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DNB ANAESTHESIA - STATISTICS: COMPLETE EXAM ANSWERS
MUST DO TOPICS (2023-2025)
1. P-VALUE + INTERPRETATION
Definition: The p-value is the probability of obtaining results as extreme as (or more extreme than) the observed data, assuming the null hypothesis is true.
Key formula concept:
- p < 0.05 → Result is statistically significant → Reject null hypothesis
- p > 0.05 → Result is NOT statistically significant → Fail to reject null hypothesis
Interpretation table (exam-ready):
| p-value | Interpretation |
|---|
| p < 0.001 | Highly significant |
| p < 0.01 | Very significant |
| p < 0.05 | Significant (threshold) |
| p > 0.05 | Not significant |
Common Misinterpretations (DNB favourite):
- p-value does NOT tell you the probability that the null hypothesis is true
- A small p-value does NOT mean a large/clinically important effect
- p-value is affected by sample size - a huge sample can make a trivial difference "significant"
- A non-significant result does NOT prove the null hypothesis
Clinical example: A new opioid reduces post-op pain. p = 0.03 means: if the drug had no effect, there is only a 3% chance of seeing this result by chance. We reject H₀ and accept the drug is effective.
2. NULL HYPOTHESIS
Null Hypothesis (H₀): States there is NO difference, NO effect, or NO association between the variables being studied. It is the "default" position.
Alternative Hypothesis (H₁ or Ha): States there IS a difference/effect/association.
Examples:
- H₀: Drug A and Drug B have equal analgesic effect (μ₁ = μ₂)
- H₁: Drug A and Drug B have different analgesic effects (μ₁ ≠ μ₂)
Process of hypothesis testing:
- State H₀ and H₁
- Choose significance level (α = 0.05 usually)
- Collect data and compute test statistic
- Calculate p-value
- If p < α → reject H₀ → accept H₁
Important: Failing to reject H₀ does NOT prove it is true. It only means there is insufficient evidence to reject it.
One-tailed vs Two-tailed tests:
- Two-tailed: Tests for difference in either direction (μ₁ ≠ μ₂)
- One-tailed: Tests for directional difference only (μ₁ > μ₂ or μ₁ < μ₂)
3. TYPE I AND TYPE II ERRORS
Memory aid: ALFA = fALse Alarm; BETA = Better miss it
| Null Hypothesis TRUE | Null Hypothesis FALSE |
|---|
| Reject H₀ | Type I Error (α) False Positive | Correct (Power = 1-β) |
| Fail to Reject H₀ | Correct (1-α) | Type II Error (β) False Negative |
Type I Error (α - False Positive):
- Rejecting a TRUE null hypothesis
- Concluding a drug works when it actually doesn't
- Probability = α (significance level, usually 0.05)
- "Crying wolf"
Type II Error (β - False Negative):
- Failing to reject a FALSE null hypothesis
- Concluding a drug doesn't work when it actually does
- Probability = β
- Power of study = 1 - β (usually set at 80% → β = 0.20)
- "Missing a real signal"
Relationship between errors:
- Decreasing α (e.g., 0.05 → 0.01) reduces Type I error but increases Type II error
- To reduce BOTH: increase sample size
Clinical relevance in anaesthesia:
- Type I Error: Adopting an ineffective drug (waste, potential harm)
- Type II Error: Rejecting an effective analgesic/anaesthetic agent (patient loses benefit)
4. ODDS RATIO (OR) + RISK RATIO - CLINICAL REFERENCE
2x2 Contingency Table (MUST memorize):
Disease + Disease -
Exposed | a | b |
Not Exposed| c | d |
Odds Ratio (OR) = (a×d) / (b×c)
- Used in: Case-control studies (you CANNOT calculate incidence/RR)
- OR = 1 → No association
- OR > 1 → Exposure increases odds of disease
- OR < 1 → Exposure is protective
Risk Ratio / Relative Risk (RR) = [a/(a+b)] / [c/(c+d)]
- Used in: Cohort studies and RCTs
- RR = 1 → No association
- RR > 1 → Exposure increases risk
- RR < 1 → Exposure protective
When OR ≈ RR: When the disease is rare (< 10% prevalence) - the rare disease assumption
Attributable Risk (AR) = Incidence in exposed - Incidence in unexposed
- Tells you how much disease is due to the exposure
Number Needed to Treat (NNT) = 1 / Absolute Risk Reduction
- Lower NNT = more effective treatment
Clinical example: OR = 2.5 for smoking and laryngeal cancer means: smokers have 2.5 times the ODDS of laryngeal cancer compared to non-smokers.
