meta-analysis in animal health and reproduction: methods and applications using stata ahmad rabiee...
TRANSCRIPT
Meta-analysis in animal health and reproduction: methods
and applications using Stata
Ahmad Rabiee Ian Lean
PO Box 660Camden 2570, NSWSBScibus.com.au
Meta-analysis
• Literature search • study quality assessment• Selection criteria• Statistical analysis • Heterogeneity• Publication bias
Methods of pooling study results
• Narrative procedure (conventional critical review method)
• Vote-counting method (significant results marked “+”, converse “–” and no significant results “neutral”)
• Combined tests (combining the probabilities obtain from two or more independent studies)
Systematic Reviews & Meta-analysis
• Systematic review is the entire process of collecting, reviewing and presenting all available evidence
• Meta-analysis is the statistical technique involved in extracting and combining data to produce a summary result
Aim of a meta-analysis
• To increase power
• To improve precision
• To answer questions not posed by the individual studies
• To settle controversies arising from apparently conflicting studies or
• To generate new hypothesis
Different types of data
• Dichotomous data (e.g. dead or live)
• Counts of events (e.g. no. of pregnancies)
• Short ordinal scales (e.g. pain score)
• Long ordinal scales (e.g. quality of life)
• Continuous data (e.g. cholesterol con.)
• Censored data or survival data (e.g. time to 1st service)
Statistical models
• Fixed effect models– Mantel-Haenszel (MH)
• Has optimal statistical power• Softwares are available for the analysis
– Peto test (modified MH method)• Recommended for non-experimental studies
• Random effect models– DerSimonian & Laird method– Bayesian method
• Regression models (Mixed model)
Fixed effect methods
• Mantel-Haenszel approach– Odd ratio– Risk ratio– Risk difference– Not recommended in review with sparse data (trials
with zero events in treatment or control group)• Peto method
– Odds ratio– Used in studies with small treatment effect and rare
events– Not a very common method– Used when the size of groups within trial are
balanced
Random effects analytic methods
• Odd ratio
• Risk ratio
• Risk difference
Dichotomous data
• Odds Ratio (OR)– The odds of the event occurring in one group divided by the
odds of the event occurring in the other group
• Relative risk or Risk Ratio (RR)– The risk of the events in one group divided by the risk of the event in the
other group
• Risk difference (RD; -1 to +1)– Risk in the experimental group minus risk in the control group
• Confidence interval (CI)– The level of uncertainty in the estimate of treatment effect– An estimate of the range in which the estimate would fall a fixed
percentage of times if the study repeated many times
Risk ratio vs. Odds ratio
• Odds ratio (OR) will always be further from the point of no effect than a risk ratio (RR)
• If event rate in the treatment group– OR & RR > 1, but– OR > RR
• If event rate in the treatment group– OR & RR < 1, but– OR < RR
Risk ratio vs. Odds ratio
• When the event is rare – OR and RR will be similar
• When the event is common– OR and RR will differ
• In situations of common events, odd ratio can be misleading
Meta-analysis features in Stata
1. metan
2. labbe
3. metacum
4. metap
5. metareg
6. metafunnel
7. confunnel
8. metabias
9. metatrim
10. metandi & metandiplot11. glst12. metamiss13. mvmeta & mvmeta_make14. metannt15. metaninf16. midas17. meta_lr18. metaparm
Source: http://www.stata.com/support/faqs/stat/meta.html
Metan in Stata
• Relative Risk (Fixed and Random effect model)• Fixedi= Fixed effect RR with inverse variance method• Fixed= M-H RR method
metan evtrt non_evtrt evctrl non_evctrl, rr fixed second(random)
favours(reduces pregnancy rate # increases pregnancy rate)
lcols(names outcome dose) by(status) sortby(outcome) force
astext(70) textsize(200) boxsca(80) xsize(10) ysize(6)
pointopt( msymbol(triangle) mcolor(gold) msize(tiny)
mlabel() mlabsize(vsmall) mlabcolor(forest_green) mlabposition(1))
ciopt( lcolor(sienna) lwidth(medium)) rfdist rflevel(95) counts
• Saving the graph in different formats
graph export "D:\Forest plot.gph", replace
graph export "D:\Forest plot.gph".png", replace
graph export "D:\Forest plot.gph".eps", replace
Forest plot using Metan (Risk Ratio)
. (0.95, 1.24)
. (0.93, 1.35)
. (0.91, 1.70)
with estimated predictive interval
with estimated predictive interval
with estimated predictive interval
.
