1 How to use this file

This file is the continuous outcome practical. It uses an eGFR dataset comparing people with sickle cell disease (SCD) with controls.

Training question: Is eGFR different between people with SCD and controls?

Primary effect measure: Mean difference (MD) because all studies report eGFR on the same scale.

Additional teaching effect measure: Standardized mean difference (SMD) to show what to do when studies measure the same construct on different scales.

Direction of effect: In this dataset, a positive MD means the mean eGFR is higher in the SCD group than in the control group.

Training note: Some studies are simulated for workshop teaching. Use the dataset to learn workflow and interpretation, not to make clinical recommendations.

1.1 Package strategy used in this practical

To keep the training simple and consistent, all three practical files use the same small package set:

{readxl} to import Excel files
{dplyr} to clean and inspect data
{meta} to run the standard meta-analyses
{knitr} to display clean tables

Teaching note: {metafor} is a powerful advanced package and is excellent for custom analyses. However, for introductory hands-on training, {meta} is more direct because it provides purpose-built functions such as metabin(), metaprop(), and metacont(). We do not use {rmeta} in these final files because it is an older package and is less suitable for a modern, reproducible training workflow.

2 1. Load packages

packages <- c("readxl", "dplyr", "meta", "knitr")
missing <- packages[!sapply(packages, requireNamespace, quietly = TRUE)]
if (length(missing) > 0) install.packages(missing)

library(readxl)
library(dplyr)
library(meta)
library(knitr)

2.1 Interpretation

What this output is: Package installation/loading.
How to interpret it: No error means the environment is ready.
Key takeaway: For continuous outcomes, the main function is metacont().

3 2. Read the Excel file as a data frame

data_file <- "SCA_Africa_Meta_10studies_final_dataset.xlsx"
if (!file.exists(data_file)) stop("Put the SCA Excel file in the same folder as this Rmd.")

cont_df <- read_excel(data_file, sheet = "1_StudyData", range = "A4:L14", col_names = TRUE)

names(cont_df) <- c(
  "No", "FirstAuthorYear", "Country", "StudyDesign", "AgeGroup",
  "nSCD", "nControl", "OverallROBINSE", "MeaneGFRSCD", "SDeGFRSCD",
  "MeaneGFRControl", "SDeGFRControl"
)

3.1 Interpretation

What this output is: Data import from the SCA Excel file.
How to interpret it: No error means the file was found and imported.
Key takeaway: Continuous meta-analysis requires sample size, mean, and standard deviation for each group.

4 3. Inspect and clean the dataset

cont_df <- cont_df %>%
  mutate(
    FirstAuthorYear = trimws(FirstAuthorYear),
    AgeGroup = trimws(AgeGroup),
    OverallROBINSE = trimws(OverallROBINSE),
    nSCD = as.numeric(nSCD),
    nControl = as.numeric(nControl),
    MeaneGFRSCD = as.numeric(MeaneGFRSCD),
    SDeGFRSCD = as.numeric(SDeGFRSCD),
    MeaneGFRControl = as.numeric(MeaneGFRControl),
    SDeGFRControl = as.numeric(SDeGFRControl)
  )

cont_df %>%
  select(FirstAuthorYear, Country, AgeGroup, nSCD, nControl,
         MeaneGFRSCD, SDeGFRSCD, MeaneGFRControl, SDeGFRControl, OverallROBINSE) %>%
  kable(caption = "eGFR dataset: SCD versus control")

