Sample size calculator with dropout and attrition built in

A sample size calculation tells you how many participants must contribute data to the primary analysis. Not everyone who is enrolled will. Some withdraw consent, move away, stop attending visits, are lost to follow-up, or have to be excluded because of a protocol deviation. If you expect a proportion d of your enrolled participants not to reach the analysis, then a proportion (1 - d) will. To end up with N evaluable participants you need enrolled participants E such that E x (1 - d) is at least N.

Solving for E gives E = N / (1 - d), rounded up to the next whole participant because you cannot enrol a fraction of a person. This is the formula the calculator uses. With N = 200 and d = 20%, E = 200 / 0.80 = 250. Check it: 20% of 250 is 50 who drop out, leaving exactly 200.

The shortcut that many people use, N x (1 + d), gives 240 for the same inputs. After 20% of 240 drop out (48 people), 192 remain, which is below the 200 the power calculation required. The shortcut always under-enrols, and the shortfall grows with the dropout rate. At 30% dropout, N = 200 would need 286 enrolled but the shortcut gives only 260. If you are reading a protocol that justifies its enrolment number this way, ask the statistician whether it was intended.

The formula is easy. The hard part is the number you put into it. Good sources are, in order of usefulness, your own pilot or earlier studies, published trials with a similar population, duration and visit burden, and registry or real-world data on adherence in your condition. Treat the figure as an assumption with a range, and look at the table to see how sensitive your enrolment is to it.

Several design features move dropout. Longer follow-up and more visits increase it. Burdensome procedures, such as repeated biopsies or imaging, increase it. Placebo arms in symptomatic conditions often lose more people when symptoms persist. Remote visits and short ePRO forms completed on a phone tend to reduce the burden, and early warning of missed visits lets sites act before a participant is lost. See patient diary software for the diary side of retention.

Separate dropout types if you can. People lost before randomization do not count against the evaluable set at all, so use the dropout rate that applies after randomization when your calculation is per randomized participant. Dropout due to treatment failure or adverse events may be handled in the analysis plan rather than treated as missing, and a statistician may define the analysis population differently from simple completers. The calculator assumes one overall dropout proportion applied equally to all arms.

Inflating enrolment protects power on paper, but every extra participant costs screening, visits, monitoring and data cleaning. For a study with 200 evaluable participants and 20% expected dropout you pay for 50 extra participants. If a better retention plan cut dropout to 10%, you would need to enrol only 223, saving 27 participants. Put both numbers in the cost-per-patient calculator and compare: a retention programme often pays for itself.

Practical retention measures are mostly unglamorous. Keep visits short and combine procedures. Offer flexible visit times and reimburse travel. Collect questionnaires on the participant's own phone, with a link that opens directly and a reminder before the window closes. Watch missed visits in real time, so the site calls the participant the same week, not at the next monitoring visit. In Capture, real-time dashboards show enrolment and activity by site, and ePRO reminders go out by email or SMS. Record the reason whenever someone stops, in a structured field, because next time your dropout assumption will come from that data. If you are planning a small study, where each lost participant is a larger share of the total, see EDC for small clinical studies and the sample size calculator to check the power you are protecting.

The calculator assumes a single, constant dropout proportion, applied equally in every arm, and that dropout is unrelated to outcome (missing completely at random). It does not account for unequal dropout between arms, dropout that depends on treatment response, time-to-event designs with staggered entry and censoring, cluster designs, or multiple imputation and mixed-model approaches that use partial data from people who leave. For time-to-event outcomes, see the survival analysis sample size calculator, which works with events rather than completers.

Ask a biostatistician when dropout is large (say above 20%), when it differs between arms, when your primary analysis will keep partial data from dropouts, when you have interim analyses, or when the protocol will be reviewed by a regulator. A statistician can also tell you whether an estimand framework changes what counts as an evaluable participant, for instance if treatment discontinuation is handled by a policy rather than by exclusion.

This is a demonstration and planning aid, not validated software. Share the inputs, not just the output, with the person who signs off the statistical analysis plan. For the underlying concept, see the glossary entry on sample size calculation.