Bit of beginner's question in terms of statistics...

How can I determine whether the treatment (patients A and B) is significantly more effective at raising PO2 levels than the placebo (patients C to E)? This would be a straightforward ANOVA if it weren't for TREATMENT and NON-TREATMENT days, the latter of which no patients received either treatment nor placebo.

I feel a 2-way ANOVA will answer this? But for some reason I feel this may be wrong.

Please could anyone explain?


  • $\begingroup$ Do you have repeated measures for the patients? $\endgroup$ – user2974951 Nov 20 '20 at 12:17
  • $\begingroup$ Yes, this data is made up of 108 observations on all patients. Equal treatment:non-treatment days ratio. $\endgroup$ – sanees_h22 Nov 20 '20 at 12:20
  • $\begingroup$ Equal treatment:non-treatment days does this mean that the treatment group received treatment half of the time, and the other half received nothing? Which half of the time? Was it determined randomly? Does the treatment effect last for many days? $\endgroup$ – user2974951 Nov 20 '20 at 12:42
  • $\begingroup$ On treatment days, patients received either a treatment or placebo. On non-treatment days, patient's didn't receive either. Treatment effect does not extend beyond the day. Days for treatment were selected randomly. $\endgroup$ – sanees_h22 Nov 20 '20 at 12:46
  • $\begingroup$ Then it looks like this can be solved using a three-way repeated measures anova or a generalized linear model with a random effect. $\endgroup$ – user2974951 Nov 20 '20 at 12:59

One approach would be to treat each participant as a separate study. For each of them estimate the mean difference between treatment days and no treatment days with its sampling variance. To take account of days do this from a model with day as a covariate (I assume the days were interleaved). The take these five estimates with their standard errors and perform a fixed effects meta-analysis to combine them with treated versus control as a moderator. The test of the moderator is then a test of the hypothesis that the PO2 levels differ between the groups.


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