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Understanding Study Design & Statistics
Dr Malachy O. Columb FRCA, FFICM
University Hospital of South ManchesterNWRAG Workshop, Bolton, May 2015
COIs: Interesting Confllicts!
Editorial Board Roles: European Journal of Anaesthesiology British Journal of Anaesthesia International Journal of Obstetric
Anesthesia
Manuscript Types
(7) Meta-analysis & systematic reviews (6) Original research – PDBRCT (5) Original research – other RCT (4) Original research – observational (3) Original research – retrospective (2) Narrative reviews – including editorials (1) Case reports, abstracts & letters
Manuscript Types
(7) Original research – PDBRCT (6) Original research – other RCT (5) Original research – observational (4) Original research – retrospective (3) Meta-analysis & systematic reviews (2) Narrative reviews – including
editorials (1) Case reports, abstracts & letters
Statistics: Definition
…the discipline concerned with the treatment of numerical data derived from groups of individuals…
Data
…are always plural…
‘Datum’ is the singular…
Types of Data
Numerical – continuous & discrete Categorical – binary, nominal, ordinal
Hypotheses Null hypothesis (HO) Alternative hypothesis (HA) P value and 95% confidence interval Two-sided by convention One-sided are rarely appropriate Equivalence, Non-inferiority, Superiority
(Margins) Inequality is the usual HA
Potencies and probabilities: One-sided P values suggest a one-sided story! Columb MO, Polley LS. Anesthesia & Analgesia 2001;92:278-9
Controlling Bias - Design
Prospective > Retrospective Double Blind > Single Blind > Unblinded Randomised Controlled Trial >
Unrandomised PDBRCT > Propensity Score Matching! PROBE (Single Blind)
Sample Size
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
Sample size
Minimum difference that is (clinically) important
Defines primary outcome! Multiple comparisons!
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
Estimate of SD
Published research Pilot data Empirical approach 1/5th – ‘one fifth’ of the range
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
One-Fifth Range
4 SD = 95.4% of values 6 SD = 99.7% of values Take 1/5th range to approximate SD 20% of the range
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
Standardised Difference
Difference / SD
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
Standardised Difference = 1.0Power and sample size estimation Armitage & Berry pp 195-202
Sample size estimate for comparison of 2 equal groups1 minimum difference to be significant1 SD
0.05 type 1 error rate, P value0.8 power
1.959964 Z 2 alpha 2 sided0.841621 Z 2 beta 1 sided
18 = minimum n for each group 20 = nonparametric
Nonparametric Adjustment
Add 16% more subjects per group!
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
Sample Size - Proportions
Power analysis and sample size calculations. Columb MO, Stevens A. Current Anaesthesia & Critical Care 2008; 19: 12-4.
Standardised Difference = 1.0Sample size estimate for comparison of 2 proportions
0.75 proportion 10.25 proportion 20.05 type 1 error rate, P value0.8 power
1.959964 Z 2 alpha 2 sided0.841621 Z 2 beta 1 sided
0.5 pooled proportion
14 = minimum n per group for uncorrected Chi square test18 = Fleiss continuity correction, minimum n per group
Descriptive Statistics
Sample Mean (SD) – 68% of data Median [interquartiles, range] Count/frequency
Inferential Statistics - Precision Population estimates; precision Differences in means, medians,
proportions Mean or mean difference Sampling theory!
Population(variable X)
Distribution of sample means(variable )
Population of means(variable )
µ
µ
Sample 1 Sample jSample 3Sample 2x1,x2.....xn x1,x2.....xn x1,x2.....xn x1,x2.....xn
1 2 3 j
......... .....
Randomization
x
100 random samples of size 4
100 random samples of size 250
100 random samples of size 50
100 random samples of size 20
Inferential Statistics - Precision SD of sampled means is the SE of mean SE mean = SD / n SEM = 68%CI, (precision) SEM x 1.96 = 95%CI (precision) Test statistic = difference / SE difference P value
Significance P value – ‘probability of the observed
difference or greater assuming the null hypothesis’
Type I or alpha error <0.05; false +ve Type II or beta error <0.20; false -ve Multiple comparisons - Bonferroni correction Corrections to 95% CI of difference
Group TestsGroups Parametric Parametric
repeated Nonparametric Nonparametric
repeated Proportions
1 One sample t
One sample t
Wilcoxon signed rank
Wilcoxon signed rank
Binomial
2 Unpaired t Paired t Mann-Whitney U
Wilcoxon matched pairs
Chi square or Fisher’s exact
>2 ANOVA Repeated measures ANOVA
Kruskal-Wallis
Friedman’s Chi square or expanded Fisher
Statistical Analyses
Correlation – Pearson, Spearman, intraclass Regression – linear, logistic, probit, survival Diagnostics – sensitivity, specificity, ROC
curves Reference intervals – normal range Agreement – kappa, Bland-Altman plots
Transformations
Table. Some useful transformations
Types of data Transformations
Positive skew, increasing variance Logarithmic = ln x, log10 x
Negative skew, decreasing variance Square power = x2
Count; Poisson distribution Square root =x
Time; survival data Inverse = 1/x
Proportion; p, Binomial distribution Logit = ln (p/1-p) Arcsin = Arcsinp
Probit = Cumulative Normal Deviate
Time-to-Event: Log Transformation
Analyses for RCT Per-Protocol (PP)
Received allocated treatment and completed protocol Largest estimate of effect size Selection bias for post-treatment withdrawals
Treatment-Received (TR) Received allocated treatment May not have completed the protocol Selection bias for pre-treatment withdrawals
Intention-to-Treat (ITT) All randomised subjects – NO WITHDRAWALS May or may not have received the intervention Underestimates true effect size of treatment Most robust analysis
MOCPASS – [email protected]
Power and sample size estimation Armitage & Berry pp 195-202
Sample size estimate for comparison of 2 equal groups
20 minimum difference to be significant20 SD
0.05 type 1 error rate, P value0.8 power
1.959964 Z 2 alpha 2 sided0.841621 Z 2 beta 1 sided
18 = minimum n for each group 20 = nonparametric
Power estimation for comparison of 2 equal groups
20 minimum difference to be significant20 SD
0.05 type 1 error rate, P value20 sample size n in each group
1.959964 Z 2 alpha 2 sided1.202314 Z 2 beta 1 sided
0.89 = power of study
Sample size estimate for comparison of 2 proportions
0.25 proportion 10.75 proportion 20.05 type 1 error rate, P value
0.8 power
1.959964 Z 2 alpha 2 sided0.841621 Z 2 beta 1 sided
0.5 pooled proportion
14 = minimum n per group for uncorrected Chi square test18 = Fleiss continuity correction, minimum n per group
Power estimation for comparison of 2 equal groups
0.25 proportion 10.75 proportion 20.05 type 1 error rate, P value
20 n per group
1.959964 Z 2 alpha 2 sided1.388312 Z 2 beta 1 sided1.002815 Z 2 beta, corrected
0.5 pooled proportion
0.917479 = power for uncorrected Chi square test0.84 = power with Fleiss continuity correction