Simple and multiple linear regression: sample size considerations.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• The "two subjects per variable" (2SPV) rule is a common heuristic for determining sample size in regression analyses.
• However, this rule may not adequately address the distinct needs of different research applications.
• Regression models are utilized in diverse fields, including etiological research and clinical practice.

Purpose of the Study:

• To critically evaluate the 2SPV rule of thumb for sample size determination in linear regression.
• To differentiate sample size considerations for etiological research versus clinical practice applications of regression.
• To propose more appropriate sample size guidelines based on established statistical principles.

Main Methods:

• Analysis of established closed-form variance formulae underlying standard errors in multiple linear regression.
• Rearrangement of these formulae to derive intuitive sample size considerations.
• Distinction between sample size requirements for etiological research (focus on coefficients) and clinical practice (focus on predicted values).

Main Results:

• The 2SPV rule is inadequate for both major uses of regression models discussed.
• Etiological research, focusing on regression coefficients, requires different sample size considerations than clinical practice.
• Clinical practice, focusing on profile-specific mean outcome levels, also has distinct sample size needs.
• Intuitive sample size considerations can be derived from underlying variance formulae for both research types.

Conclusions:

• The 2SPV rule is an oversimplification and should not be universally applied to regression sample size calculations.
• Distinct research goals in etiological studies and clinical practice necessitate tailored sample size approaches.
• Established statistical formulas provide a basis for developing more accurate and intuitive sample size guidelines for regression analyses.