eGFR dataset: SCD versus control
FirstAuthorYear	Country	AgeGroup	nSCD	nControl	MeaneGFRSCD	SDeGFRSCD	MeaneGFRControl	SDeGFRControl	OverallROBINSE
Ndour et al., 2022 *	Senegal	Mixed (4–57 y)	163	177	138.4	41.2	112.6	27.4	Low
Olawale et al., 2021 *	Nigeria	Paediatric (5–15 y)	150	50	152.3	38.6	131.5	24.7	Moderate
Suliman et al., 2020 *	Sudan	Adults (≥18 y)	32	23	118.6	30.8	98.2	20.3	Serious
Bolarinwa et al., 2012 (sim)	Nigeria	Adults	72	50	104.8	28.4	96.4	21.6	Moderate
Ephraim et al., 2015 (sim)	Ghana	Mixed	138	80	126.8	35.4	101.2	24.8	Moderate
Aloni et al., 2013 (sim)	DR Congo	Paediatric (2–15 y)	68	68	158.4	44.6	120.6	26.1	Low
Nwogoh et al., 2018 (sim)	Nigeria	Adults	60	55	109.4	27.8	94.8	20.6	Moderate
Ngo Sock et al., 2021 (sim)	Cameroon	Adults	45	40	112.4	27.8	94.6	21.3	Moderate
Fakunle et al., 2018 (sim)	Nigeria	Paediatric (3–16 y)	80	80	144.1	40.8	119.4	25.2	Moderate
Diaw et al., 2019 (sim)	Senegal	Adults	55	50	116.2	29.4	97.8	20.6	Moderate

4.1 Interpretation

What this output is: A preview table showing means, standard deviations, and sample sizes.
How to interpret it: These are the direct inputs for metacont().
Good data look like: Positive sample sizes, non-negative SDs, and comparable outcome units.
Common pitfall: Combining outcomes measured on different scales using MD. Use SMD if scales differ.

cont_df %>%
  summarise(
    studies = n(),
    missing_means = sum(is.na(MeaneGFRSCD) | is.na(MeaneGFRControl)),
    missing_sds = sum(is.na(SDeGFRSCD) | is.na(SDeGFRControl)),
    nonpositive_sample_size = sum(nSCD <= 0 | nControl <= 0, na.rm = TRUE),
    negative_sd = sum(SDeGFRSCD < 0 | SDeGFRControl < 0, na.rm = TRUE)
  ) %>%
  kable(caption = "Basic checks for continuous outcome data")

Basic checks for continuous outcome data
studies	missing_means	missing_sds	nonpositive_sample_size	negative_sd
10	0	0	0	0

4.2 Interpretation

What this output is: A validity check for continuous outcome inputs.
How to interpret it: Ideally, all problem counts are zero.
Key takeaway: Means, SDs, and sample sizes must be credible before fitting a model.
Recommended next step: Fit the mean difference model because all studies use the same eGFR scale.

5 4. Mean difference meta-analysis

m_md <- metacont(
  n.e = nSCD,
  mean.e = MeaneGFRSCD,
  sd.e = SDeGFRSCD,
  n.c = nControl,
  mean.c = MeaneGFRControl,
  sd.c = SDeGFRControl,
  studlab = FirstAuthorYear,
  data = cont_df,
  sm = "MD",
  common = FALSE,
  random = TRUE,
  method.tau = "REML",
  method.random.ci = "HK"
)

summary(m_md)

##                                   MD             95%-CI %W(random)
## Ndour et al., 2022 *         25.8000 [18.2968; 33.3032]       12.2
## Olawale et al., 2021 *       20.8000 [11.5788; 30.0212]       10.5
## Suliman et al., 2020 *       20.4000 [ 6.8831; 33.9169]        7.1
## Bolarinwa et al., 2012 (sim)  8.4000 [-0.4813; 17.2813]       10.8
## Ephraim et al., 2015 (sim)   25.6000 [17.5740; 33.6260]       11.7
## Aloni et al., 2013 (sim)     37.8000 [25.5177; 50.0823]        8.0
## Nwogoh et al., 2018 (sim)    14.6000 [ 5.7051; 23.4949]       10.8
## Ngo Sock et al., 2021 (sim)  17.8000 [ 7.3336; 28.2664]        9.4
## Fakunle et al., 2018 (sim)   24.7000 [14.1916; 35.2084]        9.4
## Diaw et al., 2019 (sim)      18.4000 [ 8.7577; 28.0423]       10.1
## 
## Number of studies: k = 10
## Number of observations: o = 1536 (o.e = 863, o.c = 673)
## 
##                           MD             95%-CI    t  p-value
## Random effects model 21.1223 [15.6679; 26.5767] 8.76 < 0.0001
## 
## Quantifying heterogeneity (with 95%-CIs):
##  tau^2 = 31.3808 [2.3198; 176.3573]; tau = 5.6019 [1.5231; 13.2800]
##  I^2 = 56.9% [12.7%; 78.7%]; H = 1.52 [1.07; 2.17]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  20.87    9  0.0133
## 
## Details of meta-analysis methods:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## - Calculation of I^2 based on Q
## - Hartung-Knapp adjustment for random effects model (df = 9)

