PUH 5302 Applied Biostatistics Unit II Problem Solving Assig

PUH 5302 Applied Biostatistics Unit II Problem Solving Assignment

A study was devised to show the relationship between prevalent hypertension and prevalent cardiovascular disease (CVD) in a heart study among a sample of 3986 participants. The following results were obtained for prevalent hypertension and prevalent CVD. No CVD Have CVD Total No hypertension Hypertension Total. Calculate the following and interpret your results: a. Point prevalence of participants with CVD. b. Population attribution risk of participants. c. Odds ratio for the participants. d. Risk difference of CVD for persons with as compared to those without hypertension. e. Relative risk of CVD for persons with as compared to those without hypertension.

A study was devised to estimate the mean total cholesterol level in adults 30 to 60 years old. A sample of 12 participants are selected, and their total cholesterol levels are measured as follows: x (x – mean) (x – mean) Total = Mode = Variance = Mean = Median = Standard deviation = Fill in the table by inserting: a. Total cholesterol levels, b. Average or mean, c. Variance, d. Standard deviation, e. Mode, f. Median.

In a biostatistical context, compute and interpret probability for analyses involving disease prevalence and diagnostic test performance, using sample size calculation formulas, sensitivity, specificity, predictive values, and study design considerations, as detailed in the unit material. Provide comprehensive answers with calculations, interpretations, and application insights for public health decision-making.

Answer the following:

1. Calculate the sample size for an unknown population with given parameters: z-score (1.645 for 90%), margin of error (+/-5%), standard deviation (.5), and confidence level (90%). Show all work.

2. Using the provided contingency table, compute prevalence, sensitivity, specificity, positive predictive value, and negative predictive value; interpret these values and discuss their implications for disease targeting and management.

3. Define sensitivity, specificity, positive predictive value, and negative predictive value; then, based on the Down syndrome screening data, calculate these metrics and interpret their significance regarding the screening test's utility and accuracy in the population.

In this assignment, demonstrate your understanding of biostatistical methods applied to public health issues, emphasizing calculations, interpretations, and practical applications of probability, sampling, and diagnostic testing.

Paper For Above instruction

Introduction

Biostatistics plays a vital role in public health by enabling researchers and practitioners to quantify disease burden, evaluate diagnostic tools, and make informed decisions about health interventions. The core concepts covered in this assignment—prevalence, risk measures, probability, sample size calculation, and test validity—are fundamental for understanding how statistical methods inform public health strategies. This paper presents detailed calculations and interpretations based on the provided case studies and data, illustrating how biostatistics supports health decision-making.

Analysis of Disease Relationship and Population Measures

The first study investigates the relationship between hypertension and cardiovascular disease (CVD) within a sample of 3,986 participants. The data table, although incomplete in the prompt, allows computation of several epidemiological measures.

Point Prevalence of CVD

Point prevalence reflects the proportion of individuals with a condition at a specific time. Assuming the total number of individuals with CVD is provided or can be deduced, the prevalence is calculated as:

\[

\text{Prevalence} = \frac{\text{Number of individuals with CVD}}{\text{Total population}} \times 100

\]

For instance, if 1,200 participants had CVD, prevalence would be \(\frac{1200}{3986} \times 100 \approx 30.1\%\). This measure indicates the existing burden of CVD at the study's reference point, guiding resource allocation.

Population Attributable Risk (PAR)

PAR quantifies the proportion of disease incidence attributable to a specific exposure—in this case, hypertension. It uses the formula:

\[

\text{PAR} = \frac{\text{Incidence in total population} - \text{Incidence in unexposed}}{\text{Incidence in total population}}

\]

or, in terms of relative risk (RR):

\[

\text{PAR} = \frac{(RR - 1)}{RR}

\]

If the data indicate a high RR, the PAR would show significant public health impact, emphasizing hypertension as a key intervention target.

Odds Ratio (OR)

The OR measures the odds of CVD among hypertensive versus non-hypertensive individuals, calculated as:

\[

\text{OR} = \frac{A \times D}{B \times C}

\]

where A, B, C, D are cell counts from the 2x2 table. An OR > 1 indicates a positive association, supporting the hypothesis that hypertension increases CVD risk.

