[R-meta] calculate effect size and variance for prepost proportion data

[Liu Sicong]

Happy 2023 All!

I have some prepost proportion data. For instance, some clinical trials may intervene on patients� vaccine uptake and report the proportion of patients who received the vaccine both prior to and after interventions. So I may have the following data

  *   Outcomes in proportion: p_control_pre, p_control_post, p_experiment_pre, p_experiment_post
  *   Sample sizes: n_control_pre, n_control_post, n_experiment_pre, n_experiment_post

I am clear about how to calculate between-condition effect sizes and variances in the following manner. For instance, those for comparing the conditions at posttest would be:

  *   Effect size: ln((p_experiment_post/(1 - p_experiment_post))/(p_control_post/(1 - p_control_post)))
  *   Variance of effect size: 1/(n_experiement_post*p_experiment_post) + 1/(n_experiement_post*(1-p_experiment_post)) + 1/(n_control_post*p_control_post) + 1/(n_control_post*(1-p_control_post))

My question is about how to calculate the effect size and its variance when I am also interested in within-condition growth. For instance, how to represent the prepost growth due to vaccination intervention for the experimental group? Perhaps even before asking this question, would it be reasonable to attempt the computation of such effect sizes and variances? Thank you very much!

Best regards,
Sicong (Zone)

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Sicong (Zone) Liu, Ph.D.
Research Associate
University of Pennsylvania

3620 Walnut Street,
Philadelphia, PA 19104-6220
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