ABSTRACT
Chapter 10 includes two important statistical issues: multiplicity and missing data. We seek to ensure the veracity of all conclusions of treatment benefit in a clinical trial, so we want to control the familywise error rate (FWER), the probability of at least one type I error. We distinguish between weak and strong control of the familywise error rate (FWER) and give examples of each. We show how to strongly control the FWER through enumeration of the different possible configurations of parameters. We then offer intuition that leads to Holm's sequentially rejective Bonferroni procedure and a clever graphical method due to Bretz et. al (2011). We then focus on the special case of independent comparisons because it motivates the Simes (1986) procedure, which leads naturally to the Hochberg (1988) procedure. Next, we illustrate the very powerful but sometimes misunderstood closure principle. It can be used to justify a large number of methods of multiple comparison adjustment. We end our discussion of multiple comparisons with the Dunnett procedure for comparison of multiple arms with the same control. We emphasize the key technique used to calculate Dunnetts's critical value, namely conditioning on the control mean to produce conditionally independent statistics. This important technique is helpful in other setting as well.
The second half of the chapter is devoted to missing data, which compromise the integrity of a trial by interfering with the ability to compare randomized arms. We define the assumption of missing completely at random (MCAR), which is very unrealistic, and contrast it with the more plausible assumption of missing at random (MAR). We then discuss several methods of dealing with missing data. One method for continuous outcomes is to use a slope to summarize the time trend; nonmissing observations can be used to estimate the slope. A principled slope analysis is accomplished through a mixed model, which gives appropriate weights to people with different numbers of missing observations. We briefly discuss likelihood based methods such as the EM algorithm, and then move to several methods of imputation, including last observation carried forward, last rank carried forward, hot deck imputation and multiple imputation. Another method of dealing with missing data is through sensitivity analyses such as a tipping point analysis. These sensitivity analyses are appealing in clinical trials because they can be used even when the MAR assumption does not hold.
