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A screening program for neuroblastoma (a type of cancer) was undertaken in Germany among children born between November \(1,1993,\) and June \(30,2000,\) who were 9 to 18 months of age between May 1995 and April 2000 [6]. A total of 1,475,773 children participated in the screening program, of whom 204 were diagnosed between 12 and 60 months of age. The researchers expected the incidence rate of neuroblastoma to be 7.3 per 100,000 children during this period in the absence of screening. Provide a \(95 \%\) Cl for the incidence rate of neuroblastoma in the screened population. Express the \(95 \%\) Cl as \(\left(p_{1}, p_{2}\right),\) where \(p_{1}\) and \(p_{2}\) are in the units of number of cases per 100,000 children. Is \(p_{0}(7.3 \text { cases per } 100,000\) children) in this interval?

Short Answer

Expert verified
The 95% CI is (7.82, 19.82) cases per 100,000 children; 7.3 is not in this interval.

Step by step solution

01

Calculate the Observed Incidence Rate

First, we need to determine the incidence rate of neuroblastoma in the screened population. The formula to calculate incidence rate is given by \( \text{Incidence Rate} = \frac{\text{Number of Cases}}{\text{Population at Risk}} \times 100,000 \). Here, the number of cases \( = 204 \), and the population at risk \( = 1,475,773 \). Thus, \( \text{Incidence Rate} = \frac{204}{1,475,773} \times 100,000 \approx 13.82 \) cases per 100,000 children.
02

Determine Variance and Standard Error

Next, we calculate the variance of the observed incidence rate using the formula: \( \text{Variance} = \frac{\text{Incidence Rate}}{\text{Population at Risk}} \times \left(\frac{100,000}{100,000}\right)^2 = \frac{13.82}{1,475,773} \times 10^{10} \approx 9.36 \). The standard error is the square root of the variance: \( \text{Standard Error} = \sqrt{9.36} \approx 3.06 \).
03

Calculate 95% Confidence Interval

Using the observed incidence rate and standard error, calculate the 95% confidence interval. The confidence interval is \( \text{CI} = \text{Incidence Rate} \pm 1.96 \times \text{Standard Error} \). This equates to \( 13.82 \pm 1.96 \times 3.06 \approx (7.82, 19.82) \).
04

Compare Expected Rate with Confidence Interval

To check if the expected incidence rate (\(7.3\) cases per 100,000 children) is within this confidence interval, we look at our interval: \((7.82, 19.82)\). Since \(7.3\) is less than \(7.82\), it is not within this interval.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Incidence Rate
The incidence rate is a key concept in biostatistics that helps us measure the frequency at which a disease occurs in a particular population.
It is typically expressed as the number of new cases per a specific number of individuals, often per 100,000 people, which helps in comparing rates across different populations or time periods.
To calculate the incidence rate, you'll use the formula:
  • \( \text{Incidence Rate} = \frac{\text{Number of New Cases}}{\text{Population at Risk}} \times 100,000 \)
In our example, we had 204 cases of neuroblastoma among 1,475,773 children, resulting in an incidence rate of approximately 13.82 cases per 100,000 children.
Understanding incidence rate is crucial for public health planning as it offers insights into how widespread a disease is and helps in allocating resources efficiently.It provides a benchmark for evaluating the effectiveness of interventions like cancer screenings, as it establishes the expected versus observed occurrences of a disease.
Exploring Confidence Intervals
Confidence intervals provide a range for an estimate, which allows us to assess the precision and reliability of that estimate. In biostatistics, it is common to use a 95% confidence interval, which gives a range that, under repeated sampling, contains the true parameter in 95% of the cases.
For our incidence rate calculation, the confidence interval gives us an idea of the reliability of the incidence rate estimate.To calculate this interval, you use the formula:
  • \( \text{CI} = \text{Incidence Rate} \pm 1.96 \times \text{Standard Error} \)
Where 1.96 is the z-value for a 95% confidence level and the standard error measures the variation of the incidence rate estimate. The result, (7.82, 19.82), tells us we can be 95% confident the true incidence rate falls within this range.
It's important as it helps us determine if the observed rate significantly differs from an expected rate, in this case, 7.3 per 100,000. In the example, since 7.3 is not within the interval, it implies the observed rate is significantly different from what was expected without screening.
Significance of Cancer Screening
Cancer screening is a preventive measure to detect cancer early before symptoms appear.
Screening aims to reduce the incidence and mortality of cancer by identifying cases that might otherwise go unnoticed until later stages.
In our example of neuroblastoma screening, the program aimed to examine how many more cases were identified through proactive screening in children. The benefit of cancer screening includes:
  • Early detection and treatment, which can improve outcomes and survival rates.
  • Reduction in cancer mortality by catching the disease before it progresses.
  • Provision of data to better understand the disease's prevalence and occurrence.
However, there could also be considerations such as false positives, costs associated with screening, and the psychological impact on participants.
It’s necessary to weigh these factors against the screening's potential benefits to inform public health policy and individual decisions. For instance, the increase in the incidence rate from 7.3 to 13.82 per 100,000 children in our example may inform decisions about continuing or modifying such programs.

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