.
.
.
.
M-H Overall (I-squared = 48.1%, p = 0.000)
Anderson & Malmo 1985
Lewis et al 1990
Lee et al 1983
Lee et al 1983
Dmitriev et al 1986Klinskii et al. 1987
Westhuysen 1980
M-H Subtotal (I-squared = 55.7%, p = 0.012)
Anderson & Malmo 1985
Roussel et al 1988
Chenault 1990
D+L Subtotal
Stevenson et al 1984
Bon Durant et al 1991
names
Pennington et al 1985Stevenson et al 1984
Lee et al 1983
Stevenson et al 1984
Chenault 1990
D+L SubtotalM-H Subtotal (I-squared = 31.2%, p = 0.058)
Goldbeck 1976
Stevenson et al 1988
Alacam et al 1986Macmillan & Taufa 1983
Lucy & Stevenson 1986
Lewis et al 1990
Grunert & Schwarz 1976
Anderson & Malmo 1985
Stevenson et al 1990
Schels & Mostafawi 1978
Schels & Mostafawi 1978
Repeat Breeder
Lee et atl 1983
Pennington et al 1985Lee et al 1985
Moller & Fielden 1981
D+L Overall
Westhuysen 1980
Lee et al 1983
Phatak et al 1986
Roussel et al 1988
Nakao et al 1983
Fielden & Moller 1983
Lewis et al 1990
Pennington et al 1985
Cycling
1st Service CP
2nd Service CP
1st Service CP
Pregnancy rate
1st Service CP1st Service CP
2nd Service CP
Pregnancy rate
Pregnancy rate
1st Service CP
2nd Service CP
Pregnancy rate
outcome
Pregnancy ratePregnancy rate
2nd Service CP
1st Service CP
1st Service CP
1st Service CP
Pregnancy rate
1st Service CP1st Service CP
1st Service CP
1st Service CP
1st Service CP
2nd Service CP
Pregnancy rate
1st Service CP
2nd Service CP
2nd Service CP
1st Service CP1st Service CP
1st Service CP1st Service CP
1st Service CP
Pregnancy rate
Pregnancy rate
1st Service CP
1st Service CP
Pregnancy rate
2nd Service CP
250
all
125
all
allall
all
all
all
125
all
all
dose
allall
all
125
all
250
all
allall
125
125
250
all
all
125
all
all
125125
allall
125
all
all
125
all
all
all
1.12 (1.08, 1.15)
1.09 (1.01, 1.17)
1.10 (0.74, 1.65)
0.93 (0.76, 1.14)
1.53 (1.27, 1.83)
1.17 (0.81, 1.71)1.54 (0.92, 2.58)
1.02 (0.75, 1.40)
1.22 (1.15, 1.31)
0.83 (0.61, 1.13)
2.10 (1.33, 3.33)
0.81 (0.66, 0.99)
1.24 (1.11, 1.38)
1.19 (0.91, 1.57)
1.10 (0.95, 1.28)
RR (95% CI)
1.18 (0.79, 1.78)1.22 (0.99, 1.51)
1.00 (0.87, 1.15)
1.04 (0.82, 1.31)
0.82 (0.67, 1.01)
1.09 (1.04, 1.13)1.08 (1.05, 1.12)
1.19 (1.02, 1.40)
1.39 (0.95, 2.04)
1.28 (0.95, 1.72)1.03 (0.93, 1.14)
1.94 (0.56, 6.73)
0.94 (0.72, 1.22)
1.20 (1.04, 1.38)
1.03 (0.85, 1.24)
1.21 (1.06, 1.39)
1.19 (0.93, 1.52)
1.39 (0.78, 2.45)
1.24 (1.07, 1.43)
1.01 (0.85, 1.18)1.00 (0.45, 2.23)
1.19 (1.02, 1.39)
1.12 (1.07, 1.17)
1.36 (0.98, 1.90)
1.24 (0.96, 1.60)
1.24 (1.07, 1.44)
1.41 (1.08, 1.84)
1.15 (1.03, 1.28)
1.10 (1.01, 1.20)
0.77 (0.41, 1.43)
0.98 (0.75, 1.28)
4144/7578
396/674
27/60
59/92
135/185
26/4620/35
12/15
1250/2586
26/59
40/45
94/242
55/100
214/495
Treatment
27/4984/144
Events,
74/92
