How Nyholt’s Method Makes Scientific Testing More Reliable

Table of Links

Abstract and 1 Introduction

1.1 Related literature

2. Types of Metrics and Their Hypothesis and 2.1 Types of metrics

   2.2 Hypotheses for different types of metrics

3. Type I and Type II Error Rates for Decision Rules including Superiority and Non-Inferiority Tests

   3.1 The composite hypotheses of superiority and non-inferiority tests

   3.2 Bounding the type I and type II error rates for UI and IU testing

   3.3 Bounding the error rates for a decision rule including both success and guardrail metrics

   3.4 Power corrections for non-inferiority testing

4. Extending the Decision Rule with Deterioration and Quality Metrics

5. Monte Carlo Simulation Study

   5.1 Results

6. Discussion and Conclusions

APPENDIX A: IMPROVING THE EFFICIENCY OF PROPOSITION 4.1 WITH ADDITIONAL ASSUMPTIONS

APPENDIX B: EXAMPLES OF GLOBAL FALSE AND TRUE POSITIVE RATES

APPENDIX C: A NOTE ON SEQUENTIAL TESTING OF DETERIORATION

APPENDIX D: USING NYHOLT’S METHOD OF EFFICIENT NUMBER OF INDEPENDENT TESTS

Acknowledgments and References

APPENDIX D: USING NYHOLT’S METHOD OF EFFICIENT NUMBER OF INDEPENDENT TESTS

As discussed above, the lack of assumption regarding the data generating process implies that under many processes the decision rule with have too low type I error rate and to high power. Although there are many alternatives to Bonferronitype corrections we have two conditions that we would like to have for any design. First, the individual metric results should have CI’s that maps to the decision rule outcome. Second, the design should allow for analytical required sample size calculations. These conditions means that most alternative multiple correction methods, such as [7] and [8] are discarded. Very few methods have confidence intervals, and even fewer are possible to integrate in the sample size calculation, due to their reliance on the p-values.

One method that fulfills our conditions is Nyholt’s method for calculating the so-called effective number of independent tests in a set of tests with arbitrary covariance structure [14]. This method is frequently applied in high-dimensional genome testing, and has been refined by several, see e.g. [11, 5]. Nyholt’s method is simple, the effective number of independent tests is given by

D.0.1 Monte Carlo simulation results with the Nyholt method Below the tables from Section 5 are repeated together with the result using Nyholts method as described above. As expected, the method improves the efficiency. This is shown by type I error rates and power closer to the intended rates under certain covariance structures.

ACKNOWLEDGMENTS

The authors would like to thank Bob Wilson for feedback on earlier drafts of this paper.

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