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Meta-análisis
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Definición El meta-análisis es una revisión sistemática de un gran número de estudios que utiliza métodos estadísticos para combinar, sintetizar e integrar la información de varios estudios independientes que son considerados por el análista como “combinables” Adaptado de: - Glass GV. Primary and Meta-analysis of research. Educational Researcher 1976;5:3-8. - Huque MF. Experiences with meta-analysis in NDA submissions. Proc
Biopharmaceutical Section of the American Statistical Association 1988;28-33. - Cook DJ, Sackett DL, Spitzer WO. Methodologic guidelines for systematic
reviews of randomized control trials in health care from the Potsdam consultation meta-analysis. J Clin Epidemiol 1995;48:168-71.
- D’Agostino RB, Weintraub M. Meta-analysis: a method for sythesizing research. Clin Pharmacol Ther 1995; 58:605-616.
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OBJETIVOS u Conclusión:
– Ganancia en precisión – Comparación crítica de los resultados – Diferencias en magnitud o sentido – Posibilidad de generalizar
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EVOLUCIÓN DEL USO DEL MÉTODO META-ANALÍTICO
Ratio articulos/mes
0,0005,000
10,00015,00020,00025,00030,00035,00040,000
1950-1959
1960-1969
1970-1979
1980-1984
1985-1989
1990-1992
(Junio)
1992(Julio)-1995
Ratio articulos/mes
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CARACTERÍSTICAS u Datos:
– Tipos de medida de los efectos – Escalas de medida – Extensión de la información
u Datos originales u Estadísticos de resumen u Estimación del efecto y errores estándar u Valores de significación
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CARACTERÍSTICAS u No independencia de los estudios
– Tiempo: momento en que se realiza el estudio
– Centro o investigador – Múltiple publicación de los resultados – Mismos sujetos (en distintos estudios)
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Ventajas y limitaciones
u Ventajas u Consideración sistemática (evaluación no
sesgada) u Cuantificación de los resultados u Aumento de precisión de los resultados u Mayor capacidad de estudiar efectos en
subgrupos u Mayor facilidad para evaluar las discrepancias
entre estudios u Mayor generalización de las conclusiones
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Ventajas y limitaciones u Limitaciones:
u La calidad está limitada por los estudios individuales
u Dificultad para establecer los criterios de inclusión u Sesgo de selección (publicación, lengua, calidad ...)
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Análisis de la heterogeneidad • Respuesta a la siguiente pregunta:
¿SON COMBINABLES LOS ESTUDIOS? • Pruebas de homogeneidad de los resultados de los
estudios individuales: - Prueba ji-cadrado Q de Cochran - Prueba ji-cuadrado de Breslow-Day
• Las pruebas de homogeneidad tienen baja potencia
para detectar la heterogeneidad • Un valor p de la prueba de homogeneidad 0.10,
sugiere heterogeneidad entre estudios y, por tanto, podría no ser válido combinar los estudios
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Egger et al. Systematic reviews in health care. London: BMJ books, 2001.
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Magnitud del efecto (1) • Los métodos estadísticos utilizados para estimar
el tamaño del efecto global de diferentes estudios se basan en Modelos de Efectos Fijos y Efectos Aleatorios
• Los Modelos de Efectos Fijos asumen un efecto
constante del tratamiento entre estudios, es decir, los tamaños de los efectos entre estudios son homogéneos o similares. - Los diferentes estudios pertenecen a una misma población - Consideran la variabilidad intra-estudio
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Magnitud del efecto (2) • Los Modelos de Efectos Aleatorios consideran que
existe una variación entre estudios - Los estudios provienen de poblaciones diferentes - Consideran la variabilidad intra e inter-estudio
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Magnitud del efecto (3) • Ninguno de los dos modelos se puede considerar
“correcto”:
- Si los estudios son homogéneos La elección entre un modelo de efectos fijos y efectos aleatorios no es importante, ya que los resultados serán idénticos
- Si los estudios no son homogéneos Es más apropiado elegir un modelo de efectos aleatorios
• Los modelos de efectos fijos y efectos aleatorios
utilizan diferentes métodos estadísticos para combinarlos resultados
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Magnitud del efecto (4)
Efectos fijos
Efectos aleatorios
Método Efecto Método Efecto
V. Cualit. Mantel-Haenszel OR, RR DerSimonian- Laird
Ratios y Diferencias
Peto OR
Basado en la varianza general
Ratios y diferencias
V. Cuantit. Diferencias tipificadas entre
medias
Cuantitativas
Diferencias tipificadas
entre medias
Cuantitativas
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Unbiased Hedges’ g estimate
u Corrections for small sample size will be made.