69/146
95/240
2894/4992
87/107
20/37
27/33174/260
10/18
58/131
112/138
50/86
304/765
64/109
17/45
123/154
146/2826/12
170/29229/44
76/154
231/492
158/283
346/605
414/655
11/32
58/125
5893/11441
1529/2828
27/66
64/93
77/161
26/5413/35
25/32
1030/2571
160/302
11/26
117/243
48/104
184/468
Control
20/4375/157
Events,
75/93
83/182
117/243
4863/8870
73/107
40/103
23/36582/896
2/7
60/127
95/140
654/1156
235/717
54/109
15/55
94/146
136/2646/12
139/28430/62
58/146
177/469
38/96
293/589
371/647
13/29
54/114
100.00
14.81
0.65
1.60
2.07
0.600.33
0.40
23.81
1.32
0.35
2.94
1.18
4.76
(M-H)
0.541.81
Weight
1.88
1.86
2.93
76.19
1.84
0.53
0.556.59
0.07
1.53
2.37
2.28
6.11
1.36
0.34
2.43
3.540.15
3.550.63
1.50
4.56
1.43
7.47
9.39
0.34
1.42
%
1.12 (1.08, 1.15)
1.09 (1.01, 1.17)
1.10 (0.74, 1.65)
0.93 (0.76, 1.14)
1.53 (1.27, 1.83)
1.17 (0.81, 1.71)1.54 (0.92, 2.58)
1.02 (0.75, 1.40)
1.22 (1.15, 1.31)
0.83 (0.61, 1.13)
2.10 (1.33, 3.33)
0.81 (0.66, 0.99)
1.24 (1.11, 1.38)
1.19 (0.91, 1.57)
1.10 (0.95, 1.28)
RR (95% CI)
1.18 (0.79, 1.78)1.22 (0.99, 1.51)
1.00 (0.87, 1.15)
1.04 (0.82, 1.31)
0.82 (0.67, 1.01)
1.09 (1.04, 1.13)1.08 (1.05, 1.12)
1.19 (1.02, 1.40)
1.39 (0.95, 2.04)
1.28 (0.95, 1.72)1.03 (0.93, 1.14)
1.94 (0.56, 6.73)
0.94 (0.72, 1.22)
1.20 (1.04, 1.38)
1.03 (0.85, 1.24)
1.21 (1.06, 1.39)
1.19 (0.93, 1.52)
1.39 (0.78, 2.45)
1.24 (1.07, 1.43)
1.01 (0.85, 1.18)1.00 (0.45, 2.23)
1.19 (1.02, 1.39)
1.12 (1.07, 1.17)
1.36 (0.98, 1.90)
1.24 (0.96, 1.60)
1.24 (1.07, 1.44)
1.41 (1.08, 1.84)
1.15 (1.03, 1.28)
1.10 (1.01, 1.20)
0.77 (0.41, 1.43)
0.98 (0.75, 1.28)
4144/7578
396/674
27/60
59/92
135/185
26/4620/35
12/15
1250/2586
26/59
40/45
94/242
55/100
214/495
Treatment
27/4984/144
Events,
74/92
69/146
95/240
2894/4992
87/107
20/37
27/33174/260
10/18
58/131
112/138
50/86
304/765
64/109
17/45
123/154
146/2826/12
170/29229/44
76/154
231/492
158/283
346/605
414/655
11/32
58/125
reduces pregnancy rate increases pregnancy rate
1.149 1 6.73
Forest plot using Metan (SMD)
. (-0.53, 1.13)
. (-0.37, 0.80)
. (-0.11, 0.32)
with estimated predictive interval
with estimated predictive interval
with estimated predictive interval
Heterogeneity between groups: p = 0.000I-V Overall (I-squared = 79.2%, p = 0.000)
New York study
California study-2
Uchida at al.
D+L Subtotal
Kincaid and Socha.
D+L Overall
Texas study1
Snead et al.
Mexico study
California study-3
McKay et al
Toni et al.
Monardes et al.
California study-4
Reference
A
New York study1
I-V Subtotal (I-squared = 84.3%, p = 0.000)
Campbell et al.
D+L Subtotal
Nocek et al. (Year 2)
I-V Subtotal (I-squared = 27.5%, p = 0.199)
Ferguson et al.California study-1
Ballantine et al.
Colorado study
Nocek et al. (Year 1)
Texas study2
Lean et al.
