Biostats homework

Question

3. A study estimates that the rate of preventable Adverse Drug Events (ADEs) in hospital is 35%. Preventable ADEs typically result from inappropriate care or medication errors, such as errors in commission and omission. In a hospital, 5 randomly selected patients reported experiencing an ADE. Let X represent the number of preventable ADE, i.e., X ~ b(5, 0.35)

 

a. Calculate the probability of preventable ADEs of the five patients and present them in tabular form as we did in class; (Hint: There are 6 possible outcomes.)

b. Present the probability distribution of preventable ADEs in a bar-like graph.

Answer 1

To calculate the probability of preventable Adverse Drug Events (ADEs) for the five patients, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

1. P(X = k) is the probability of exactly k preventable ADEs.
2. n is the total number of trials (5 patients in this case).
3. k is the number of successful trials (the number of preventable ADEs).
4. p is the probability of a single success (the probability of a preventable ADE).

In this case, n = 5, and p = 0.35. You want to find the probabilities for k from 0 to 5.

Here are the probabilities in tabular form:

--------------------------------

| k | P(X = k) |

--------------------------------

| 0 | 0.1785 |

| 1 | 0.3087 |

| 2 | 0.2670 |

| 3 | 0.1234 |

| 4 | 0.0213 |

| 5 | 0.0011 |

--------------------------------

To present the probability distribution of preventable ADEs in a bar-like graph, you can create a bar chart where the x-axis represents the number of preventable ADEs (k) and the y-axis represents the corresponding probabilities. Here's an example of how you can plot this in R:

# Probability distribution data

k_values <- 0:5

probabilities <- dbinom(k_values, size = 5, prob = 0.35)

# Create a bar chart

barplot(probabilities, names.arg = k_values, xlab = "Number of Preventable ADEs", ylab = "Probability", main = "Probability Distribution of Preventable ADEs")