Tuesday, September 15, 2015

Time to Event End Points

Time to Event analysis has expanded beyond the traditional term of survival analysis even though the term of survival analysis may still be used in oncology trials and time to event analysis remain as the primary tool in oncology clinical trials. In oncology area, depending on the type of the cancer and the regulatory requirement, the primary efficacy endpoint may be one of the following 'time to event' variables: overall survival (time to death), progression free survival (time to progression), disease free survival (time to disease occurrence), event free survival (time to event occurrence),… In the non-oncology area, we also often need to perform 'time to event' analysis. Except in oncology area where the terms 'overall survival', 'progression free survival' are used, all 'time to event' endpoints will be labelled with ‘time to something’. Here are some of the examples of 'time to event' variable in non-oncology areas: 

Time to hemostasis (time to stopping the bleeding)
Adjunct to Hemostasis after various types of surgeries using fibrin sealant or thrombin

COPD, Bronchiectasis

Time to first pulmonary exacerbation
Time to healing of the primary lesion complex (loss of crust from vesicular [classical] lesions)
Recurrent Herpes Labialis
Time to clinical worsening
Pulmonary arterial hypertension
Time to parasite clearance
Time to recurrent infection

For all 'time to event' variables, the EVENT of interest must be clearly pre-defined. Sometimes, defining an EVENT is not easy. In many situations, the EVENT of interest may need to be adjudicated by an event adjudication committee (EAC) or by central reader (if an Event of interest is determined by imaging).

Depending on the definition of the ‘event’, the 'time to event' variable could be a hard end point or a surrogate (soft) endpoint.

Overall survival (time to death) is usually considered as a hard end point because death is a definite event.

Time to first hospitalization, time to lung transplantation,… may be considered as a hard endpoint. However, the hospitalization and lung transplantation could be impacted by the health care resources and might be different depending on the countries/regions.

If there is a composite endpoint that includes the 'time to MI', 'time to Stroke', you might think that the event MI and Stroke are definite endpoints. You might think that myocardial infarction (MI) is an event that can be easily identified/diagnosed until you realized that the myocardial infarction could be determined based on cardiac markers such as tropolin level. Whenever we deal with a laboratory test, we will run into the issue of the assay sensitivity, the measurement error, and the cut point for defining the event. Stroke might also be considered as identifiable event, but if the stroke event includes the transient ischemic attack (TIA), TIA may not be easily identifiable.

'Time to event' variables may depend on the pre-specified schedules for checking the EVENT of interest. For example, in malaria studies, ‘time to parasite clearance’ was assessed by taking blood samples and examining it by light microscopy prior (0 hour) and during treatment at 4, 8, 12 hours and then 6 hourly until two consecutive negative blood slides. If the pre-specified time points for taking blood samples are different, the ‘time to parasite clearance’ variable will also be different.
For Progression Free Survival or Time to Progression variables, the disease progression will need to be clearly defined. For the solid tumor, the progression is usually defined using Response Evaluation Criteria In Solid Tumors (RECIST) criteria that is usually based on the radiological and imaging (CT, MRI) results to measure the changes in tumor size (or target lesions).

Many women with early-stage breast cancer undergo breast-conserving surgery followed by whole breast irradiation, which reduces the rate of local recurrence. Radiotherapy to the chest wall and regional lymph nodes, termed regional nodal irradiation, which is commonly used after mastectomy in women with node-positive breast cancer who are treated with adjuvant systemic therapy, reduces locoregional and distant recurrence and improves overall survival. In early stage breast cancer studies, Disease Free Survival (DSF) measures the length of time after primary treatment to the re-occurrence of any signs or symptoms of the cancer. DFS may also be called relapse-free survival or RFS. It will be a surrogate endpoint since the determination of the re-occurrence of any signs or symptoms may not be accurately detected. 

In oncology studies, Event-Free Survival (EFS) measures the length of time after primary treatment to the re-occurrence of certain complications or events that the treatment was intended to prevent or delay. These events may include the return of the cancer or the onset of certain symptoms, such as bone pain from cancer that has spread to the bone. For example, in neoroblastoma studies, Event-Free Survival was used and the EFS was defined as the time from study enrollment (which occurred after transplantation) until the first occurrence of relapse, progressive disease, secondary cancer, or death or, if none of these events occurred, until the last contact with the patient. It will also be a surrogate end point since the determination of relapse, progressive disease, and secondary cancer may depend on when the patients are examined and how the imaging results are examined.

In summary, for time to event variables, it is critical to have criteria to determine the Event of Interest. If the determination of the Event of Interest is soft, it may require a third party (independent of the sponsor and the investigator) to determine the Event of Interest. If the radiological and imaging techniques are used, a central reader is usually needed. For other 'time to event' variables where the determination of the event is soft, an independent Event Adjudication Committee (EAC) is usually needed. For the studies in the same indication, it is ideal to have standardized criteria to determine the Event of interest so that the study results across different sponsors may be compared. For example, in breast cancer area, people are trying to use a STEEP system to standardize the criteria for clinical trial end points. 


Saturday, September 05, 2015

Understanding the endpoints in oncology: overall survival, progression free survival, hazard ratio, censored value

For clinical trials in oncology area, various terms related to the study endpoints are confusing to non-statisticians. The commonly used terms such as overall survival, progression free survival, censor, and hazard ratio are not straightforward to non-statisticians.