5.1 Interpretation

What this output is: A random-effects meta-analysis of mean differences in eGFR.
How to interpret it: The pooled MD is 21.122 (95% CI 15.668 to 26.577). A positive value means higher mean eGFR in the SCD group.
Heterogeneity: I2 = 56.9%, tau2 = 31.3808, Q-test p = 0.013.
Key takeaway: The MD is clinically interpretable because the outcome unit is the same across studies.
What cannot be concluded: This observational comparison does not prove that SCD causes the difference; confounding and selection bias may remain.
Common pitfall: Ignoring units. The MD is only meaningful when studies use comparable measurement units.

6 5. Mean difference summary table

summary_cont(m_md, "Mean difference: eGFR SCD vs control") %>%
  mutate(
    Estimate = fmt_num(Estimate),
    Lower_95_CI = fmt_num(Lower_95_CI),
    Upper_95_CI = fmt_num(Upper_95_CI),
    Tau2 = fmt_num(Tau2, 4),
    I2_percent = fmt_num(I2_percent, 1),
    Q_p_value = fmt_p(Q_p_value)
  ) %>%
  kable(caption = "Pooled mean difference using random-effects REML and Hartung-Knapp CI")

Pooled mean difference using random-effects REML and Hartung-Knapp CI
Analysis	Studies	Estimate	Lower_95_CI	Upper_95_CI	Tau2	I2_percent	Q_p_value
Mean difference: eGFR SCD vs control	10	21.122	15.668	26.577	31.3808	56.9	0.013

6.1 Interpretation

What this output is: A compact table of the pooled MD and heterogeneity statistics.
How to interpret it: The estimate is the average difference in eGFR between SCD and control groups.
Good vs. concerning: A narrow CI suggests precision; high I2 suggests important variation across studies.
Recommended next step: Inspect the forest plot.

7 6. Mean difference forest plot

forest(
  m_md,
  prediction = TRUE,
  print.tau2 = TRUE,
  print.I2 = TRUE,
  leftcols = c("studlab", "n.e", "mean.e", "sd.e", "n.c", "mean.c", "sd.c"),
  leftlabs = c("Study", "SCD n", "SCD mean", "SCD SD", "Control n", "Control mean", "Control SD"),
  rightcols = c("effect", "ci", "w.random"),
  rightlabs = c("MD", "95% CI", "Weight"),
  xlab = "Mean difference in eGFR"
)

7.1 Interpretation

What this output is: A forest plot of study-level and pooled mean differences.
How to interpret it: Squares show study estimates; horizontal lines show CIs; the diamond is the pooled MD.
Key takeaway: A diamond to the right of zero indicates higher eGFR in the SCD group.
Common pitfall: Assuming the biggest study is always the most valid study. Weight reflects precision, not risk of bias.

8 7. Standardized mean difference analysis

This section is included for teaching. Use SMD when studies measure the same construct using different scales. Here, MD remains the preferred primary analysis because all studies report eGFR on the same scale.

m_smd <- metacont(
  n.e = nSCD,
  mean.e = MeaneGFRSCD,
  sd.e = SDeGFRSCD,
  n.c = nControl,
  mean.c = MeaneGFRControl,
  sd.c = SDeGFRControl,
  studlab = FirstAuthorYear,
  data = cont_df,
  sm = "SMD",
  common = FALSE,
  random = TRUE,
  method.tau = "REML",
  method.random.ci = "HK"
)

summary(m_smd)

