Prevalence Ratio Meta-analysis

Packages

library(tidyverse)

── Attaching packages ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
✔ ggplot2 3.2.0     ✔ purrr   0.3.2
✔ tibble  2.1.3     ✔ dplyr   0.8.3
✔ tidyr   1.0.0     ✔ stringr 1.4.0
✔ readr   1.3.1     ✔ forcats 0.4.0
── Conflicts ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

First try

(
  mtprop <-
    meta::metaprop(
      event = num,
      n = denom,
      studlab = study,
      byvar = droplevels(tgroup),
      data = df
    )
)

                  proportion           95%-CI %W(fixed) %W(random) byvar
Manos, 1999           0.3947 [0.3638; 0.4262]        --         --     1
Bergeron, 2000        0.4324 [0.3387; 0.5298]        --         --     1
Lytwyn, 2000          0.4035 [0.2756; 0.5418]        --         --     1
Shlay, 2000           0.3128 [0.2485; 0.3830]        --         --     1
Morin, 2001           0.2917 [0.2452; 0.3416]        --         --     1
Rebello, 2001         0.4133 [0.3008; 0.5330]        --         --     3
Solomon, 2001         0.5676 [0.5470; 0.5879]        --         --     1
Zielinski, 2001       0.3474 [0.2837; 0.4155]        --         --     3
Kulasingam, 2002      0.5111 [0.4498; 0.5722]        --         --     1
Pretorius, 2002       0.3224 [0.2928; 0.3532]        --         --     1
Cuzick, 2003          0.2602 [0.1852; 0.3470]        --         --     3
Guyot, 2003           0.5217 [0.3059; 0.7318]        --         --     3
Lonky, 2003           0.4604 [0.4007; 0.5210]        --         --     1
Wensveen, 2003        0.4527 [0.3708; 0.5365]        --         --     1
Bruner, 2004          0.2688 [0.1821; 0.3708]        --         --     2
Rowe, 2004            0.4400 [0.3804; 0.5009]        --         --     1
Andersson, 2005       0.4423 [0.3047; 0.5867]        --         --     1
Dalla Palma, 2005     0.6987 [0.6202; 0.7695]        --         --     1
Giovannelli, 2005     0.2283 [0.1472; 0.3275]        --         --     1
Kendall, 2005         0.3410 [0.3302; 0.3520]        --         --     1
Nieh, 2005            0.7424 [0.6199; 0.8422]        --         --     1
Bergeron, 2006        0.4441 [0.4215; 0.4669]        --         --     1
Kelly, 2006           0.7255 [0.5826; 0.8411]        --         --     2
Kiatpongsan, 2006     0.3889 [0.2879; 0.4974]        --         --     1
Ko, 2006              0.4010 [0.3810; 0.4213]        --         --     2
Monsonego, 2006       0.4789 [0.3588; 0.6008]        --         --     1
Moss, 2006            0.4564 [0.4402; 0.4727]        --         --     3
Selvaggi, 2006        0.3958 [0.3586; 0.4339]        --         --     2
Wright, 2006          0.3409 [0.3149; 0.3675]        --         --     2
Cuschieri, 2007       0.6053 [0.5319; 0.6753]        --         --     3
Ronco, 2007           0.3144 [0.2814; 0.3488]        --         --     1
You, 2007             0.4629 [0.4340; 0.4919]        --         --     2

Number of studies combined: k = 32

                     proportion           95%-CI  z p-value
Fixed effect model       0.4072 [0.4013; 0.4132] --      --
Random effects model     0.4269 [0.3842; 0.4706] --      --

Quantifying heterogeneity:
tau^2 = 0.2318; H = 6.44; I^2 = 97.6%

Quantifying residual heterogeneity:
H = 4.81 [4.33; 5.35]; I^2 = 95.7% [94.7%; 96.5%]

Test of heterogeneity:
      Q d.f.  p-value             Test
 740.38   31 < 0.0001 Likelihood-Ratio

Results for subgroups (fixed effect model):
                                 k proportion           95%-CI      Q  tau^2   I^2
byvar = ASCUS                   20     0.3979 [0.3905; 0.4054] 562.93 0.2371 97.3%
byvar = ASC-US                   6     0.4003 [0.3875; 0.4132]  63.59 0.2535 98.0%
byvar = BORDERLINE DYSKARYOSIS   6     0.4516 [0.4367; 0.4665]  45.10 0.1961 91.0%

Test for subgroup differences (fixed effect model):
                    Q d.f.  p-value
Between groups  41.96    2 < 0.0001
Within groups  671.62   29 < 0.0001