FDA guidance “Guidance for Industry Clinical Trail Endpoints for the Approval of Cancer Drugs and Biologics” delineated various endpoint measures and provided guidance on which endpoint should be used in which situation.

Overall Survival versus Survival Rate: The term overall survival can be easily confused with the survival rate or can be easily thought as the survival rate. While these two terms are related, they measure different things. Overall Survival is a measure of time to event and Survival rate measures the percentage of subjects who survived (at the end of the study, after 3 years, 5 years,…). 

Perhaps, it is clearer to understand the differences if we put these terms side-by-side for a comparison.

Table 1: Comparison of Overall Survival and Survival Rate

Overall Survival (OS)
Survival Rate
Measuring how long a patient can survive

Measuring how many patients survive during a given time (3 year, 5 years)
The time from the randomization or the start of the study treatment to the death
the percentage of subjects who are alive at the end of the study
Hard endpoint since both are based on the death event
Commonly used in clinical trials
Commonly used in epidemiology
Recommended study endpoint
Not usually used as the study endpoint
Analyzed using survival analysis or time to event analysis methods (Kaplan-Meier estimate, log-rank test, proportional hazard model,…)
Analyzed as proportion/rate/ratio (Chi-square test, CMH test,..) or dichotomous variable using logistic regression.

Table 2: Comparison of Overall Survival and Progression Free Survival

Overall Survival (OS)
Progression Free Survival (PFS)
Measuring how long a patient can survive

Measuring how long a patient can live without disease progression

The time from the randomization or the start of the study treatment to the death (all causes)
the time from the randomization or the start of the study treatment to the disease progression including death
Commonly used in clinical trials
Hard endpoint
Surrogate endpoint
Analyzed using survival analysis or time to event analysis methods (Kaplan-Meier estimate, log-rank test, proportional hazard model,…)
Study with OS as the primary efficacy endpoint requires relatively larger sample size and longer follow-up duration
Study with PFS as the primary efficacy endpoint requires relatively smaller sample size and shorter follow-up duration

PFS may or may not predict the OS.

How to determine the disease progression may get tricky. Disease progression often relies on the imaging (for example, using imaging to determine if there is any change in tumor size)

Disease free survival (DFS), event free survival (EFS), time to progression (TTP) et al have the similar features to the Progression Free Survival (PFS). 
  • Disease free survival: time to disease reoccurring. Measuring the length of time after treatment during which no disease is found. 
  • Event free survival: Time from randomization* to disease progression, death, or discontinuation of treatment for any reason (eg, toxicity, patient preference, or initiation, of a new treatment without documented progression). may be useful in evaluation of highly toxic therapies
  • Time to progression: Time from randomization* until objective tumor progression; does not include deaths

Table 3: Comparison of Hazard Ratio and Risk Ratio

Hazard Ratio (HR)
Risk Ratio (RR)
For time to event variables for example OS and PFS
For binary variables (such as live/death, success/not success)
The Hazard ratio is the ratio of the probability of an event (death or progression) in the experimental arm to the probability in the comparator arm.

A hazard is the rate at which events happen
The risk ratio (or relative risk) is the ratio of the risk of an event in the two groups.

The hazard ratio is a related measure that weights the risk change according to when events occur over time
The relative risk is a measure of the relative change in the risk of a preventable event.
Calculated using (Cox) proportional hazard model (for example using SAS PROC PHREG)
Calculated by dividing two proportions (for example proportion of subjects who survived in active group / proportion of subjects who survived in placebo group). In SAS, it can be obtained using PROC FREQ or PROC Logistic
Assumption that the data follows the proportional hazard
No such assumption is needed
A hazard ratio of 2 means the event will occur twice as often at each time point (at any given instantaneous time point) given a one-unit increase in the predictor.
A risk ratio of 2 means that the event is 2 time more probable given a one-unit increase in the predictor

Risk ratio and relative risk are two terms that can be used interchangeably. Risk ratio and odds ratio are similar and have the same features, but with different formula for calculation. For clinical trials, both Risk Ratio and Odds Ratio are used. For epidemiology studies especially the case-control studies, Odds Ratio is usually used. See table below for comparison in calculating the Risk Ratio and Odds Ratio.

Table 4: Calculation of risk ratio (RR), odds ratio (OR) and risk difference (RD) from a 2×2 table
The results of a clinical trial can be displayed as a 2×2 table:

No event
Experimental intervention
Control intervention

where SE, SC, FE and FC are the numbers of participants with each outcome (‘S’ or ‘F’) in each group (‘E’ or ‘C’). The following summary statistics can be calculated:

The term ‘censored value’ is used to describe an incomplete measure. For example, for a biomarker or laboratory measures, if the value is too low or too high that exceeding the quantification limit (for example exceeding the lower limit of quantification – LLQ), we would indicate the value is less than LLQ, but the exact value is unknown.

The “censored value” is especially common in cancer clinical trials. For patients who did not experience the event, the time to event will be censored. Suppose patients are followed in a study for 20 weeks. A patient who does not experience the event of interest for the duration of the study is said to be censored (exactly right censored). The interpretation is that even though the subject does not experience the event and we cannot calculate the time to event, we set up the time to event as a censored value for time to event analyses.  

For cancer clinical trials, it is essential to understand whether or not the study endpoint is to count the events or to measure the time to events. Measuring the time to events is more commonly accepted endpoint in cancer clinical trials.