##                                 SMD            95%-CI %W(random)
## Ndour et al., 2022 *         0.7417 [ 0.5217; 0.9618]       23.1
## Olawale et al., 2021 *       0.5809 [ 0.2558; 0.9061]       10.6
## Suliman et al., 2020 *       0.7464 [ 0.1915; 1.3013]        3.6
## Bolarinwa et al., 2012 (sim) 0.3230 [-0.0401; 0.6862]        8.5
## Ephraim et al., 2015 (sim)   0.7989 [ 0.5133; 1.0845]       13.7
## Aloni et al., 2013 (sim)     1.0287 [ 0.6704; 1.3869]        8.7
## Nwogoh et al., 2018 (sim)    0.5890 [ 0.2150; 0.9630]        8.0
## Ngo Sock et al., 2021 (sim)  0.7067 [ 0.2672; 1.1463]        5.8
## Fakunle et al., 2018 (sim)   0.7249 [ 0.4048; 1.0451]       10.9
## Diaw et al., 2019 (sim)      0.7137 [ 0.3183; 1.1091]        7.1
## 
## Number of studies: k = 10
## Number of observations: o = 1536 (o.e = 863, o.c = 673)
## 
##                         SMD           95%-CI     t  p-value
## Random effects model 0.7042 [0.5830; 0.8253] 13.15 < 0.0001
## 
## Quantifying heterogeneity (with 95%-CIs):
##  tau^2 = 0 [0.0000; 0.0745]; tau = 0 [0.0000; 0.2729]
##  I^2 = 0.0% [0.0%; 62.4%]; H = 1.00 [1.00; 1.63]
## 
## Test of heterogeneity:
##     Q d.f. p-value
##  8.87    9  0.4490
## 
## Details of meta-analysis methods:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## - Calculation of I^2 based on Q
## - Hartung-Knapp adjustment for random effects model (df = 9)
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)

8.1 Interpretation

What this output is: A standardized mean difference model.
How to interpret it: The pooled SMD is 0.704 (95% CI 0.583 to 0.825) standard deviation units.
Key takeaway: SMD is useful for combining different scales, but it is less directly clinically interpretable than MD.
Common pitfall: Reporting SMD when MD is available and clinically meaningful.

forest(m_smd, prediction = TRUE, print.tau2 = TRUE, print.I2 = TRUE, xlab = "Standardized mean difference")

8.2 Interpretation

What this output is: A forest plot of standardized mean differences.
How to interpret it: Effects are expressed in SD units rather than clinical eGFR units.
Recommended next step: Prefer MD for the main report when all studies use the same eGFR scale.

9 8. Sensitivity to tau-squared estimator

This section asks: Would the mean-difference result change if we used a different estimator for between-study variance?

The only thing we change below is method.tau.

fit_md <- function(data, tau_method = "REML") {
  metacont(
    n.e = nSCD,
    mean.e = MeaneGFRSCD,
    sd.e = SDeGFRSCD,
    n.c = nControl,
    mean.c = MeaneGFRControl,
    sd.c = SDeGFRControl,
    studlab = FirstAuthorYear,
    data = data,
    sm = "MD",
    common = FALSE,
    random = TRUE,
    method.tau = tau_method,
    method.random.ci = "HK"
  )
}

md_tau <- bind_rows(
  summary_cont(fit_md(cont_df, "REML"), "REML"),
  summary_cont(fit_md(cont_df, "DL"),   "DL"),
  summary_cont(fit_md(cont_df, "SJ"),   "SJ")
)

md_tau %>%
  mutate(
    Estimate = fmt_num(Estimate),
    Lower_95_CI = fmt_num(Lower_95_CI),
    Upper_95_CI = fmt_num(Upper_95_CI),
    Tau2 = fmt_num(Tau2, 4),
    I2_percent = fmt_num(I2_percent, 1),
    Q_p_value = fmt_p(Q_p_value)
  ) %>%
  kable(caption = "Sensitivity of pooled MD to tau-squared estimator")

Sensitivity of pooled MD to tau-squared estimator
Analysis	Studies	Estimate	Lower_95_CI	Upper_95_CI	Tau2	I2_percent	Q_p_value
REML	10	21.122	15.668	26.577	31.3808	56.9	0.013
DL	10	21.121	15.668	26.575	31.1663	56.9	0.013
SJ	10	21.155	15.679	26.632	40.6733	56.9	0.013

9.1 Interpretation

What this output is: A comparison of MD results under different heterogeneity estimators.
How to interpret it: Similar estimates suggest that the conclusion is not strongly dependent on the tau2 estimator.
Key takeaway: Model assumptions should be checked and reported.
Common pitfall: Using only one estimator and assuming the result is robust.