Results for subgroups (random effects model):
                                 k proportion           95%-CI      Q  tau^2   I^2
byvar = ASCUS                   20     0.4285 [0.3745; 0.4843] 562.93 0.2371 97.3%
byvar = ASC-US                   6     0.4223 [0.3241; 0.5272]  63.59 0.2535 98.0%
byvar = BORDERLINE DYSKARYOSIS   6     0.4265 [0.3347; 0.5236]  45.10 0.1961 91.0%

Test for subgroup differences (random effects model):
                    Q d.f. p-value
Between groups   0.01    2  0.9946

Details on meta-analytical method:
- Random intercept logistic regression model
- Maximum-likelihood estimator for tau^2
- Logit transformation
- Clopper-Pearson confidence interval for individual studies

Second try

(meta <- meta::metaprop(event = event.e,
             n = n.e, studlab = paste(author, year),
             byvar = cut(year, 3),
             data = Olkin95[1:20,]))

                  proportion           95%-CI %W(fixed) %W(random) byvar
Fletcher 1959         0.0833 [0.0021; 0.3848]        --         --     1
Dewar 1963            0.1905 [0.0545; 0.4191]        --         --     1
Lippschutz 1965       0.1395 [0.0530; 0.2793]        --         --     1
European 1 1969       0.2410 [0.1538; 0.3473]        --         --     2
European 2 1971       0.1850 [0.1469; 0.2282]        --         --     2
Heikinheimo 1971      0.1005 [0.0640; 0.1481]        --         --     2
Italian 1971          0.1159 [0.0712; 0.1750]        --         --     2
Australian 1 1973     0.0985 [0.0653; 0.1410]        --         --     3
Frankfurt 2 1973      0.1275 [0.0696; 0.2081]        --         --     3
Gormsen 1973          0.1429 [0.0178; 0.4281]        --         --     3
NHLBI SMIT 1974       0.1321 [0.0548; 0.2534]        --         --     3
Brochier 1975         0.0333 [0.0041; 0.1153]        --         --     3
Euro Collab 1975      0.1686 [0.1159; 0.2331]        --         --     3
Frank 1975            0.1091 [0.0411; 0.2225]        --         --     3
Valere 1975           0.2245 [0.1177; 0.3662]        --         --     3
Klein 1976            0.2857 [0.0839; 0.5810]        --         --     3
UK-Collab 1976        0.1258 [0.0906; 0.1686]        --         --     3
Austrian 1977         0.1051 [0.0751; 0.1420]        --         --     3
Australian 2 1977     0.2033 [0.1361; 0.2852]        --         --     3
Lasierra 1977         0.0769 [0.0019; 0.3603]        --         --     3

Number of studies combined: k = 20

                     proportion           95%-CI  z p-value
Fixed effect model       0.1375 [0.1245; 0.1516] --      --
Random effects model     0.1371 [0.1160; 0.1614] --      --

Quantifying heterogeneity:
tau^2 = 0.0835; H = 1.47; I^2 = 53.5%

Quantifying residual heterogeneity:
H = 1.49 [1.14; 1.94]; I^2 = 54.8% [23.1%; 73.4%]

Test of heterogeneity:
     Q d.f. p-value             Test
 43.12   19  0.0012 Likelihood-Ratio

Results for subgroups (fixed effect model):
                      k proportion           95%-CI     Q  tau^2   I^2
byvar = (1959,1965]   3     0.1447 [0.0820; 0.2428]  0.71      0  0.0%
byvar = (1965,1971]   4     0.1549 [0.1320; 0.1810] 13.68 0.1137 72.7%
byvar = (1971,1977]  13     0.1278 [0.1122; 0.1452] 23.25 0.0669 45.4%

Test for subgroup differences (fixed effect model):
                   Q d.f. p-value
Between groups  3.43    2  0.1799
Within groups  37.63   17  0.0028

Results for subgroups (random effects model):
                      k proportion           95%-CI     Q  tau^2   I^2
byvar = (1959,1965]   3     0.1447 [0.0820; 0.2428]  0.71      0  0.0%
byvar = (1965,1971]   4     0.1514 [0.1076; 0.2088] 13.68 0.1137 72.7%
byvar = (1971,1977]  13     0.1304 [0.1069; 0.1583] 23.25 0.0669 45.4%

Test for subgroup differences (random effects model):
                    Q d.f. p-value
Between groups   0.61    2  0.7358

Details on meta-analytical method:
- Random intercept logistic regression model
- Maximum-likelihood estimator for tau^2
- Logit transformation
- Clopper-Pearson confidence interval for individual studies