P
Griffiths et al.Early-Mid-late
Early-Mid
Early
Early-Mid
Early-Mid
Early-Mid
Early-Mid-late
Early-Mid
Early-Mid-late
Early-Mid-late
Early
Early-Mid
Lact
Early-Mid-late
Early-Mid
Early-Mid-late
Early-Mid-lateEarly-Mid
Early-Mid-late
Early-Mid-late
Early-Mid-late
Early-Mid-late
Early-Mid-late
Early-Mid-lateTMR+15
TMR
TMR
TMR
TMR
TMR
TMR
TMR
Pasture
Comp
TMR
TMR
Diet
TMR
TMR+10
TMR
TMRTMR
TMR
TMR
TMR
TMR
PMR (Pasture+TMR)
Pasture
0.20 (0.14, 0.26)
0.22 (-0.03, 0.47)
0.10 (-0.17, 0.37)
-0.25 (-0.88, 0.37)
0.30 (0.08, 0.52)
-0.08 (-0.74, 0.57)
0.22 (0.09, 0.35)
0.18 (-0.08, 0.43)
-0.05 (-0.56, 0.45)
0.63 (0.22, 1.05)
0.03 (-0.34, 0.41)
-0.03 (-0.22, 0.15)
0.17 (-0.12, 0.46)
-0.13 (-0.79, 0.54)
0.01 (-0.32, 0.35)
SMD (95% CI)
0.11 (-0.21, 0.43)
0.30 (0.22, 0.38)
0.18 (-0.32, 0.69)
0.10 (0.01, 0.20)
0.98 (0.69, 1.27)
0.10 (0.02, 0.18)
0.06 (-0.28, 0.39)0.13 (-0.19, 0.44)
0.36 (0.11, 0.61)
0.36 (0.08, 0.63)
1.25 (0.96, 1.54)
0.11 (-0.04, 0.27)
-0.00 (-0.18, 0.17)
0.18 (0.01, 0.35)
2498
125, 37.8 (5.03)
105, 44.6 (8.81)
20, 44.4 (1.97)
18, 41.7 (5.94)
161, 40.6 (10.9)
30, 33.9 (6.99)
46, 37.3 (2.68)
50, 43.8 (6.08)
229, 17.1 (3.03)
90, 34.8 (5.88)
17, 36.7 (8.45)
50, 43.8 (6.08)
(SD); TreatmentN, mean
93, 29.8 (10.2)
1296
30, 35.7 (6.02)
102, 43.5 (2.02)
1202
63, 28.6 (3.96)105, 44.6 (8.81)
128, 41.8 (3.39)
104, 36.8 (5.25)
107, 37.6 (2.07)
315, 36.2 (8.87)
233, 25.7 (4.27)
277, 17.5 (4.99)
2488
125, 36.7 (5.03)
109, 43.7 (8.98)
20, 44.9 (1.97)
18, 42.2 (5.94)
94, 38.8 (8.34)
30, 34.2 (5.31)
46, 35.6 (2.68)
62, 43.5 (6.77)
229, 17.2 (3.03)
90, 33.8 (5.88)
18, 37.8 (8.7)
109, 43.7 (8.98)
(SD); ControlN, mean
65, 28.7 (9.39)
1176
30, 34.6 (6.02)
106, 41.5 (2.06)
1312
73, 28.4 (3.91)62, 43.5 (6.77)
123, 40.6 (3.33)
103, 34.8 (5.6)
109, 35 (2.09)
313, 35.2 (7.96)
276, 25.7 (4.32)
278, 16.6 (5)
100.00
5.13
4.41
0.82
0.74
4.88
1.24
1.81
2.28
9.45
3.70
0.72
2.83
(I-V)Weight
3.15
48.87
1.23
3.83
%
51.13
2.793.21
5.09
4.20
3.72
12.94
10.43
11.40
0.20 (0.14, 0.26)
0.22 (-0.03, 0.47)
0.10 (-0.17, 0.37)
-0.25 (-0.88, 0.37)
0.30 (0.08, 0.52)
-0.08 (-0.74, 0.57)
0.22 (0.09, 0.35)
0.18 (-0.08, 0.43)
-0.05 (-0.56, 0.45)
0.63 (0.22, 1.05)
0.03 (-0.34, 0.41)
-0.03 (-0.22, 0.15)
0.17 (-0.12, 0.46)
-0.13 (-0.79, 0.54)
0.01 (-0.32, 0.35)
SMD (95% CI)
0.11 (-0.21, 0.43)
0.30 (0.22, 0.38)
0.18 (-0.32, 0.69)
0.10 (0.01, 0.20)
0.98 (0.69, 1.27)
0.10 (0.02, 0.18)
0.06 (-0.28, 0.39)0.13 (-0.19, 0.44)
0.36 (0.11, 0.61)
0.36 (0.08, 0.63)
1.25 (0.96, 1.54)
0.11 (-0.04, 0.27)
