Hello everyone. In this lecture we'll be talking about one way we get those numbers that we need to put it into our power in sample size analysis. So we'll be talking about how to find those inputs through a literature review process. We're going to talk about what inputs are needed and describe how to find them in the literature. You may recall that in order to perform a power sample size calculation, we have to specify the design, the statistical test, the criterion and the final key inputs for our power or sample size analysis that we've talked about. Some of the inputs that are needed for power analysis simply come from the experimental setup. What are the outcomes? What are the predictors? How many times is there a repeated measurement on the outcomes? Is there a baseline covariate? Is there a clustering? These are all things you should be fairly familiar with given the experience in exercises up to this point. The five key inputs for power and sample size analysis however, need to be found in external sources. We're going to talk about what those inputs are and how we find them. In order to conduct power and sample size calculations, we have to specify the design, the test, the criterion and the inputs. Since we have talked about all of these things in previous lectures, I'm going to move on, but feel free to pause and read these reminders of what these aspects of studies are. I do want to talk about this last point however, that inputs provide information about expected results of the study. This is why we are discussing this lecture in the first place. We're in a kind of quandary when we need to do power and sample size analysis. Because if we already knew all the inputs we needed, then we would simply know the results of the experiment. So when we're in a situation in which we're trying to predict the future, we don't actually know what the inputs are for power and sample size, so we have to make educated guesses. Here are the five inputs of the design. You should have a pretty good idea of what all of these inputs are, but let's go through them quickly. Clustering refers to the organization of the participants in the resulting shared experience of certain groups. Predictors are our indicator variables or independent variables. Covariates are variables we use to reduce group differences in increased power, although I don't believe we've had any examples with covariates yet. You know what repeated measures are from all of the talks and examples of longitudinal studies and the response is the outcome variable that you're looking at. Here, you can see various statistical tests. On the left are the multivariate model for repeated measures tests and on the right are the univariate model for repeated measures tests. Remember, multivariate models have more than one outcome variable and univariate models have a single outcome variable. You need to specify a criterion. That's the first thing you'd click in GLIMMPSE when it says solve in for. You must first solve for either power or sample size. If you choose to solve for power, you must provide a specific sample size. If you choose to solve for sample size, you must provide a specific power. The wavelengths works, you provide the smallest group size and information about the design in order to apply the total sample size. For example, if you specify that you have a one-to-one randomization, meaning there is an equal amount of people in each group, the smallest group is 10, this means the total sample size is 10 in the treatment plus 10 in the control, which is 20. A two-to-one randomization means there's double the amount in one group as the other. That means if there's 10 in the control group, which is the smallest group, the treatment group has 20 giving a total of 30 participants. Remember, we need five key inputs for power and sample size. Here they are. We have to provide predictors to hypothesis, the hypothesis mean or slopes or just the mean difference, the hypothesized standard deviations and correlations and the type one error. As you can see, inputs three through five are numeric. We're going to talk about how to get values for these key numeric inputs by focusing on the literature review process. In a literature review, you look at past studies and publications that are relevant to your current research goals. In this situation, we'll be doing this to find values for our key numeric inputs for power and sample size analysis. The standard deviation, the correlation between measurements and the scientifically meaningful detectable differences are numeric inputs for power in sample size analysis that are typically unknown before you run a study. That's where the literature review comes in. By the way, when we say scientifically meaningful difference, we mean something that may not be statistically significant, but it's still meaningful to science. For example, something that improves the quality of life for people in a medical study about health even though the change is not statistically significant. The literature review can help us with the standards for our desired power and type one error. These will vary by field. 0.8 is common, however, we usually recommend using 0.9 or 0.95. Remember to always to consider the ethics when making decisions as well. Type one error is simply set to 0.05. It can also be 0.01 for a more conservative analysis. Also remember to always watch for multiple comparison problems with Bonferroni adjustments if necessary. When heading into a literature review, it is important to have a plan. You want to identify questions of interests upfront. Essentially, think about what kind of information or inputs you are looking for. One example could be an unknown correlation value. Make sure you know exactly what you want to search for, so your search can be efficient and effective. Throughout the literature review, you also want to carefully document the results of your search. It's helpful to make a table like this. The author, title, design, etc. Then you can put down the numeric values for those studies which can help us with our estimates. We'll