Testing for Equivalence or Noninferiority chapter 21

An Example Compare the treatment effects of two drugs ( peak plasma concentration) Statistically Null hypothesis: x-y=0 Alternative hypothesis: X-Y=!0 Set a significant level (0.05) P value and CI Clinically or scientifically a generic drug tends to be prove it works just the same as a standard or reference drug. How? Equivalence zone/margin; equivalence testing

Equivalent Zone Ratio of Peak Concentrations The zone of equivalence is defined using scientific criteria with range 80 to 125% from report of Food and Drug Administration (FDA). As shown in this figure, the zone does not appear symmetrical around the 100 %; whereas it is symmetrical in a practical sense due to both symmetrical reciprocals (1/0.8=1.25;1/1.25=0.8) (%) 80% 125%

Mean within the Equivalence Zone A B C Ratio of Peak Concentrations (%) mean Figure shows data from three drugs where the mean of ratio of peak concentrations is within the zone of equivalence, but cannot prove equivalence. From FDA, two drugs are defined to be bioequivalent, when CI within the equivalence zone. As seen in this graph, the data demonstrate drugs B and C are equivalent to the standard drug; whereas the result is inconclusive for drug A.

Mean outside the Equivalence Zone D E F Ratio of Peak Concentrations (%) mean Figure shows data from three drugs where the mean ratio of peak concentrations is in the not equivalence one, but cannot prove the drugs are not equivalent. According to FDA’s criteria, as seen in this graph, drug F is not equivalent to standard drug, and for D and E, the data are inconclusive.

Usual Statistical Hypothesis Testing Is Not Helpful Statistically in this case Null hypothesis: ratio=100% ( CI includes 100%) Alternative hypothesis: ratio=!100% (100% sits outside of CI) A,B and D drugs meet null hypothesis, while C,E and F reject it. However, as we had known, B and C drugs are equivalent to a standard drug, and F is not equivalent.

Hypothesis Testing to Equivalence..significantly>80%..significantly<125% AND Two null hypotheses with one-tail test respectively Alternatives: the mean value of the ratio is greater than 0.80 the mean value of the ratio is less than 1.25 Applying the idea of statistical hypothesis testing to equivalence testing Two drugs are proven equivalent when both of alternatives are met.

Noninferiority Trials To prove that a new treatment is not worse than the standard treatment All parts of CI must be to the right of the lower border of the equivalence zone. Before testing, make 100% sure the works of the standard drug

Gaussian or Not? Chapter 24

The Gaussian Distribution Is an Unreachable Ideal Ideal data includes extremes: very low negative numbers super-high positive values Real data cannot meet those extremes, such as blood pressure and weight. Why do many tests rely on the it? Simulated data have shown statistical tests based on the Gaussian distribution is useful and robust, especially for the equal sample size. The data for test is required to enough close to the Gaussian distribution rather than equal it.

Distribution of 12 sample size from a Gaussian distribution with mean of and SD of 0.40 via randomly simulation. Distribution of 130 sample size from a Gaussian distribution with mean of and SD of 0.41 via randomly simulation. What a Gaussian distribution really looks like

Testing for Normality D'Agostino's K-squared test: Combinated the skewness and kurtosis, and both are equivalent to zero under an ideal Gaussian distribution. Others, positive or negative. Other tests: Shapiro-Wilk test Kolmogorov-Smirnov test Darling-Anderson test

The Interpreting of Results of Test Hypothesis: (null hypotheses, alternative hypotheses ) P value: Answer to what is the probability of obtaining a sample that deviates from a Gaussian distribution as much as (more/ less than ) this sample does. High P value and low P value Note: When null hypothesis is accepted, it does not demonstrate the sample is Gaussian distribution, only say this sample is consistent with Gaussian distribution. With the increasing of sample size, the evidence would be stronger.

What to do when data fail into a normality test Choices for a small P value (1) Transform your data (2) Outliers (3) Follow your statistical conclusion (4) Switch to non-parametric tests (will be shown in chapter 41) (before switch, should be careful, especially for the small size of sample)

Does it make sense to ask whether a particular data set is Gaussian?(No) Normality test is to demonstrate whether the data is consistent with normal distribution rather than whether the data is Gaussian. Should a normality test be run as part of every experiment?(not necessarily) Solution: a particular study without comparisons or scientific questions and plenty of data points, according to this kind of data obtained, it will be more convinced to see whether its distribution is consistent with normal distribution via normality test?