σµµ
δ ce −=
1431−
−=m
Jm
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛
−+−=⎟
⎠
⎞⎜⎝
⎛−
−=94
3114
31ee nn
gm
gd
2−+= ec nnm
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Effect size interpretation
u Since effect sizes are non-dimensional measurements (no units), some conventions have been proposed[1],[2]: – small≈0.20, – medium≈0.50 – large≈0.80
– [1] Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
– [2] Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155-159.
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Análisis se sensibilidad
EFFECTS MODEL
RELATIVE LIVE-BIRTH RATIO
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
FIXEDRANDOM FIXEDRANDOM
FAVOURS CONTROLFAVOURS TREATMENT
Homogeneity testP = 0.06 (<<0.10)
Homogeneity testP = 0.63 (>>0.10)
Data from Jeng GT et al. JAMA 1995; 274:830-836.
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Análisis de la correlación CORRELATION BETWEEN THE EFFECT SIZE AND SAMPLE SIZE
SAMPLE SIZE
0.00.20.40.60.81.01.21.41.61.82.02.22.4
100140180220260300340380420
ODDS RATIO
r2 = 0.01b = 0.0009p = 0.70
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Análisis de la robustez
• Análisis del sesgo de publicación y/o inclusión selectiva de estudios positivos
• Correlación entre la magnitud del efecto y
el tamaño muestral de los estudios.
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u Los métodos utilizados para detectar la introducción del sesgo de publicación en un meta-análisis son:
– Funnel plot – El análisis de la asimetria del funnel plot
u Si el número de estudios incluidos en el meta-análisis es pequeño, el funnel plot es poco útil. En este caso, el mejor método es comparar el tamaño del efecto global entre los estudios publicados y no publicados
u En un meta-análisis basado en todos los estudios originales, no es necesario analizar el sesgo de publicación
Análisis del sesgo de publicación y/o inclusión selectiva de estudios positivos (3)
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Funnel plot
PublishedUnpublishedOverall OR
DEMONSTRATION OF FUNNEL PLOT
ODDS RATIO
SAMPLE SIZE
0
20
40
60
80
100
120
140
160
180
200
220
0.20.40.60.81.01.21.41.61.82.0
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Funnel plot
PublishedOverall OR
DEMONSTRATION OF FUNNEL PLOT
ODDS RATIO
SAMPLE SIZE
0
20
40
60
80
100
120
140
160
180
200
220
0.20.40.60.81.01.21.41.61.82.02.2
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Presentación gráfica
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Conclusiones (1) 1. El meta-análisis es un herramienta valida y
poderosa para la síntesis de la investigación siempre y cuando se aplique de forma adecuada (justificación, protocolo, etc.)
2. La utilización no crítica del meta-análisis puede
llevar a conclusiones erróneas. Las principales críticas que se realizan a un meta-análisis son:
- Sesgo de publicación y/o inclusión selectiva de estudios positivos - Heterogeneidad entre estudios - Correlación entre el tamaño del efecto y el tamaño de la muestra
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Conclusiones (2) 3. Únicamente cuando estos problemas son
debidamente considerados y analizados por medio de:
- Análisis de la asimetría del funnel plot - Pruebas de homogeneidad - Análisis de la correlación entre el tamaño del efecto y el tamaño de la muestra de los estudios Es posible aplicar esta técnica estadística para combinar los estudios de forma que los resultados globales sean científicamente validos
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Meta-análisis Ejemplo
Ferran Torres [email protected]
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u Effects of plantago ovata husk on lipid metabolism.
A meta-analysis
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Selection of studies
u Identified 26 studies =>18 were valid according to the predefined criteria
u Excluded studies. – Most of them (7 of 8) insufficient information
on descriptive statistics to calculate the meta-analysis estimates from those studies;
– the other one was erroneously pre-selected since only insoluble fiber was used in that trial.
