Designs and sample size in medical resarch
- 1. Design and Sample Size (and Analysis) A. Indrayan PhD(OhioState), FAMS, FRSS, FASc
- 2. Study design Objective of study: Descriptive Analytical Strategy: Sample survey Case series Census Observational Experimental (Intervention) Method: Random Nonrandom (Purposive) Prospective (Follow-up) Cross- sectional Retros- pective Laboratory experiment Clinical trial Field trial Type: Mixed in stages SRS Haphazard Volunteers Longitudinal Case-control Chemical Therapeutic Prophylactic SyRS Snowball Cohort Nested case-control Cell Diagnostic Screening StRS Convenience Other No control Animal Prophylactic CRS/Area Quota Cohort can be historical (retrospective) or Cases and controls can be prospectively Screening MRS Referred concurrent recruited PPS With control Without control Consecutive Sequential Randomised (RCT if trial) Non- randomised Blind Open Layout for experiments/trials: -Cross-over, repeated measures -One-way, two-way, factorial, etc. Single Double Triple
- 3. Descriptive Studies • Existing status – unless you know this, how do you plan to proceed (what percentage of people of age 60+ have cataract in India, profile of cases of benign prostatic hyperplasia) • No cause-effect (or antecedent-outcome)
- 4. Descriptive Studies • Case series (HIV in SFO) • Case studies • Sample surveys (SRS) Primary methodology for surveys: • Sample design • Random, nonrandom, etc.
- 5. Analytical Studies • Antecedent–outcome relationship • Aetiology, risk factors, cause-effect, etc. Two types: Observational and Experimental
- 6. Observational Studies (Epidemiological Studies) • Naturally occurring events (Nature’s experiments) • No human intervention (obesity and hypertension) • Intervention is harmful or not easily implementable (smoking)
- 7. Types of Observational Studies • Ecological studies (population based variables – dietary pattern and diabetes) • Retrospective (case-control) • Prospective (cohort) • Cross-sectional (different from surveys) • There must be an antecedent and an outcome
- 9. Experimental Studies • Clinical trials on patients (treatment modalities and ) • Field trials on population at large (iron supplementation to girls) • Laboratory experiments on animals (pharmacological), biological material (tissues, swabs, blood specimen, etc.)
- 10. Clinical Trial Ethics • Intervention must have been established as potentially beneficial in preclinical phases • Inclusion and exclusion criteria (for mortality end point do not take persons of old age, people likely to be harmed with side effects or otherwise not included) • Informed consent (self selection) – bias? • Protection of interest of the subjects (Individual interest more important than societal gains unless explicitly stated) • Done in standard conditions (bias under control) • Done in phases • Helsinki Declaration
- 11. Clinical Trials Methodology • Random selection of subjects (consecutive or random numbers) • Controls – self (placebo effect confounded) or parallel (matched, unmatched) • Random allocation (individual or cluster) • Blinding (Double blind RCT gold standard) • Masking
- 12. Clinical Trial Designs • One-way, two-way, factorial, partially factorial • Crossover • Up-and-down • Two-stage • Adaptive
- 13. Laboratory Experiments • Standard conditions (in lab. and in subjects) so less variation and less sample size • Same designs • Harmful intervention can be tried in lower animals and they can be sacrificed if carried out as per guidelines
- 15. Sample size is required for planning Statistical requirement may conflict with available resources Sample size Reliability Hard to execute Large sample Small sample Easy to do
- 16. Should be neither too small nor too big • Small sample may fail to provide sufficient evidence – unethical in case of experiments as the exposure is unnecessary (but good for pilot/exploratory/phase-1 trial) • Large sample is also waste of resources if smaller sample can provide convincing evidence
- 17. Some researchers expect a statistician to give a sample size just on the basis of the title of research Just as a physician can not prescribe without knowing fully about pain, a statistician can not suggest a sample size without some basic information
- 18. Sample size depends on –1 Statistical parameter under investigation: • Mean/Median • Proportion (Prevalence, Probability) • Rate (Incidence, Mortality) • Ratio (OR, RR, Hazard ratio) • Coefficient (Regression, Correlation) • Difference
