# Biostatistics Case Studies 2014 Youngju Pak, PhD. Biostatistician [email protected] Session 2:...

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REI Summer Fellowship Biostatistics

Biostatistics Case Studies 2014Youngju Pak, [email protected] 2: Sample Size & Power for Inequality and Equivalence Studies II1What we have leaned in session 1? Info Needed for Study Size: Comparing Means (Inequality test)Effect (clinically meaningful difference)Subject variabilityType I error (1.96 for =0.05; 2.58 for =0.01)Power (0.842 for 80% power; 1.645 for 95% power)Free sample size calculations: www.stat.uiowa.edu/~rlenth/Power(1.96 + 0.842)22SD2 2N =Case Study

Ophthalmology 2006; 113:70-76.

AbstractPrimary Outcome and Study Size

Study Size - Page 72 bottom of column 1: Primary Outcome - Page 72 middle of column 1: Needs ConsensusPIs GambleTesting inequality vs. equivalence.Hypotheses for testing inequality:Ha: | mean(treatment ) - mean (control ) | 0H0: | mean(treatment ) - mean (control ) | = 0 Hypotheses for testing inequality:Ha : 1< mean(trt1) mean (trt2) < 2H0 : mean(trt1) mean (trt2) 1 Non-Inferiority or mean(trt1) mean (trt2) 2 Graphical presentation of equivalence testWith our regular t-tests, to conclude there is a substantial difference you must observe a difference large enough to conclude it is not due to sampling error

To conclude there is not a substantial difference you must observe a difference small enough to reject that closeness is not due to sampling error from distributions centered on large effects

Non-Inferiority Study Usually a new treatment or regimen is compared with an accepted treatment or regimen or standard of care. The new treatment is assumed inferior to the standard and the study is designed to show overwhelming evidence that it is at least nearly as good, i.e., non-inferior. It usually has other advantages, e.g., oral vs. inj. A negative inferiority study fails to detect inferiority, but does not necessarily give evidence for non-inferiority. The accepted treatment is usually known to be efficacious already, but an added placebo group may also be used. How to determine Sample Size? For IOP study, we haveHa: mean IOP change uf mean IOP change f < 1.5 H0: mean IOP change uf mean IOP change f 1.5 thus, we are only interested in the upper limit of the difference Non-inferiority one-sided T-test Thus we reject the H0 if Signal/ Noise < some clinical value.But N for a non-inferiority test require more complicated parameters such as the non-centrality parameter of the t-distribution (a Two One Sided T-test is usually used for the equivalence test ).

Lets run a softwarefrom www.stat.uiowa.edu/~rlenth/PowerInformation you will need Equivalence Margin Non-Inferiority Margin(NIM) =1.5 for the IOP studyAssumed mean difference in change of IOP between two groups -> usually zero difference assumed but it is assumed 0.5 for the IOP studySD of changes of IOP = 3.5 (usually set to 2.5%) since the confidence level of the confidence interval is (100-2 x ) %Sample size for IOP study

Three dimensional power curve for a non-inferiority test

How do we determine if the fixed method is noninferior to the unfixed method? Regardless of study aim to prove treatments equivalent or to prove them different - inference can be based on: Primary Outcome: IOP reduction D= Duf Df , where Df = mean IOP reduction with fixed therapyTypical superiority/inferiority study:Compare to 0.

Non-inferiority study:Compare to 2, a pre-specified margin of equivalence (1.5 here).= 95% CI for D(= Duf Df ) = true (population) values for D

Typical Analysis: Inferiority or SuperiorityH0: Duf Df = 0H1: Duf Df 0Aim: H1 therapies differ = 0.05 & N=2194 Power = 80% when =1, SD=3.5Fixed is inferior= 95% CI for D = true (population) values for D

Fixed is superior00Du Df[Not used in this paper]0No difference detectedDu DfDu DfTypical Analysis: Inferiority OnlyH0: Du Df 0H1: Du Df > 0Aim: H1 fixed is inferior = 0.025 & N=2194 Power = 80% for when =1, SD=3.5Fixed is inferior= 95% CI for Du Df= true (population) values for D

00Duf Df[Not used in this paper]0Inferiority not detectedDuf DfDuf Df( = 0.05 N=2153 )Non-InferiorityH0: Du Df 1.5H1: Du Df < 1.5Aim: H1 fixed is non-inferior = 0.025 & N=2194 Power = 80% for When = 0.5, NIM=1.5Fixed is non-inferior= 95% CI for Du Df= true (population) values for D

00Duf Df[As in this paper]0Non-Inferiority not detectedDuf DfDuf Df1.51.5Fixed is inferior1.5Inferiority and Non-InferiorityFixed is non-inferior= 95% CI for Du Df = true (population) values for D000Neither is detectedDuf Df1.51.5Fixed is inferior01.5Fixed is non-clinically inferiorD^uf = 9.0 D^f = 8.7 D^ = 0.3 95% CI = -0.1 to 0.7Observed Results:Fixed is non-inferior01.51.5Conclusions: GeneralNegligibly inferior would be a better term than non-inferior. All inference can be based on confidence intervals.Pre-specify the comparisons to be made. Cannot test for both non-inferiority and superiority. Power for only one or for multiple comparisons, e.g., non-inferiority and inferiority. Power can be different for different comparisons. Very careful consideration must be given to choice of margin of equivalence (1.5 here). You can be risky and gamble on what expected differences will be (0.5 here), but the study is worthless if others in the field would find your margin too large.

FDA Guidelines : http://www.fda.gov/downloads/drugs/guidancecomplianceregulatoryinformation/guidances/ucm202140.pdf

Where, M1= Full effect of the active control compare with the placebo effectM2= NI MarginSelf-QuizGive an example in your specialty area for a superiority /inferiority study. Now modify it to an equivalence study. Now modify it to a non-inferiority study. T or F: The main point about non-inferiority studies is that we are asking whether a treatment is as good or better vs. worse than another treatment, so it uses a one-sided test.Power for a typical superiority test is the likelihood that you will declare treatment differences (p