of the following: cough, sputum, wheezing, dyspnea, or chest tightness with a duration of at least 3 days requiring treatment with antibiotics or systemic steroids.” The primary analysis was based on a log-rank test of the difference between the two treatment groups in the time to the first exacerbation, with no adjustments for baseline covariates. A Cox proportional-hazards  model was used to adjust for differences in prespecified, prerandomization factors that might predict the risk of acute exacerbations of COPD.

The primary outcome was the effect of simvastatin on the exacerbation rate, which was defined as the number of exacerbations per person-year.

COPD exacerbation rates in the two study groups were compared with the use of a rate ratio. The independence of individual exacerbations was ensured by considering participants to have had two separate exacerbations if the onset dates were at least 14 days apart. Exacerbation rates in each group and the between-group differences were analyzed with the use of negative binomial regression modeling and time-weighted intention-to-treat analyses with adjustments of confidence intervals for between-participant variation (overdispersion).

FDA recommended the time to first exacerbation as the primary efficacy endpoint over the use of frequency of exacerbations as primary endpoints. The time to first exacerbation will be analyzed using log-rank test or Cos proportional hazard model.
Even though the FDA agrees that the frequency of exacerbations may be a clinically relevant endpoint; however, there are several statistical issues and challenges in providing a reliable and unbiased estimate of treatment effect using this endpoint:
  • Dependencies of exacerbation on previous exacerbations within patients
  • Effect of influential cases as it can potentially impact the results
  • Distinguishing between early vs. late exacerbations as a function of time
  • Distinguishing between first vs. subsequent exacerbations within patients
  • Investigator biases in assessing the number of events (e.g. events occurring close together)


Paul M Brown, Alberta Children's Hospital Research Institute said...

Dr Deng, thanks for this summary. Incidentally, we just published on this topic ie recurrent events versus composite endpoints: We showed the former approach can offer superior power. I feel somewhat obliged to promote the more thorough analysis. I find composites are quite wasteful with data, among other issues. I enjoy your blog, especially as a fellow SAS user. Cheers

Paul M Brown, Alberta Children's Hospital Research Institute said...
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