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pooling multiple arms from the same trial, or multiple studies from the same research group sharing subjects, introduces non-independence",{"type":23,"tag":118,"props":909,"children":910},{},[911,916],{"type":23,"tag":36,"props":912,"children":913},{},[914],{"type":29,"value":915},"Studies estimating the same quantity",{"type":29,"value":917}," — the PICO framework (Population, Intervention, Comparator, Outcome) must be sufficiently similar across studies; pooling apples and oranges inflates heterogeneity meaninglessly",{"type":23,"tag":118,"props":919,"children":920},{},[921,926],{"type":23,"tag":36,"props":922,"children":923},{},[924],{"type":29,"value":925},"Log-scale for ratio measures",{"type":29,"value":927}," — odds ratios, risk ratios, and hazard ratios must be log-transformed before pooling (the forest plot x-axis should use log scale); pooling raw ORs is incorrect",{"type":23,"tag":118,"props":929,"children":930},{},[931,936],{"type":23,"tag":36,"props":932,"children":933},{},[934],{"type":29,"value":935},"Minimum number of studies",{"type":29,"value":937}," — fixed-effect pooling is valid with ≥ 2 studies, but random-effects estimation of τ² is unreliable with fewer than 5–10 studies; with few studies, use a Bayesian approach or report only the fixed-effect estimate",{"type":23,"tag":118,"props":939,"children":940},{},[941,946],{"type":23,"tag":36,"props":942,"children":943},{},[944],{"type":29,"value":945},"Publication bias awareness",{"type":29,"value":947}," — funnel plot asymmetry and Egger's test are heuristics, not definitive; small-study effects (genuine associations between study size and effect due to clinical reasons) can mimic publication bias",{"type":23,"tag":24,"props":949,"children":951},{"id":950},"related-tools",[952],{"type":29,"value":953},"Related Tools",{"type":23,"tag":32,"props":955,"children":956},{},[957,959,965,966,972,974,979,981,987,989,995],{"type":29,"value":958},"Use the ",{"type":23,"tag":155,"props":960,"children":962},{"href":961},"/tools/survival-curve",[963],{"type":29,"value":964},"Survival Curve Generator",{"type":29,"value":61},{"type":23,"tag":155,"props":967,"children":969},{"href":968},"/tools/cox-proportional-hazards",[970],{"type":29,"value":971},"Cox Proportional Hazards Model",{"type":29,"value":973}," to generate study-level hazard ratios that you then pool in a meta-analysis. Use the ",{"type":23,"tag":155,"props":975,"children":976},{"href":4},[977],{"type":29,"value":978},"Forest Plot Generator",{"type":29,"value":980}," within this tool — the forest plot is built-in. Use the ",{"type":23,"tag":155,"props":982,"children":984},{"href":983},"/tools/chi-square-test",[985],{"type":29,"value":986},"Chi-Square Test Calculator",{"type":29,"value":988}," to analyze individual 2×2 tables before pooling. Use the ",{"type":23,"tag":155,"props":990,"children":992},{"href":991},"/tools/correlation-matrix",[993],{"type":29,"value":994},"Correlation Matrix Calculator",{"type":29,"value":996}," to explore associations among study-level moderators before running meta-regression.",{"type":23,"tag":24,"props":998,"children":1000},{"id":999},"frequently-asked-questions",[1001],{"type":29,"value":1002},"Frequently Asked Questions",{"type":23,"tag":32,"props":1004,"children":1005},{},[1006,1011,1013,1017,1019,1023],{"type":23,"tag":36,"props":1007,"children":1008},{},[1009],{"type":29,"value":1010},"When should I use fixed-effect vs random-effects meta-analysis?",{"type":29,"value":1012},"\nUse the ",{"type":23,"tag":36,"props":1014,"children":1015},{},[1016],{"type":29,"value":73},{"type":29,"value":1018}," when all studies were conducted under essentially identical conditions (same protocol, population, intervention dose) and you believe there is one true effect that all studies are estimating — typically pre-specified in a protocol or when analyzing tightly controlled laboratory replication studies. Use the ",{"type":23,"tag":36,"props":1020,"children":1021},{},[1022],{"type":29,"value":80},{"type":29,"value":1024}," (almost always in practice) when studies differ in any clinically meaningful way — different populations, dosages, follow-up times, or outcome definitions — because these differences introduce real variability in the true effect. The random-effects model accounts for this between-study variance (τ²) and produces wider, more honest confidence intervals. Choosing fixed-effect because it gives a more significant result is not valid.",{"type":23,"tag":32,"props":1026,"children":1027},{},[1028,1033,1035,1040,1042,1047,1049,1054,1056,1061,1063,1069],{"type":23,"tag":36,"props":1029,"children":1030},{},[1031],{"type":29,"value":1032},"What does a prediction interval mean and why is it wider than the confidence interval?",{"type":29,"value":1034},"\nThe ",{"type":23,"tag":36,"props":1036,"children":1037},{},[1038],{"type":29,"value":1039},"95% confidence interval",{"type":29,"value":1041}," (CI) on the pooled estimate describes uncertainty about the ",{"type":23,"tag":139,"props":1043,"children":1044},{},[1045],{"type":29,"value":1046},"mean",{"type":29,"value":1048}," true effect across studies — it shrinks as you add more studies. The ",{"type":23,"tag":36,"props":1050,"children":1051},{},[1052],{"type":29,"value":1053},"95% prediction interval",{"type":29,"value":1055}," (PI) describes where 95% of ",{"type":23,"tag":139,"props":1057,"children":1058},{},[1059],{"type":29,"value":1060},"future individual study",{"type":29,"value":1062}," true effects are expected to fall, accounting for the between-study variance τ². The PI is always wider than the CI when τ² > 0. Example: if the pooled OR = 0.75 ",{"type":23,"tag":1064,"props":1065,"children":1066},"span",{},[1067],{"type":29,"value":1068},"95% CI 0.65–0.87",{"type":29,"value":1070}," but the 95% PI = 0.45–1.25, the treatment is beneficial on average but might be ineffective (OR > 1 possible) in some subpopulations. Reporting only the CI without the PI overstates the consistency of evidence when I² is high.",{"type":23,"tag":32,"props":1072,"children":1073},{},[1074,1079],{"type":23,"tag":36,"props":1075,"children":1076},{},[1077],{"type":29,"value":1078},"How do I interpret I² and when is heterogeneity a problem?",{"type":29,"value":1080},"\nI² = 0–25%: low heterogeneity — studies are fairly consistent and pooling is straightforward. I² = 25–50%: moderate heterogeneity — worth investigating potential moderators but pooling is still reasonable. I² = 50–75%: high heterogeneity — a single pooled estimate may be misleading; explore subgroup analysis or meta-regression to find sources. I² > 75%: very high heterogeneity — question whether pooling is appropriate at all; may need to report studies narratively. Note that I² depends on sample size (more studies → more power to detect heterogeneity) — report τ² alongside I² to describe the magnitude of between-study variation in effect size units.",{"type":23,"tag":32,"props":1082,"children":1083},{},[1084,1089,1093,1095,1100,1102,1106,1108,1113],{"type":23,"tag":36,"props":1085,"children":1086},{},[1087],{"type":29,"value":1088},"What is publication bias and how do I detect it?",{"type":23,"tag":36,"props":1090,"children":1091},{},[1092],{"type":29,"value":801},{"type":29,"value":1094}," occurs because studies with statistically significant or large effects are more likely to be published than null results, making the published literature systematically biased toward larger effects. In a ",{"type":23,"tag":36,"props":1096,"children":1097},{},[1098],{"type":29,"value":1099},"funnel plot",{"type":29,"value":1101}," (effect size vs standard error), the studies should form a symmetric inverted funnel if there is no bias. Asymmetry — typically an absence of small studies on the left side of the null — suggests that small null or negative studies were never published. ",{"type":23,"tag":36,"props":1103,"children":1104},{},[1105],{"type":29,"value":693},{"type":29,"value":1107}," formally tests for this asymmetry. The ",{"type":23,"tag":36,"props":1109,"children":1110},{},[1111],{"type":29,"value":1112},"trim-and-fill method",{"type":29,"value":1114}," imputes missing studies to symmetrize the funnel and re-estimates the pooled effect after correction. However, funnel asymmetry can also result from genuine small-study effects (different populations or doses in smaller studies) rather than publication bias — the interpretation always requires clinical judgment.",{"type":23,"tag":32,"props":1116,"children":1117},{},[1118,1123,1125,1130],{"type":23,"tag":36,"props":1119,"children":1120},{},[1121],{"type":29,"value":1122},"Can I meta-analyze studies that reported different effect measures?",{"type":29,"value":1124},"\nNo — you cannot directly pool, for example, odds ratios from some studies and risk differences from others. However, you can convert between measures if you have the raw data: risk difference and relative risk can be derived from each other given the baseline risk; OR can be approximately converted to RR using the formula RR ≈ OR / (1 − p₀ + p₀ × OR) where p₀ is the control group event rate. Alternatively, use the ",{"type":23,"tag":36,"props":1126,"children":1127},{},[1128],{"type":29,"value":1129},"standardized mean difference (SMD)",{"type":29,"value":1131}," for continuous outcomes where studies used different measurement scales — the SMD divides the mean difference by the pooled SD, making all studies dimensionless and directly comparable.",{"title":7,"searchDepth":1133,"depth":1133,"links":1134},2,[1135,1136,1137,1142,1143,1144,1145,1146],{"id":26,"depth":1133,"text":30},{"id":109,"depth":1133,"text":112},{"id":173,"depth":1133,"text":176,"children":1138},[1139,1141],{"id":180,"depth":1140,"text":183},3,{"id":350,"depth":1140,"text":353},{"id":513,"depth":1133,"text":516},{"id":717,"depth":1133,"text":720},{"id":880,"depth":1133,"text":883},{"id":950,"depth":1133,"text":953},{"id":999,"depth":1133,"text":1002},"markdown","content:tools:063.meta-analysis.md","content","tools/063.meta-analysis.md","tools/063.meta-analysis","md",{"loc":4},1775502471922]