Four Step Data Analysis, Different Hypothesis Tests
Generally, sample statistics include: quantitative data:
  mean, variance, standard deviation, median, quartiles, range,....
  mean difference, ratio of medians
discrete data, failuretime data:
  proportion, percentage (depending on time)
  difference between proportions, numbers needed to treat, odds ratios, relative risks, hazard ratios,....
The current chapter will particularly focus on the discrete data and failuretime data. The quantitative data analyses have been covered in the Chap. 6. Discrete data can answer many questions in trials like those given underneath.
How large is the response rate How many patients have sideeffects?
How many patients were alive (after 5 years)?
Is the response rate under treatment A larger than under B?
Are there more “sideeffects” after than before treatment?
What is the optimal dose?
Study design: (a.o.)
trials, cohorts, casecontrol studies crosssectional vs followup measurements Data type: (a.o.)
quantities, binary, categorical, ordinal variables censored variables
The required data analysis is dependent on (1) the study design and (2) the type of data. Four steps are, often, mentioned to constitute a proper data analysis:
step 1 summarize the data
 calculate statistics
step 2 provide the reliability of the statistics
  standard error (se), confidence interval (ci) step 3 hypothesis testing
  pvalues, significance level step 4 regression analysis
  (causal) association, confounder correction, prediction, explained variation,....
The fourth step regression will be the subject of the Chap. 7, and will not be addressed here. The general situation with randomized controlled trials is, that they have representative random samples from a target population. The ultimate conclusion of a trial is very relevant to the sample, but much more to the target population of the trial, as explained the underneath graph.
This somewhat peculiar situation of trials explains much of the analysis steps taken.
1 sample 1 measurement 
2 samples 1 measurement 
>2 samples 1 measurement 

Quantitative 
one sample ttest/ Wileoxon test 
unpaired ttest / Mann Whitney test 
ANOVA, Kruskal Wallis test 
Discrete 
Zor ehisquared test 
Zor ehisquared test 
ehisquared test 
Censored 
(kaplanmeier) 
logrank test 
logrank test 
1 sample 2 measurements 
1 sample >2 measurements 
>1 samples >1 measurement 

Quantitative 
paired ttest / Wileoxon test 
mm ANOVA/ Friedman test 
mm ANOVA 
Discrete 
Mc Nemar test 
Cochran’s Q test 
r.e. logistic regression 
Censored 
stratified logrank test 
stratified logrank test 
fRailty models 
Above an overview of relevant tests for data analysis including those of discrete data analysis is given (ANOVA=analysis of variance, r.e.=random effects). Many hypothesis tests are possible, and each of them has its own place in the area of statistical data analysis. In this chapter the most relevant procedures will now be explained with examples from practice.