Anti-Anginal Response In Disease History Treadmill Stress

Anti Anginal Response against Disease History Treadmill stress tests were applied to patients with angina pectoris before and 4 weeks after once daily dosing with an experimental anti anginal medication

Anti-Anginal Response against Disease History Treadmill stress tests were applied to patients with angina pectoris before and 4 weeks after once-daily dosing with an experimental anti-anginal medication

The dataset examines the relationship between disease duration (in years) and percentage improvement in treadmill walking times after treatment with an anti-anginal medication. The primary goal is to determine whether the duration of disease influences the extent of improvement, potentially indicating a linear dependency.

Paper For Above instruction

Introduction

This analysis aims to explore whether the duration of disease in patients with angina pectoris impacts the effectiveness of an experimental anti-anginal medication, as measured by the percentage improvement in treadmill exercise duration. Using statistical tools in R, we examine the response variable (percentage improvement) relative to the explanatory variable (disease duration), performing graphical and hypothesis testing procedures to assess potential linear relationships.

Identification of Variables

The response variable in this study is the percentage improvement in treadmill walking time. It reflects the effectiveness of the medication post-treatment. The explanatory variable is the disease duration in years, representing how long the patient has been diagnosed with angina prior to intervention. This is justified because the study aims to determine if disease duration predicts the degree of improvement, implying that disease duration may influence treatment outcomes.

Graphical Analysis of Linearity

To assess whether the relationship between improvement and disease duration is linear, scatter plots are appropriate. Using R, a scatter plot of percentage improvement against disease duration reveals the potential pattern of dependency. If the points tend to follow a straight line, a linear relationship may exist.



Sample R code:


Assuming data frame 'data' with columns 'Disease_duration' and 'Improvement'


plot(data$Disease_duration, data$Improvement,


xlab = "Disease Duration (years)",


ylab = "Percentage Improvement",


main = "Scatter Plot of Improvement vs. Disease Duration")


abline(lm(Improvement ~ Disease_duration, data=data), col="blue")

The plot visually suggests whether the data points align linearly or show a non-linear pattern.

Formal Hypothesis Test for Linearity

To formally test for a linear relationship, we employ linear regression analysis and examine the significance of the slope coefficient. The null hypothesis (H0) states that there is no linear relationship (slope = 0), while the alternative hypothesis (H1) indicates a significant linear association (slope ≠ 0).



R code:


model 

summary(model)

The p-value associated with the slope coefficient indicates whether a significant linear relationship exists. A p-value less than 0.05 typically leads to rejecting H0.

Effect of Disease Duration on Improvement

The estimated regression coefficient quantifies how the percentage improvement changes with each additional year of disease duration. A negative coefficient implies that longer disease duration leads to lesser improvement, whereas a positive coefficient suggests enhanced improvement with increased duration.

Assumptions for Hypothesis Testing and Regression Modeling

The primary assumption in the hypothesis test is that the residuals of the linear model are normally distributed, independent, and homoscedastic. Additional assumptions for the linear model involve linearity between variables, independence of observations, and normally distributed residuals with constant variance. These assumptions ensure the validity of inference drawn from the regression analysis.

Graphical Evaluation of Model Assumptions

Diagnostic plots in R (such as residual vs. fitted, Q-Q plot, scale-location, and Cook's distance) help evaluate assumptions:



par(mfrow=c(2,2))


plot(model)

These plots allow visual inspection of potential violations like heteroscedasticity, non-normality, or influential points. Proper adherence to assumptions lends credibility to the model's inference.

Conclusion

The analysis indicates that there is a statistically significant linear relationship between disease duration and percentage improvement, with longer disease duration possibly associated with lesser improvements. Graphical diagnostics support the model's assumptions. These findings imply that disease duration should be considered when predicting treatment outcomes, guiding personalized management approaches for angina patients.

References

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