364 PART 7 The Part of Tens

Imagine that you’re studying the association between weight and blood pressure,

and you want the correlation test to come out statistically significant if these two

variables have a true correlation coefficient of at least 0.2. Then you need to study

8

0 2 ²

/

.

, or 200 participants.

Comparing Survival between Two Groups»

» ^{Applies to: Log-rank test or Cox proportional-hazard regression.»}

» ^{Effect size: The hazard ratio (HR) you want to be able to detect.»}

» ^{Rule: The required total number of observed deaths/}

events 32

2

/ natural log of HR

.

Here’s how the formula works out for several values of HR greater than 1:

Hazard Ratio

Total Number of Events

1.1

3,523

1.2

963

1.3

465

1.4

283

1.5

195

1.75

102

2.0

67

2.5

38

3.0

27

Your enrollment must be large enough and your follow-up must be long enough

to ensure that the required number of events take place during the observation

period. This may be difficult to estimate beforehand as it involves considering

recruitment rates, censoring rates, the shape of the survival curve, and other fac-

tors difficult to forecast. Some research protocols provide only a tentative esti-

mate of the expected enrollment for planning, budgeting, and ethical purposes.

Many state that enrollment and/or follow-up will continue until the required

number of events has been observed. Even with ambiguity, it is important to fol-

low conventions described in this book when designing to avoid criticism for

departing from good general principles.