1. Basic Statistical Concepts

2. Chapter 2 Reading instructions 2.1 Introduction: Not very important 2.2 Uncertainty and probability: Read 2.3 Bias and variability: Read 2.4 Confounding and interaction: Read 2.5 Descriptive and inferential statistics: Repetition 2.6 Hypothesis testing and p-values: Read 2.7 Clinical significance and clinical equivalence: Read 2.8 Reproducibility and generalizability: Read

3. Bias and variability Bias: Systemtic deviation from the true value Design, Conduct, Analysis, Evaluation Lots of examples on page 49-51

4. Bias and variability Larger study does not decrease bias ; Drog X - Placebo -7-4-10 mm Hg -7-4-10 Drog X - Placebo mm Hg Drog X - Placebo -7-4-10 n=40 n=200N=2000 Distribution of sample means: = population mean Population mean bias

5. Bias and variability There is a multitude of sources for bias Publication bias Selection bias Exposure bias Detection bias Analysis bias Interpretation bias Positive results tend to be published while negative of inconclusive results tend to not to be published The outcome is correlated with the exposure. As an example, treatments tends to be prescribed to those thought to benefit from them. Can be controlled by randomization Differences in exposure e.g. compliance to treatment could be associated with the outcome, e.g. patents with side effects stops taking their treatment The outcome is observed with different intensity depending no the exposure. Can be controlled by blinding investigators and patients Essentially the I error, but also bias caused by model miss specifications and choice of estimation technique Strong preconceived views can influence how analysis results are interpreted.

6. Bias and variability Amount of difference between observations True biological: Temporal: Measurement error: Variation between subject due to biological factors (covariates) including the treatment. Variation over time (and space) Often within subjects. Related to instruments or observers Design, Conduct, Analysis, Evaluation

7. Raw Blood pressure data Baseline8 weeks Placebo Drug X DBP (mmHg) Subset of plotted data

8. Bias and variability Unexplained variation Variation in observations = Explained variation +

9. Bias and variability Drug A Drug B Outcome Is there any difference between drug A and drug B?

10. Bias and variability Y=μ A +βx Y=μ B +βx μAμA μBμB x=age Model:

11. Confounding Predictors of treatm ent Predictors of outcome Confounders Treatment allocation Treatment allocation A B Outcome

12. Example Smoking Cigarettes is not so bad but watch out for Cigars or Pipes (at least in Canada) VariableNon smokersCigarette smokers Cigar or pipe smokers Mortality rate*20.220.535.5 Cochran, Biometrics 1968 *) per 1000 person-years %

13. Example Smoking Cigaretts is not so bad but watch out for Cigars or Pipes (at least in Canada) VariableNon smokersCigarette smokers Cigar or pipe smokers Mortality rate*20.220.535.5 Average age54.950.565.9 Cochran, Biometrics 1968 *) per 1000 person-years %

14. Example Smoking Cigaretts is not so bad but watch out for Cigars or Pipes (at least in Canada) VariableNon smokersCigarette smokers Cigar or pipe smokers Mortality rate*20.220.535.5 Average age54.950.565.9 Adjusted mortality rate* 20.226.424.0 Cochran, Biometrics 1968 *) per 1000 person-years %

15. Confounding The effect of two or more factors can not be separated Example:Compare survival for surgery and drug R Life long treatment with drug Surgery at time 0 Surgery only if healty enough Patients in the surgery arm may take drug Complience in the drug arm May be poor Looks ok but: Survival Time

16. Confounding Can be sometimes be handled in the design Example: Different effects in males and females Imbalance between genders affects result Stratify by gender R A B Gender M F R R A A B B Balance on average Always balance

17. Interaction The outcome on one variable depends on the value of another variable. ExampleInteraction between two drugs R A A B B Wash out A=AZD1234 B=AZD1234 + Clarithromycin

18. Interaction 19.75 (µmol*h/L) 36.62 (µmol*h/L) AUC AZD1234: AUC AZD1234 + Clarithromycin: Ratio:0.55 [0.51, 0.61] AZD1234 Example: Drug interaction

19. Interaction Example:Treatment by center interaction Average treatment effect: -4.39 [-6.3, -2.4] mmHg Treatment by center: p=0.01 What can be said about the treatment effect?