-0.00 (-0.18, 0.17)
0.18 (0.01, 0.35)
2498
125, 37.8 (5.03)
105, 44.6 (8.81)
20, 44.4 (1.97)
18, 41.7 (5.94)
161, 40.6 (10.9)
30, 33.9 (6.99)
46, 37.3 (2.68)
50, 43.8 (6.08)
229, 17.1 (3.03)
90, 34.8 (5.88)
17, 36.7 (8.45)
50, 43.8 (6.08)
(SD); TreatmentN, mean
93, 29.8 (10.2)
1296
30, 35.7 (6.02)
102, 43.5 (2.02)
1202
63, 28.6 (3.96)105, 44.6 (8.81)
128, 41.8 (3.39)
104, 36.8 (5.25)
107, 37.6 (2.07)
315, 36.2 (8.87)
233, 25.7 (4.27)
277, 17.5 (4.99)
reduces milk yield increases milk yield
0-1.54 0 1.54
Forest plot using Metan (WMD)
. (0.31, 2.81)
. (-0.68, 1.51)
. (-1.05, 2.91)
with estimated predictive interval
with estimated predictive interval
with estimated predictive interval
Heterogeneity between groups: p = 0.000I-V Overall (I-squared = 72.2%, p = 0.000)
D+L Subtotal
Griffiths et al.
Nocek et al. (Year 2)
Campbell et al.Snead et al.
Uchida at al.
Colorado study
A
Ferguson et al.
California study-4Ballantine et al.
New York study1
Texas study1
Kincaid and Socha.
I-V Subtotal (I-squared = 38.3%, p = 0.113)
California study-2
Reference
New York study
I-V Subtotal (I-squared = 37.0%, p = 0.080)Nocek et al. (Year 1)
Lean et al.
California study-1
California study-3
Texas study2
McKay et al
D+L Subtotal
Monardes et al.
D+L Overall
Toni et al.
Mexico studyP
Early-Mid-late
Early-Mid-late
Early-MidEarly-Mid
Early
Early-Mid-late
Early-Mid-late
Early-MidEarly-Mid-late
Early-Mid-late
Early-Mid
Early-Mid
Early-Mid
Lact
Early-Mid-late
Early-Mid-late
Early-Mid-late
Early-Mid
Early-Mid
Early-Mid-late
Early-Mid-late
Early
Early-Mid-late
Early-Mid-late
Pasture
TMR
TMR+10TMR
TMR
TMR
TMR
TMRTMR
TMR
TMR
TMR
TMR
Diet
TMR+15
TMR
PMR (Pasture+TMR)
TMR
TMR
TMR
Pasture
TMR
Comp
TMR
1.12 (0.90, 1.35)
0.42 (-0.03, 0.87)
0.90 (0.07, 1.73)
2.00 (1.45, 2.55)
1.10 (-1.95, 4.15)-0.32 (-3.46, 2.82)
-0.50 (-1.72, 0.72)
1.94 (0.46, 3.42)
0.22 (-1.11, 1.55)
0.09 (-2.29, 2.47)1.20 (0.37, 2.03)
1.10 (-1.98, 4.18)
1.80 (-0.58, 4.18)
-0.50 (-4.38, 3.38)
0.35 (0.03, 0.67)
0.91 (-1.47, 3.29)
WMD (95% CI)
1.10 (-0.15, 2.35)
1.90 (1.58, 2.22)2.60 (2.05, 3.15)
-0.01 (-0.76, 0.74)
1.04 (-1.34, 3.42)
0.22 (-2.16, 2.60)
0.96 (-0.36, 2.28)
-0.10 (-0.65, 0.45)
1.56 (1.05, 2.07)
-1.10 (-6.78, 4.58)
0.93 (0.42, 1.44)
1.00 (-0.72, 2.72)
1.70 (0.60, 2.80)
2498
277, 17.5 (4.99)
102, 43.5 (2.02)
30, 35.7 (6.02)30, 33.9 (6.99)
20, 44.4 (1.97)
104, 36.8 (5.25)
63, 28.6 (3.96)
50, 43.8 (6.08)128, 41.8 (3.39)
93, 29.8 (10.2)
161, 40.6 (10.9)
18, 41.7 (5.94)
1202
105, 44.6 (8.81)