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Statistical issues on the results (1) u Poor quality of information
u withdrawals and descriptive results: u Complete available descriptive data, n, mean and
dispersion (SD or SE), for the baseline subtracted effect was found only for one study (Williams 1995).
– SD (or SE to derive the SD): u Estimated from baseline and final values by using
correlation coefficients from other published data. u If baseline or final SD not available: SD for the baseline
difference was directly imputed from other published data. u cross-over design
– Intrasubject correlation for the estimation of the SD of the treatment differences has been ignored for the cross-over design because of (a) it was not available and (b) this is conservative since it leads to less significant results.
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Statistical issues on the results (2)
u Treatment arms u 2 per study except 1:
– (MacMahon 1998): The mentioned study was a three arm trial with a control group (n=74) and 2 active doses of 7 G/d (n=101), and 10.5G/d (n=91).
– Half the sample size of the control group (n=37; 74/2) was used for the comparison between each active group.
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Statistical issues on the results (3)
u Potential Publication Bias
– (a) The biggest studies have the lowest magnitude effect for Total Cholesterol, although the direction of the effect is positive for all of them.
– (b) There are probably some unpublished small studies with negative results, although the bigger studies are positive.
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Statistical issues on the results (3)
u Heterogeneity and sensibility analysis
– (a) The biggest studies have the lowest magnitude effect for Total Cholesterol, although the direction of the effect is positive for all of them.
– (b) There are probably some unpublished small studies with negative results, although the bigger studies are positive.
=>
– Pooled results too heterogeneous u very cautious with the conclusions u fixed effects not valid
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Meta-analysis estimations u Significant effect for
– Total Cholesterol (p<0.001) – LDL (p<0.001)
u “Marginally significant“ – Triglycerides (p=0.213 but p=0.021 for
the fixed effect approach) u No effect:
– HDL (p=0.886 and p=0.178 for the fixed effect approach)
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.80 ( -0.93 , -0.68 )
Study ANDERSON 1988
BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 SUMMERBELL 1994
WOLEVER 1994 WILLIAMS 1995
WEINGAND 1997 MACMAHON 1998 MACMAHON 1998
RODRIGUEZ-MORAN 1998 ANDERSON 1999
Pooled(fixed effects)
Fibern: mean(SD)
13: -0.940(0.152) 40: -0.250(0.072) 19: -0.340(0.151) 30: -0.337(0.119) 27: -0.510(0.529) 27: -0.520(0.363) 21: -0.550(0.416) 20: -0.363(0.565) 59: -0.337(0.407) 20: 0.070(0.447) 18: -0.810(0.177) 19: -0.450(0.159) 18: -0.290(0.407) 26: -0.544(0.133) 23: -0.180(0.407)101: -0.670(0.407) 91: -0.700(0.407) 62: -0.673(0.169) 14: -0.119(0.407)
n=522
Controln: mean(SD)
13: -0.230(0.320) 35: 0.010(0.219) 19: -0.020(0.242) 28: 0.052(0.179) 27: -0.070(0.364) 25: -0.240(0.133) 23: 0.000(0.225) 20: -0.130(0.134) 59: -0.018(0.407) 20: 0.080(0.358) 18: -0.620(1.169) 18: -0.170(0.296) 18: 0.270(0.407) 24: -0.299(0.177) 23: 0.080(0.407) 37: -0.610(0.407) 37: -0.610(0.407) 63: -0.440(0.746) 15: 0.372(0.407)
