Question

The article "Spray Flu Vaccine May Work Better Than Injections for Tots" (San Luis Obispo Tribune, May 2,2006 ) described a study that compared flu vaccine administered by injection and flu vaccine administered as a nasal spray. Each of the 8000 children under the age of 5 that participated in the study received both a nasal spray and an injection, but only one was the real vaccine and the other was salt water. At the end of the flu season, it was determined that \(3.9 \%\) of the 4000 children receiving the real vaccine by nasal spray got sick with the flu and \(8.6 \%\) of the 4000 receiving the real vaccine by injection got sick with the flu. a. Why would the researchers give every child both a nasal spray and an injection? b. Use the given data to estimate the difference in the proportion of children who get sick with the flu after being vaccinated with an injection and the proportion of children who get sick with the flu after being vaccinated with the nasal spray using a \(99 \%\) confidence interval. Based on the confidence interval, would you conclude that the proportion of children who get the flu is different for the two vaccination methods?

Short answer

a) The researchers give every child both a nasal spray and an injection to eliminate biases and placebo effects. b) The 99% confidence interval is computed based on the difference in proportions and the standard error. If 0 does not fall within this interval, there is significant evidence at the 99% confidence level that the proportion of children who get sick is different for the two vaccination methods.

Step-by-step solution

Interpretation of Research Methodology

The researchers gave every child both a nasal spray and an injection to eliminate any bias that could occur from knowing which type of vaccination - either nasal spray or injection - a child received. This methodology, known as a 'blind' experiment, controls for placebo effects and ensures that any difference in outcomes can be attributed to the type of vaccine administered, not to preconceived notions or psychological effects.

Calculation of Proportions

First, calculate the proportion of children who got sick after receiving each type of vaccine. For the nasal spray, it's \(0.039 (or 3.9\% of 4000)\). For the injection, it's \(0.086 (or 8.6\% of 4000)\).

Estimation of Difference in Proportions

Next, subtract the proportion of children who got sick after receiving the nasal spray vaccine from the proportion of children who got sick after receiving the injection vaccine. This gives an estimated difference of \(0.086 - 0.039 = 0.047\).

Computation of Standard Error

The standard error for the difference in proportions is calculated using the formula \(\sqrt{\frac{p1*(1-p1)}{n1} + \frac{p2*(1-p2)}{n2}}\). Where \(p1 = 0.039\), \(n1 = 4000\), \(p2 = 0.086\), and \(n2 = 4000\).

Compute Confidence Interval

Based on the difference in proportions and the standard error, the 99% confidence interval is calculated by finding \(± Z \times SE\), where \(Z\) is the z-score associated with a 99% confidence level. The z-score for a 99% confidence level is about 2.58.

Interpretation of Results

Compare 0 to the computed 99% confidence interval to conclude whether the proportion of children who get the flu is different for the two vaccination methods. If 0 is not within the interval, then there is significant evidence that the two vaccination methods produce different results.

Key concepts

Research Methodology

Understanding the research methodology in studies involving medical treatments is crucial for interpreting the results accurately. In the vaccine study example, each child received both a nasal spray and an injection to maintain the integrity of the results. By using this approach, the researchers aimed to ensure that neither the participants nor the administrators knew which was the real vaccine and which was a placebo, a practice known as blinding.

Blinding is critical in eliminating various biases that could influence the outcome, such as the placebo effect or the health care provider's expectations influencing the behavior or reporting of symptoms. Research methodology that includes such rigorous techniques ensures that the results can be attributed solely to the efficacy of the vaccine rather than external factors.

Blind Experiment

A blind experiment is a powerful tool in clinical research. Blinding can happen at several levels, but the most common are single-blind and double-blind studies. In a single-blind experiment, the participant is unaware of what treatment they are receiving, which helps to prevent bias based on their expectations. In the study of flu vaccines, this approach was used to ensure that the children's or caregivers' responses were not influenced by knowing which vaccine was administered.

A double-blind experiment goes a step further by keeping both the participant and the researcher or physician administering the treatment unaware of which is the active treatment and which is the placebo. This method prevents both patients' and researchers' preconceptions from affecting the results.

Placebo Effects

The placebo effect is a fascinating phenomenon where an individual experiences real changes in health after receiving a treatment with no therapeutic value, like a sugar pill, saline injection, or, in our example, salt water. Placebos are used in clinical trials to act as a control group against which the actual treatment's effectiveness is measured. The placebo effect can result from a person's expectations of how the treatment should work, underscoring the mind's powerful role in physical health.

In the vaccine study, salt water was used as a placebo to ensure that any differences in flu rates could be attributed to the actual vaccines rather than psychological factors or the body's natural healing process. It helps researchers to determine whether the improvement in patients is due to the treatment itself and not because of the patients' belief in the treatment.

Proportion Calculation

Proportions play a vital role in statistics, particularly in epidemiological and clinical research. When calculating proportions, you're essentially looking to find what fraction of a whole is represented by a particular outcome. In our vaccine study, we looked at the proportion of children who got sick with flu after receiving each form of vaccination.

To calculate the proportion, one would divide the number of children who had the flu by the total number of children who received that vaccine. So, for the nasal spray, the proportion is \(0.039\) when converted from 3.9%, and for those receiving the injection, it's \(0.086\). These proportions are crucial for making comparisons and determining efficacy between the different vaccines.

Standard Error Computation

The standard error (SE) is a statistical term that measures the accuracy with which a sample distribution represents a population. When computing the standard error of the difference in proportions, it helps us understand the variability of that estimated difference. In the context of the flu vaccine example, the standard error was calculated using the formula \(\sqrt{\frac{p1*(1-p1)}{n1} + \frac{p2*(1-p2)}{n2}}\), where \(p1\) is the proportion of children who got sick with the nasal spray, \(n1\) is the number of children who received the nasal spray, \(p2\) is the proportion of children who got sick with the injection, and \(n2\) is the number of children who received the injection.

This standard error computation is then used to construct a confidence interval, giving us a range in which we are reasonably sure the true difference in proportions lies. We can say with 99% confidence that the true difference between the two vaccination methods falls within the calculated interval, provided that 0 is not within that interval.