10 9. Leave-one-out analysis

loo_md <- metainf(m_md, pooled = "random")
summary(loo_md)

## Leave-one-out meta-analysis
## 
##                                            MD             95%-CI  p-value
## Omitting Ndour et al., 2022 *         20.4958 [14.3775; 26.6142] < 0.0001
## Omitting Olawale et al., 2021 *       21.1914 [14.9377; 27.4452] < 0.0001
## Omitting Suliman et al., 2020 *       21.2010 [15.0621; 27.3399] < 0.0001
## Omitting Bolarinwa et al., 2012 (sim) 22.6062 [17.8249; 27.3875] < 0.0001
## Omitting Ephraim et al., 2015 (sim)   20.5545 [14.4286; 26.6804] < 0.0001
## Omitting Aloni et al., 2013 (sim)     19.7301 [15.1625; 24.2978] < 0.0001
## Omitting Nwogoh et al., 2018 (sim)    21.9172 [15.9853; 27.8491] < 0.0001
## Omitting Ngo Sock et al., 2021 (sim)  21.4931 [15.3479; 27.6383] < 0.0001
## Omitting Fakunle et al., 2018 (sim)   20.7715 [14.6382; 26.9048] < 0.0001
## Omitting Diaw et al., 2019 (sim)      21.4558 [15.2668; 27.6448] < 0.0001
##                                                                          
## Random effects model                  21.1223 [15.6679; 26.5767] < 0.0001
##                                         tau^2    tau   I^2
## Omitting Ndour et al., 2022 *         35.0045 5.9165 57.9%
## Omitting Olawale et al., 2021 *       39.1461 6.2567 61.7%
## Omitting Suliman et al., 2020 *       36.7829 6.0649 61.6%
## Omitting Bolarinwa et al., 2012 (sim) 10.2410 3.2001 34.2%
## Omitting Ephraim et al., 2015 (sim)   35.5302 5.9607 58.7%
## Omitting Aloni et al., 2013 (sim)     16.0349 4.0044 39.4%
## Omitting Nwogoh et al., 2018 (sim)    32.4092 5.6929 57.1%
## Omitting Ngo Sock et al., 2021 (sim)  37.1589 6.0958 60.9%
## Omitting Fakunle et al., 2018 (sim)   36.5497 6.0456 60.7%
## Omitting Diaw et al., 2019 (sim)      37.9332 6.1590 61.1%
##                                                           
## Random effects model                  31.3808 5.6019 56.9%
## 
## Details of meta-analysis methods:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Calculation of I^2 based on Q
## - Hartung-Knapp adjustment for random effects model (df = {8, 9})

forest(loo_md, xlab = "Mean difference in eGFR")

10.1 Interpretation

What this output is: The pooled MD recalculated after omitting one study at a time.
How to interpret it: Compare each omit-one estimate with the original pooled MD: 21.122 (95% CI 15.668 to 26.577).
Observed range: Leave-one-out MDs range from 19.730 to 22.606.
Key takeaway: If the direction and magnitude remain similar, the result is not driven by one study.
Common pitfall: Removing influential studies without methodological justification.

11 10. Galbraith/radial plot

galbraith_plot(m_md, main = "Galbraith plot: eGFR mean difference")

11.1 Interpretation

What this output is: A diagnostic radial plot for the MD model.
How to interpret it: Points outside the approximate +/-1.96 reference limits may be outliers or sources of heterogeneity.
Key takeaway: Investigate unusual studies; do not delete them automatically.
Recommended next step: Check study design, population, eGFR measurement, and extracted means/SDs.

12 11. Funnel plot and Egger test

funnel(m_md, xlab = "Mean difference", main = "Funnel plot: eGFR mean difference")

egger_md <- metabias(m_md, method.bias = "linreg", k.min = 3)
egger_md

## Linear regression test of funnel plot asymmetry
## 
## Test result: t = 0.40, df = 8, p-value = 0.6974
## Bias estimate: 1.2409 (SE = 3.0777)
## 
## Details:
## - multiplicative residual heterogeneity variance (tau^2 = 2.5562)
## - predictor: standard error
## - weight:    inverse variance
## - reference: Egger et al. (1997), BMJ

12.1 Interpretation

What this output is: A funnel plot and Egger test for small-study effects/asymmetry.
How to interpret it: Funnel asymmetry or a small p-value may reflect small-study effects, reporting bias, heterogeneity, or chance.
Observed result: Egger test p = 0.697.
Key takeaway: This is a diagnostic signal, not proof of publication bias.
Common pitfall: Over-interpreting funnel asymmetry with few studies.