n= 648
Fiber vs Placebo effect in lipid reduction. Total CholesterolHedges unbiased g, Fixed effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-1.01 ( -1.31 , -0.70 )
Study ANDERSON 1988
BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 SUMMERBELL 1994
WOLEVER 1994 WILLIAMS 1995
WEINGAND 1997 MACMAHON 1998 MACMAHON 1998
RODRIGUEZ-MORAN 1998 ANDERSON 1999
Pooled(random effects)
Fibern: mean(SD)
13: -0.940(0.152) 40: -0.250(0.072) 19: -0.340(0.151) 30: -0.337(0.119) 27: -0.510(0.529) 27: -0.520(0.363) 21: -0.550(0.416) 20: -0.363(0.565) 59: -0.337(0.407) 20: 0.070(0.447) 18: -0.810(0.177) 19: -0.450(0.159) 18: -0.290(0.407) 26: -0.544(0.133) 23: -0.180(0.407)101: -0.670(0.407) 91: -0.700(0.407) 62: -0.673(0.169) 14: -0.119(0.407)
n=522
Controln: mean(SD)
13: -0.230(0.320) 35: 0.010(0.219) 19: -0.020(0.242) 28: 0.052(0.179) 27: -0.070(0.364) 25: -0.240(0.133) 23: 0.000(0.225) 20: -0.130(0.134) 59: -0.018(0.407) 20: 0.080(0.358) 18: -0.620(1.169) 18: -0.170(0.296) 18: 0.270(0.407) 24: -0.299(0.177) 23: 0.080(0.407) 37: -0.610(0.407) 37: -0.610(0.407) 63: -0.440(0.746) 15: 0.372(0.407)
n= 648
Fiber vs Placebo effect in lipid reduction. Total CholesterolHedges unbiased g, Random effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-1.0 -0.7 -0.4 -0.1 0.1 0.3 0.5 0.7 0.9
-0.31 ( -0.37 , -0.24 )
Study ANDERSON 1988
BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 SUMMERBELL 1994
WOLEVER 1994 WILLIAMS 1995
WEINGAND 1997 MACMAHON 1998 MACMAHON 1998
RODRIGUEZ-MORAN 1998 ANDERSON 1999
Pooled(random effects)
Fibern: mean(SD)
13: -0.940(0.152) 40: -0.250(0.072) 19: -0.340(0.151) 30: -0.337(0.119) 27: -0.510(0.529) 27: -0.520(0.363) 21: -0.550(0.416) 20: -0.363(0.565) 59: -0.337(0.407) 20: 0.070(0.447) 18: -0.810(0.177) 19: -0.450(0.159) 18: -0.290(0.407) 26: -0.544(0.133) 23: -0.180(0.407)101: -0.670(0.407) 91: -0.700(0.407) 62: -0.673(0.169) 14: -0.119(0.407)
n=522
Controln: mean(SD)
13: -0.230(0.320) 35: 0.010(0.219) 19: -0.020(0.242) 28: 0.052(0.179) 27: -0.070(0.364) 25: -0.240(0.133) 23: 0.000(0.225) 20: -0.130(0.134) 59: -0.018(0.407) 20: 0.080(0.358) 18: -0.620(1.169) 18: -0.170(0.296) 18: 0.270(0.407) 24: -0.299(0.177) 23: 0.080(0.407) 37: -0.610(0.407) 37: -0.610(0.407) 63: -0.440(0.746) 15: 0.372(0.407)
n= 648
Fiber vs Placebo effect in lipid reduction. Total CholesterolDifference of means (mmol/L), Random effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.03 ( -0.39 , 0.33 )
Study ANDERSON 1988
BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 SUMMERBELL 1994
WOLEVER 1994 WILLIAMS 1995
WEINGAND 1997 RODRIGUEZ-MORAN 1998
ANDERSON 1999
Pooled(random effects)
Fibern: mean(SD)
13: -0.090(0.042) 40: 0.050(0.066) 19: -0.020(0.080) 30: 0.026(0.168) 27: 0.060(0.168) 27: -0.020(0.099) 21: -0.020(0.057) 20: 0.026(0.100) 59: -0.026(0.055) 20: -0.020(0.224) 18: 0.130(0.154) 19: -0.010(0.070) 18: -0.040(0.030) 26: 0.106(0.094) 23: 0.055(0.168) 62: 0.440(0.454) 14: 0.005(0.168)
n=448
Controln: mean(SD)
13: -0.090(0.141) 35: 0.030(0.058) 19: -0.020(0.072) 28: 0.078(0.168) 27: 0.140(0.168) 25: 0.000(0.072) 23: -0.010(0.024) 20: 0.000(0.094) 59: -0.013(0.059) 20: -0.040(0.134) 18: 0.130(0.120) 18: 0.070(0.085) 18: 0.040(0.030) 24: 0.039(0.031) 23: -0.185(0.168) 63: 0.078(0.044) 15: 0.017(0.168)
