Meta Analysis Rerun 21.03.25

#### 1. Load packages ----
library(metafor)
library(meta)
library(metaforest)
library(dplyr)
library(tidyverse)
library(readxl)
library(grid)
library(gridExtra)

#### 2. Load the data ----
data1 <- read.csv("../data/WI_MA_data_25.02.25.csv")

#### 3. Process the data ----
# Calculate effect sizes using escalc() for all data
data1 <- escalc(measure="MD", m1i=mn_exp, sd1i=std_exp, n1i=n_exp, 
                m2i=mn_ctl, sd2i=std_ctl, n2i=n_ctl, data=data1, 
                slab=paste(author, year, sep=", "))

# Split data into MIP and MEP datasets
data_MIP <- data1 %>% filter(RMP == "MIP")
data_MEP <- data1 %>% filter(RMP == "MEP")

#### 4. Meta-analysis for MIP ----
# Random-effects model with Hartung-Knapp adjustment
MIP_rma <- rma(yi, vi, data = data_MIP, method = "REML", test = "knha")

# Fixed-effect model
MIP_fe <- rma(yi, vi, data = data_MIP, method = "FE")

# Create meta object for forest plot
MIP_meta <- metacont(
  n.e = data_MIP$n_exp, mean.e = data_MIP$mn_exp, sd.e = data_MIP$std_exp, 
  n.c = data_MIP$n_ctl, mean.c = data_MIP$mn_ctl, sd.c = data_MIP$std_ctl, 
  data = data_MIP, studlab = data_MIP$author,
  common = TRUE, random = TRUE,
  method.random.ci = TRUE,  # Hartung-Knapp adjustment
  prediction = TRUE,  # Include prediction interval
  sm = "MD"
)

#### 5. Meta-analysis for MEP ----
# Random-effects model with Hartung-Knapp adjustment
MEP_rma <- rma(yi, vi, data = data_MEP, method = "REML", test = "knha")

# Fixed-effect model
MEP_fe <- rma(yi, vi, data = data_MEP, method = "FE")

# Create meta object for forest plot
MEP_meta <- metacont(
  n.e = data_MEP$n_exp, mean.e = data_MEP$mn_exp, sd.e = data_MEP$std_exp, 
  n.c = data_MEP$n_ctl, mean.c = data_MEP$mn_ctl, sd.c = data_MEP$std_ctl, 
  data = data_MEP, studlab = data_MEP$author,
  common = TRUE, random = TRUE,
  method.random.ci = TRUE,  # Hartung-Knapp adjustment
  prediction = TRUE,  # Include prediction interval
  sm = "MD"
)

1 MIP MA Results

#### 6. Create Forest Plots ----

#### MIP Forest Plot ----
# Set minimal margins (bottom, left, top, right)
par(mar = c(2, 4, 1, 2))  

forest(MIP_meta,
       leftcols = c("studlab", "n.e", "mean.e", "sd.e", "n.c", "mean.c", "sd.c"),
       leftlabs = c("Author", "n", "Mean", "SD", "n", "Mean", "SD"),
       rightcols = c("effect", "ci"),
       rightlabs = c("MD", "95% CI"),
       comb.fixed = TRUE,
       comb.random = TRUE,
       prediction = TRUE,
       print.tau2 = TRUE,
       print.I2 = TRUE,
       print.H = TRUE,  # Add H^2 statistic
       col.predict = "red",  # Prediction interval in red
       col.diamond = "blue",  # Confidence interval in blue
       hetstat = TRUE,
       overall = TRUE,
       overall.hetstat = TRUE,
       test.overall.common = TRUE,
       test.overall.random = TRUE,
       main = "Maximum Inspiratory Pressure (MIP) generation in wind instrumentalists vs. controls",
       fontsize = 8,     # Reduced from 10 to 8
       cex = 0.8,        # Added to control element size
       xlim = c(-50, 50), # Adjust as needed for your data range
       header.height = 0.5) # Reduce header height

# Display the image with no extra padding in the document
knitr::include_graphics("MIP_forest_plot.png", dpi = 300)

#### 7. Summary Statistics ----

# Print Analyses
MIP_meta

Number of studies: k = 4
Number of observations: o = 211 (o.e = 120, o.c = 91)

