Question

In: Statistics and Probability

Background The prevalence of peanut allergy among children in Western countries has doubled in the past...

Background
The prevalence of peanut allergy among children in Western countries has doubled in the past 10 years, and peanut allergy is becoming apparent in Africa and Asia. We evaluated strategies of peanut consumption and avoidance to determine which strategy is most effective in preventing the development of peanut allergy in infants at high risk for the allergy.
Methods
We randomly assigned 640 infants with severe eczema, egg allergy, or both to consume or avoid peanuts until 60 months of age. Participants, who were at least 4 months but younger than 11 months of age at randomization, were assigned to separate study cohorts on the basis of preexisting sensitivity to peanut extract, which was deter- mined with the use of a skin-prick test — one consisting of participants with no measurable wheal after testing and the other consisting of those with a wheal mea- suring 1 to 4 mm in diameter. The primary outcome, which was assessed indepen- dently in each cohort, was the proportion of participants with peanut allergy at 60 months of age.
Results
Among the 530 infants in the intention-to-treat population who initially had nega- tive results on the skin-prick test, the prevalence of peanut allergy at 60 months of age was 13.7% in the avoidance group and 1.9% in the consumption group (P<0.001). Among the 98 participants in the intention-to-treat population who initially had positive test results, the prevalence of peanut allergy was 35.3% in the avoidance group and 10.6% in the consumption group (P=0.004). There was no significant between-group difference in the incidence of serious adverse events. Increases in levels of peanut-specific IgG4 antibody occurred predominantly in the consumption group; a greater percentage of participants in the avoidance group had elevated titers of peanut-specific IgE antibody. A larger wheal on the skin-prick test and a lower ratio of peanut-specific IgG4:IgE were associated with peanut allergy.
Conclusions
The early introduction of peanuts significantly decreased the frequency of the devel- opment of peanut allergy among children at high risk for this allergy and modulated immune responses to peanuts.

a) What is the research question that these investigators are trying to answer?

b) Identify the treatment and response variable.

c) Was this a controlled experiment or an observational study? Explain.

d) What is the answer to the research question?

e) Is the conclusion appropriate for the methods used to collect data? (Can the authors infer causality?)

f) To what population do the conclusions apply?

g) Do the p-values suggest that introducing peanuts at an earlier age was effective in reducing peanut allergies? (Hint: What does the size of this p-value indicate?)

Solutions

Expert Solution

a) The researchers are trying to identify a strategy that would decrease the prevalence of peanut allergy in infants. For this, they are using a strategy of either giving peanuts or not giving peanuts in the early infancy between 8 and 11 months. Hence they are trying to answer whether giving an early peanut rich diet can decrease the prevalence of peanut allergy in the infants.

b) The treatment variable is an explanatory variable. It determines the treatment options provided in a given study. Here the treatment options are whether to have a peanut-rich diet or not.

The response variable is the one that is measured as a result of varying the explanatory or the treatment variable. Hence the response variable here is the prevalence of peanut allergy.

c) The subjects were assigned to groups in a randomized fashion. The groups weren't inherent based on some pre-existing traits. And hence whether a certain subject would receive peanut-diet or not was randomized. Hence this is an instance of a randomized study with appropriate controls. Therefore it is a controlled experiment and not an observational study.

d) The experiment was performed as mentioned in the question and the prevalence of peanut-allergy was assessed in the individuals based on whether they were treated with a peanut-rich diet or not. And as can be seen, there was a significant decrease in the prevalence of peanut allergy when the subjects were treated with a peanut-rich diet. This was observed irrespective of whether the infants had tested positive or negative for the skin-prick test.

Thus, the conclusion based on these results is that irrespective of their prior condition, if the infants are provided with a peanut-rich diet in the period between 4 and 11 months, their chance of having peanut allergy decreases.

e) The experiment was designed in a controlled fashion. This is not merely an observational study. Hence there is causality that can be inferred from here. And hence the results are reliable.

f) The population from which the children were selected isn't mentioned here. However, all of these are infants with either eczema or egg allergy or both. Hence the results apply to the infants who have these conditions.

g) The p-value is a measure of the probability that the results obtained are due to chance. Here, in both the cases (whether the infants were positive or negative to the skin prick test), the p-values for the prevalence of peanut allergy shows a value less than 0.05. This value is for the difference in the prevalence with or without treatment a peanut-rich diet. Hence, the conclusion drawn that the introduction of peanuts at an earlier age is effective in reducing peanut allergies is statistically significant. This is what the p-value indicates. That there is less than 5% chance of the resuls being due to random chance event.


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