13 12. Trim-and-fill sensitivity analysis

tf_md <- trimfill(m_md)
summary(tf_md)

##                                   MD             95%-CI %W(random)
## Ndour et al., 2022 *         25.8000 [18.2968; 33.3032]       12.2
## Olawale et al., 2021 *       20.8000 [11.5788; 30.0212]       10.5
## Suliman et al., 2020 *       20.4000 [ 6.8831; 33.9169]        7.1
## Bolarinwa et al., 2012 (sim)  8.4000 [-0.4813; 17.2813]       10.8
## Ephraim et al., 2015 (sim)   25.6000 [17.5740; 33.6260]       11.7
## Aloni et al., 2013 (sim)     37.8000 [25.5177; 50.0823]        8.0
## Nwogoh et al., 2018 (sim)    14.6000 [ 5.7051; 23.4949]       10.8
## Ngo Sock et al., 2021 (sim)  17.8000 [ 7.3336; 28.2664]        9.4
## Fakunle et al., 2018 (sim)   24.7000 [14.1916; 35.2084]        9.4
## Diaw et al., 2019 (sim)      18.4000 [ 8.7577; 28.0423]       10.1
## 
## Number of studies: k = 10 (with 0 added studies)
## Number of observations: o = 1536 (o.e = 863, o.c = 673)
## 
##                           MD             95%-CI    t  p-value
## Random effects model 21.1223 [15.6679; 26.5767] 8.76 < 0.0001
## 
## Quantifying heterogeneity (with 95%-CIs):
##  tau^2 = 31.3808 [2.3198; 176.3573]; tau = 5.6019 [1.5231; 13.2800]
##  I^2 = 56.9% [12.7%; 78.7%]; H = 1.52 [1.07; 2.17]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  20.87    9  0.0133
## 
## Details of meta-analysis methods:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## - Calculation of I^2 based on Q
## - Hartung-Knapp adjustment for random effects model (df = 9)
## - Trim-and-fill method to adjust for funnel plot asymmetry (L-estimator)

funnel(tf_md, xlab = "Mean difference", main = "Trim-and-fill: eGFR mean difference")

13.1 Interpretation

What this output is: An exploratory adjustment for funnel plot asymmetry.
How to interpret it: Compare the adjusted MD with the original pooled MD.
Key takeaway: Large changes suggest sensitivity to possible missing evidence or asymmetry.
Limitation: Trim-and-fill should not be treated as a definitive correction.

14 13. Subgroup analysis by overall risk of bias

m_md_rob <- metacont(
  n.e = nSCD,
  mean.e = MeaneGFRSCD,
  sd.e = SDeGFRSCD,
  n.c = nControl,
  mean.c = MeaneGFRControl,
  sd.c = SDeGFRControl,
  studlab = FirstAuthorYear,
  data = cont_df,
  sm = "MD",
  common = FALSE,
  random = TRUE,
  method.tau = "REML",
  method.random.ci = "HK",
  subgroup = OverallROBINSE
)

summary(m_md_rob)