- 19. Sample size depends on –2 • Estimation/Test of hypothesis • Design (Descriptive/Analytical) • Layout (Independent/Matching/Repeated measures, One-way/Two-way/Etc.) • Sampling method (SRS/Cluster/Etc.) • Any subgroups • Non-response • Number of variables to be simultaneously considered
- 20. Two types of statistical inference Estimation Test of hypothesis Requirement of basic information is different for the two setups
- 21. I. ESTIMATION Basic equation: L = zα/2*SE(t) n is in the denominator of all SEs • Variability in different measurements (quantitative); prevalence or proportion (qualitative) • Minimum degree of precision (width of CI) – Margin of error • Least confidence you can afford
- 22. II. TEST OF HYPOTHESIS Basic equation: Power = P(Z ≥ zα when the specified medically important difference is present; n would occur on the right side of the equation • Variability in different measurements (quantitative); prevalence or proportion (qualitative) • Minimum difference that would be considered medically important • Statistical power (The probability of detecting the specified difference when present) • Level of significance (The probability of incorrectly rejecting a null) – one-tail or two-tail
- 23. Adjustments • Expected nonresponse or dropouts (bias) • Sampling other than SRS • Number of covariates in the study • Cross-classifications – sub-groups
- 24. TOOLS FOR SAMPLE SIZE • Formula (different for small samples) • Online calculator (http://www.stat.ubc.ca/~rollin/stats/ssize , http://statpages.org/#Power , http://hedwig.mgh.harvard.edu/sample_size/size.html ) • Nomogram • Table • Thumb rule
- 25. 100 0.02 1000 900 800 700 600 500 400 300 250 150 100 75 Prevalence rate Cluster size Number of Clusters 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 450 400 350 300 250 225 200 175 150 500 100 90 80 70 60 50 45 40 35 30 25 20 15 125 200 100 90 80 70 60 50 40 35 30 25 20 15 45 10 5 450 400 350 300 250 225 175 150 125 500 90 80 70 60 50 150 125 100 175 200 450 350 300 250 225 400 500 45 40 35 30 25 20 15 10 5 150 125 100 90 80 70 60 400 350 300 250 225 200 175 450 500 45 40 35 30 25 20 15 10 50 450 400 350 300 250 225 200 500 175 150 125 100 80 70 60 50 45 40 35 30 25 20 15 10 125 100 90 80 70 60 50 40 35 30 25 20 15 10 400 300 250 225 200 175 150 350 450 500 5 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.06 0.07 0.05 0.04 0.015 0.03 0.025 0.020 0.010 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.06 0.04 0.07 0.05 0.015 0.03 0.025 0.020 0.010 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.06 0.04 0.07 0.05 0.015 0.03 0.025 0.020 0.010 0.18 0.20 0.22 Ratio of D & B (D /B -lines) a =0.20 a =0.10 a =0.05 Number of clusters ( C -lines) a =0.05 a =0.10 a =0.20 P -line L=10% of P L=20% of P L=20% of P L=10% of P L=10% of P L=20% of P L = Precision required on either side of P , a = Size of critical region (Confidence = 1-a ) Prevalence rate (P )
- 26. Thumb Rules • Normative studies: 200 per group Clinical trials – • Big trial: Minimum 300 per group—each centre in case multicentric • Medium trial: Minimum 100 per group • Small trial (PG thesis): Minimum 30 per group Observational studies – • Case-control: Minimum 30 cases with rarest exposure in case of medium sized study and minimum of 5 cases in case small scale (PG thesis) study • Cohort: Minimum 30 cases with rarest outcome in case of medium sized study and minimum of 5 cases in case small scale (PG thesis) study Regressions • Logistic: Minimum 5 cases in rarest cross-classification • Quantitative regression: Minimum 10 subjects per regressor
- 27. Resource limitations • Many times, time and resources do not allow a study on the required sample size. • Do reverse calculation for the sample size you can cover and find power of your study. Say that the power of the study would be so much and not more, in view of the resource limitations. • In case of really small sample and non- Gaussian conditions, use non-parametric or exact methods.
- 28. Analysis – 1 (broad aspects only) Depends on design and the type of measurements (quantitative, qualitative, ordinal) • For descriptive studies (Profiles, prevalence, patterns) – percentages, cross- tabulations, mean, SD, quartiles, percentiles, box plot, distribution pattern, Kaplan-Meier for durations, rates and ratios, confidence intervals,
- 29. Analysis – 2 • For analytical studies (correlations with cause-effect overtones, differences between groups in percentages and averages) – various correlations, chi-square test, Student t-test, ANOVA, ANCOVA, logistic regression (odds ratios), quantitative regression, Cox regression (hazard ratios), agreement analysis, log-rank, ROC curves,