(SD); Treatment
125, 37.8 (5.03)
1296107, 37.6 (2.07)
233, 25.7 (4.27)
105, 44.6 (8.81)
50, 43.8 (6.08)
315, 36.2 (8.87)
N, mean
229, 17.1 (3.03)
17, 36.7 (8.45)
90, 34.8 (5.88)
46, 37.3 (2.68)
2488
278, 16.6 (5)
106, 41.5 (2.06)
30, 34.6 (6.02)30, 34.2 (5.31)
20, 44.9 (1.97)
103, 34.8 (5.6)
73, 28.4 (3.91)
109, 43.7 (8.98)123, 40.6 (3.33)
65, 28.7 (9.39)
94, 38.8 (8.34)
18, 42.2 (5.94)
1312
109, 43.7 (8.98)
(SD); Control
125, 36.7 (5.03)
1176109, 35 (2.09)
276, 25.7 (4.32)
62, 43.5 (6.77)
62, 43.5 (6.77)
313, 35.2 (7.96)
N, mean
229, 17.2 (3.03)
18, 37.8 (8.7)
90, 33.8 (5.88)
46, 35.6 (2.68)
100.00
7.30
16.42
0.540.51
3.39
2.31
2.86
0.897.30
0.53
0.89
0.34
50.14
0.89
(I-V)
3.24
49.8616.42
9.00
0.89
0.89
2.90
Weight
16.42
0.16
1.71
4.21
%
1.12 (0.90, 1.35)
0.42 (-0.03, 0.87)
0.90 (0.07, 1.73)
2.00 (1.45, 2.55)
1.10 (-1.95, 4.15)-0.32 (-3.46, 2.82)
-0.50 (-1.72, 0.72)
1.94 (0.46, 3.42)
0.22 (-1.11, 1.55)
0.09 (-2.29, 2.47)1.20 (0.37, 2.03)
1.10 (-1.98, 4.18)
1.80 (-0.58, 4.18)
-0.50 (-4.38, 3.38)
0.35 (0.03, 0.67)
0.91 (-1.47, 3.29)
WMD (95% CI)
1.10 (-0.15, 2.35)
1.90 (1.58, 2.22)2.60 (2.05, 3.15)
-0.01 (-0.76, 0.74)
1.04 (-1.34, 3.42)
0.22 (-2.16, 2.60)
0.96 (-0.36, 2.28)
-0.10 (-0.65, 0.45)
1.56 (1.05, 2.07)
-1.10 (-6.78, 4.58)
0.93 (0.42, 1.44)
1.00 (-0.72, 2.72)
1.70 (0.60, 2.80)
2498
277, 17.5 (4.99)
102, 43.5 (2.02)
30, 35.7 (6.02)30, 33.9 (6.99)
20, 44.4 (1.97)
104, 36.8 (5.25)
63, 28.6 (3.96)
50, 43.8 (6.08)128, 41.8 (3.39)
93, 29.8 (10.2)
161, 40.6 (10.9)
18, 41.7 (5.94)
1202
105, 44.6 (8.81)
(SD); Treatment
125, 37.8 (5.03)
1296107, 37.6 (2.07)
233, 25.7 (4.27)
105, 44.6 (8.81)
50, 43.8 (6.08)
315, 36.2 (8.87)
N, mean
229, 17.1 (3.03)
17, 36.7 (8.45)
90, 34.8 (5.88)
46, 37.3 (2.68)
reduces milk yield increases milk yield
0-6.78 0 6.78
Homogeneity
• Meta-analysis should only be considered when a group of trials is sufficiently homogeneous in terms of participations, interventions and outcomes to provide a meaningful summary
Examination for heterogeneity
• Examination for “heterogeneity” involves determination of whether individual differences between study outcomes are greater than could be expected by chance alone.
• Analysis of “heterogeneity” is the most important function of MA, often more important than computing an “average” effect.
Differences between studies
• By different investigators
• In different settings
• In different countries
• In different ways
• For different length of time
• To look at different outcomes
• Etc.
