22 November 2020

Introduction

Two students requested help to set up their research. The research is part of their Orthopedic training. For this research, the effect is to be investigated of a treatment method.

An example hypothesis.
H0: The decompression method does not have an effect compared to the placebo treatment.
H1: There is a significant relation between the decompression therapy and the cure-rates of patients.

Trial setup I

case control

  • A sample-size of n subjects
  • Two groups (real treatment and placebo treatment)
  • Measurement of effect

Method

case control

Subject meeting requirements received:

  • Manual decompression treatment
  • Manual placebo treatment

Results I

## # A tibble: 12 x 2
##    Treatment  Outcome  
##    <chr>      <chr>    
##  1 decompress Cured    
##  2 placebo    Cured    
##  3 placebo    Not cured
##  4 placebo    Cured    
##  5 placebo    Not cured
##  6 placebo    Cured    
##  7 decompress Cured    
##  8 placebo    Not cured
##  9 decompress Cured    
## 10 placebo    Not cured
## 11 placebo    Not cured
## 12 placebo    Cured

Results II

Contingency table showing how many subjects were cured after receiving different treatments.
Treatment Placebo Total
Outcome? Cured 28 48 76
Not cured 10 114 124
Total 38 162 200

Results III

Pearson’s Chi-square test: \(\chi^{2} = \sum \frac{(observed_{ij} - model_{ij})^{2}}{model_{ij}}\)

contingency table

Results IV

contingency table

df p_0.05 p_0.01
1 3.84 6.63
2 5.99 9.21
3 7.81 11.34
4 9.49 13.28
5 11.07 15.09

Conclusion

The value of \(\chi^{2}\) was 25.36,
degree of freedom is one,
significant at p < 0.001.

The H0 is rejected.

There was as a significant association between the type of treatment and whether or not the patient was cured.

Discussion

  • Cure might not be TRUE or FALSE, but more like on a scale,
  • Maybe bias for gender, BMI, age, etc.