                          MD              95%-CI  z|t  p-value
Common effect model  20.8060 [ 13.7368; 27.8753] 5.77 < 0.0001
Random effects model 17.5094 [-13.1490; 48.1678] 1.82   0.1667
Prediction interval          [-47.5076; 82.5264]              

Quantifying heterogeneity (with 95%-CIs):
 tau^2 = 322.5526 [68.0641; >3225.5258]; tau = 17.9597 [8.2501; >56.7937]
 I^2 = 86.9% [68.4%; 94.6%]; H = 2.76 [1.78; 4.29]

Test of heterogeneity:
     Q d.f.  p-value
 22.87    3 < 0.0001

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 = 3)
- Prediction interval based on t-distribution (df = 3)

# Display summary statistics for MIP
cat("\nSummary for Maximum Inspiratory Pressure (MIP):\n")

Summary for Maximum Inspiratory Pressure (MIP):

cat("Random-effects model (with Hartung-Knapp adjustment):\n")

Random-effects model (with Hartung-Knapp adjustment):

print(MIP_rma)

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

tau^2 (estimated amount of total heterogeneity): 322.5526 (SE = 309.7010)
tau (square root of estimated tau^2 value):      17.9597
I^2 (total heterogeneity / total variability):   85.74%
H^2 (total variability / sampling variability):  7.01

Test for Heterogeneity:
Q(df = 3) = 22.8665, p-val < .0001

Model Results:

estimate      se    tval  df    pval     ci.lb    ci.ub    
 17.5094  9.6336  1.8175   3  0.1667  -13.1490  48.1678    

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\nFixed-effect model:\n")

Fixed-effect model:

print(MIP_fe)

Fixed-Effects Model (k = 4)

I^2 (total heterogeneity / total variability):   86.88%
H^2 (total variability / sampling variability):  7.62

Test for Heterogeneity:
Q(df = 3) = 22.8665, p-val < .0001

Model Results:

estimate      se    zval    pval    ci.lb    ci.ub      
 20.8060  3.6068  5.7685  <.0001  13.7368  27.8753  *** 

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\nHeterogeneity statistics:\n")

Heterogeneity statistics:

cat("I² =", formatC(MIP_rma$I2, digits=1, format="f"), "%\n")

I² = 85.7 %

cat("H² =", formatC(MIP_rma$H2, digits=2, format="f"), "\n")

H² = 7.01 

cat("τ² =", formatC(MIP_rma$tau2, digits=4, format="f"), "\n\n")

τ² = 322.5526 

1.1 Study Characteristics

• Number of studies: 3 independent studies were included in this meta-analysis

• Total sample size: 129 participants across all studies

• Experimental group: 73 participants (wind instrumentalists)

• Control group: 56 participants (non-instrumentalists/controls)

1.2 Effect Size Estimates

• Common effect model (previously called fixed-effect model):

  • Mean difference: 23.71 units.
    This indicates a pooled effect size of 23.71 units (on the outcome measure) favoring one group over the other under the assumption that all studies share the same true effect size.

  • 95% Confidence interval: [15.17 to 32.26]
    The true effect size is likely to fall between 15.17 and 32.26 with 95% confidence.

  • Statistical significance z-score: 5.44
    This shows how many standard deviations the observed effect size (23.7135) is away from null (zero effect).

  • Statistical significance p-value: < 0.0001
    The p-value is highly significant, meaning the observed effect size is unlikely to have occurred by chance under the null hypothesis.

  • Interpretation: Under the assumption that all studies are measuring the same true effect, wind instrumentalists demonstrate significantly higher values (likely Maximum Inspiratory Pressure) compared to controls, with an average difference

Interpretation of the Common Effect Model:

Under the common effect assumption, the meta-analysis suggests a strong and statistically significant mean difference of approximately 23.71, with high confidence in the precision (narrow 95% CI). However, this assumes homogeneity in the effects across studies, which is likely invalid given the high heterogeneity observed (discussed below).

• Random effects model:

  • Mean difference: 18.30 units
    Under the random effects model, which accounts for variability in effect sizes across studies, the pooled MD is 18.30.

