Pruebas no parametricas, correlacion y regresion lineal

Introduction to Non-Parametric Statistical Tests

Overview of the Session

• The session begins with a focus on non-parametric statistical tests, following previous discussions on parametric tests like the Student's t-test and ANOVA.

• The instructor mentions that they will also cover two additional parametric tests that differ due to the absence of nominal variables.

Case Study Reading

• The class engages in reading a case study titled "Clinical Trial in Postpartum Depression," which involves Dr. David Wang's research on a new therapy for postpartum depression.

• Participants are encouraged to take notes on interesting terms as they read through the case details about the study involving 50 women assigned to an exercise program versus usual care.

Key Findings from Dr. Wang's Study

Results and Challenges

• Dr. Wang found that women who participated in the exercise program showed lower scores on the Hamilton Rating Scale for Depression compared to those receiving standard care.

• After submitting his manuscript, he received feedback indicating issues with his choice of statistical analysis, specifically using linear regression for data that may not meet parametric assumptions.

Concerns About Statistical Methods

• Dr. Wang expresses concerns about switching from parametric to non-parametric methods, fearing loss of efficiency and significance in results due to ranking data instead of using raw values.

• He contemplates how to control for age differences and whether he can change his analysis method at this stage of research.

Discussion on Statistical Analysis Approaches

Clinical Relevance and Data Categorization

• To enhance clinical relevance, categorizing responses based on a 50% reduction in Hamilton scores is suggested as a common approach accepted by medical communities.

• The importance of understanding outcomes when discussing statistics is emphasized, particularly regarding how different types of depression among participants complicate statistical design choices.

Parametric vs Non-parametric Tests

• The instructor outlines conditions under which parametric tests can be used: numerical outcomes must be normally distributed with equal variances across samples; otherwise, non-parametric tests should be considered due to their less strict requirements.

Understanding Non-parametric Tests

Types of Non-parametric Tests Covered

• The session introduces several non-parametric alternatives: Mann–Whitney U test (analogous to t-test), Wilcoxon signed-rank test (for paired samples), and Kruskal-Wallis test (for multiple groups). Each serves specific scenarios where traditional parametrics fail due to data distribution issues or sample size limitations.

Practical Application Example

• An example involving children treated with antibiotics versus symptomatic management for acute otitis media illustrates how ordinal scales are analyzed using rankings rather than means when conducting non-parametric tests like Mann–Whitney U test or Wilcoxon signed-rank test for related samples.

Chi-Squared Test Overview

Exploring Categorical Variables

• A discussion arises around comparing categorical variables using chi-squared tests since no parametric options exist for such comparisons; both independent treatment groups show improvement rates based on categorical responses (yes/no).

Conclusion and Importance

• Emphasis is placed on understanding when each type of statistical test should be applied based on variable types—categorical versus numerical—and ensuring proper methodology before analyzing data sets is crucial for valid conclusions in health sciences research contexts.

Understanding Statistical Tests: Chi-Squared and T-Tests

Importance of Comparing Proportions

• The essence of the chi-squared test is to compare proportions, especially when denominators differ. Standardization involves dividing responses by the total number of patients.

• While the T-test compares means, in this context, we focus on proportions to assess treatment effectiveness.

Calculating Effectiveness

• For example, with silver nitrate treatment, 14 out of 20 patients responded (70%), compared to only 35% for talc. This highlights a significant difference in response rates.

• The chi-squared test evaluates if this difference is statistically significant by comparing observed frequencies against expected frequencies under the null hypothesis.

Interpreting P-values

• A P-value less than 0.05 indicates rejection of the null hypothesis, suggesting a significant difference between groups.

• The null hypothesis posits no difference in clinical improvement between treatments; rejecting it implies one treatment is more effective.

Hypothesis Testing and Statistical Significance

Null vs. Alternative Hypotheses

• The null hypothesis states there are no differences between groups; the alternative suggests a significant difference exists.

• In this case, rejecting the null confirms that silver nitrate has a significantly better clinical response than talc.

Considerations for Chi-Squared Test

• It's crucial to have at least five observations per cell in contingency tables; otherwise, results may be unstable and require alternative tests like Fisher's exact test.

Practical Application: Conducting Chi-Squared Tests

Example Analysis Steps

• An example using NHFS data illustrates how to import datasets and perform statistical tests using software commands.

