Sample size calculation for longitudinal data of abdominal aortic aneurysm

Abstract

Sample size calculation is a crucial step in all experimental design. In clinical research and drug development activities, it is required in order to be able to demonstrate a presumed statistical effect of a drug or a treatment. Today many sample size calculation algorithms and formulas exist. However, in this work an algorithm based on the results of Liu and Liang (1997) is tested and used to predict the right sample size based on data from a study involving 211 patients with abdominal aortic aneurysm (also known as AAA). In this study the growth of the diameter of the aneurysm was monitored over time and the slope of that growth was calculated. Since no information about treatment effect was provided, a statistically significant reduction of the slope by 20% was chosen to replace the lack. More precisely, we want to calculate the sample size required to demonstrate a desired effect of growth reduction by 20% of a treatment at the statistical power of 80%.

The aim of this work was not only to examine statistically the abdominal aortic aneurysm data from placebo patients and the involved variables but also to evaluate the “longpower” package existing in the programming language R to calculate the sample size for longitudinal data.

The statistical model chosen for this work was a linear mixed model with TIME as a random and fixed variable and logarithm of aneurysm diameter at baseline (AD0) as a fixed variable. Non-equidistant TIME measured the intervals of ultrasound screenings in years whereas AD0 was measured in mm.

The formula of Liu and Liang (1997) using “longpower” package in R computed a required sample size of 420 patients with a power of 80% and reduction of TIME slope by 20%. In order to verify the sample size of 420 a simulation for the control and the treatment groups were run. A two-sample t-test showed statistically significant difference in means of logarithms of aneurysm diameters for simulated control and treatment groups at the significance level of less than 0.1%.

Moreover, a linear mixed model using simulated data for 210 placebo and 210 treatment patients to investigate a cross effect of TIME*TREATMENT as fixed and random variable gave a statistically significant difference between the control and the treatment groups at the significance level of less than 0.1%.

To test the number 2*210 patients, another simulation of 2*105 patients were run. Two-sample t-tests showed statistically significant difference in means of logarithms of aneurysm diameters for these simulated control and treatment groups at the significance level of less than 0.1%. Investigation of the cross effect of TIME*TREATMENT in a linear mixed model showed statistically significance at the significance level of less than 0.1% for the simulation of 2*105 patients.

Although both sample sizes of 2*210 and 2*105 were acceptable from statistical standpoint, power calculations revealed that the sample size of 2*210 gave a power of 73% whereas 2*105 gave only a power of 61%. Finally, the sample size of 420 (2*210) was verified by the simulations.