Studies differ in 3 basic ways
• Clinical diversity: Variability in the participants, interventions and outcomes studied
• Methodological diversity: Variability in the trial design and quality
• Statistical heterogeneity: Variability in the treatment effects being evaluated in the different trials. This is a consequence of clinical and/or methodological diversity among the studies
Methods for estimation of heterogeneity
• Conventional chi-square (χ2) analysis (P>0.10)• I2= [(Q-df)/Q x 100% (Higgins et al. 2003), where
Q is the chi-squared statistic; df is its degrees of freedom
• Graphical test-forest plots (OR or RR and confidence intervals)
• L’Abbe plots (outcome rates in treatment and control groups are plotted on the vertical and horizontal axes)
• Galbraith plot • Regression analysis• Comparing the results of fixed and random effect
models (a crude assessment of heterogeneity)
L’Abbe plot0
.25
.5.7
51
Even
t ra
te g
roup
1
0 .25 .5 .75 1Event rate group 2
0.2
5.5
.75
1E
ven
t ra
te g
roup
10 .25 .5 .75 1
Event rate group 2
Null Odds ratioRisk ratio Studies
labbe evtrt non evtrt evctrl nonevctrl, rr(1.21) null labbe evtrt nonevtrt evctrl nonevctrl, rr(1.21) or(1.30) null
Galbraith plot
b/se
(b)
1/se(b)
b/se(b) Fitted values
0 11.5116
-2-2
0
2
4.72877
b/se
(b)
1/se(b)
b/se(b) Fitted values
0 14.9965
-2-2
0
2
3.8419
galbr logrr selogES (dichotomous data)
Strategies for addressing heterogeneity
• Check again that the data are correct• Do not do a meta-analysis• Ignore heterogeneity (fixed effect model)• Perform a random effects meta-analysis• Change the effect measure (e.g. different
scale or units)• Split studies into subgroups• Investigate heterogeneity using meta-
regression• Exclude studies
Sensitivity analysis(sub-group)
• A process for re-analysing the same data set
• A range of principles used, depends on– Choice of statistical test– Inclusion criteria– Inclusion of both published and unpublished
Meta-regression
• To investigate whether heterogeneity among results of multiple studies is related to specific characteristics of the studies (e.g. dose rate)
• To investigate whether particular covariate (potential ‘effect modifier’) explain any of the heterogeneity of treatment effect between studies
• Can find out if there is evidence of different effects
in different subgroups of trials
• It is appropriate to use meta-regression to explore sources of heterogeneity even if an initial overall test for heterogeneity is non-significant
Meta-regression-1
metareg _ES bcalving acalving full_lact monen_other bstcode apcode, wsse(_seES) bsest(reml)
Meta-regression Number of obs = 23
REML estimate of between-study variance tau2 = .04357
% residual variation due to heterogeneity I-squared_res = 65.24%
Proportion of between-study variance explained Adj R-squared = 51.05%
Joint test for all covariates Model F(6,16) = 3.50
With Knapp-Hartung modification Prob > F = 0.0209
-------------------------------------------------------------------------------------------------------------
_ES | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+-----------------------------------------------------------------------------------------------
bcalving | -.0028578 .0031445 -0.91 0.377 -.0095239 .0038083
acalving | -.0007429 .0013228 -0.56 0.582 -.0035472 .0020613
full_lact | .3517979 .2544234 1.38 0.186 -.1875556 .8911513
other s| .3403943 .1278838 2.66 0.017 .0692928 .6114959
bstcode | -.0333014 .1370641 -0.24 0.811 -.3238642 .2572614
apcode | .4589506 .1391693 3.30 0.005 .1639249 .7539762
_cons | -.3564435 .2521411 -1.41 0.177 -.8909586 .1780717
-----------------------------------------------------------------------------------------------------------
Meta-regression
metareg _ES full_lact monen_other apcode, wsse(_seES) bsest(reml)
Meta-regression Number of obs = 23
REML estimate of between-study variance tau2 = .04134
% residual variation due to heterogeneity I-squared_res = 66.02%
Proportion of between-study variance explained Adj R-squared = 53.55%
Joint test for all covariates Model F(3,19) = 6.63
With Knapp-Hartung modification Prob > F = 0.0030
---------------------------------------------------------------------------------------------------------
_ES | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+-------------------------------------------------------------------------------------------
full_lact | .3138975 .117573 2.67 0.015 .0678144 .5599807
others | .3640601 .124601 2.92 0.009 .1032672 .6248529
apcode | .4385834 .1253647 3.50 0.002 .1761921 .700974
_cons | -.4478162 .1598295 -2.80 0.011 -.7823432 -.1132892
-------------------------------------------------------------------------------------------------------
Funnel Plots
Publication bias
+ve results more likely To be published (publication bias) To be published rapidly (time lag bias) To be published in English (language bias) To be published more than once (multiple
publications bias) To be cited by others (citation bias)
Sources of Bias
Bias arising from the studies included in the review
Bias arising from the way the review is done
Publication bias is only one of the possible reasons for asymmetrical funnel plot
Funnel plot should been seen as a means of examining “small study effect”
Publication bias
Funnel plot
Publication bias exists (asymmetrical)
Publication bias doesn’t exists (symmetrical)For continuous data- Effect size plotted vs SE or
sample sizeFor dichotomous data- LogOR or RR vs logSE or
sample size
Fail Safe Number (F)
Z= (∑ ES/1.645)2-N: (where N= no of papers; ∑ ES is summed of effect size over all studies)- for calculation of unpublished studies that would be required to negate the results of a significantly positive ES analysis.