5. SAMPLE SIZE CALCULATION
Why it matters: Too small → miss real effects (Type II error). Too large → wasteful, unethical.
Formula (observational study):
N = Z²pq / d²
Where:
- Z = Z-value for desired confidence level (Z = 1.96 for 95% CI)
- p = expected prevalence/proportion
- q = 1 - p
- d = allowable error (precision)
Factors that INCREASE sample size required:
- Smaller effect size (harder to detect)
- Lower α (more stringent significance level)
- Higher desired power (less β)
- Greater variability in the outcome
- Rare disease/outcome
- Two-tailed test vs one-tailed
Power analysis: Usually conducted to achieve 80% power (β = 0.20) at α = 0.05.
DNB exam tip: The question often asks "what factors affect sample size" - remember: effect size, α level, power (1-β), and variability.
6. RANDOMIZATION + BLINDING - CONCEPTS IN RCT
Randomization
Definition: Process of assigning participants to groups by chance, so each participant has an equal probability of being in any group.
Purpose: Eliminates selection bias and distributes confounders (known and unknown) equally.
Types of Randomization:
| Type | Description |
|---|
| Simple | Coin flip equivalent; may give unequal groups |
| Block | Ensures equal group sizes (e.g., blocks of 4 or 6) |
| Stratified | Randomizes within strata (e.g., age groups, ASA grade) first, then randomizes |
| Cluster | Entire groups (wards, hospitals) randomized together |
| Minimization | Dynamic allocation to maintain balance on key variables |
Blinding (Masking)
Definition: Keeping participants, investigators, or both unaware of treatment allocation to prevent bias.
| Type | Who is blinded? |
|---|
| Single-blind | Patient only |
| Double-blind | Patient + clinician/researcher |
| Triple-blind | Patient + clinician + statistician |
Why blinding matters:
- Prevents performance bias (patients behaving differently)
- Prevents detection/assessment bias (observer unconsciously rating differently)
- Minimizes the placebo effect
- Reduces reporting bias
Allocation concealment vs blinding:
- Allocation concealment = preventing knowledge of UPCOMING assignment (before randomization) - prevents selection bias
- Blinding = preventing knowledge of CURRENT assignment (after randomization) - prevents performance/detection bias
7. SENSITIVITY AND SPECIFICITY
The 2x2 Diagnostic Table:
Disease + Disease -
Test + | TP | FP |
Test - | FN | TN |
Sensitivity = TP / (TP + FN)
- "How good is the test at detecting disease when it IS present"
- A HIGH sensitivity test, when NEGATIVE, RULES OUT disease
- Mnemonic: SnNout (Sensitive test, Negative result = rules OUT)
Specificity = TN / (TN + FP)
- "How good is the test at correctly identifying those WITHOUT disease"
- A HIGH specificity test, when POSITIVE, RULES IN disease
- Mnemonic: SpPin (Specific test, Positive result = rules IN)
Positive Predictive Value (PPV) = TP / (TP + FP)
- Probability of disease given a positive test
- Affected by disease prevalence
Negative Predictive Value (NPV) = TN / (TN + FN)
- Probability of no disease given a negative test
Likelihood Ratios:
- LR+ = Sensitivity / (1 - Specificity)
- LR- = (1 - Sensitivity) / Specificity
Trade-off: Increasing sensitivity decreases specificity (and vice versa). Visualized by the ROC curve.
Clinical context in anaesthesia:
- Pre-op tests: High sensitivity preferred (don't miss sick patients)
- Confirmatory tests: High specificity preferred (avoid unnecessary cancellations)
VERY LIKELY TOPICS
8. IMPACT FACTOR OF A JOURNAL
Definition: A metric indicating the average number of citations received per paper published in a journal over the past 2 years.