  • 95% Confidence interval: [-40.13 to 76.73]
    The wide interval indicates uncertainty surrounding the overall effect size, as the true mean may range from a large negative effect to a substantial positive effect.

  • Statistical significance: t = 1.35, p = 0.3102
    z-score: 1.35
    The observed effect is only 1.35 standard deviations away from zero, indicating weak evidence against the null hypothesis.
    p-value: 0.3102
    The result is not statistically significant at common thresholds (e.g., 0.05), suggesting insufficient evidence for a consistent mean difference across studies.

  • Interpretation: When allowing for between-study heterogeneity, the estimated mean difference favors wind instrumentalists but is not statistically significant. The wide confidence interval crosses zero, indicating uncertainty about the true direction of effect.

• Prediction interval: [-94.82 to 131.42]

  • Interpretation: This wide interval expresses the range within which the effect size for a future study is expected to fall, given the observed between-study variability. The large spread emphasizes the uncertainty and inconsistency across studies.

Interpretation of the Random Effects Model:

The random effects model accounts for heterogeneity in effect sizes and provides a less precise estimate. Although the mean difference is positive (18.30), the high between-study variability leads to wide confidence and prediction intervals, resulting in a non-significant overall effect.

1.3 Heterogeneity Assessment

• Tau² = 502.79 [96.16 to >5027.92]

  • Interpretation: This represents the estimated variance of true effects between studies. The large value indicates substantial true differences in effect sizes across studies.

• Tau = 22.42 [9.81 to >70.91]

  • Interpretation: This is the standard deviation of true effects, suggesting that studies differ from the mean effect by approximately ±22.42 units on average.

  • There is considerable uncertainty about the magnitude of heterogeneity, but the lower bound is still relatively large, confirming substantial between-study variability.

• I² = 90.7% [75.5% to 96.4%]

  • Interpretation: Approximately 91% of the observed variance in effect sizes reflects real differences in the true effect rather than sampling error. According to conventional thresholds, this represents very high heterogeneity.

• H = 3.28 [2.02 to 5.31]

  • Interpretation: The H statistic represents the ratio of the total amount of variability to the amount expected from sampling error alone. The value of 3.28 indicates that there is 3.28 times more total variation than would be expected if all studies shared a common effect size.

  • A value of 3.28 is consistent with substantial heterogeneity.

• Cochran’s Q test: Q = 21.46, df = 2, p < 0.0001

  • Interpretation: This test strongly rejects the null hypothesis of homogeneity across studies, confirming the presence of significant between-study variability.

Interpretation of Heterogeneity:

The meta-analysis demonstrates very high heterogeneity, evidenced by large tau², high I² (90.7%), and significant Q test results (p < 0.0001). These findings suggest that the effects vary significantly across studies, likely due to differences in study populations, methodologies, or other unexplained factors.

1.4 Overall Interpretation

This meta-analysis reveals a complex picture regarding the difference in respiratory muscle performance (likely Maximum Inspiratory Pressure) between wind instrumentalists and controls:

1. Common Effect Model:

   • Suggests a significant positive mean difference of 23.71, with narrow confidence intervals and a very small p-value, indicating strong evidence for an effect under the assumption of homogeneity. However, this assumption is invalidated by the observed heterogeneity.

2. Random Effects Model:

   • Provides a lower pooled effect size of 18.30 and wide confidence intervals spanning from negative to positive values. The non-significant p-value (0.31) and broad prediction intervals highlight the uncertainty caused by high study heterogeneity.

3. Heterogeneity Metrics:

   • Substantial heterogeneity (τ² = 502.79, I² = 90.7%) indicates large variability in effect sizes across studies, meaning the pooled result may not represent a consistent effect.

4. Overall Conclusion:

   • While the common effect model suggests a strong, statistically significant effect, the high degree of heterogeneity suggests caution in interpreting the pooled estimate. The variability among studies reduces confidence in a single pooled effect size, and future research should explore the sources of heterogeneity to better understand the underlying differences.

5. Conflicting models:

   • The common effect model suggests a significant positive effect favoring wind instrumentalists, while the random effects model—which is more appropriate given the high heterogeneity—shows a non-significant effect with wide confidence intervals.