n=456
Fiber vs Placebo effect in lipid reduction. HDLHedges unbiased g, Random effects
Control better Fiber better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-1.02 ( -1.36 , -0.69 )
Study ANDERSON 1988
BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 SUMMERBELL 1994
WOLEVER 1994 WILLIAMS 1995
WEINGAND 1997 MACMAHON 1998 MACMAHON 1998
RODRIGUEZ-MORAN 1998 ANDERSON 1999
Pooled(random effects)
Fibern: mean(SD)
13: -0.840(0.264) 40: -0.310(0.081) 19: -0.160(0.100) 30: -0.337(0.224) 27: -0.480(0.448) 27: -0.590(0.283) 21: -0.560(0.385) 20: -0.389(0.372) 59: -0.332(0.096) 20: 0.040(0.358) 18: -1.090(0.216) 19: -0.440(0.194) 18: -0.260(0.016) 26: -0.613(0.093) 23: -0.320(0.427)101: -0.630(0.427) 91: -0.710(0.427) 62: -0.725(0.427) 14: -0.179(0.427)
n=522
Controln: mean(SD)
13: -0.110(0.321) 35: 0.000(0.232) 19: -0.140(0.252) 28: -0.104(0.144) 27: -0.140(0.523) 25: -0.200(0.147) 23: -0.130(0.211) 20: -0.130(0.099) 59: -0.057(0.200) 20: -0.060(0.358) 18: -0.850(0.941) 18: -0.250(0.261) 18: 0.280(0.316) 24: -0.221(0.238) 23: -0.020(0.427) 37: -0.580(0.427) 37: -0.580(0.427) 63: -0.440(0.427) 15: 0.281(0.427)
n=648
Fiber vs Placebo effect in lipid reduction. LDLHedges unbiased g, Random effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.88 ( -1.01 , -0.75 )
Study ANDERSON 1988
BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 SUMMERBELL 1994
WOLEVER 1994 WILLIAMS 1995
WEINGAND 1997 MACMAHON 1998 MACMAHON 1998
RODRIGUEZ-MORAN 1998 ANDERSON 1999
Pooled(fixed effects)
Fibern: mean(SD)
13: -0.840(0.264) 40: -0.310(0.081) 19: -0.160(0.100) 30: -0.337(0.224) 27: -0.480(0.448) 27: -0.590(0.283) 21: -0.560(0.385) 20: -0.389(0.372) 59: -0.332(0.096) 20: 0.040(0.358) 18: -1.090(0.216) 19: -0.440(0.194) 18: -0.260(0.016) 26: -0.613(0.093) 23: -0.320(0.427)101: -0.630(0.427) 91: -0.710(0.427) 62: -0.725(0.427) 14: -0.179(0.427)
n=522
Controln: mean(SD)
13: -0.110(0.321) 35: 0.000(0.232) 19: -0.140(0.252) 28: -0.104(0.144) 27: -0.140(0.523) 25: -0.200(0.147) 23: -0.130(0.211) 20: -0.130(0.099) 59: -0.057(0.200) 20: -0.060(0.358) 18: -0.850(0.941) 18: -0.250(0.261) 18: 0.280(0.316) 24: -0.221(0.238) 23: -0.020(0.427) 37: -0.580(0.427) 37: -0.580(0.427) 63: -0.440(0.427) 15: 0.281(0.427)
n=648
Fiber vs Placebo effect in lipid reduction. LDLHedges unbiased g, Fixed effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.15 ( -0.39 , 0.09 )
Study
ANDERSON 1988 BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 WILLIAMS 1995
WEINGAND 1997 RODRIGUEZ-MORAN 1998
ANDERSON 1999
Pooled(random effects)
Fibern: mean(SD)
13: -0.210(0.058) 40: 0.030(0.302) 19: -0.135(0.214) 30: -0.011(0.320) 27: -0.240(0.293) 27: 0.200(0.516) 21: 0.080(0.455) 20: 0.102(0.630) 59: 0.006(0.308) 20: 0.240(0.805) 18: 0.450(1.008) 26: -0.142(0.249) 23: 0.002(0.781) 62: -0.554(0.781) 14: 0.165(0.781)
n=412
Controln: mean(SD)
13: 0.190(0.479) 35: -0.050(0.102) 19: 0.030(0.201) 28: 0.000(0.088) 27: -0.140(0.313) 25: -0.120(0.185) 23: 0.300(0.791) 20: 0.000(0.224) 59: 0.150(0.345) 20: 0.920(1.163) 18: 0.410(0.351) 24: -0.232(0.137) 23: 0.002(0.781) 63: -0.181(0.781) 15: 0.342(0.781)
n=419
Fiber vs Placebo effect in lipid reduction. TriglyceridesHedges unbiased g, Random effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-0.16 ( -0.30 , -0.02 )
