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analyses:viechtbauer2007b [2021/11/08 15:54] – Wolfgang Viechtbaueranalyses:viechtbauer2007b [2022/08/03 11:24] (current) – Wolfgang Viechtbauer
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 17 98 186 80 189  0.2189 0.0120   6.30     1     21.9        6 17 98 186 80 189  0.2189 0.0120   6.30     1     21.9        6
 </code> </code>
-Variables ''ai'' and ''ci'' indicate the number of participants with significant improvements between baseline and the follow-up assessment in the treatment and the placebo group, respectively, variables ''n1i'' and ''n2i'' are the corresponding group sizes, variable ''yi'' is the log of the relative improvement rate (i.e., the improvement rate in the treatment group divided by the improvement rate in the placebo group), ''vi'' is the corresponding sampling variance, ''dosage'' is the weekly dosage (in grams) of the //Hypericum// extract used in each study, ''major'' indicates whether a study was restricted to participants with major depression or not (1 or 0, respectively), ''baseline'' denotes the average score on the Hamilton Rating Scale for Depression (HRSD) at baseline (i.e., before treatment begin), and ''duration'' indicates the number of treatment weeks before response assessment. Variables ''yi'' and ''vi'' are not actually included in the original dataset and were added by means of the ''escalc()'' function.+Variables ''ai'' and ''ci'' indicate the number of participants with significant improvements between baseline and the follow-up assessment in the treatment and the placebo group, respectively, variables ''n1i'' and ''n2i'' are the corresponding group sizes, variable ''yi'' is the log of the relative improvement rate (i.e., the improvement rate in the treatment group divided by the improvement rate in the placebo group), ''vi'' is the corresponding sampling variance, ''dosage'' is the weekly dosage (in grams) of the //Hypericum// extract used in each study, ''major'' indicates whether a study was restricted to participants with major depression or not (1 or 0, respectively), ''baseline'' denotes the average score on the Hamilton Rating Scale for Depression (HRSD) at baseline (i.e., before the treatment), and ''duration'' indicates the number of treatment weeks between the baseline and the response assessment. Variables ''yi'' and ''vi'' are not actually included in the original dataset and were added by means of the ''escalc()'' function.
  
 Note that, for illustration purposes, only a subset of the data from the Linde et al. (2005) meta-analysis are actually included in this example. Therefore, no substantive interpretations should be attached to the results of the analyses given below. Note that, for illustration purposes, only a subset of the data from the Linde et al. (2005) meta-analysis are actually included in this example. Therefore, no substantive interpretations should be attached to the results of the analyses given below.
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 </code> </code>
 <code output> <code output>
-   ai n1i ci n2i   yi dosage major baseline duration ci.lb ci.ub  +   ai n1i ci n2i   yi dosage major baseline duration ci.lb ci.ub 
-1  20  25 11  25 1.82   2.66     0     19.5        8  1.12  2.95 +1  20  25 11  25 1.82   2.66     0     19.5        8  1.12  2.95
 2  14  20  9  20 1.56   6.30     0     12.5        4  0.89  2.73 2  14  20  9  20 1.56   6.30     0     12.5        4  0.89  2.73
 . .
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 Given that the true (log) relative rates are apparently heterogeneous, we can consider two possibilities: Given that the true (log) relative rates are apparently heterogeneous, we can consider two possibilities:
  
-  - We can interpret the model estimate obtained above as an estimate of the (weighted) average of the true log relative rates for these 17 studies. This is the so-called fixed-effects model, which allows us to make a //conditional// inference (about the average effect) that only pertains to this set of studies.+  - We can interpret the model estimate obtained above as an estimate of the (weighted) average of the true log relative rates for these 17 studies. This is the so-called fixed-effects model, which allows us to make a //conditional// inference (about the average effect) that only pertains to this set of studies. For a more in-depth discussion of the fixed-effects model, see [[https://wviechtb.github.io/metafor/reference/misc-models.html|here]].
   - We can model the heterogeneity in the true log relative rates and apply a random-effects model. This allows us to make an //unconditional// inference about a larger population of studies from which the included set of studies are assumed to be a random selection.   - We can model the heterogeneity in the true log relative rates and apply a random-effects model. This allows us to make an //unconditional// inference about a larger population of studies from which the included set of studies are assumed to be a random selection.
  
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 Model Results: Model Results:
  
-estimate    se  zval  pval  ci.lb  ci.ub  +estimate    se  zval  pval  ci.lb  ci.ub 
-    0.45  0.09  4.87  <.01   0.27   0.63  *** +    0.45  0.09  4.87  <.01   0.27   0.63  ***
  
 --- ---
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 dat$dosage <- dat$dosage * dat$duration dat$dosage <- dat$dosage * dat$duration
 </code> </code>
-The baseline HRSD score will be used to reflect the severity of the depression in the patients. Since these two variables may interact, their product will also be included in the model. Finally, for easier interpretation, we will also center the variables at (roughly) their means when including them in the model.+The baseline HRSD score will be used to reflect the severity of the depression in the patients. Since these two variables may interact, their product will also be included in the model. Finally, for easier interpretation, we will center the variables at (roughly) their means when including them in the model.
  
