1
Online depository
Likelihood ratio analysis1-7
Deeks and Altman3 suggest that likelihood ratios have more powerful properties, making them
more appropriate in clinical use, than sensitivity and specificity alone. Practically, a good test
should have a Positive Likelihood Ratio (LR+) of at least 2.0 and a Negative Likelihood Ratio
(LR-) of 0.5 or less.7 This would correspond to an AUC of roughly 0.75. A better test would
have likelihood ratios of 5 and 0.2, respectively, and this corresponds to an AUC of around 0.92.
Even better would be likelihood ratios of 10 and 0.1, which corresponds roughly to an AUC of
0.97. Similar to ours, such an approach is also used in Christ-Crain et al.5 and Grover and
Pittman.6
Power analysis
As stated in the Introduction section, our null hypothesis (H0) was μ1=μ2 [the mean PnCPAP was
not different between responders (μ1) and non-responders (μ2)] whereas the alternative
hypothesis (H1) was μ1<μ2 (the mean PnCPAP of non-responders was greater than that of
responders). Accordingly, the effect size (Δ0) and the power (i.e., 1-β) should be calculated with
the following formula: Δ0=(μ1-μ2)/σ, 1-β=Pr{t0<-t(φ, 2α)}, φ= n1+n2-2, where σ is the population
standard deviation, β is the Type II error, φ is the degree of freedom, α is the Type I error set at
0.05, n1 is the number of responders, and n2 is the number of non-responders.8 Statistically, n1
and n2 were assumed to be equal (i.e., n1=n2) to each other in the formula. This was favourable
in our study because the overall success rate of oral appliance therapy has been reported to be
approximately 50%1 (i.e., n1⋍n2) when criterion 2 is applied.
However, since the present study
was the first which investigated the relationship between oral appliance treatment outcome and
2
PnCPAP, no previous reports provided an estimate of μ1 or μ2 to determine Δ0. Accordingly, in
addition to its uses for planning, power analysis was utilized after analyses of μ1 and μ2 had been
completed to determine the actual power achieved, so that the results could be properly
interpreted.9 In this case, σ was set at 3 cmH2O by reference to previous literature.10 The ratio
n2/n1, which is known to affect the power, was also checked simultaneously. The relationship
between the total sample size (i.e., n1+n2) and the power was examined using Microsoft®
Excel-based free software.11 The sample size was regarded as acceptable if the power exceeded
0.80.
The effect size and the power in the present study were 1.02 and 0.81 at criterion 1
(μ1=7.50±2.55, μ2=10.56±3.45; mean±standard deviation), 1.10 and 0.87 at criterion 2
(μ1=7.71±2.70, μ2=11.0±3.36), and 0.94 and 0.76 at criterion 3 (μ1=8.63±3.19, μ2=11.46±3.33),
respectively. These results suggest that the total sample size for this study was acceptable.
Hence it was considered that further recruitment of patients was not necessary.
Sample size and generalisability of the results
The number of randomly selected study samples appears rather small when the total pool of
potentially eligible patients is considered.
However, we speculate that generalizability is
maintained for the following reasons.
First, patient selection was performed with the use of the RANDBETWEEN function
that is available in Microsoft® Excel. This method is introduced by Morizane.12 Second, we
compared some diagnostic variables between the subjects whose data were analyzed (i.e., N=35)
and the eligible patients who were not selected for analyses in the study (i.e., N=407-35=372)
(Table 1 of the online depository).13 Statistical significance was observed not only in four
3
variables including optimal positive airway pressure (PnCPAP) but also in terms of age between
the two populations. However, age appeared not to effect the results because there was no
significant age difference between responders and non-responders (Table 1 in the text) and also
because age per se did not contribute to the likelihood of treatment success with oral appliances
(Table 3 in the text).
Table 1. Characteristics of analysed and non-analysed subjects.
Diagnostic Characteristics
Analysed
sample
Number
Age (yrs)
BMI (kg/m2)
PnCPAP(cm H2O)
AHI on the diagnostic polysomnography (/hr)
nadir SaO2 on the diagnostic polysomnography (%)
35
55 (41-66) *
26 (24-29)
9 (7-13)
37 (24-60)
80 (71-84)
*: p<0.05 versus non-analysed sample.
variables.
Non-analysed
sample
p value
374
47 (40-56)
27 (25-30)
9 (7-10)
43 (29-63)
76 (69-82)
0.04
0.06
0.61
0.13
0.07
Mann-Whitney U tests were used to compare the
4
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