Survival Analysis

Major innovation in computational speed

Compute power by formula rather than simulation even when accrual rates, hazard rates, and attrition rates vary from one time interval to the next.

Graph power as a function of study duration, accrual patterns, treatment effect, attrition, or any other parameter in just seconds and get a clear picture of that factor's impact in your study.

This speed is made possible by the new algorithm which bypasses the simulation, coupled with an extremely powerful interface. With any other program, the same task would require many hours of tedious computation.

Power Analysis for Suvival Analysis

Survival analysis is used when subjects will be followed over a period of time, and we want to compare the proportion of subjects surviving at each point in time.  Survival analysis is used most often in clinical trials, and the term “Survival” comes from these studies where the outcome is, quite literally, survival.  However, the method can be used to track the time to any event (such as time to success) and is used in many other fields, as well.  The program will compute power for studies that compare survival rates in two groups

• How study duration and accrual affect power

  As a rule, the longer the study duration, the higher the power, since a longer period of observation allows us to observe more events.  

  For a given number of patients and a given study duration power is higher to the extent that patients are entered earlier (and followed longer).  Specifically,

  Power is higher if patients are entered prior to the study, rather than during the study.

  Power is higher is the accrual period is short, rather than long

  For a given accrual period power is highest if the accrual rate is initially high; is lower if the accrual rate is constant; and is lowest if the accrual rate increased over time

  These rules all follow from the fact that the earlier a patient is entered, the longer that patient can be followed before the study ends.  The impact of accrual rates on power will vary from one study to the next.  For example, if patients will be followed for 10 years, it doesn’t matter much if they are accrued over 2 months or over 6 months.  By contrast, if patients will be followed for only a year, then this may be an important distinction.

• How hazard rates and the hazard ratio affect power

Power is driven in part by the number of events in the study.  That is, the hazard rate must be high enough so that the event rate in the two groups can be compared.  For this reason, if the hazard rate is very low, power will be adversely affected.  As long as the hazard rates will yield a fair number of events the primary factor affecting power will be the hazard ratio, or the ratio of hazard rates in one group as compared to the other group.

• How attrition affects power

Attrition affects the number of patients actually in the study, and so the lower the attrition rate, the higher the power.  The best case is when there is no attrition.  If attrition exists, a low rate is preferable to a high one.  If attrition varies it will have more of an impact if it takes place early in the study, since this will result in the loss of more data.  Beyond these simple rules, the impact of attrition in any given study depends on a host of other factors.  For example, if the hazard rates are high then most patients will die before they have a chance to drop out and the impact of attrition may be low.  By contrast, if the the hazard rates are low and patients are expected to be alive (and followed) for many years, then even a modest attrition rate can severely impact the sample size and power.

Design Options available in the program

• Options for study design

  The program allows the user to select from among three options for accrual, two for hazard rates, and three for attrition, yielding a total of 18 options for study design.  The options selected here are used to configure the interactive screen, report, tables and graphs.  The program will compute power for a survival analysis study for two groups, using the log rank test.

•  Options for accrual

§         Accrual is Prior to the Study.   All subjects are accrued, and waiting, before the study actually begins so that all subjects enter the study on Day 1.  If the follow-up period is 24 months, this means that each subject will be followed for the full 24 months unless that subject dies (for example) or drops out of the study for some other reason. 

§         Accrual is Constant.  Subjects will be entered into the study over a period of time, at a constant rate.  For example, we may plan to enter subjects over a period of 6 months and then to follow them for an additional 18 months after the last one is entered.  The first subject could be followed for as long as 24 months while the last one entered could be followed for no more than 18 months. 

§         Accrual Varies.  The accrual rate varies.  For example, we may plan to enter a small number of patients per month for 3 months, as recruiting efforts are being refined, and then to increase the entry rate after that.  Or, we may plan to enter some patients before the study begins and additional patients after the study is underway.   If this option is selected you will not be able to include accrual time as a variable in tables and graphs.

• Options for hazard rates

§         Hazard rate is constant.  The hazard rate is constant over time.  For example, if the hazard rate will be 5% for one group and 10% for the other group for all time periods in the study. 

§         Hazard rate varies.  The hazard rate varies from one time period to the next.  For example, if the hazard rates in the two groups are initially 2% vs 4% but later rise to 5% vs 10%.  The rates in the two groups may be proportional but this is not required.

• Options for attrition

§         No attrition.  No patients will be lost to attrition.  This might be the case, for example, if the study will last for only a brief period of time and the intervention takes place at the start (e.g. surgery vs. no surgery) rather than on an ongoing basis.

§         Attrition is constant.  Select this option if the attrition rate will be constant throughout the study and will be the same for both groups.  This might be appropriate, for example, if the only reason for attrition is likely to be patients moving away from the geographic area.  If this option is selected, attrition can be included as a variable in the tables and graphs.

§         Attrition varies.  This option allows you to provide an attrition rate separately for each time interval and for each group.  For example, you might expect that the attrition rate is high initially, as some patients re-think their commitment to the study, and then levels off.   Or, you might expect the attrition to be higher in one treatment group than another.   If this option is selected, attrition cannot be included as a variable in the tables and graphs.

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