Assessing Differences Between Groups

• Questions arise about age differences between genders or weight differences related to ischemic heart disease—both can be analyzed using appropriate statistical tests like T-tests or chi-squared tests based on variable types.

Exploring Associations Between Variables

Investigating Health Conditions

• Analyzing cholesterol levels among diabetics versus non-diabetics shows significant differences that can be assessed through statistical testing.

Correlation Between Diabetes and Ischemic Heart Disease

• Tabulating diabetes status against ischemic heart disease prevalence reveals associations that warrant further investigation through chi-squared analysis.

Advanced Statistical Concepts: Regression and Correlation

Understanding Correlation Coefficients

• Correlation measures linear relationships between two continuous variables; Pearson's correlation assesses strength and directionality but does not imply causation.

Regression Analysis for Predictive Modeling

• Regression models help predict outcomes based on independent variables while accounting for confounding factors—essential for understanding complex health relationships.

Understanding Ventricular Function and Predictive Modeling

Introduction to Ventricular Function

• The main focus is on ventricular function measurement using continuous variables with a normal distribution, specifically mean arterial pressure as the independent variable.

Predictive Modeling in Cardiology

• A dataset of 10 patients is introduced, highlighting their systolic blood pressures and ejection fractions. The goal is to determine if blood pressure can predict ejection fraction.

• Reference is made to existing predictive models like cardiovascular risk indices, including the Framingham scale, which uses multiple variables to calculate risk scores.

Regression Analysis Basics

• Regression involves selecting an optimal line on a scatter plot for prediction purposes, utilizing a formula that includes constants and an independent variable. The intercept (B0) and slope (Beta1) are defined.

• The least squares method will be used to calculate these parameters in statistical software (Stata). Beta1 indicates the relationship between the independent variable (blood pressure) and the dependent variable (ejection fraction).

Error Measurement in Predictions

• Each patient's data may deviate from the predicted line due to random error; this deviation's significance lies in understanding whether Beta1 equals zero or not, indicating no association between variables.

Implementing Regression in Stata

• Instructions are provided for running regression analysis in Stata, where results yield coefficients for both intercept and slope based on input data regarding ejection fraction and blood pressure.

Example Calculation of Ejection Fraction

• An example calculation shows how to derive expected ejection fraction from given blood pressure values using derived coefficients from regression output. For instance, substituting a blood pressure of 120 yields an estimated ejection fraction of approximately 66.7%.

Multivariable Regression Models

• Discussion transitions into multivariable regression models that allow inclusion of confounding variables such as age or gender while quantifying their associations with outcomes like ejection fraction. This enhances predictive accuracy by adjusting for other factors affecting results.

Practical Applications: Data Analysis Examples

Correlation Exercises Using FFQ Database

• Transitioning into practical exercises with a food frequency questionnaire database involving 2143 patients; initial tasks include calculating descriptive statistics like average weight and BMI using commands like "summarize."

Scatter Plots and Correlation Coefficients

• A scatter plot is created between weight and BMI showing strong correlation due to BMI's dependence on weight calculations; further correlation tests reveal significant relationships between dietary iron intake and total iron levels among participants.

Exploring Exercise Impact on BMI

• An analysis investigates the correlation between hours of exercise performed by individuals against their BMI, revealing an inverse relationship where increased exercise correlates with lower BMI values—statistically significant despite low correlation strength.

Advanced Regression Techniques

Energy Intake vs Age Analysis

• Utilizing energy intake data from FFQ alongside age as predictors through linear regression analysis reveals insights about how energy consumption varies with age; interpretation focuses on understanding intercept values when age equals zero—often non-interpretable contextually but mathematically relevant nonetheless.

Hypothesis Testing within Regression Framework

• Hypothesis testing examines whether age significantly affects energy intake levels; findings indicate that changes in energy consumption correlate negatively with increasing age—a statistically significant result allowing rejection of null hypotheses regarding independence between these variables.

Conclusion: Key Takeaways

Summary Insights

• Emphasis placed on understanding linear regression fundamentals including coefficient interpretation, hypothesis testing relevance, model fitting techniques via statistical software.

• Future sessions planned to cover more complex topics such as multivariate regression analyses along with survival modeling techniques essential for comprehensive research methodologies.

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