Formula:
Impact Factor (year X) = Citations in year X to articles published in years (X-1) and (X-2) / Total articles published in years (X-1) and (X-2)
Example: IF for 2024 = Citations received in 2024 for papers published in 2022-23 ÷ Total papers published in 2022-23
Significance:
- Higher IF = more influential/widely-read journal
- Important for: journal selection, career advancement, grant applications
- Common high-IF anaesthesia journals: Anesthesiology, British Journal of Anaesthesia, Anaesthesia
Limitations (frequently asked):
- Varies by specialty - cannot compare across fields
- Encourages publication bias toward positive/exciting results
- Review articles inflate IF (naturally get more citations)
- Self-citation manipulation possible
- Only reflects journal-level impact, not individual article quality
- Time lag - doesn't capture long-term influential papers
Alternatives:
- h-index (individual researcher impact)
- Eigenfactor score (accounts for quality of citing journals)
- Altmetric score (social media/news mentions)
- CiteScore
9. STANDARD DEVIATION (SD) AND STANDARD ERROR (SE)
Standard Deviation (SD):
- Measures variability/spread of individual data points around the mean
- Describes the sample itself
- Does NOT change substantially with larger samples
- Used when describing data
Formula: SD = √[Σ(x - x̄)² / (n-1)]
Standard Error (SE):
- Measures how precisely the sample mean estimates the population mean
- SE = SD / √n
- Gets smaller as n increases (more precise estimate with larger samples)
- Used when making inferences about population
Key difference for exams:
| SD | SE |
|---|
| Describes spread of data | Describes precision of mean estimate |
| Does not depend on n | Gets smaller as n increases |
| Use in descriptive statistics | Use in inferential statistics |
| Used to draw error bars showing variability | Used for confidence intervals |
Normal Distribution (68-95-99.7 rule):
- Mean ± 1 SD = 68% of data
- Mean ± 2 SD = 95% of data
- Mean ± 3 SD = 99.7% of data
10. CONFIDENCE INTERVAL (CI) - Linked to P-value
Definition: A range of values within which the true population parameter is expected to lie, with a specified level of confidence (usually 95%).
Interpretation of 95% CI: If we repeated the study 100 times, 95 of those CIs would contain the true population parameter.
Key rules for interpreting CI in exams:
| CI for difference in means | Interpretation |
|---|
| Does NOT include 0 | Statistically significant (p < 0.05) |
| Includes 0 | NOT statistically significant (p > 0.05) |
| CI for ratio (OR, RR) | Interpretation |
|---|
| Does NOT include 1 | Statistically significant |
| Includes 1 | NOT statistically significant |
CI width affected by:
- Sample size (larger n → narrower CI → more precise)
- Confidence level (99% CI is wider than 95% CI)
- Variability of data
Relationship with p-value: If 95% CI for OR does not include 1 → p < 0.05 (significant). These are two ways of expressing the same thing.
11. BIAS IN CLINICAL TRIALS
Definition: Systematic error that leads to incorrect estimation of the true effect.
Types of bias (exam favourite):
| Bias | Definition | How to reduce |
|---|
| Selection bias | Non-random selection into study groups | Randomization |
| Allocation bias | Researcher influences group assignment | Allocation concealment |
| Performance bias | Different care given to groups apart from intervention | Blinding |
| Detection/Observer bias | Outcome assessed differently between groups | Blinding of assessors |
| Recall bias | Cases remember exposure better than controls | Prospective design; case-control problem |
| Reporting bias | Selective reporting of outcomes | Pre-registration of trials |
| Publication bias | Positive results more likely to be published | Funnel plot, grey literature search |
| Attrition bias | Differential loss to follow-up | Intention-to-treat analysis |
| Confounding | Third variable affects both exposure and outcome | Randomization, multivariable analysis |
Intention-to-Treat (ITT) analysis: Analyze participants in the group they were randomized to, regardless of whether they completed the intervention. Preserves randomization benefits and gives real-world efficacy.
12. RCT (RANDOMIZED CONTROLLED TRIAL)
Definition: An experimental study where participants are randomly allocated to receive an intervention or control, with outcomes compared prospectively.