6. Substantial heterogeneity:

   • All heterogeneity measures (I², H, and τ²) consistently indicate very high between-study variability, suggesting that the effect of wind instrument playing on respiratory muscle performance likely varies considerably based on factors not accounted for in this analysis.

7. Limited evidence base:

   • With only three studies and a modest total sample size (129 participants), the precision of estimates is limited, as reflected in the wide confidence and prediction intervals.

8. Clinical implications:

   • While the common effect model suggests a positive effect of approximately 24 units (which may be clinically meaningful depending on the scale), the high heterogeneity and non-significant random effects model suggest caution in drawing firm conclusions.

9. Research implications:

   • More studies are needed to identify factors that may explain the substantial heterogeneity observed. These could include differences in musical experience, type of wind instrument, training intensity, or methodological variations across studies.

The most appropriate conclusion is that while there is some evidence suggesting wind instrumentalists may have higher respiratory muscle performance compared to controls, the effect varies substantially across studies, and the current evidence is insufficient to draw firm conclusions about the size or consistency of this effect.

1.5 Interpretation of MIP Effect Size

Clinical Significance of a 24 cmH₂O Difference in Maximum Inspiratory Pressure

A difference of 24 cmH₂O in Maximum Inspiratory Pressure (MIP) between wind instrumentalists and controls represents a moderate to large effect based on the following evidence:

Reference to Normal Values

Normal MIP values in healthy adults typically range from approximately 70-120 cmH₂O for men and 50-90 cmH₂O for women, with variations by age. A difference of 24 cmH₂O represents roughly 20-35% of these reference values, which is substantial (ATS/ERS Statement, 2002; Evans & Whitelaw, 2009).

Clinical Significance Thresholds

While there isn’t a universally established minimal clinically important difference (MCID) for MIP, respiratory intervention studies often consider improvements of 10-15 cmH₂O to be clinically meaningful (Romer & McConnell, 2004; Formiga et al., 2018). At 24 cmH₂O, this difference exceeds typical intervention effect thresholds.

Relationship to Respiratory Dysfunction

MIP values below 60-80 cmH₂O are frequently used as thresholds for diagnosing inspiratory muscle weakness (Sclauser Pessoa et al., 2014; Laveneziana et al., 2019). An increase of 24 cmH₂O could potentially move someone from a classification of weakness to normal function.

Functional Implications

This magnitude of difference could translate to meaningful improvements in exercise capacity, reduced dyspnea, and potentially better respiratory reserve during physical exertion (Lötters et al., 2002; Hill et al., 2006).

Training Effects

In studies of dedicated respiratory muscle training programs, improvements of 15-30% in MIP are typically reported after weeks or months of specific training (Illi et al., 2012; HajGhanbari et al., 2013). A 24 cmH₂O difference suggests that wind instrument playing may provide respiratory muscle training effects comparable to dedicated respiratory exercise programs.

References

American Thoracic Society/European Respiratory Society. (2002). ATS/ERS Statement on respiratory muscle testing. American Journal of Respiratory and Critical Care Medicine, 166(4), 518-624.

Evans, J. A., & Whitelaw, W. A. (2009). The assessment of maximal respiratory mouth pressures in adults. Respiratory Care, 54(10), 1348-1359.

Formiga, M. F., Roach, K. E., Vital, I., Urdaneta, G., Balestrini, K., Calderon-Candelario, R. A., Campos, M. A., & Cahalin, L. P. (2018). Reliability and validity of the test of incremental respiratory endurance measures of inspiratory muscle performance in COPD. International Journal of Chronic Obstructive Pulmonary Disease, 13, 1569-1576.

HajGhanbari, B., Yamabayashi, C., Buna, T. R., Coelho, J. D., Freedman, K. D., Morton, T. A., Palmer, S. A., Toy, M. A., Walsh, C., Sheel, A. W., & Reid, W. D. (2013). Effects of respiratory muscle training on performance in athletes: a systematic review with meta-analyses. Journal of Strength and Conditioning Research, 27(6), 1643-1663.

Hill, K., Jenkins, S. C., Philippe, D. L., Cecins, N., Shepherd, K. L., Green, D. J., Hillman, D. R., & Eastwood, P. R. (2006). High-intensity inspiratory muscle training in COPD. European Respiratory Journal, 27(6), 1119-1128.

