[MUSIC] So a little bit about some of the practicalities of computing sample size in clinical trials. So what if there are no prior data and this is not uncommon, especially for a novel intervention. One of the conventional approaches would be to conduct a pilot study and I'll talk about how you would compute the sample size needs for a pilot study in just a moment. Or to just do the best that you can to make reasonable estimates likely to be conservative, reasonable estimates. Remember however, that conservative estimates usually translate into larger sample sizes. What do you do if the sample size you've calculated is too big, you can't afford to do a study that is that larger? You won't be able to find that many patients. One approach if you can't figure out how to redesign your study to do things differently is to calculate what you think you could show with a sample size that you could actually obtain. So if your calculation of your sample size says that your study needs to have 1500 people and you don't think that you could possibly afford a study or complete a study that had more than 1000 people and you can maybe attempt to show what would be found in a trial with 1000 people? What kind of detectable difference with a reasonable power would that result? And is that adequate? Will that help advance the scientific understanding of the thing you're attempting to study or you can estimate the precision. For example the 95% confidence interval for the difference between the two groups with some fixed sample size and would that be an advance in the scientific understanding. It's very common when calculating sample sizes to present a table that shows the trade offs between different degrees of power and different assumptions about the detectable difference or the the rate of your outcome measure in the control group. And then often on a table like that, you would highlight the particular intersection of power and detectable difference that you have chosen as the primary design characteristics for your study. Lots of software options available to help calculate sample size here on the slide, we've cataloged a few of them, including some online sample size calculators that can accommodate a fairly broad range of different trial designs and then some classic installed software designs and I'm going to show a couple of examples calculating sample size using some of these options. So let's imagine we had an example trial that we were going to assess a drug's response on a laboratory measure. So this would be a continuous measure, outcome will analyze this using a standard T test. And for the purposes of this example, we assume or perhaps there are literature that suggests that the laboratory measure will have a response in the placebo group of 20. And we hope or think that our intervention might get us a response or measure of the value of 12 in the treated group. And We assume or that were able to determine that the standard deviation of whatever our outcome laboratory measure is is 25 and we'll assume that it's the same in both groups As noted before. A fairly typical value for alpha is 0.05 as shown on the slide here And well for purposes of this example assume a power of 0.85. So in 85% power common to use values of .8.85.9 in various circumstances. And so the question we're asking is with these assumptions with a drug that we think will have a treatment effect of eight notice that the intervention group here is averages eight below the placebo group, With a standard deviation of 25. And assuming a type one error of 0.05 and Targeting a power of 85%. How many people do I need to enroll in my study? Remember that we noted earlier that often you'll inflate your sample size calculation for some estimate of missing data. Afterwards, these estimates, I'm going to show you do not account for that missing data. So, here is the ps website showing one way that it's possible to calculate the sample size. So along the right hand edge, we see graphs this. This particular website shows graphs of the results of the sample size calculation on the left hand side. I've specified the type one error is 10.5 Specifically the standard deviation is 25. This particular website asks me to express the ratio of control individuals to experimental or intervention, that this again for a two arm study. So I've set that ratio at one, this would be the same as reflecting an allocation ratio of 1-1. The difference in the means of the two populations, as we said, for purposes of illustration will be eight And I've specified the power of 0.85. And then this particular website computes automatically for me the sample size needs in each of the two groups. So that number 177 is the number needed in each of the two groups. The total would be double that. And this site also shows me a 95% confidence interval with this is essentially the detectable difference. And then on the grass on the right hand side, the left most panel, we can see the trade offs between sample size and power with the dotted lines reflecting exactly what we've specified. So at an 85% power sample size needs. And then it shows here in the little box, it's inset what the sample size needs would be for a power of 72%. And it shows here that the end needed per group would be 127. And on the right hand panel it shows us the tradeoffs between sample size and detectable difference and as you can see here If the detectable difference, the difference that we wanted to be able to detect was not eight, but perhaps larger than eight, say 10 sample sized need goes down dramatically. And likewise, if the two groups are more similar, if the detectable difference goes to as small as seven sample size, need to go up fairly dramatically. And then on the bottom it just shows us a plot of the detectable difference with a 95% confidence interval. The second of the two websites we showed, it has a simpler interface. And so here we are specified again to ask it to give us a sample size calculation using a two sided test I specify here, instead of specifying the difference between the two groups, it asks us to give them the means of each of the two groups. So I've put in 12 and 20 And then the standard deviation of five, It again asks us to specify the ratio of the two arms. So I've specified that ratio as one, I can plug in the alpha of .05 and the power of .85. And here I get a total sample size, not a sample size per group of 3 51 that's essentially the same as the previous one with a little bit of difference in some of the rounding. Here's the third website and even simpler interface again, to specify alpha. Here, we specify the beta instead of the power. So remember the power is one minus beta. So here the beta is 10.15 and they asked us to specify the proportion of subjects that are in group one And then it fixes the proportion of groups and the other group from that first one so .5 in each of the two groups, that's an allocation ratio. Again of 1-1. Here we specify the effect size like the first website instead of just the individual means in the two groups and then the standard deviation on this website, you click the calculate button, it gives you a couple of parameters about the z values that we discussed earlier And then down at the bottom, it shows us the number needed in each of the two groups and the total is 352 which again is essentially the same as the previous two estimates with a little bit of rounding again, none of these have accounted for missing data. And then finally 1/4 example showing the same calculations using the package SAs And so the code that generates the sample size calculation is shown at the top of specifying the two group means of 12 and 20 same as before. I specify the power. I have not in this example specified the alpha but it has assumed an alpha of .05 if it's not specified, I did specify the power Then down at the bottom, it shows you all the fixed scenario elements reflecting what we've put in for those things and also the assumed value of alpha. And it calculates a total sample size of 354, again very close to the other ones within a degree of rounding. And here it's not able to give us an exact in For a power of exactly 85%. It rounded to the nearest whole individual and the power At that level is 85.1%, not just .85. So a few final points to summarize what we've learned here. Sample size calculations are necessary and fundamental for good trial design. Their important both for practical and ethical considerations. There are many assumptions that you have to make when calculating the sample size needs for a particular trial. Often the trial will involve trade offs between these assumptions. If the assumption about the effect sizes not correct and your sample size calculations might have to account for that in a different way. And often when designing a trial it's useful to consider different scenarios, different values for a detectable difference, different values for variability to see what effect that those have on your final sample size. However, I would caution against choosing assumptions and scenarios that minimize the sample size. A sample size that is too small does not allow you to answer the question or increases the risk that you will be unable to answer the question. Wow Yeah