##                                   MD             95%-CI %W(random)
## Ndour et al., 2022 *         25.8000 [18.2968; 33.3032]       12.2
## Olawale et al., 2021 *       20.8000 [11.5788; 30.0212]       10.5
## Suliman et al., 2020 *       20.4000 [ 6.8831; 33.9169]        7.1
## Bolarinwa et al., 2012 (sim)  8.4000 [-0.4813; 17.2813]       10.8
## Ephraim et al., 2015 (sim)   25.6000 [17.5740; 33.6260]       11.7
## Aloni et al., 2013 (sim)     37.8000 [25.5177; 50.0823]        8.0
## Nwogoh et al., 2018 (sim)    14.6000 [ 5.7051; 23.4949]       10.8
## Ngo Sock et al., 2021 (sim)  17.8000 [ 7.3336; 28.2664]        9.4
## Fakunle et al., 2018 (sim)   24.7000 [14.1916; 35.2084]        9.4
## Diaw et al., 2019 (sim)      18.4000 [ 8.7577; 28.0423]       10.1
##                              OverallROBINSE
## Ndour et al., 2022 *                    Low
## Olawale et al., 2021 *             Moderate
## Suliman et al., 2020 *              Serious
## Bolarinwa et al., 2012 (sim)       Moderate
## Ephraim et al., 2015 (sim)         Moderate
## Aloni et al., 2013 (sim)                Low
## Nwogoh et al., 2018 (sim)          Moderate
## Ngo Sock et al., 2021 (sim)        Moderate
## Fakunle et al., 2018 (sim)         Moderate
## Diaw et al., 2019 (sim)            Moderate
## 
## Number of studies: k = 10
## Number of observations: o = 1536 (o.e = 863, o.c = 673)
## 
##                           MD             95%-CI    t  p-value
## Random effects model 21.1223 [15.6679; 26.5767] 8.76 < 0.0001
## 
## Quantifying heterogeneity (with 95%-CIs):
##  tau^2 = 31.3808 [2.3198; 176.3573]; tau = 5.6019 [1.5231; 13.2800]
##  I^2 = 56.9% [12.7%; 78.7%]; H = 1.52 [1.07; 2.17]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  20.87    9  0.0133
## 
## Results for subgroups (random effects model):
##                             k      MD               95%-CI   tau^2    tau     Q
## OverallROBINSE = Low        2 30.7744 [-44.3408; 105.8896] 45.0373 6.7110  2.67
## OverallROBINSE = Moderate   7 18.5789 [ 12.9506;  24.2072] 16.6230 4.0771 10.30
## OverallROBINSE = Serious    1 20.4000 [  6.8831;  33.9169]      --     --  0.00
##                             I^2
## OverallROBINSE = Low      62.6%
## OverallROBINSE = Moderate 41.8%
## OverallROBINSE = Serious     --
## 
## Test for subgroup differences (random effects model):
##                   Q d.f. p-value
## Between groups 3.70    2  0.1575
## 
## Details of meta-analysis methods:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-Profile method for confidence interval of tau^2 and tau
## - Calculation of I^2 based on Q
## - Hartung-Knapp adjustment for random effects model (df = 9)

forest(m_md_rob, xlab = "Mean difference in eGFR", prediction = TRUE, print.tau2 = TRUE)

14.1 Interpretation

What this output is: A subgroup analysis by overall ROBINS-E judgement.
How to interpret it: Compare pooled MDs across risk-of-bias categories and inspect the test for subgroup differences.
Key takeaway: If higher-risk studies show larger or different effects, risk of bias may influence the pooled estimate.
Common pitfall: Treating subgroup analysis as proof of bias. It is exploratory unless pre-specified and well-powered.
Recommended next step: Use risk-of-bias sensitivity analysis and GRADE certainty assessment when preparing final conclusions.

15 14. Report-ready wording

Using a random-effects mean difference meta-analysis with REML estimation of between-study variance and Hartung-Knapp confidence intervals, the pooled mean difference in eGFR between SCD and control groups was 21.122 (95% CI 15.668 to 26.577). Positive values indicate higher mean eGFR in the SCD group. Heterogeneity was I2 = 56.9%, tau2 = 31.3808, Q-test p = 0.013. Because the studies are observational and some entries are simulated for training, the result should be interpreted as a methodological exercise rather than a clinical conclusion.

16 15. Key learning points

Use metacont() for continuous outcomes with group means, SDs, and sample sizes.
Use MD when all studies report the same outcome scale.
Use SMD when studies measure the same construct on different scales.
Interpret direction carefully: here, positive MD means higher eGFR in SCD.
Always examine heterogeneity, influence, small-study effects, and risk of bias before drawing conclusions.

Practical Meta-Analysis 3: Continuous Outcomes

Mean difference and standardized mean difference workflow using a consistent, simple {meta} package approach

Evidence Synthesis Training Course

13 May 2026