Illi, S. K., Held, U., Frank, I., & Spengler, C. M. (2012). Effect of respiratory muscle training on exercise performance in healthy individuals: a systematic review and meta-analysis. Sports Medicine, 42(8), 707-724.

Laveneziana, P., Albuquerque, A., Aliverti, A., Babb, T., Barreiro, E., Dres, M., Dubé, B. P., Fauroux, B., Gea, J., Guenette, J. A., Hudson, A. L., Kabitz, H. J., Laghi, F., Langer, D., Luo, Y. M., Neder, J. A., O’Donnell, D., Polkey, M. I., Rabinovich, R. A., … Verges, S. (2019). ERS statement on respiratory muscle testing at rest and during exercise. European Respiratory Journal, 53(6), 1801214.

Lötters, F., van Tol, B., Kwakkel, G., & Gosselink, R. (2002). Effects of controlled inspiratory muscle training in patients with COPD: a meta-analysis. European Respiratory Journal, 20(3), 570-576.

Romer, L. M., & McConnell, A. K. (2004). Respiratory muscle training in healthy humans: resolving the controversy. International Journal of Sports Medicine, 25(4), 284-293.

Sclauser Pessoa, I. M., Franco Parreira, V., Fregonezi, G. A., Sheel, A. W., Chung, F., & Reid, W. D. (2014). Reference values for maximal inspiratory pressure: a systematic review. Canadian Respiratory Journal, 21(1), 43-50.

2 MEP MA Results

#### 6. Create Forest Plots ----
# MEP Forest Plot
# Set smaller margins (bottom, left, top, right)
par(mar = c(2, 4, 1, 2))  

forest(MEP_meta,
       leftcols = c("studlab", "n.e", "mean.e", "sd.e", "n.c", "mean.c", "sd.c"),
       leftlabs = c("Author", "n", "Mean", "SD", "n", "Mean", "SD"),
       rightcols = c("effect", "ci"),
       rightlabs = c("MD", "95% CI"),
       comb.fixed = TRUE,
       comb.random = TRUE,
       prediction = TRUE,
       print.tau2 = TRUE,
       print.I2 = TRUE,
       print.H = TRUE,
       col.predict = "red",
       col.diamond = "blue",
       hetstat = TRUE,
       overall = TRUE,
       overall.hetstat = TRUE,
       test.overall.common = TRUE,
       test.overall.random = TRUE,
       main = "Maximum Expiratory Pressure (MEP) generation in wind instrumentalists vs. controls",
       fontsize = 8,
       cex = 0.8,
       xlim = c(-50, 50),
       header.height = 0.5)  # Reduce header height

# Close the device
dev.off()

null device 
          1 

# Display the image with no extra padding in the document
knitr::include_graphics("MEP_forest_plot.png", dpi = 300)

#### 7. Summary Statistics ----

# Print Analyses
MEP_meta

Number of studies: k = 3
Number of observations: o = 185 (o.e = 107, o.c = 78)

                          MD              95%-CI  z|t p-value
Common effect model  15.3436 [  7.0355; 23.6518] 3.62  0.0003
Random effects model 21.1392 [-17.2307; 59.5091] 2.37  0.1412
Prediction interval          [-39.8221; 82.1005]             

Quantifying heterogeneity (with 95%-CIs):
 tau^2 = 122.8165 [0.0000; >1228.1648]; tau = 11.0823 [0.0000; >35.0452]
 I^2 = 50.2% [0.0%; 85.6%]; H = 1.42 [1.00; 2.64]

Test of heterogeneity:
    Q d.f. p-value
 4.02    2  0.1341

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 = 2)
- Prediction interval based on t-distribution (df = 2)

# Display summary statistics for MEP
cat("\nSummary for Maximum Expiratory Pressure (MEP):\n")

Summary for Maximum Expiratory Pressure (MEP):

cat("Random-effects model (with Hartung-Knapp adjustment):\n")

Random-effects model (with Hartung-Knapp adjustment):

print(MEP_rma)

Random-Effects Model (k = 3; tau^2 estimator: REML)

tau^2 (estimated amount of total heterogeneity): 122.8165 (SE = 251.1952)
tau (square root of estimated tau^2 value):      11.0823
I^2 (total heterogeneity / total variability):   50.13%
H^2 (total variability / sampling variability):  2.01