Hierarchy of evidence (highest to lowest):
- Systematic review / Meta-analysis
- RCT ← Gold standard for therapeutic efficacy
- Cohort study
- Case-control study
- Cross-sectional study
- Case reports/series
- Expert opinion
Key features of a good RCT:
- Randomization (eliminates selection bias)
- Allocation concealment
- Blinding (double-blind ideal)
- Adequate sample size (power calculation done)
- Intention-to-treat analysis
- Pre-registered protocol
- Reported per CONSORT guidelines
CONSORT checklist (2010): 25-item checklist for reporting RCTs. Includes: title, abstract, introduction, methods (eligibility, outcomes, randomization, blinding, sample size), results (flow diagram, baseline, analysis), discussion, and registration details. Accompanied by a CONSORT flow diagram showing participant progress through each stage.
13. ROC CURVE (Receiver Operating Characteristic)
Definition: A graphical plot showing the diagnostic ability of a test across all possible cut-off thresholds, plotting sensitivity (y-axis) vs 1-specificity (x-axis).
Area Under the Curve (AUC):
| AUC value | Interpretation |
|---|
| 1.0 | Perfect test |
| 0.9-1.0 | Excellent |
| 0.8-0.9 | Good |
| 0.7-0.8 | Fair |
| 0.6-0.7 | Poor |
| 0.5 | Useless (no better than chance) |
Uses of ROC curve:
- Compare diagnostic tests (the test with higher AUC is better)
- Select optimal cut-off point (point closest to top-left corner)
- At the optimal cut-off, sensitivity and specificity are maximized together
Relationship: Moving the cut-off point changes sensitivity and specificity inversely - every point on the ROC curve represents a different threshold.
RECENT TOPICS
14. CONSORT GUIDELINES
Full form: Consolidated Standards of Reporting Trials
Purpose: A standardized checklist to ensure complete and transparent reporting of RCTs so readers can assess validity and applicability.
Key components:
- 25-item checklist covering: title, abstract, introduction, methods, results, discussion, and other information (trial registration, protocol access, funding)
- CONSORT flow diagram (must-know): Shows number of participants at each stage:
- Assessed for eligibility
- Excluded (with reasons)
- Randomized
- Allocated to each arm
- Lost to follow-up (with reasons)
- Discontinued (with reasons)
- Analyzed (including ITT)
Why CONSORT matters: Poor reporting leads to inability to replicate studies, assess bias, or apply results. CONSORT compliance is required by most major anaesthesia journals.
15. PICO FRAMEWORK (Research Question Framing)
Full form: Population - Intervention - Comparison - Outcome
| Element | Description | Example |
|---|
| Population | Who is the study about? | Adult patients undergoing laparoscopic cholecystectomy |
| Intervention | What intervention/exposure? | Dexmedetomidine infusion |
| Comparison | Compared to what? | Propofol infusion |
| Outcome | What outcome measured? | Hemodynamic stability and recovery time |
PICO example (anaesthesia):
"In adult patients undergoing general anaesthesia (P), does use of BIS monitoring (I) compared to standard clinical monitoring (C) reduce the incidence of intraoperative awareness (O)?"
Why PICO matters:
- Structures the research question clearly
- Guides database search strategy in systematic reviews
- Helps define inclusion/exclusion criteria
- Part of CONSORT and systematic review protocols
EXTRA TOPICS (From Second Image)
16. TYPES OF RESEARCH STUDIES
Research Studies
│
├── Observational (no intervention)
│ ├── Descriptive
│ │ ├── Case report
│ │ ├── Case series
│ │ └── Cross-sectional (prevalence study)
│ └── Analytical
│ ├── Case-control (retrospective; calculates OR)
│ └── Cohort (prospective; calculates RR, AR)
│
└── Experimental (intervention by researcher)
├── RCT (randomized; gold standard)
├── Non-randomized controlled trial
└── Community trial
17. CASE-CONTROL vs COHORT STUDY
| Feature | Case-Control | Cohort |
|---|
| Direction | Backward (effect → cause) | Forward (cause → effect) |
| Timing | Retrospective | Usually prospective |
| Start point | Disease present | No disease initially |
| Measure | Odds Ratio (OR) | RR, AR, Incidence |
| Bias | Recall bias | Loss to follow-up bias |
| For rare outcomes | Yes | Difficult (need huge n) |
| For rare exposures | Less ideal | Yes |
| Multiple exposures | Can study many | Less efficient |
| Multiple outcomes | Less efficient | Can study many |
| Cost/time | Low | High |
| Ethical issues | Less (no new exposure) | More (may expose to harm) |
18. META-ANALYSIS AND FOREST PLOT
Meta-analysis: Statistical technique that pools quantitative results from multiple studies to produce a single, more precise effect estimate.
