Meta-regression using data from a HTA (Acellular Dermal Matrix)
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Author: Xuanqian Xie I would like to illustrate the meta-regression using the data from recent published HTA report (

Author: Xuanqian Xie


I would like to illustrate the meta-regression using the data from recent published HTA report (Nicolau et al. 2012).  I selected total of complications as interested outcomes, because it was the commonest outcomes and was reported in 7 of 10 studies, and the number of events of this outcomes are relatively large.

I used the Restricted maximum likelihood (REML)(proc mixed in SAS, but I used R package, metaphor, here) in meta-regression because as far as I know, other methods is rarely used in the meta-regression.

I selected 4 covariates, difference in age, difference in BMI, ratio of smoking and ratio of X-ray therapy. Basically, only the Ratio of X-ray therapy moderately influences the RR.   Now, I summarize the results below.

 

Reference:

Nicolau I, Xie X, McGregor M and Dendukuri N. Evaluation of Acellular Dermal Matrix for Breast Reconstruction: An Update. Montreal (Canada): Technology Assessment Unit (TAU) of the McGill University Health Centre (MUHC); 2012 June 4. Report no. 59. 42p. Available from: http://www.mcgill.ca/tau/sites/mcgill.ca.tau/files/muhc_tau_2012_59_dermalmatrix.pdf

 

#Date of creating the data for the analysis: February 2012.

#Last date of modification: May 1st 2012

#Software package: R 2.12, metafor package

 

#1 Meta-analysis

#1.1 estimator: REML

#1.2 Test by the DerSimonian-Laird estimator

#2 meta-regression

# 2.1: Age

# 2.2: BMI

# 2.3: Smoke

# 2.4: X-ray therapy

 

1.       Age

Six eligible articles.

1.1Meta-analysis: 

Random-Effects Model (k = 6; tau^2 estimator: REML)

tau^2 (estimate of total amount of heterogeneity): 0.1744 (SE = 0.1608)

Model Results:

estimate       se     zval     pval    ci.lb    ci.ub         

  0.3391   0.2075   1.6345   0.1022  -0.0675   0.7457  

Please note: RR= exp (estimate)

1.2Meta-regression

Mixed-Effects Model (k = 6; tau^2 estimator: REML)

tau^2 (estimate of residual amount of heterogeneity): 0.2275 (SE = 0.2255)

Test of Moderators (coefficient(s) 2):

QM(df = 1) = 0.0077, p-val = 0.9299

Model Results:

          estimate      se     zval    pval    ci.lb   ci.ub  

intrcpt     0.3352  0.2600   1.2894  0.1973  -0.1743  0.8447  

Age_diff   -0.0061  0.0690  -0.0880  0.9299  -0.1414  0.1293  

 

1.3Interprtation

a. Age_diff does not impact the RR.

b. The moderator, Age_diff, increases the heterogeneity, tau^2  .

 

2. BMI

Five eligible articles.

2.1Meta-analysis: 

Random-Effects Model (k = 5; tau^2 estimator: REML)

tau^2 (estimate of total amount of heterogeneity): 0.1725 (SE = 0.1677)

Model Results:

estimate       se     zval     pval    ci.lb    ci.ub         

  0.2663   0.2187   1.2179   0.2233  -0.1623   0.6949         

2.2Meta-regression

Mixed-Effects Model (k = 5; tau^2 estimator: REML)

tau^2 (estimate of residual amount of heterogeneity): 0.2312 (SE = 0.2467)

Test of Moderators (coefficient(s) 2):

QM(df = 1) = 0.0916, p-val = 0.7621

Model Results:

          estimate      se    zval    pval    ci.lb   ci.ub  

intrcpt     0.2570  0.2478  1.0369  0.2998  -0.2288  0.7427  

BMI_Diff    0.0276  0.0913  0.3027  0.7621  -0.1513  0.2066 

2.3Interprtation

a. BMI_Diff does not impact the RR.

b. The moderator, BMI_Diff, increases the heterogeneity, tau^2  .

 

3. Smoking

Four eligible articles.