Test for Heterogeneity:
Q(df = 2) = 4.0189, p-val = 0.1341

Model Results:

estimate      se    tval  df    pval     ci.lb    ci.ub    
 21.1392  8.9177  2.3705   2  0.1412  -17.2307  59.5091    

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\nFixed-effect model:\n")

Fixed-effect model:

print(MEP_fe)

Fixed-Effects Model (k = 3)

I^2 (total heterogeneity / total variability):   50.23%
H^2 (total variability / sampling variability):  2.01

Test for Heterogeneity:
Q(df = 2) = 4.0189, p-val = 0.1341

Model Results:

estimate      se    zval    pval   ci.lb    ci.ub      
 15.3436  4.2389  3.6197  0.0003  7.0355  23.6518  *** 

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cat("\nHeterogeneity statistics:\n")

Heterogeneity statistics:

cat("I² =", formatC(MEP_rma$I2, digits=1, format="f"), "%\n")

I² = 50.1 %

cat("H² =", formatC(MEP_rma$H2, digits=2, format="f"), "\n")

H² = 2.01 

cat("τ² =", formatC(MEP_rma$tau2, digits=4, format="f"), "\n")

τ² = 122.8165 

2.1 Study Characteristics

• Number of studies: 2 independent studies were included in this meta-analysis

• Total sample size: 103 participants across both studies

• Experimental group: 60 participants (wind instrumentalists)

• Control group: 43 participants (non-instrumentalists/controls)

2.2 Effect Size Estimates

• Common effect model (fixed-effect model):

  • Mean difference: 30.84 cmH₂O
    This means that, under the assumption that the studies estimate a single true effect (i.e., fixed effect model), the experimental group shows an average improvement (or increase) of 30.84 units compared to the control group.

  • 95% Confidence interval: [10.61 to 51.07]
    The CI indicates that the true effect is likely between 10.61 and 51.07 units, with 95% confidence. This excludes zero, meaning the result is statistically significant.

  • Statistical significance: z = 2.99, p = 0.0028
    The p-value is statistically significant (p < 0.05), meaning there is strong evidence to reject the null hypothesis (i.e., no difference between groups).

  • Interpretation: Under the assumption that both studies are measuring the same true effect, wind instrumentalists demonstrate significantly higher Maximum Expiratory Pressure (MEP) compared to controls, with an average difference of approximately 31 cmH₂O.

• Random effects model:

  • Mean difference: 31.35 cmH₂O
    This is the average effect size when assuming variability in the true effect across studies (due to heterogeneity).

  • 95% Confidence interval: [-119.67 to 182.37]
    The confidence interval here is wide and crosses zero, meaning the result is not statistically significant.

  • Statistical significance: t = 2.64, p = 0.2307
    The result is not statistically significant (p > 0.05). This suggests uncertainty about the true difference between groups when accounting for heterogeneity.

  • Interpretation: When allowing for between-study heterogeneity, the estimated mean difference still favors wind instrumentalists but is not statistically significant. The wide confidence interval crossing zero reflects substantial uncertainty about the true effect, largely due to the Hartung-Knapp adjustment with only 2 studies (df = 1).

• Prediction interval: [-152.37 to 215.06]

  • Interpretation: This extremely wide interval represents the range in which the true effect of a new study would be expected to fall with 95% certainty. The very wide range reflects both the limited number of studies and between-study variability.

  • This wide interval highlights substantial uncertainty about the variability in potential outcomes. The inclusion of both negative and positive values indicates that future studies could show either a benefit or no effect at all.

2.3 Heterogeneity Assessment

• Tau² = 67.78

  • Interpretation: This represents the estimated variance of true effects between studies. The moderate value suggests some differences in true effects across studies.

• Tau = 8.23

  • Interpretation: This is the standard deviation of true effects, suggesting that studies differ from the mean effect by approximately ±8.23 cmH₂O on average.

• I² = 23.5%

  • Interpretation: Approximately 23.5% of the observed variance reflects real differences in the true effect rather than sampling error. According to conventional thresholds, this represents low-to-moderate heterogeneity.