 We can fit a mixed-effects meta-regression model with these moderators to the data with: We can fit a mixed-effects meta-regression model with these moderators to the data with:
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 Model Results: Model Results:
  
-                                 estimate      se     zval    pval    ci.lb   ci.ub  +                                 estimate      se     zval    pval    ci.lb   ci.ub 
-intrcpt                            0.4763  0.0876   5.4342  <.0001   0.3045  0.6480  ***  +intrcpt                            0.4763  0.0876   5.4342  <.0001   0.3045  0.6480  *** 
-I(dosage - 34)                    -0.0058  0.0100  -0.5846  0.5588  -0.0254  0.0138       +I(dosage - 34)                    -0.0058  0.0100  -0.5846  0.5588  -0.0254  0.0138 
-I(baseline - 20)                  -0.0672  0.0352  -1.9086  0.0563  -0.1363  0.0018    .  +I(baseline - 20)                  -0.0672  0.0352  -1.9086  0.0563  -0.1363  0.0018    . 
-I(dosage - 34):I(baseline - 20)   -0.0016  0.0034  -0.4555  0.6487  -0.0083  0.0052      +I(dosage - 34):I(baseline - 20)   -0.0016  0.0034  -0.4555  0.6487  -0.0083  0.0052
  
 --- ---
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  1.26  0.99  1.61  0.77  2.07  1.26  0.99  1.61  0.77  2.07
 </code> </code>
-So, for a low baseline HRSD score (i.e., mildly depressed patients), the estimated average relative improvement rate is quite high (2.67 with 95% CI: 1.46 to 4.88), but at a high baseline HRSD score (i.e., more severely depressed patients), the estimated average relative improvement rate is low (1.26 with 95% CI: 0.99 to 1.61) and in fact not significantly different from 1.+So, for a low baseline HRSD score (i.e., for mildly depressed patients), the estimated average relative improvement rate is quite high (2.67 with 95% CI: 1.46 to 4.88), but at a high baseline HRSD score (i.e., for more severely depressed patients), the estimated average relative improvement rate is low (1.26 with 95% CI: 0.99 to 1.61) and in fact not significantly different from 1.
  
 As shown in Figure 3 in the article, we can illustrate these results with a scatterplot of the data, superimposing a line (or rather: curve after the back-transformation) with the estimated average relative improvement rate based on the model for different baseline HRSD scores, holding the total dosage value constant at 34. This figure can be re-created with: As shown in Figure 3 in the article, we can illustrate these results with a scatterplot of the data, superimposing a line (or rather: curve after the back-transformation) with the estimated average relative improvement rate based on the model for different baseline HRSD scores, holding the total dosage value constant at 34. This figure can be re-created with:
 <code rsplus> <code rsplus>
-size <- 1 / sqrt(dat$vi) +xvals   <- seq(12, 24, by=0.1) - 20 
-size <- 0.15 * size / max(size) +modvals <- cbind(0, cbind(xvals, 0)) 
- +preds   <- predict(res, modvals)
-modvals <- cbind(0, cbind(seq(12, 24, by=0.1)) - 20, 0) +
-preds   <- predict(res, modvals, transf=exp)+
  
-plot(NA, NA, xlab="Baseline HRSD Score", ylab="Relative Rate", xlim=c(12,24), ylim=c(0.5,4.0), bty="l") +regplot(res, mod=3, pred=preds, xvals=xvals, 
-abline(h=seq(1, 4, by=0.5), col="lightgray") +        shade=FALSE, bty="l", las=1, digits=1, transf=exp, 
-abline(v=seq(14, 24, by=2), col="lightgray") +        xlim=c(12,24)-20, ylim=c(0.5,4), xaxt="n", 
-lines(modvals[,2] + 20, preds$pred, col="darkgray", lwd=2) +        xlab="Baseline HRSD Score", ylab="Relative Rate") 
-lines(modvals[,2] + 20, preds$ci.lb, col="darkgray", lty="dashed", lwd=2) +axis(side=1, at=seq(12, 24, by=2) - 20, labels=seq(12, 24, by=2))
-lines(modvals[,2] + 20, preds$ci.ub, col="darkgray", lty="dashed", lwd=2) +
-symbols(dat$baseline, exp(dat$yi), circles=size, inches=FALSE, add=TRUE, bg="black")+
 </code> </code>
  
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 ==== References ==== ==== References ====
  
-Linde, K., Berner, M., Egger, M., & Mulrow, C. (2005). St John's wort for depression: Meta-analysis of randomised controlled trials. //British Journal of Psychiatry, 186//, 99--107. +Linde, K., Berner, M., Egger, M., & Mulrow, C. (2005). St John's wort for depression: Meta-analysis of randomised controlled trials. //British Journal of Psychiatry, 186//, 99--107.
  
-Viechtbauer, W. (2007). Accounting for heterogeneity via random-effects models and moderator analyses in meta-analysis. //Zeitschrift für Psychologie / Journal of Psychology, 215//(2), 104--121. +Viechtbauer, W. (2007). Accounting for heterogeneity via random-effects models and moderator analyses in meta-analysis. //Zeitschrift für Psychologie / Journal of Psychology, 215//(2), 104--121.
  
analyses/viechtbauer2007b.txt · Last modified: 2022/08/03 11:24 by Wolfgang Viechtbauer