Basic Statistical Concepts

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

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sources for bias Publication bias Positive results tend to be published while negative of inconclusive results tend to not to be published Selection bias The outcome is correlated with the exposure.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

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

7. Placebo DBP (mmHg) Drug X Baseline 8 weeks Raw Blood pressure data Subset of plotted data

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

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

10. Model: Y=μB+βx μB Y=μA+βx μA x=age Bias and variability

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

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

14. Example Smoking Cigaretts is not so bad but watch out for Cigars or Pipes (at least in Canada) *) per 1000 person-years % Cochran, Biometrics 1968

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

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

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

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

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. Confirmatory analysis: Hypothesis Results 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. Explorative analysis: Results Hypothesis Conclusion?

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

25. Statistical model: Observations from a class of distribution functions Hypothesis test: Set up a null hypothesis: H0: and an alternative H1: Hypothesis testing, p-values Reject H0 if Significance level Rejection region p-value: The smallest significance level for which the null hypothesis can be rejected.

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

27. Example Objective: To compare sitting diastolic blood pressure (DBP) lowering effect of hypersartan 16 mg with that of hypersartan 8 mg 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 treatment effect i = 1,2,3 {16 mg, 8 mg, 4 mg} yij = μ + τi + β(xij - x··) + εij Model: Null hypoteses (subsets of ): H01: τ1 = τ2 (DBP) H02: τ1 = τ2 (SBP) H03: τ2 = τ3 (DBP) H04: τ2 = τ3 (SBP) Parameter space:

28. Example contined This is a t-test where the test statistic follows a t-distribution Rejection region: 0 -c c P-value: The null hypothesis can pre rejected at 0 -4.6 -2.8

29. P-value says nothing about the size of the effect! Example: Simulated data. The difference between treatment and placebo is 0.3 mmHg A statistical significant difference does NOT need to be clinically relevant!

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

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. Cochran Mantel Haenszel p-value = 0.0007 Statistically significant! Clinically significant? Health economically relevant?