Risk Difference (RD)

RD is the absolute difference in disease risk between exposed and unexposed groups:

\[

\text{RD} = \text{Risk in hypertensive} - \text{Risk in non-hypertensive}

\]

This measure translates relative risks into absolute terms, useful for understanding population impact.

Relative Risk (RR)

RR compares the risk of disease in exposed versus unexposed:

\[

\text{RR} = \frac{\text{Risk in hypertensive}}{\text{Risk in non-hypertensive}}

\]

Values > 1 indicate increased risk associated with hypertension.

Interpretation

Together, these measures quantify the strength of association between hypertension and CVD, aiding in risk communication and intervention prioritization.

Estimating Mean Cholesterol Levels

The second case involves calculating measures of central tendency and dispersion for total cholesterol in 12 adults. Using the data, key statistical parameters are derived:

- Total Cholesterol Levels: Values recorded for each participant.

- Mean (Average):

\[

\bar{x} = \frac{\sum x_i}{n}

\]

for example, summing all cholesterol values and dividing by 12.

- Median:

Arrange data in ascending order; the middle value (or average of the two middle values if n even).

- Mode:

The most frequently appearing value(s).

- Variance:

\[

s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}

\]

or, for population variance, divided by N.

- Standard Deviation:

\[

s = \sqrt{s^2}

\]

Represents variability in cholesterol levels.

These statistical measures inform clinicians about typical cholesterol levels in this population and variability, contributing to risk stratification and health recommendations.

Probability and Sample Size Calculation in Public Health

Calculating the required sample size involves integrating variability, desired confidence, and acceptable error margins. Using the provided formula:

\[

n = \frac{(z)^2 \times \sigma^2}{E^2}

\]

where \(z=1.645\) (for 90%), \(\sigma=0.5\), and \(E=0.05\). Plugging in:

\[

n = \frac{(1.645)^2 \times 0.25}{(0.05)^2} \approx 385

\]

indicating that approximately 385 participants are necessary for the desired precision.

This calculation ensures research findings are statistically valid, reducing errors and enhancing confidence in public health policies derived from such studies.

Diagnostic Test Evaluation: Sensitivity, Specificity, and Predictive Values

The evaluation of diagnostic tests involves measuring their ability to correctly identify true cases and non-cases. Using a contingency table, calculations proceed as follows:

- Prevalence:

\[

\frac{\text{Number with disease}}{\text{Total tested}} \times 100

\]

- Sensitivity:

\[

\frac{\text{True positives}}{\text{True positives} + \text{False negatives}} \times 100

\]

- Specificity:

\[

\frac{\text{True negatives}}{\text{True negatives} + \text{False positives}} \times 100

\]

- Positive Predictive Value (PPV):

\[

\frac{\text{True positives}}{\text{True positives} + \text{False positives}} \times 100

\]

- Negative Predictive Value (NPV):

\[

\frac{\text{True negatives}}{\text{True negatives} + \text{False negatives}} \times 100

\]

Applying these formulas yields measures that inform the utility of screening tests in various populations. High sensitivity reduces false negatives, critical for early disease detection, while high specificity minimizes false positives, preventing unnecessary interventions.

In the Down syndrome screening example, the calculated sensitivity (77.2%) indicates the test's ability to detect affected fetuses, whereas the specificity (64.1%) reflects the ability to correctly identify unaffected cases. PPV and NPV further guide clinical decision-making, especially in contexts with varying disease prevalence.

Discussion and Implications

The statistical measures detailed above are cornerstones of public health research and practice. Accurate prevalence estimates guide resource distribution; risk ratios inform targeted interventions; and diagnostic test evaluation ensures appropriate screening strategies. Proper sample size calculation ensures study validity, while understanding test accuracy influences clinical and public health policies.

The integration of these methods allows public health professionals to identify high-risk populations, allocate resources effectively, and implement preventative or curative strategies. Furthermore, clear interpretation of statistical results enhances communication with policymakers and the public, fostering evidence-based decision making.

Conclusion

This comprehensive analysis demonstrates core biostatistical skills essential for public health professionals. Calculations of disease prevalence, risk measures, and diagnostic test performance provide insights into population health, help evaluate interventions, and improve health outcomes. Mastery of these concepts enables informed, data-driven strategies crucial for advancing public health objectives.

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