1. On average, how much did HbA1c levels decreased at the 1-month, 3-months and 1-year cohorts?



The first step is to evaluate the amount of missing values per cohort in the data set, this will allow us to asses the strength of evidence visualized comparing HbA1c levels between postoperative cohorts (1-month, 3-months, 6-months, 1-year).

Variable Recorded Values Missing Values % Miss Values
Preop HbA1c 653 181 21.70
1-Month HbA1c 206 628 75.30
3-Month HbA1c 475 359 43.05
6-Month HbA1c 410 424 50.84
Year HbA1c 290 544 65.23


The initial visualization of the data shows outliers that are clinically incompatible, this dificults a cualitative evaluation of the boxplots.

Once outliers that make no sense clinically are eliminated (their values are changed to missing), an initial evaluation of their distribution is possible as it is shown in the following figure.

Are these subsets normally distributed? (Checking for assumptions of normality)

We start with quantile-quantile plots (Q-Q plots) to visually evaluate for normality in the data:

Winning trick: the closer datapoints line up with the line proposed by the Q-Q plot, the closer the data is to a normal distribution.

Shapiro-Wilk’s test for Normality

##        variables statistic      p_value
## 1    Preop HbA1c 0.8312335 1.101613e-25
## 2  HbA1c 1-month 0.8586827 1.770142e-12
## 3 HbA1c 3-months 0.8817955 2.204902e-18
## 4 HbA1c 6-months 0.8740162 1.371731e-17
## 5   HbA1c 1-year 0.8527173 6.367683e-16

The results show a p-value < 0.05 for all the variables which is interpreted as the distribution of all variables are significantly different than a normal distribution. This means that the subsets will have to be analyzed with non-parametric methods.

Evaluating for differences in means of groups

The following table shows the means, medians and standard deviations (SD) of the HbA1c levels at the specific post-operative cohort in time:
Variables mean_hba1c median SD
Preop HbA1c 6.14 5.8 1.13
HbA1c 1-month 5.93 5.7 0.93
HbA1c 3-months 5.63 5.5 0.73
HbA1c 6-months 5.56 5.4 0.69
HbA1c 1-year 5.50 5.3 0.79

Kruskal-Wallis Test

## 
##  Kruskal-Wallis rank sum test
## 
## data:  HbA1c_value by Group
## Kruskal-Wallis chi-squared = 188.85, df = 4, p-value < 2.2e-16

The result of the Kruskal-Wallis test shows a p-value < 0.0000000000000016, therefore it is concluded that there are significant differences between the treatment groups.

To be able to know the pairs of groups that are different a multiple pairwise-comparison test has to be implemented.

Pairwise Wilcoxon Test between groups

## 
##  Pairwise comparisons using Wilcoxon rank sum test 
## 
## data:  melted$HbA1c_value and melted$Group 
## 
##             hba1c_preop one_hba1c three_hba1c six_hba1c
## one_hba1c   0.0510      -         -           -        
## three_hba1c < 2e-16     8.1e-05   -           -        
## six_hba1c   < 2e-16     1.8e-07   0.0552      -        
## year_hba1c  < 2e-16     5.4e-11   2.0e-05     0.0051   
## 
## P value adjustment method: BH

The results of the multiple pairwise-comparison, according to the p-values, show statistical significant differences between the following variables:

  • hba1c_preop with:
    • three_hba1c
    • six_hba1c
    • year_hba1c
  • one_hba1c with:
    • three_hba1c
    • six_hba1c
    • year_hba1c
  • three_hba1c with:
    • year_hba1c
  • six_hba1c with:
    • year_hba1c