Hello everyone. Now that we know we are going to have some missing data, we're going to talk about what you can do about it. So, we'll review the definition of missing data, power, dropout, and how missing data can cause problems. We'll be using an example that you should be very familiar with by now, the dental procedures study that looks at pain levels over time based on audio treatment to show an account for missing data. Remember, when we see missing data, we need to think about why it is missing. Once we do that, if we can safely decide that the data is missing at random, we can simply adjust the sample size by making some simple calculations. Let's quickly review the example once again. Patients have a root canal procedure during which different groups received different audio treatments, testing to see if using a sensory focus results in a different pattern of memory pain than patients who do not take part in the sensory focus. After patients were randomly assigned to the sensory focus group or the control group, those in the sensory focus group listen to audio instructions to focus on physical sensations of their mouths. The control group listen to an audio about initial topic. Here's the flowchart for the study. You can see that measurements of pain recall were collected three times, immediately following the root canal and six and 12 months later. Based on these measurements, the researchers were looking to compare the experiences of the two groups. Specifically, the goal was to compare patterns of memory of pain over time between sensory focus in the control group. Here's our null, that there is no difference in pattern of memory of pain over time between groups. The researchers planned or repeated measurement analysis of variance to test the time by treatment interaction, which allows us to examine the differences in the pattern of pain over time between groups. They claimed to fit a general linear multivariate model using memory of pain as an outcome and using group assignment as predictors. Once again, we don't dive deep into data analysis in this course, as our concern is to teach about power analysis. But researchers shows you a statistical test, we've talked about this statistical test a couple times, the Hotelling-Lawley test, to test the interaction between group and time with an Alpha of 0.01. Researchers noticed missing data, investigated it, and understood the missing data pattern. They figured out that over a year's worth of time, they could expect a 25 percent loss to follow up. Researchers knew this because from running a dental clinic for a long time, they had experiences with asking people about their memory of pain. They recognized that patients left the clinic because their insurance status changed or because their employers changed their insurance programs. So, they not only understood the rate at which patients were leaving, but they also understood why they were leaving. Knowing this information helped them reach the realization that leaving was unassociated with memory of pain and any factor they could measure that could be influencing the study. Now we're going to go through a sample size summary to show what at first graph looks like and how we adjust for missing data. Here's a first draft, which starts off by describing our analysis plan, includes estimates we picked up from previous studies. We've highlighted the key components of the summary that we want to see when you guys write a sample size summary. As you can see, this includes the model, test, interaction, and key values like standard deviation. The sample size summary goes on to describe important correlation values including the expectations of decaying over time. Finally, it goes into the desired power, type I error rate, and the mean difference. The calculated sample size for all of these values is given as 44 participants. But remember that calculated sample size of 44 does not account for the missing data that we expect to occur. Therefore, it must be adjusted. If you remember based on prior knowledge and experience, we can expect 25 percent loss to follow up. So, we use the value in the following calculation. We take our unadjusted samples size and divide it by one minus the percentage of loss to follow up that we expect in decimal form. As you can see here, that gives us a larger sample size accounting for the missing data of 58.6. Obviously, we cannot recruit 0.6 of a participant, so we want to round up. Makes sure, though, to round up to a number that is divisible by the number of groups. In this example, there are two groups: sensory focus and control. If we take 58.6 and rounded to 59, that number is not divisible by two. So, we round up to 60, as this may seem easy to have two groups of size 30. One thing to note, as you are leading the sample size, rounding up further, do not forget about the ethics lecture we're talking about in subsequent lectures. This is an example where patients are receiving root canal procedures that they would have already have gone, though we do not need to worry. However, if something were negatively affecting or hurting people in some way, there would definitely be ethical considerations to inflating the sample size like this. After calculating the suggested sample size, makes sure to revise the sample summary section so it includes the new information. Here you can see an example of the revision. Recently published results give slightly better adjustment, as we include this paper from stats in medicine, which gave more approximations to adjust for missing data. Let's do a quick review summary for accounting for missing data. First, do your preliminary calculations to come up with the original sample size for your study. Then use the equation here to adjust your sample size. Finally, make sure to describe the sample size you started with, with the anticipated lost to follow up, then the new adjusted sample size, all in your sample size summary. That's it for this lecture. Thank you for your time.