https://file.aiquickdraw.com/mathbot/file/1726537282698t17jla07.jpg

### 1. **Study Design:**
The study described in the image appears to be a **cohort study**. This is because a group of individuals was followed, and the exposure to a risk factor (hepatitis B viral infection, measured by HBsAg positivity) was observed, along with the outcome (liver cancer). Participants were classified into exposed (HBsAg positive) and non-exposed (HBsAg negative) groups, and the incidence of liver cancer was tracked in each group.

### 2. **Measure of Association (Risk Ratio):**
To calculate the risk ratio (relative risk, RR), we use the following formula:

\[
RR = \frac{\text{Risk in exposed group}}{\text{Risk in non-exposed group}}
\]

- **Risk in the exposed group (HBsAg positive):**
  \[
  \text{Risk} = \frac{152}{3454} = 0.044
  \]

- **Risk in the non-exposed group (HBsAg negative):**
  \[
  \text{Risk} = \frac{9}{19253} = 0.00047
  \]

Now, the risk ratio:
\[
RR = \frac{0.044}{0.00047} = 93.62
\]

Thus, the relative risk (RR) is **93.62**, indicating that those who are HBsAg positive are about 93 times more likely to develop liver cancer compared to those who are HBsAg negative.

For the **95% Confidence Interval (CI)**, we need further statistical details (like standard error or variance), but it is generally calculated using statistical software for this type of epidemiological study.

### 3. **Hypotheses:**

- **Null Hypothesis (H₀):** Hepatitis B viral infection (HBsAg positivity) does not increase the risk of liver cancer (i.e., RR = 1).
- **Alternative Hypothesis (H₁):** Hepatitis B viral infection increases the risk of liver cancer (i.e., RR > 1).

Given the risk ratio of 93.62, the result strongly suggests an association between HBV infection and liver cancer. This indicates that **HBV is likely a causal factor** for liver cancer, especially if the 95% confidence interval excludes 1.

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Do you want more details on any of the calculations or concepts?

### 5 Related Questions:
1. How do you interpret a risk ratio of greater than 1 in epidemiological studies?
2. What other study designs could be used to investigate the relationship between HBV and liver cancer?
3. How can confounding factors affect the results of a cohort study?
4. How would you compute a 95% confidence interval for the relative risk?
5. What are the key differences between a cohort study and a case-control study?

### Tip:
Always ensure to assess potential confounders in cohort studies, as they may influence the observed association between the exposure and the outcome.

Dr. R.P. Beasley and his colleagues are interested in the association of hepatitis B viral infection (HBV) and liver cancer in Taiwan. What type of study design is described? Calculate the appropriate measure of association for this study and state hypotheses. Does HBV cause liver cancer?

This page discusses a cohort study analyzing the relationship between hepatitis B infection (HBsAg) and liver cancer in Taiwan. It calculates the risk ratio (RR = 93.62) and explores whether HBV infection increases the risk of liver cancer.

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