20. Descriptive and inferential statistics The presentation of the results from a clinical trial can be split in three categories: Descriptive statistics Inferential statistics Explorative statistics

21. Descriptive and inferential statistics Descriptive statistics aims to describe various aspects of the data obtained in the study. Listings. Summary statistics (Mean, Standard Deviation…). Graphics.

22. Descriptive and inferential statistics Inferential statistics forms a basis for a conclusion regarding a prespecified objective addressing the underlying population. HypothesisResults Confirmatory analysis: Conclusion

23. Descriptive and inferential statistics Explorative statistics aims to find interesting results that Can be used to formulate new objectives/hypothesis for further investigation in future studies. ResultsHypothesis Explorative analysis: Conclusion?

24. Hypothesis testing, p-values and confidence intervals Objectives Variable Design Statistical Model Null hypothesis Estimate p-value Confidence interval Results Interpretation

25. Hypothesis testing, p-values Statistical model: Observations from a class of distribution functions Hypothesis test: Set up a null hypothesis: H 0: and an alternative H 1 : Reject H 0 if p-value: Rejection region The smallest significance level for which the null hypothesis can be rejected. Significance level

26. Confidence intervals A confidence set is a random subset covering the true parameter value with probability at least. Let(critical function) Confidence set: The set of parameter values correponding to hypotheses that can not be rejected.

27. Example y ij = μ + τ i + β (x ij - x ·· ) + ε ij Variable: The change from baseline to end of study in sitting DBP (sitting SBP) will be described with an ANCOVA model, with treatment as a factor and baseline blood pressure as a covariate Null hypoteses (subsets of ): H 01 : τ 1 = τ 2 (DBP) H 02 : τ 1 = τ 2 (SBP) H 03 : τ 2 = τ 3 (DBP) H 04 : τ 2 = τ 3 (SBP) Objective: To compare sitting diastolic blood pressure (DBP) lowering effect of hypersartan 16 mg with that of hypersartan 8 mg Model: treatment effect i = 1,2,3 {16 mg, 8 mg, 4 mg} Parameter space:

28. Example contined HypothesisVariableLS MeanCI (95%)p-value 1: 16 mg vs 8 mgSitting DBP-3.7 mmHg[-4.6, -2.8]<0.001 2: 16 mg vs 8 mgSitting SBP-7.6 mmHg[-9.2, -6.1]<0.001 3: 8 mg vs 4 mgSitting DBP-0.9 mmHg[-1.8, 0.0]0.055 4 : 8 mg vs 4 mgSitting SBP-2.1 mmHg[-3.6, -0.6]0.005 This is a t-test where the test statistic follows a t-distribution Rejection region: P-value: The null hypothesis can pre rejected at 0 -cc 0 -4.6-2.8

29. P-value says nothing about the size of the effect! No. of patients per groupEstimation of effectp-value 101.94 mmHg0.376 100-0.65 mmHg0.378 10000.33 mmHg0.129 100000.28 mmHg<0.0001 1000000.30 mmHg<0.0001 A statistical significant difference does NOT need to be clinically relevant! Example: Simulated data. The difference between treatment and placebo is 0.3 mmHg

30. Statistical and clinical significance Statistical significance: Clinical significance: Health ecominical relevance: Is there any difference between the evaluated treatments? Does this difference have any meaning for the patients? Is there any economical benefit for the society in using the new treatment?

31. Statistical and clinical significance A study comparing gastroprazole 40 mg and mygloprazole 30 mg with respect to healing of erosived eosophagitis after 8 weeks treatment. DrugHealing rate gastroprazole 40 mg87.6% mygloprazole 30 mg84.2% Cochran Mantel Haenszel p-value = 0.0007 Statistically significant! Health economically relevant? Clinically significant?