Treatments

Positive control = Standard treatment on the farm Treatment = Decision support tool

Outcomes

The primary outcome will be absence of recurrence of clinical mastitis

Sample size assumptions

Non-inferiority design

library(epiR)
epi.ssninfb(treat = 0.7, control = 0.7, delta = 0.075, n = NA, r = 1, 
   power = 0.80, nfractional = FALSE, alpha = 0.05)
## $n.total
## [1] 924
## 
## $n.treat
## [1] 462
## 
## $n.control
## [1] 462
## 
## $delta
## [1] 0.075
## 
## $power
## [1] 0.8

924 cows are needed to show that the decision support tool is not worse (no worse than 7.5 percentage points lower) than the industry standard treatment

Adjustments to sample size for loss to follow-up

We expect that loss to follow-up will be 20%

924 * 1.2
## [1] 1108.8

We need an additional 100 cows for the pilot-study.

924 * 1.2 + 100
## [1] 1208.8

The final number of cows required is 1209

Paragraph

We expect that 30% of cows will have a recurrence event for clinical mastitis. Therefore, 70% of cows will have an absence of recurrence (i.e. our primary outcome). We expect that the outcome will be the same (70%) in cows randomised to the decision support tool. We believe that a reduction in absence of recurrence of ≤7.5% points will be acceptable to producers. Therefore, we will use a non-inferiority hypothesis test to evaluate if this is the case. As convention, we will use an alpha of 0.05 and desired power of 0.8. Under these assumptions, 924 cows are needed to show that the decision support tool is not inferior than the industry standard treatment (i.e. no worse than 7.5 percentage points lower). This calculation was conducted in R using the epi.ssninfb function within the EpiR package (see analysis log at this address: https://rpubs.com/samrowe/cm22_sample_size). To recruit this many cases into our data set, an addition 20% are needed to account for loss to follow-up (n = 1109). Finally, an additional 100 cows are required for the pilot study. In summary, 1209 cows are required for this study.

Revised sample size 2024-02-28

We wish to nest a therapeutic trial within the existing non-inferiority design, where 2 positive controls are included and compared.

This will be a superiority design where two antibiotics will be compared to each other for bacteriological cures. The target population is cows with non-severe klebsiella mastitis. Our sample population will be cows with non-severe mastitis, which will be approximately 50% klebsiella - it will be unknown which cases are caused by klebsiella or other bacteria at the time of enrollment. Therefore enough cases will need to be enrolled to retrospectively apply our inclusion criteria.

Outcome of interest = bacteriological cure. Expected bacteriological cure with narrow spectrum antibiotic = 0.4. Expected bacteriological cure with broad spectrum antibiotic = 0.6.

epi.sssupb(treat = 0.6, control = 0.4, delta = 0.05, n = NA, power = 0.8, r = 1, nfractional = FALSE, alpha = 0.05)
## $n.total
## [1] 264
## 
## $n.treat
## [1] 132
## 
## $n.control
## [1] 132
## 
## $delta
## [1] 0.05
## 
## $power
## [1] 0.8
n <- epi.sssupb(treat = 0.6, control = 0.4, delta = 0.05, n = NA, power = 0.8, r = 1, nfractional = FALSE, alpha = 0.05)$n.treat

Inflate sample size to account for missing data 10% probability of missing a milk sampling. 0.9^2 = 0.81. Therefore need expect to lose 19% of recruits. This means we need to inflate sample size by 1/0.81 = 1.23. Below is the number of klebsiella cases needed per group for the treatment trial

n_kleb_cases <- round(n*1.23,0)
n_kleb_cases
## [1] 162

Inflate sample size to account for non-klebsiella isolates. Assume 50% of cases are Klebsiella.

n_any_path_cases <- n_kleb_cases * 2
n_any_path_cases
## [1] 324

Therefore the total number of additional cases to recruit for this study is show below

n_any_path_cases * 2
## [1] 648