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## CHAPTER OBJECTIVES

• Identify and describe situations where a research design is not amenable to bivariate statistical analysis

• Define and describe the causes (i.e., confounders, omitted variables, mediators, effect modifiers) and consequences (i.e., bias or inefficiency) of inappropriately using bivariate statistical analysis

• Explain how linear regression is commonly used in the drug literature to account for these causes and consequences

• Describe and appropriately interpret the coefficient estimates and predictions produced by linear regression

• Describe how the coefficient estimates and predictions produced by linear regression, when properly interpreted, can be used to evaluate a research hypothesis

## KEY TERMINOLOGY

• Bayesian regression analysis

• Biased

• Bivariate linear regression

• Coefficient estimates

• Confounder

• Confounding effect

• Credible interval

• Dummy variables

• Effect modification

• Effect modifier

• Equal-tail credible interval

• Highest posterior density (HPD) credible interval

• Inefficient

• Interaction

• Linear regression

• Mediating effect

• Mediator

• Moderator

• Moderator effect

• Multiple linear regression

• Omitted variable

• Ordinary least squares (OLS)

• Residual

• R-squared (R2)

• Simple linear regression

• Standardized coefficients

• Unstandardized coefficients

## INTRODUCTION

In an ideal experimental setting, a researcher has complete control over study design and implementation. This complete control over the experiment allows the researcher to anticipate and account for potential sources of bias that might affect the outcome of the experiment. Once all major sources of bias have been identified and accounted for, the remaining sources of error can be adjusted for in a traditional randomized controlled trial (RCT). These can include minor variability in laboratory methods and measurement errors in the resulting data. Random sampling methodologies, as well as the random assignment of patients to treatment and control groups, are sufficient to ensure that these minor differences “average out” across the groups and do not bias or otherwise influence the results of the experiment. As a result, experimental data can be used to statistically test the researcher’s null hypothesis in a fairly straightforward manner.

Unfortunately, in many practical settings the researcher does not have full control over the design of a study. For example, many types of observational studies use secondary data such as administrative claims previously collected by third party payers for nonresearch purposes.1 Similarly, in certain types of clinical studies, ethical considerations prohibit researchers from employing randomization or conducting experiments.2 Third, some research must be collected through survey techniques, where study participants may not be willing or able to respond to all questions posed by a researcher.3 Without the ability to control the study design to adjust for possible biases inherent in these designs, it is difficult to argue that the results add anything substantial to the current states of knowledge and clinical practice. This is problematic, given the wide array of topics and issues in clinical and administrative pharmacy practice that can only be investigated using observational study designs.

The approach used by most clinical and academic researchers in these instances is to apply ...

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