often list the results of this in our power analysis. We would say something like, we reviewed all papers that had the keywords pain recall and longitudinal comprising of 86 papers. Among these papers, standard deviation estimates for the score of pain recall range from 0.98-1.02. We chose the highest possible value observed in the literature for the standard deviation. We think that we'll get in the trial in order to produce a conservative power analysis, something like that. It is good to show the reviewers that you are careful when you're doing thoughtful and deliberate research. Here we have a new example to show you how you can use literature review to find numeric inputs for power or sample size analysis. Researchers are looking to compare the pattern of weight gain over pregnancy for two treatment groups. So what they're looking for is the time by treatment interaction. This is a common design. They are looking at specific pregnant women, those at risk for gestational diabetes. Here we have our treatment and control, either a diet intervention or a standard of care. Measurements will be made six times throughout pregnancy. Here you can see some of the details of the study. The analysis is a repeated measures ANOVA looking at differences between groups. The null is that there will be no difference between treatment and control. The planned test is the Hotelling-Lawley test, and there you see the Type 1 error rate and that we have a covariate. We're going to control for pretty pregnant body mass index as a covariate. The rationale is that recommended weight gain is based on women's body mass index before pregnancy. So women who are obese or overweight are recommended to gain less weight than women who are standard weight or underweight. Here's an example of a table that would be made documenting the results of the literature review. Citations are on the left, then the mean and standard error of the weight gain for treatment and control groups, then we see the sample size. Finally, we looked at what the treatment is. As you can see, none of the treatments are exactly the treatment that's planned for our example study. We need to keep that in consideration. So which values should we use? The numbers actually are fairly consistent. We see the control group gaining about the same amount of weight. We see a definite decrease in weight gain in the treatment group, and all that didn't really seem to differ much based on what the treatment was. Often we chose the biggest of the three estimates or smallest of the three estimates. We need to make sure why we justified these decisions we make and always think about the ethical considerations. You can also summarize your unpublished data from one of your similar studies. This is helpful because correlations are rarely published in studies. Here we have an unpublished data from a similar study, this allowed us to get an estimate of the correlation between measurements. You can see there are multiple differences in means and standard deviations cited in the table. So, what do we do to deal with this uncertainty? Well we can use a power curve. A power curve is a graphical description of what the power is as a function of something else, which in this case could be the means or standard deviations. We'll talk more about these later in the lecture and about the graphics. We can also consider many different values of mean differences that are close to the expected difference. We consider different values of variances, and we use the experimental situation to guide the choice of what kind of estimate we want. A conservative estimate refers to getting a small sample size. A liberal means ongoing to lean more towards having a large sample size on. This decision should be based on the experimental situation and ethical considerations. Think about is the treatment hurting anyone. Let's take a look at how using power curves can help you with uncertainty. You can draw several curves for different estimates and for desired power, you can look at the value of the estimate. Let's take a look at a couple of examples so it makes more sense. Here's a graphic with multiple curves. You can see that the higher the variance, the lower the power which makes sense based on our previous lectures. Here our desired power of 0.9, you can see that at 0.9, the curves are starting to flatten out which is why we usually use it. Here is the range of uncertainty. We can look at what the mean difference is. We could detect if we wanted a power of 0.9 even with uncertainty about the variants. Often, this kind of graphic will show up in a grant with an explanation. We'd say something like, we're not sure about the variants is because we could not find it in the literature, but as you can see here, if the variance is any of these values we can still detect mean differences around negative 1-1.7. Make sure to be careful about unpublished numbers. Also, be careful differentiating between standard errors and standard deviations. These are different things, making a mistake by mixing result will lead to incorrect power analysis result. Let's do a review summary for this lecture. We can use the literature review to get unknown numeric inputs that we need for power or sample size analysis. This key numeric inputs include means, standard deviations, and correlation. Also, make sure you plan your literature review and then document your progress. You want to head into your literature review with a plan, identifying questions of input search, you want answers to such as unknown correlations or the types of designs in a given field, and make sure you have some search terms to find what you are looking for. Finally, these values you get from the literature review are estimates, you need to account for uncertainty involved with these estimates. You can use a power curve considering different values for the estimates you find and make decisions based on an experimental context as to whether you should have a conservative or more liberal estimate. That wraps up this lecture on the literature review. Thank you for your time.
