Exercise 1.1 (p. 11)

Migraine and acupuncture, Part I.

A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 89 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 46 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. 

library(kableExtra)

group <- c('treatment', 'control', 'total')
yes <- c(10, 2, 12)
no <- c(33, 44, 77)
col_total <- c(43, 46, 89)

pain_free <- data.frame(group = group, yes = yes, no = no, total = col_total)

# HTML table
kbl(pain_free, caption = "Migraine patients: pain free 24 hours after treatment") %>%
  kable_styling(bootstrap_options = "striped",
                full_width = F)
Migraine patients: pain free 24 hours after treatment
group yes no total
treatment 10 33 43
control 2 44 46
total 12 77 89
  1. What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture?

We take the number of pain free treatment patients (row: treatment, column: yes) and divide it by the total number of patients in the treatment group (row: treatment, column: total). The percentage (23.25%) is shown below. 

pf_treatment = 10 / 43
pf_treatment
## [1] 0.2325581
  1. What percent were pain free in the control group?

We take the number of pain free control patients (row: control, column: yes) and divide it by the total number of patients in the treatment group (row: control, column: total). The percentage (4.35%) is shown below. 

pf_control = 2 / 46
pf_control
## [1] 0.04347826
  1. In which group did a higher percent of patients become pain free 24 hours after receiving acupuncture?

The treatment group.

pf_treatment > pf_control
## [1] TRUE
  1. Your findings so far might suggest that acupuncture is an effective treatment for migraines for all people who suffer from migraines. However this is not the only possible conclusion that can be drawn based on your findings so far. What is one other possible explanation for the observed difference between the percentages of patients that are pain free 24 hours after receiving acupuncture in the two groups?

Random error / chance and the limited sample size (< 100 total patients) could have played a role in the difference in percentages. For example, maybe the treatment group was treated by an experienced acupuncture practitioner and the control group was treated by an inexperienced acupuncture practitioner … and thus the control group was actually irritated (rather than held stable) by its acupuncture treatment. While early findings certainly point toward acupuncture as an effective treatment for patients who suffer from migraines, more data would be required to rule out the possibility of random error / chance and draw a more convincing conclusion.