Statistics for the intensivist (3) ICU Fellowship Training Radboudumc
Comparison of means Single observed mean with hypothesized value Two means arising from paired data Two means from unpaired data Confidence intervals and t-tests (as long as certain assumptions are met)
Single observed mean with hypothesized value Admission albumin IC 23.3 ± 6.6 g/l (N = 23409) Normal mean value 40 g/l Is admission albumin for ICU patients really lower than in normal patients or is this difference based on coincidence? Null hypothesis states that there is no difference in albumin levels between ICU admission patients and normal people Calculate confidence interval (and perform a hypothesis test)
Single observed mean with hypothesized value Calculate the 95% confidence interval of the mean 23.3 ± 1.96 6.6/ 23409 = (23.22, 23.38) Albumin concentration in normal population is well outside this range How likely is this found difference if in reality there is no difference one sample t-test t = (sample mean - hypothesized mean)/sesample mean = (23.3-40)/0.08 = -208,75 Number of SE s that separates the sample mean from the hypothesized mean P < 0.0001
Comparison of two means arising from paired data What is the effect of fluid administration on renal perfusion in critically ill patients? Measurement of resistivity index (renal interlobar artery doppler) before and after volume expansion in 49 patients with acute circulatory failure Measurement of urine output three hours before and after FC Moussa MD. Crit Care 2015;19:250
Renal Resistive Index Measuring changes in renal perfusion A B Normal values < 0.70 RI = (A - B)/A Schnell D. Intensive Care Med 2012;38:1751-1760
1 100 0,9 90 Resistivity index 0,8 0,73 0,7 0,6 0,71 MAP (mmhg) 80 70 60 0,5 Before After 50 Before After 80 200 Pulse pressure (mmhg) 70 60 50 40 UP (ml/hr) 160 120 80 40 30 Before After 0 Before After Increase in urine output predicted by changes in RI but not by changes in systemic hemodynamics Moussa MD. Crit Care 2015;19:250
Comparison of two means arising from paired data Is the decrease in resistivity index from 0.73 to 0.71 after a FC a genuine effect or simply due to chance Null hypothesis states that there is no difference in RI after a FC The two sets of data come from the same patients and are thus not independent The paired t-test concentrates on the differences between the pairs of measurement rather than the measurements themselves
An example Null hypothesis: mean of differences in ScvO2 = 0 t-test compares observed mean of differences with 0 95% CI 6.8 ± 2.26 2.4 = (1.4, 12.2) t = (sample mean of differences - 0)/SEsample mean of differences = (6.8)/2.4 = 2.87 P = 0.02
Comparison of two means arising from unpaired data Effect of levosimendan vs nitroglycerin on diastolic function undergoing CABG (N = 30) 12 Levosimendan Nitroglycerin 11 E/e 10 9 9.5 ± 1.25 8 8 ± 0.69 7 6 Baseline After infusion Malik V. J Cardiovasc Pharmacol 2015
Comparison of two means arising from unpaired data Null hypothesis: there is no difference between the E/e after infusion of levosimendan or nitroglycerin Confidence intervals: Levosimendan (7.62, 8.38) and NTG (8.81, 10.19) t-test focusses on differences between means and calculates a SD and SE of the mean difference and incorporates different sample sizes If SE of mean difference is known 95% CI can be calculated Student t test: t = difference in sample means/se of difference in sample means P = 0.01
Assumptions and limitations for t-tests Normal distribution is essential (for the samples or the differences) Student unpaired t-test also SD s should be approximately equal Otherwise: non-parametric tests If you want to compare three groups: ANOVA
Non-parametric tests When the assumptions of normality are not met Require no or very little assumptions to be made about the data Sign test Wilcoxon signed rank test Wilcoxon rank sum or Mann-Withney test
Sign test Compare a single sample with hypothesized value (replaces one-sample or paired t-test) 10 8 6 4 2 0 0-3 6.01-9 12.01-15 18.01-21 24.01-27 Liu D. PloS ONE 2015;10:e0129450
Sign Observations of exactly 1 are dropped Null hypothesis states that procalcitonin cannot predict mortality How likely is it that you would find 16/16 studies with a positive effect of procalcitonin on mortality prediction if in fact procalcitonin has no effect?
Sign test P-values based on binomial distribution Determine the smalles number of either or - signs (in this case 0) Determine from table or computer Disadvantage: no effect estimate Inthis case highly unlikely that procalcitonin cannot predict mortality in ICU patients
Sign test in paired samples - - Smallest number = 2 For 10 observations P = 0.11 Remember Paired t-test p = 0.02
Wilcoxon signed rank test Accounts for the magnitude of the observations (in contrast to sign test which gives simple or -) 5 steps: state null hypothesis, rank all observations in increasing order of magnitude ignoring their sign, allocate a sign, calculate sum of all positive ranks and negative ranks and determine the smaller one, calculate appropriate p-value
Wilcoxon signed rank test R = 235678910 = 50 R- = 14 = 5 P-value from computer/table Remember Paired t-test p = 0.02
Mann-Whitney test Non-parametric alternative to the unpaired t-test (to compare two independent groups) 3 steps: rank all observations in increasing order of magnitude independent where they come from, add up the ranks in the smaller of the two groups, calculate p-value from table or computer
Mann-Whitney example Does a sedation protocol decreases the total amount of propofol? to have a significance of 0.05 S should be outside these numbers or computer P > 0.05
Advantages and disadvantages No or very limited assumptions about the format of the data - useful for dealing with outliers Simple to carry out by hand Useful in the analysis of ordered categorial data
Advantages and disadvantages Lack power as compared with more traditional approaches especially with small sample size Geared towards hypothesis testing rather than estimation of effect size
NVE (Vt/EAdi) during weaning with NAVA 12 patients with prolonged (> 4 D) MV - 10 ARDS and 2 COPD Failed SBT on PSV 7 - afterwards NAVA60%SBT Comparison of NVE during NAVA60%SBT versus NVE on first unsuccessful SBT and on the day of successful SBT Student s t-test and Wilcoxon s matched-pair signed-rank test for means and medians Rozé H. BJA 2013;111:955-960
Rozé H. BJA 2013;111:955-960