0.2
.4.6
.81
se(S
MD
)
-2 -1 0 1 2Standardized mean difference (SMD)
Funnel plot with pseudo 95% confidence limits0
.2.4
.6.8
se(S
MD
)
-2 -1 0 1 2Standardized mean difference (SMD)
Funnel plot with pseudo 95% confidence limits
0.2
.4.6
.8S
tand
ard
err
or
-2 -1 0 1 2Effect estimate
Funnel plot with pseudo 95% confidence limits
0
.2
.4
.6
.8
Sta
nd
ard
err
or
-2 -1 0 1 2Effect estimate
Studies
0.01
0.05
0.1
Filled funnel plot with pseudo 95% confidence limits
th
eta
, fill
ed
s.e. of: theta, filled0 .2 .4 .6 .8
-2
-1
0
1
2
Funnel plot (continuous data)metabias _ES _seES, egger
Contour-enhanced funnel plotconfunnel _ES _seES
Trim & Fillmetatrim _ES _seES, funnel print
Continuous data
0.2
.4.6
se(l
og
RR
)
-1 -.5 0 .5 1 1.5log_ES
Funnel plot with pseudo 95% confidence limits
0
.2
.4
.6
Sta
nd
ard
err
or
-2 -1 0 1 2Effect estimate
Studies
0.01
0.05
0.1
Filled funnel plot with pseudo 95% confidence limits
th
eta
, fil
led
s.e. of: theta, filled0 .2 .4 .6
-1
0
1
2
Funnel plot metabias _logES _selogES, egger
Contour-enhanced funnel plotconfunnel _logES _selogES
Trim & Fill metatrim _logES _selogES, funnel print
Dichotomus data
Testing for funnel plot asymmetry-1
Cochrane group suggests that that tests for funnel plot asymmetry should be used in only a minority of meta-analyses (Ioannidis 2007)
Begg’s rank correlation test (adjusted rank correlation-low power) This test is NOT recommended with any type of data
Eggers linear regression test (regression analysis-low power) This test is mainly recommended for continuous data
Testing for funnel plot asymmetry-2
Peters (2006) & Harbord (2006) tests These tests are suitable for dichotomous data
with odds ratios False-positive results may occur in the presence
of substantial between-study heterogeneity
For dichotomous outcomes with risk ratios (RR) or risk differences (RD)
Firm guidance is not yet available
Correcting for publication bias
Trim and fill method (tail of the side of the funnel plot with smaller trials chopped off)
Fail safe N (required studies to overturn positive results)
Modelling for the probability of studies not published
Conclusion: there is no definite answer for assessing the presence of publication bias
Influence analysis
0.85 1.39 0.92 2.11 2.34
Beckett (1998)
Duffield (1998)
Heuer (2001)
Duffield (2002)
Green_A (2004)
Green_B (2004)
Green_C (2004)
Green_D (2004)
Green_E (2004)
Green_F (2004)
Melendez (2006)
Lower CI Limit Estimate Upper CI Limit Meta-analysis estimates, given named study is omitted
metaninf nt mean_t sd_t nc mean_c sd_c, label(namevar=study year) random cohen
References
• www.stata.com/support/faqs/stat/meta.html
• Cochrane Collaboration Open learning material for reviewers (2002)
• Higgins et al. (2001). BMJ 327: 557-560
• Sterne et al. (2001). BMJ 323: 101-105
• Whitehead A (2002). Meta-analysis of Controlled Clinical Trials