3.1Meta-analysis: 

Random-Effects Model (k = 4; tau^2 estimator: REML)

tau^2 (estimate of total amount of heterogeneity): 0.2608 (SE = 0.2807)

Model Results:

estimate       se     zval     pval    ci.lb    ci.ub          

  0.3919   0.2946   1.3303   0.1834  -0.1855   0.9693 

3.2Meta-regression

Mixed-Effects Model (k = 4; tau^2 estimator: REML)

tau^2 (estimate of residual amount of heterogeneity): 0.3008 (SE = 0.4050)

Test of Moderators (coefficient(s) 2):

QM(df = 1) = 0.5390, p-val = 0.4629

Model Results:

          estimate      se     zval    pval    ci.lb   ci.ub  

intrcpt    -0.3541  1.0708  -0.3307  0.7409  -2.4528  1.7446  

Smoke_RR    1.1324  1.5425   0.7341  0.4629  -1.8908  4.1555 

3.3Interprtation

a. Smoke_RR does not impact the RR.

b. The moderator, Smoke_RR, increases the heterogeneity, tau^2  .

 

4. X-ray therapy

Five eligible articles.

4.1Meta-analysis: 

Random-Effects Model (k = 5; tau^2 estimator: REML)

tau^2 (estimate of total amount of heterogeneity): 0.0096 (SE = 0.0563)

Model Results:

estimate       se     zval     pval    ci.lb    ci.ub         

  0.5490   0.1263   4.3469   <.0001   0.3014   0.7965      ***

4.2Meta-regression

Mixed-Effects Model (k = 5; tau^2 estimator: REML)

tau^2 (estimate of residual amount of heterogeneity): 0 (SE = 0.0609)

Test of Moderators (coefficient(s) 2):

QM(df = 1) = 3.3731, p-val = 0.0663

Model Results:

         estimate      se     zval    pval    ci.lb   ci.ub   

intrcpt    1.7292  0.6470   2.6728  0.0075   0.4612  2.9972  **

XRT_RR    -1.0793  0.5877  -1.8366  0.0663  -2.2311  0.0725   .

 

Predicted RR (XRT_RR from 07 to 1.5)

     pred    se  ci.lb  ci.ub  cr.lb  cr.ub X.intrcpt X.XRT_RR

1  2.6477    NA 1.6147 4.3416 1.6147 4.3416         1     0.70

2  2.5086    NA 1.6095 3.9100 1.6095 3.9100         1     0.75

3  2.3768    NA 1.6013 3.5278 1.6013 3.5278         1     0.80

4  2.2519    NA 1.5889 3.1916 1.5889 3.1916         1     0.85

5  2.1336    NA 1.5706 2.8986 1.5706 2.8986         1     0.90

6  2.0215    NA 1.5435 2.6476 1.5435 2.6476         1     0.95

7  1.9153    NA 1.5044 2.4385 1.5044 2.4385         1     1.00

8  1.8147    NA 1.4495 2.2720 1.4495 2.2720         1     1.05

9  1.7194    NA 1.3770 2.1469 1.3770 2.1469         1     1.10

10 1.6290    NA 1.2892 2.0585 1.2892 2.0585         1     1.15

11 1.5435    NA 1.1919 1.9987 1.1919 1.9987         1     1.20

12 1.4624    NA 1.0916 1.9591 1.0916 1.9591         1     1.25

13 1.3855    NA 0.9932 1.9330 0.9932 1.9330         1     1.30

14 1.3128    NA 0.8996 1.9157 0.8996 1.9157         1     1.35

15 1.2438    NA 0.8124 1.9043 0.8124 1.9043         1     1.40

16 1.1784    NA 0.7320 1.8971 0.7320 1.8971         1     1.45

17 1.1165    NA 0.6587 1.8927 0.6587 1.8927         1     1.50

 

 RR_base_XRT <- exp (0.5490);

RR_base_XRT= 1.731521

> RR_base_XRT_lb <- exp(rr_XRT1$ci.lb); RR_base_XRT_lb

[1] 1.351804

> RR_base_XRT_ub <- exp(rr_XRT1$ci.ub); RR_base_XRT_ub

[1] 2.217737

4.3Interprtation

a. XRT_RR  moderately influence RR (p=0.066).

b. The moderator, XRT_RR  , reduces the heterogeneity, tau^2 , to zero .

c. The predicted RR when XRT_RR=1, is 1.9153(95% Cl, 1.5044, 2.4385). Without adjustment of covariate, the RR is 1.73(95% Cl, 1.35, 2.21).