ANOVA is significant but also demonstrates non-inferiority

Question

I have data that is looking at comparing a cheap (T) to expensive (V) ultrasound device with the hopes that the cheap is the same as expensive. There was 4 different examiners that used 4 different views to determine the presence of osteophytes. I have used a generalised mixed-effects logistic regression followed by an ANOVA and non-inferiority test.

glmer(OSTEOPHYTES ~ DEVICE + Examiner + VIEW + (1 | ID), data = TVOPL, family = binomial,
                  nAGQ = 10)

The ANOVA is significant for DEVICE (Pr(>|z|) = 0.00514), meaning there is a difference in the two devices (Reject Null hypothesis). However, when I do a non-inferiority (LRT) test:

subset_data <- subset(TVOPL, DEVICE %in% c("V", "T"))
vinno_model <- glmer(OSTEOPHYTES ~ Examiner + VIEW + (1 | ID), data = subset_data, family = binomial(link = "logit"), control = glmerControl(optimizer = "bobyqa"))
tablet_model <- glmer(OSTEOPHYTES ~ DEVICE + Examiner + VIEW + (1 | ID), data = subset_data, family = binomial(link = "logit"), control = glmerControl(optimizer = "bobyqa"))
lrt_result <- anova(vinno_model, tablet_model, test = "LRT")
summary(lrt_result)

It is significant Pr(>Chisq) = 0.00495 determining that the cheap device is noninferior to the expensive device by the specified margin. When I subset the data into each view, it also can come up with the opposite. The ANOVA is not significant, but also not non-inferior. How do I interpret this in terms of results due to conflicting outcomes? Also is it possible to use non-inferiority with the data set including all views, then, ANOVA for each View (A,B,C,D) as I want to know which view is the best.

Answer 1

Your understanding of a non-inferiority test is wrong, I fear. It has nothing to do with a small p value of a LRT.

In your case, you would specify a margin for the true effect $\theta$ of DEVICE to be "like zero". For instance, 0.02. This leads to traditional hypotheses

• $H_o$: $\theta \le -0.02$ and
• $H_1$: $\theta > -0.02$ (non-inferiority, the thing that you want to show)

Then, you would calculate a lower one-sided 95% CI for $\theta$ and show that it is larger than -0.02. If yes, you would reject $H_o$ in favour of non-inferiority.

Furthermore, you seem to do pairwise comparisons. This will make the non-inferiority consideration much more complicated (as it is completely different from showing superiority, one cannot simply apply a Bonferroni correction or similar).