Sample Size Calculation Without Considering Dropout Rate

When planning for clinical trials, sample size calculation is a two-step or three-step process. For clinical trials with continuous variable or categorical variable as primary efficacy endpoint, the sample size calculation is usually a two-step process: the step 1 is to calculate the sample size based on the effect size / standard deviation for continuous variable; difference in rate/proportions and the control group rate/proportion for categorical variable. The step 2 is to apply the dropout rate to calculate the number of subjects needed to be randomized. I had an earlier post “sample size considering the dropout rate” to state that the calculation to account for the dropout rate should be by dividing (1-dropout rate), not by multiplying (1+dropout rate).

For clinical trials with time to event variables, the sample size calculation is usually involved in three steps:

• Step 1: Estimate the number of events needed based on hazard ratio, median survival time, or event rate at a specified time frame
• Step 2: Estimate the number of subjects needed to obtain the required number of events based on the accrual time, the follow-up, or the overall study duration
• Step 3: Estimate the total sample size by considering the dropout rate.

Applying the dropout rate in clinical trials with time to event endpoint is not straightforward. The dropout rate is usually not a constant throughout the study (during the accrual period and during the follow-up period).

To calculate the sample size for studies with time to event variables, I usually use Cytel’s EAST software. To deal with the dropout rate, the EAST software user manual suggests a ‘trial and error’ method. With this method, we will need to provide an initial dropout rate (expressed in ‘probability of dropout’ or ‘hazard for dropout’). We then check the summary of the sample size estimation. The number of dropouts is displayed, and the dropout rate can easily be calculated by dividing the number of dropouts by the number of subjects. If the calculated dropout rate is different from the assumptions, we can then go back to revise the initial input – do this several times until the calculated dropout rate from EAST matches the assumed dropout rate.

I recently run into two scenarios where the sample size calculation does not need to consider the dropout rate.

• Sample size calculation for an animal study (pigs for example) with a time to event variable. The pigs used in the experiment will be confined in a facility. There is no lost-to-follow-up or anything situation like that. There is no need for us to consider the dropout rate if we try to estimate the number of pigs needed for an experiment. 

• Sample size calculation for a metastatic non-small cell lung cancer (NSCLC) study with overall survival as the primary efficacy endpoint. The median survival time for metastatic NSCLC patients is usually short. In other words, the mortality rate for NSCLC patients is high. In this situation, the number of subjects who lost to follow-up is generally small (less than 5%) and we may not need to apply the dropout rate in calculating the number of subjects to be randomized. A friend of mine who is an expert in NSCLC clinical trials told me that in their studies with OS as primary efficacy endpoint, they will calculate the number of death events needed, and then simply add 25-30% more patients on top of the number of death events to account for a small proportion of subjects who may live much longer. For example, based on the hazard ratio, accrual time, and follow-up time, if the calculated number of death events is 200 events, we can simply have a sample size of 250-260 subjects randomized (25-30% more than the number of death events). 

Here are some recent trials from New England Journal of Medicine where there was no mention of dropout rate in sample size calculations:

• Durvalumab after Chemoradiotherapy in Stage III Non–Small-Cell Lung Cancer and the study protocol
• Nivolumab versus Docetaxel in Advanced Squamous-Cell Non–Small-Cell Lung Cancer and the study protocol
• Atezolizumab for First-Line Treatment of Metastatic Nonsquamous NSCLC and the study protocol
• Dimopoulos 2018 Phase 3 Trial of Ibrutinib plus Rituximab in Waldenström’s Macroglobulinemia
• A Randomized, Double-Blind, Placebo-Controlled, Phase 3 Study of Ibrutinib or Placebo in Combination with Rituximab in Subjects with Waldenström’s Macroglobulinemia

• Pembrolizumab plus Chemotherapy in Metastatic Non–Small-Cell Lung Cancer