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I've been asked to help determine the design of an RCT. The design is primarily interested in the benefit of using a laser on some dental procedure in addition to a local anti-biotic and scaling, versus just the anti-biotic and scaling.

The outcome us gum attachment loss. A dentist will probe the area between the tooth and gum to measure the depth where there is no attachment between the two. This is done on a tooth by tooth basis and is measured in mm. The aim of the RCT is to determine efficacy of the laser (meaning, does attachment loss decrease when using the laser in addition to drug and scaling).

Because there are two groups (Laser + drug + scaling v. drug + scaling), it would be easy to suggest randomizing subjects to one of the two and measure attachment loss on a single tooth or set of teeth. I would run an ANCOVA controlling for baseline attachment loss plus other clinical factors associated with attachment loss (like smoking status).

I believe there is the option to also use patients as controls for themselves, which should improve efficiency. Under the assumption that all teeth in the mouth are exchangeable, the proposition would be:

  • Randomly select one side of the mouth to receive treatment (laser + drug + scaling) and the other receive control (drug + scaling).

  • Match two teeth on either side on baseline attachment loss.

  • Treat those teeth and measure improvement after treatment.

  • Compare the difference in attachment loss between the two teeth and perform a regression on this.

To be clear, if $y_t$ was the attachment loss after treatment on the treated tooth, and $y_c$ was the attachment loss after treatment on the control tooth, then the ANCOVA would be on $\delta = y_t - y_c$.

I'm interested in the knowing if I my conception on matching teeth is valid and if the analysis I good, or if there is some other analysis I might be able to perform which might be better suited.

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This split-mouth design is pretty common in dental research and sounds pretty reasonable. You want to make sure the sides are truly randomly selected (and at least vaguely comparable a-priori, because otherwise e.g. comparing one side that barely needed treatment vs. side that was in a really bad shape might not be ideal) and similarly the selection of the teeth to be matched. You also want to do as much as possible to minimize bias in the outcome assessment (ideally done by a person that's not aware which side was treated which way, or for consistency reasons always by the same person for all patients).

Analysis-wise, forming a subject difference is one way of proceeding that makes perfect sense. An alternative is to run e.g. a model with a subject random effect (modeling the average for each side), or to even model separately each tooth.

Given that you intend to always use two teeth per side, the different options shouldn't make too much of a difference. However, this also limits you:

  • Patients with only one side needing treatment (or only needing treatment for one tooth on one of the two sides) cannot be used (while with the last option that would be possible).
  • You cannot adjust for any covariates on a tooth level (e.g. some pre-treatment assessment, something you can measure from an X-ray or whatever else might make sense), while with the last option you could.
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  • $\begingroup$ I'm fond of the idea of a subject random effect. It might be feasible for us to measure all teeth within each treatment, meaning I could estimate a model in which teeth are nested within subject with a fixed effect of treatment and other covariates as Jacob mentions. $\endgroup$ Mar 15, 2023 at 1:59
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I like the idea of randomizing each side of the mouth for each patient, and also matching teeth. I wonder if it's best to match by position of the teeth (i.e. using symmetry of the mouth) rather than by baseline loss, especially since you're also controlling for baseline loss. I'm not sure what the consequences of the different matching would be.

In terms of modeling, I would use a random effects model. Enumerate the teeth on the right side from $t=1,..,T$, and assume that each of these teeth can be matched to the left side. For each measurement (2T measurements per subject) we note the subject, the tooth, the side, the treatment/control status, and covariates of the patients. Then the model in lme4 would be

fit <- lmer(y~ treatment + covariates + (1|subject) + (1|subject:tooth), data = dat)

and you would look at the coefficient for treatment

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