Forest plot (exam essential):
- Each horizontal line = one study; length = confidence interval
- Box = point estimate (size proportional to study weight)
- Diamond at bottom = pooled effect estimate
- Vertical line at 1 (for ratios) or 0 (for differences) = "line of no effect"
- If CI of a study crosses the line of no effect → that study alone is non-significant
- If the diamond crosses the line of no effect → overall pooled result is non-significant
Heterogeneity:
- I² statistic: Measures % of variability due to true heterogeneity (not chance)
- I² < 25%: Low heterogeneity
- I² 25-75%: Moderate
- I² > 75%: High (pooling questionable)
- Cochran's Q test: p < 0.05 = significant heterogeneity
Statistical models:
- Fixed-effects model: All studies measure same true effect
- Random-effects model: True effect varies between studies (used when heterogeneity is present)
Publication bias: Assessed by funnel plot (asymmetric funnel = publication bias likely) and Egger's test.
19. NON-PARAMETRIC TESTS
When to use: When data is not normally distributed, ordinal data, or small samples.
| Parametric Test | Non-parametric Equivalent | Use |
|---|
| Independent t-test | Mann-Whitney U test | Compare 2 independent groups |
| Paired t-test | Wilcoxon signed-rank test | Compare 2 related groups |
| One-way ANOVA | Kruskal-Wallis test | Compare 3+ independent groups |
| Pearson correlation | Spearman's rank correlation | Correlation (non-normal data) |
Key features of non-parametric tests:
- Based on ranks, not raw values
- No assumption of normal distribution
- Less statistical power than parametric tests (if normality holds)
- More appropriate for small samples, skewed data, outliers
20. ANOVA (Analysis of Variance)
Use: Compare means of THREE or more groups simultaneously.
Why not multiple t-tests? Multiple comparisons inflate Type I error rate. ANOVA keeps overall α at 0.05.
Test statistic: F-ratio = Variance BETWEEN groups / Variance WITHIN groups
- Large F → Groups differ more than expected by chance
Types:
- One-way ANOVA: One independent variable (factor)
- Two-way ANOVA: Two independent variables + tests for interaction
- Repeated measures ANOVA: Same subjects measured multiple times
Post-hoc tests (done after significant ANOVA to find which groups differ):
- Tukey's HSD (most common)
- Bonferroni correction
- Scheffé test
Assumptions: Normality, homogeneity of variance (Levene's test), independence.
Non-parametric alternative: Kruskal-Wallis test.
21. EVIDENCE-BASED MEDICINE (EBM)
Definition: Conscientious, explicit, and judicious use of current best evidence in making decisions about individual patient care (Sackett, 1996).
Three pillars of EBM:
- Best available research evidence
- Clinical expertise of the clinician
- Patient values and preferences
Steps in EBM (5-step approach):
- Ask - Frame clinical question (using PICO)
- Acquire - Search literature (PubMed, Cochrane)
- Appraise - Critically evaluate evidence
- Apply - Implement in clinical practice
- Assess - Evaluate outcomes
22. LEVELS OF EVIDENCE AND GRADES OF RECOMMENDATION
Oxford Levels of Evidence (simplified):
| Level | Study Type |
|---|
| 1a | Systematic review of RCTs |
| 1b | Well-designed RCT |
| 2a | Systematic review of cohort studies |
| 2b | Individual cohort study |
| 3a | Systematic review of case-control studies |
| 3b | Individual case-control study |
| 4 | Case series |
| 5 | Expert opinion |
GRADE System Recommendations:
- Grade A: Consistent Level 1 evidence
- Grade B: Consistent Level 2-3 evidence or extrapolation from Level 1
- Grade C: Level 4 evidence or extrapolation from 2-3
- Grade D: Level 5 or troublingly inconsistent evidence
23. PRIMARY vs SECONDARY RESEARCH
| Feature | Primary Research | Secondary Research |
|---|
| Data | Original, newly collected | Already existing data |
| Examples | RCT, cohort study, case-control | Systematic review, meta-analysis, literature review |
| Time/Cost | High | Lower |
| Bias control | Researcher controls design | Limited by quality of original studies |
| Purpose | Generate new knowledge | Synthesize existing knowledge |
