Basic Concepts in Calculations of Sample Size & Statistical Power
Todd Alonzo1

1University of Southern California

Synopsis

The Overview of Biostatistical Data Analysis Methods is comprised of the following 3 parts:

  • Part 1: Basic concepts in calculations of sample size and statistical power
  • Part 2: ROC Analysis in diagnostic medicine
  • Part 3: Statistical prognostic/predictive modelling of quantitative imaging biomarkers (QIBs)

Part 1: Basic concepts in calculations of sample size and statistical power

This is is the second lecture on the foundations of imaging studies, with a focus on determining the sample size required for the study. We will provide the rationale for performing sample size calculations. The process of calculating sample size and power calculations will be presented as four building blocks. We will discuss each block with an example included for each. Two errors, Type I and II errors, can be made during hypothesis testing. Two classic diagnostic accuracy studies, representing prospective and retrospective designs, will be compared. As an alternative design to superiority studies, non-inferiority and equivalence study designs will be discussed.

-Reasons for performing sample size calculations

  • To minimize the risk of making the wrong conclusion from your study
  • To plan for your study’s needs
  • To determine if a study is feasible

-Sample size calculations takes place after you have specified your study’s primary objective

-Building blocks of sample size calculations

  • State statistical hypothesis and/or what you want to estimate
  • Plan the statistical analysis
  • Make assumptions about your study data
  • Calculate sample size

-Example

-Hypothesis testing decisions

  • fail to reject null hypothesis
  • reject null hypothesis

-Result of hypothesis testing decisions

  • Type 1 and 2 errors
  • Power

-Impact of study design on required sample size

  • Retrospective study design
  • Prospective study design
  • Unpaired design

-Alternatives to superiority hypothesis

  • Non-inferiority
  • Equivalence

Part 2: ROC Analysis in diagnostic medicine

This is the second lecture on statistical methods used in imaging studies, with a focus on Receiver Operating Characteristic (ROC) analysis in diagnostic medicine. We will use an example to motivate the need for ROC analysis. Sensitivity and specificity are commonly used to compare the accuracy of two modalities, but they have disadvantages: (1) conclusions may be different for them so it is not clear which modality has better performance; (2) requires dichotomizing non-binary modality results. ROC analysis graphically displays both sensitivity and specificity for all possible cutpoints. The area under the ROC curve, which ranges from 0.5 (poor discrimination) to 1 (perfect discrimination), is commonly used to summarize ROC curves. Approaches for comparing ROC curves will be presented along with advantages and disadvantages of using ROC analysis.

-Motivating Sample

-Problems with sensitivity, specificity

-Receiver operating characteristic curves

  • Sensitivity and specificity illustrated together
  • All possible cutpoints included

-Construction of an ROC curve

-Area under ROC curve (AUC)

  • Definition
  • Interpretation
  • Example

-Estimation of ROC curve and AUC

-Different ROC curve applications

-Comparing ROC curves

-ROC curve advantages and disadvantages

Part 3: Statistical prognostic/predictive modelling of quantitative imaging biomarkers (QIBs)

This is the second lecture on statistical methods used in imaging studies, with a focus on methods for statistical prognostic/predictive modeling of quantitative imaging biomarkers (QIBs). We will begin with the definitions of QIBs. We will then discuss survival curves and time-to-event analysis and how they are useful for assessing the performance of prognostics biomarkers. Studies can benefit from the use of statistical modeling so we will discuss when studies need statistical modeling, the basics of models, and a comparison of different types of modelling. A description of the Cox Proportional Hazards model will be provided along with interpretation of model results.

-Quantitative imaging biomarkers (QIBs)

  • Definition
  • Examples

-Prognostic Biomarker

  • Ideal
  • Example

-Survival curves

  • Definition
  • Estimation
  • Example

-Comparison of survival curves

-Statistical modeling

  • Motivation

-Modelling basics

  • Independent variable
  • Mathematical function
  • Dependent variable

-Cox proportional hazards model

  • Definition
  • Interpretation
  • Example

Acknowledgements

No acknowledgement found.

References

No reference found.
Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)