Study
ANDERSON 1988 BELL 1989 BELL 1990 LEVIN 1990 NEAL 1990
ANDERSON 1991 ANDERSON 1992 EVERSON 1992
SPRECHER 1993 SPRECHERON 1993
MACIEJKO 1994 WILLIAMS 1995
WEINGAND 1997 RODRIGUEZ-MORAN 1998
ANDERSON 1999
Pooled(fixed effects)
Fibern: mean(SD)
13: -0.210(0.058) 40: 0.030(0.302) 19: -0.135(0.214) 30: -0.011(0.320) 27: -0.240(0.293) 27: 0.200(0.516) 21: 0.080(0.455) 20: 0.102(0.630) 59: 0.006(0.308) 20: 0.240(0.805) 18: 0.450(1.008) 26: -0.142(0.249) 23: 0.002(0.781) 62: -0.554(0.781) 14: 0.165(0.781)
n=412
Controln: mean(SD)
13: 0.190(0.479) 35: -0.050(0.102) 19: 0.030(0.201) 28: 0.000(0.088) 27: -0.140(0.313) 25: -0.120(0.185) 23: 0.300(0.791) 20: 0.000(0.224) 59: 0.150(0.345) 20: 0.920(1.163) 18: 0.410(0.351) 24: -0.232(0.137) 23: 0.002(0.781) 63: -0.181(0.781) 15: 0.342(0.781)
n=419
Fiber vs Placebo effect in lipid reduction. TriglyceridesHedges unbiased g, Fixed effects
Fiber better Control better
Estimates with 95% confidence intervals
Absolute Baseline Reduction
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Subgroups u SS with ES>1
– Cholesterol and LDL u fiber food supplement compound u intake duration between 4 and 8 weeks u daily doses >10G/d
u Moderate SS ES – >8 weeks regimens
u -0.7 cholesterol and -0.8 LDL
u SS with ES≈1 – periods of study publication: no clear trend
u Adult population: replication of the main pooled effect because only 2 studies on childhood.
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Group P value
Hedges’ g estimator (random)
95% Lower Limit
95% Upper Limit
Main pooled effect 0.000 -1.007 -1.311 -0.703 Type of fiber
Fiber food supplement compound 0.000 -1.134 -1.561 -0.707 Diet or Cereals supplements 0.000 -0.869 -1.313 -0.426
Duration of fiber Intake <=4 weeks 0.310 -0.670 -1.966 0.625 >4 to <=8 weeks 0.000 -1.171 -1.539 -0.803 >8 weeks 0.024 -0.672 -1.255 -0.088
Daily dose < 5 G/d 0.939 -0.024 -0.644 0.596 >= 5 to 10 G/d 0.005 -0.908 -1.542 -0.275 >10 G/d 0.000 -1.123 -1.477 -0.769
Population Non Adults 0.303 -0.786 -2.282 0.711 Adults 0.000 -1.032 -1.350 -0.714
Year of publication 1988-1990 0.000 -1.807 -2.418 -1.196 1991-1993 0.001 -0.786 -1.234 -0.338 1994-1997 0.000 -0.971 -1.456 -0.486 >=1998 0.016 -0.370 -0.673 -0.068
Cholesterol
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LDL Group
P value
Hedges’ g estimator (random)
95% Lower Limit
95% Upper Limit
Main pooled effect 0.000 -1.023 -1.356 -0.690 Type of fiber
Fiber food supplement compound 0.000 -1.191 -1.569 -0.813 Diet or Cereals supplements 0.002 -0.833 -1.360 -0.306
Duration of fiber Intake <=4 weeks 0.437 -1.023 -3.601 1.555 >4 to <=8 weeks 0.000 -1.115 -1.447 -0.783 >8 weeks 0.036 -0.765 -1.480 -0.051
Daily dose < 5 G/d 0.389 0.274 -0.349 0.897 >= 5 to 10 G/d 0.022 -0.950 -1.761 -0.139 >10 G/d 0.000 -1.154 -1.457 -0.851
Population Non Adults 0.441 -0.942 -3.338 1.454 Adults 0.000 -1.029 -1.354 -0.704
Year of publication 1988-1990 0.001 -1.192 -1.891 -0.493 1991-1993 0.003 -1.102 -1.834 -0.370 1994-1997 0.001 -1.245 -2.008 -0.481 >=1998 0.008 -0.453 -0.788 -0.118
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Meta-análisis Ejemplo
Ferran Torres [email protected]
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Example u Fleiss JL The statistical basis of meta-analysis.