• H = 1.14

  • Interpretation: The H statistic value of 1.14 indicates there is 1.14 times more total variation than would be expected if both studies shared a common effect size, suggesting modest heterogeneity.

  • A value close to 1 indicates low heterogeneity, which aligns with the I² findings.

• Cochran’s Q test: Q = 1.31, df = 1, p = 0.2528

  • Interpretation: This test fails to reject the null hypothesis of homogeneity across studies. However, with only 2 studies, the Q test has low power to detect heterogeneity.

  • This is the weighted sum of squared differences between the individual study effects and the pooled effect. A low value indicates little heterogeneity.

  • The lack of statistical significance (p > 0.05) indicates that there is no evidence of substantial heterogeneity between studies.

2.4 Meta-Analysis Methods

• Inverse variance method: Appropriate weighting of studies based on precision

• REML estimator for tau²: A robust method for estimating between-study variance

• Hartung-Knapp adjustment: A conservative approach that widens confidence intervals when there are few studies

• Prediction interval based on t-distribution: Appropriate for small numbers of studies

2.5 Overall Interpretation

This meta-analysis of Maximum Expiratory Pressure (MEP) between wind instrumentalists and controls presents a nuanced picture:

1. Under the Common Effect Model:

   • The pooled estimate of the average difference between groups (MD = 30.84) is statistically significant, with a relatively narrow confidence interval that excludes zero. This suggests a clear benefit of the intervention.

2. Under the Random Effects Model:

   • The pooled mean difference (MD = 31.35) is not statistically significant due to the very wide confidence interval that includes zero, indicating considerable uncertainty in the estimated effect when variability across studies (heterogeneity) is considered.

3. Heterogeneity:

   • Heterogeneity is low to moderate (I² = 23.5%), supported by the non-significant Q-test (p = 0.2528). This suggests that the observed study results are relatively consistent with each other.

4. Prediction Interval:

   • The wide prediction interval ([−152.37, 215.06]) underscores the uncertainty about what the true effect might be in a new or future study.

5. Conclusion:

   • While the fixed effects model suggests a statistically significant benefit, the random effects model introduces substantial uncertainty in the pooled effect. This is likely due to the small number of studies (k = 2) and their moderate heterogeneity. More studies are needed to confirm the findings and reduce uncertainty.

6. Evidence of effect:

   • Both models estimate a similar mean difference of approximately 31 cmH₂O favoring wind instrumentalists, which would be clinically meaningful if confirmed.

7. Statistical significance discrepancy:

   • The common effect model shows statistical significance (p = 0.0028), while the random effects model with Hartung-Knapp adjustment does not (p = 0.2307). This discrepancy is primarily due to the conservative adjustment with only 2 studies.

8. Moderate heterogeneity:

   • The heterogeneity measures (I² = 23.5%, H = 1.14) suggest some variability between the true effects of the two studies, but not extreme differences.

9. Limited evidence base:

   • With only two studies and 103 total participants, the precision of estimates is limited, as reflected in the extremely wide confidence and prediction intervals in the random effects model.

10. Clinical implications:

    • A difference of approximately 31 cmH₂O in MEP represents a clinically meaningful difference in expiratory muscle strength. This would be expected given the expiratory demands of wind instrument playing, which requires controlled and often forceful exhalation.

11. Research implications:

    • More studies are needed to increase precision and allow for exploration of factors that might influence the relationship between wind instrument playing and expiratory muscle strength.

The appropriate conclusion is that there is preliminary evidence suggesting wind instrumentalists may have higher MEP compared to controls, with an estimated difference of approximately 31 cmH₂O. However, due to the limited number of studies, this finding should be considered tentative until confirmed by additional research.

2.6 Interpretation of MIP Effect Size

A difference of 31 cmH₂O in Maximum Expiratory Pressure (MEP) between wind instrumentalists and controls represents a clinically significant effect based on the following evidence:

Reference to Normal Values

Normal MEP values in healthy adults typically range from approximately 100-200 cmH₂O for men and 70-140 cmH₂O for women, varying by age. A difference of 31 cmH₂O represents roughly 15-30% of these reference values, which is substantial (ATS/ERS Statement, 2002; Evans & Whitelaw, 2009). Harik-Khan et al. (1998) showed that even normal aging results in only about a 15-20% decline in MEP over decades, putting this 31 cmH₂O difference into perspective.

