Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The...

Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The format is in Table 13.49. Three separate two-period cross-over studies were performed, based on different groups of subjects. Study 1 compared 0.625 mg estrogen with placebo. Study 2 compared 1.25 mg estrogen with placebo. Study 3 compared $1.25 \mathrm{mg}$ estrogen with 0.625 mg estrogen. Subjects received treatment for 4 weeks in each active-treatment period; a 2 -week washout period separated the two active-treatment periods. Suppose we are planning a new study similar in design to study $1 .$ How many participants do we need to study to detect an underlying 3 -mm Hg treatment effect for SBP with 80\% power assuming there is no carry-over effect and we perform a two-sided test with $\alpha=.05$ ?

Refer to Data Set ESTROGEN.DAT at www.cengagebrain .com. The format is in Table 13.49.
Three separate two-period cross-over studies were performed, based on different groups of subjects. Study 1 compared 0.625 mg estrogen with placebo. Study 2 compared 1.25 mg estrogen with placebo. Study 3 compared $1.25 \mathrm{mg}$ estrogen with 0.625 mg estrogen. Subjects received treatment for 4 weeks in each active-treatment period; a 2 -week washout period separated the two active-treatment periods.
Suppose we are planning a new study similar in design to study $1 .$ How many participants do we need to study to detect an underlying 3 -mm Hg treatment effect for SBP with 80\% power assuming there is no carry-over effect and we perform a two-sided test with $\alpha=.05$ ?

Key Concepts

Type I Error (Alpha Level) and Two-Sided Test

The Type I error rate, or alpha level, defines the threshold for statistical significance, determining the probability of falsely rejecting the null hypothesis when it is actually true. A two-sided test is used when changes in either direction (increase or decrease) are considered important, and the alpha level is split between the two tails of the distribution.

Sample Size Estimation

Sample size estimation involves calculating the number of participants needed to achieve a desired level of power for detecting a specified treatment effect, given a particular alpha level. This calculation takes into account the effect size, variability in the data, and assumptions about the study design, such as the absence of carry-over effects in a crossover study.

Treatment Effect (Effect Size)

The treatment effect, or effect size, represents the magnitude of difference expected between different treatments. It is a crucial parameter in study design as it directly influences the sample size needed to detect a statistically significant difference between treatment conditions.

Statistical Power

Statistical power is the probability that a study will detect a true effect when one exists. Typically, power is set at a certain level (for example, 80%), ensuring that the study is sufficiently sensitive to identify a clinically meaningful difference if it is present.

Washout Period

A washout period is the time interval between administrations of different treatments in a crossover study. Its purpose is to allow any effects of the previous treatment to dissipate before the next treatment begins, thereby minimizing the risk of carry-over effects that could confound the results.

Crossover Study Design

A crossover study design is a type of clinical trial where each participant receives multiple interventions sequentially, with a period of time between treatments. This design allows subjects to serve as their own controls, which can increase the efficiency of the study and reduce variability due to inter-subject differences.

Carry-over Effect

A carry-over effect occurs when the effects of a treatment persist into subsequent treatment periods in a crossover study. Minimizing or assuming no carry-over effects is essential to correctly attribute observed outcomes to the current treatment rather than lingering effects from earlier treatments.

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