Statistical Methods in Medical research 1993; 2: 121-145.
Results of seven placebo-controlled randomised studies of the effect of aspirin in preventing death after myocardial infarction
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StudyAAS Placebo AAS Placebo
MRC-1 49 67 615 624CDP 44 64 758 771MRC-2 102 126 832 850GASP 32 38 317 309PARIS 85 104 810 812AMIS 246 219 2267 2257ISIS-2 1570 1720 8587 8600
deaths Total patients
Studies of aspirin in myocardial infarction
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Study OR y=ln(OR) se{lnOR} w Prop weightMRC-1 0.72 0.49 1.06 -0.33 0.19 26.3 2.9%CDP 0.68 0.46 1.01 -0.38 0.20 25.1 2.8%MRC-2 0.80 0.61 1.06 -0.22 0.14 49.3 5.4%GASP 0.80 0.49 1.32 -0.22 0.25 15.6 1.7%PARIS 0.79 0.54 1.16 -0.23 0.19 27.1 3.0%AMIS 1.13 0.94 1.37 0.12 0.10 104.3 11.4%ISIS-2 0.90 0.83 0.97 -0.11 0.04 665.1 72.9%
95% CI
8.910=∑ iw3.99yw ii −=∑Pooled estimate of ln(OR) =
OR = 0.90 (0.84 0.96)
11.08.9103.99
−=−
Meta-analysis of Aspirin trials
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Graphical representation
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Study OR y=ln(OR) se{lnOR} w Prop weightMRC-1 0.72 0.49 1.06 -0.33 0.19 26.3 2.9%CDP 0.68 0.46 1.01 -0.38 0.20 25.1 2.8%MRC-2 0.80 0.61 1.06 -0.22 0.14 49.3 5.4%GASP 0.80 0.49 1.32 -0.22 0.25 15.6 1.7%PARIS 0.79 0.54 1.16 -0.23 0.19 27.1 3.0%AMIS 1.13 0.94 1.37 0.12 0.10 104.3 11.4%ISIS-2 0.90 0.83 0.97 -0.11 0.04 665.1 72.9%
95% CI
Fixed OR = 0.90 (0.84 0.96)
Study OR y=ln(OR) var Prop weightMRC-1 0.72 0.46 1.10 -0.33 0.05 8.0%CDP 0.68 0.43 1.05 -0.38 0.05 8.0%MRC-2 0.80 0.57 1.12 -0.22 0.03 13.0%GASP 0.80 0.46 1.36 -0.22 0.07 5.0%PARIS 0.79 0.52 1.20 -0.23 0.05 9.0%AMIS 1.13 0.86 1.48 0.12 0.02 21.0%ISIS-2 0.90 0.72 1.10 -0.11 0.01 36.0%
95% CI
Random OR= 0.88 95%CI : (0.77 ; 0.99)
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10.4%-14.2% = 3.8%
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Meta-análisis Normativas
Ferran Torres [email protected]
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Guias y Normativas u ICH - E9: Statistical Principles for Clinical Trials Note
for Guidance on Statistical Principles for Clinical Trials. CMP/ICH/363/96. September 1998
u CPMP/EWP/2330/99: Validity and Interpretation of Pooled Analyses, and one Pivotal study
u The Potsdam International Consultation on Meta-analysis Potsdam, Germany, March 1994
u Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. http://www.prisma-statement.org/
u QUORUM. Statement. Lancet 1999; 354: 1896-1900.