Clinical Significance Thresholds

While there isn’t a universally established minimal clinically important difference (MCID) specifically for MEP, respiratory muscle training studies often consider improvements of 15-20 cmH₂O to be clinically meaningful (Gosselink et al., 2011; Dall’Ago et al., 2006). At 31 cmH₂O, this difference substantially exceeds typical intervention effect thresholds.

Relationship to Respiratory Dysfunction

MEP values below 60 cmH₂O are often used as thresholds for diagnosing expiratory muscle weakness and cough insufficiency (Szeinberg et al., 1988; Bach & Saporito, 1996). An increase of 31 cmH₂O could potentially move someone from a classification of weakness to normal function or from normal to superior expiratory strength.

Functional Implications

This magnitude of difference could translate to meaningful improvements in cough efficacy, secretion clearance, and speech production. Expiratory muscle strength is particularly important for effective coughing, which requires MEP of at least 60 cmH₂O for effective airway clearance (Kang & Bach, 2000; Suárez et al., 2002).

Training Effects

In studies of dedicated respiratory muscle training programs targeting expiratory muscles, improvements of 10-25% in MEP are typically reported after weeks of specific training (Weiner et al., 2003; Mota et al., 2007). A 31 cmH₂O difference suggests that wind instrument playing provides substantial expiratory muscle training effects that may exceed those of some dedicated respiratory exercise programs.

References

American Thoracic Society/European Respiratory Society. (2002). ATS/ERS Statement on respiratory muscle testing. American Journal of Respiratory and Critical Care Medicine, 166(4), 518-624.

Bach, J. R., & Saporito, L. R. (1996). Criteria for extubation and tracheostomy tube removal for patients with ventilatory failure: A different approach to weaning. Chest, 110(6), 1566-1571.

Dall’Ago, P., Chiappa, G. R., Guths, H., Stein, R., & Ribeiro, J. P. (2006). Inspiratory muscle training in patients with heart failure and inspiratory muscle weakness: A randomized trial. Journal of the American College of Cardiology, 47(4), 757-763.

Evans, J. A., & Whitelaw, W. A. (2009). The assessment of maximal respiratory mouth pressures in adults. Respiratory Care, 54(10), 1348-1359.

Gosselink, R., De Vos, J., van den Heuvel, S. P., Segers, J., Decramer, M., & Kwakkel, G. (2011). Impact of inspiratory muscle training in patients with COPD: what is the evidence? European Respiratory Journal, 37(2), 416-425.

Harik-Khan, R. I., Wise, R. A., & Fozard, J. L. (1998). Determinants of maximal inspiratory pressure. The Baltimore Longitudinal Study of Aging. American Journal of Respiratory and Critical Care Medicine, 158(5 Pt 1), 1459-1464.

Kang, S. W., & Bach, J. R. (2000). Maximum insufflation capacity: vital capacity and cough flows in neuromuscular disease. American Journal of Physical Medicine & Rehabilitation, 79(3), 222-227.

Mota, S., Güell, R., Barreiro, E., Solanes, I., Ramírez-Sarmiento, A., Orozco-Levi, M., Casan, P., Gea, J., & Sanchis, J. (2007). Clinical outcomes of expiratory muscle training in severe COPD patients. Respiratory Medicine, 101(3), 516-524.

Suárez, A. A., Pessolano, F. A., Monteiro, S. G., Ferreyra, G., Capria, M. E., Mesa, L., Dubrovsky, A., & De Vito, E. L. (2002). Peak flow and peak cough flow in the evaluation of expiratory muscle weakness and bulbar impairment in patients with neuromuscular disease. American Journal of Physical Medicine & Rehabilitation, 81(7), 506-511.

Szeinberg, A., Tabachnik, E., Rashed, N., McLaughlin, F. J., England, S., Bryan, C. A., & Levison, H. (1988). Cough capacity in patients with muscular dystrophy. Chest, 94(6), 1232-1235.

Weiner, P., Magadle, R., Beckerman, M., Weiner, M., & Berar-Yanay, N. (2003). Specific expiratory muscle training in COPD. Chest, 124(2), 468-473.