24. SAMPLING TECHNIQUES
| Type | Description | Use |
|---|
| Simple random | Every individual has equal chance (lottery) | Homogeneous population |
| Systematic random | Every nth person selected | Ordered lists |
| Stratified random | Divide into strata, then randomly sample from each | Heterogeneous population, ensure subgroup representation |
| Cluster | Groups (clusters) randomly selected; all in cluster included | Geographically dispersed populations |
| Multistage | Cluster sampling done in multiple stages | Large national surveys |
| Convenience | Whoever is available | Pilot studies (high bias) |
| Purposive | Researcher handpicks subjects | Qualitative research |
| Snowball | Existing subjects recruit next (chain referral) | Hard-to-reach populations |
25. RESEARCH ETHICS AND INFORMED CONSENT
Helsinki Declaration: Foundation of research ethics globally. Key principles:
- Participant welfare > scientific interest
- Informed consent mandatory
- Independent ethics committee review required
- Vulnerable populations require extra protection
- Protocol must be publicly registered
Components of valid informed consent:
- Disclosure (full information about study)
- Comprehension (patient understands)
- Voluntariness (no coercion)
- Competence (legal capacity)
- Decision (explicit agreement)
Ethical principles (Belmont Report):
- Respect for persons (autonomy)
- Beneficence (maximize benefits)
- Justice (fair distribution)
26. PUBLICATION ETHICS AND PLAGIARISM
Plagiarism: Presenting another's work/ideas as your own without proper attribution.
Types:
- Direct plagiarism (copy-paste)
- Self-plagiarism (republishing own prior work)
- Mosaic/patchwork plagiarism (mixing own and others' text)
- Inadvertent plagiarism
Prevention: Turnitin/iThenticate software; proper citation; paraphrasing with acknowledgment.
Predatory journals: Journals that charge publication fees without proper peer review. Beall's list identifies predatory publishers.
Authorship criteria (ICMJE): Must fulfill ALL of:
- Substantial contribution to conception/design or data
- Drafting or critically revising the manuscript
- Final approval of published version
- Accountability for all aspects of the work
Ghost authorship: Listed as author without contribution. Honorary/Gift authorship: Contributing without meeting criteria. Both are unethical.
QUICK REVISION TABLE
| Topic | Key Number/Formula |
|---|
| P-value threshold | p < 0.05 = significant |
| Type I error | α = 0.05 (false positive) |
| Type II error | β = 0.20 → Power = 80% |
| Sample size formula | N = Z²pq/d² |
| SD vs SE | SE = SD/√n |
| 95% CI | Mean ± 1.96 × SE |
| Normal distribution | 68-95-99.7 rule |
| OR formula | (ad)/(bc) in 2×2 table |
| Sensitivity | TP/(TP+FN) - SnNout |
| Specificity | TN/(TN+FP) - SpPin |
| AUC (perfect test) | 1.0 |
| AUC (useless test) | 0.5 |
| I² (low heterogeneity) | < 25% |
| Impact factor formula | Citations in year X / Articles published in (X-1 and X-2) |
---All 26 topics from your notes and the PDF are covered above. Here's a quick guide to how it's organized:
Must Do (Topics 1-7):
- P-value, Null Hypothesis, Type I/II errors, Odds Ratio/Risk Ratio, Sample Size, Randomization + Blinding, Sensitivity/Specificity
Very Likely (Topics 8-13):
- Impact Factor, SD vs SE, Confidence Intervals, Bias in trials, RCT structure, ROC curve
Recent (Topics 14-15):
- CONSORT guidelines + flow diagram, PICO framework
Extra/Additional (Topics 16-26):
- Study types, Case-control vs Cohort comparison table, Meta-analysis + Forest plot, Non-parametric tests, ANOVA, EBM, Levels of evidence, Primary vs Secondary research, Sampling techniques, Research ethics, Publication ethics
A few exam tips specific to DNB Anaesthesia:
- The 2x2 contingency table is the backbone - learn it once and you can derive OR, RR, sensitivity, specificity, PPV, NPV from it
- SnNout / SpPin mnemonics are frequently tested
- Forest plots - know how to read them (whether diamond crosses the line of no effect)
- For CONSORT, know the flow diagram stages by name
- I² > 75% = pooling data in meta-analysis is questionable