Howard Appendix 1 and 2

Appendix 1

Effect of antiplatelet and/or anticoagulation medication on the risk of tympanic barotrauma in hyperbaric oxygen therapy patients and development of a predictive model

Adam E Howard

Appendix 2

The resulting equation for calculating the logit of the categorical outcome variable MEBt is given:

                     (Eq. 2)

Where the point estimate for the intercept (α₁) comparing no MEBt with (MEBt I or ≥II) was 2.5246 (SE 0.4752), and for comparing (no MEBt or MEBt I) with MEBt ≥II the (α₂) intercept was 3.2009 (SE 0.4853). Two examples for translating this result into interpretable odds and probabilities are now given.

Example 1: A 55-year-old male

The logit for comparing no MEBt with (MEBt I or ≥II), (using α₁):

= 2.5246 - (0.3421*0) - (0.0148*55)

= 2.5246 – 0 – 0.814

= 1.7106

The odds of a 55-year-old male having no MEBt are e^1.7106 which = 5.5 times the odds of having either MEBt I or ≥II.

The probability of a 55-year-old male having no MEBt:

= e^1.7106 / (1+ e^1.7106)

= 5.53 / 6.53

= 85%

The logit for comparing (no MEBt or MEBt I) with MEBt ≥II, (using α₂):

= 3.2009 - (0.3421*0) - (0.0148*55)

= 3.2009 – 0 – 0.814

= 2.3869

The odds of a 55-year-old male having no MEBt or MEBt I are e^2.3869 which = 10.9 times the odds of having MEBt ≥II.

The probability of a 55-year-old male having MEBt ≥II

= 1-[the probability of having either no MEBt or MEBt I]:

= 1-[e^2.3869 / (1+ e^2.3869)]

= 1-[10.88 / 11.88]

= 1-92%

=8%.

Therefore, the probabilities of each of the three outcomes for a 55-year-old male are: no MEBt (85%), MEBt I (7%) and MEBt ≥II (8%), total=100%.

Example 2: A 65-year-old female

The logit for comparing no MEBt with (MEBt I or ≥II), (using α₁):

= 2.5246 - (0.3421*1) - (0.0148*65)

= 2.5246 – 0.3421 – 0.962

= 1.2205

The odds of a 65-year-old female having no MEBt are e^1.2205 which = 3.4 times the odds of having either MEBt I or ≥II.

The probability of a 65-year female having no MEBt:

= e^1.2205 / (1+ e^1.2205)

= 3.39 / 4.39

= 77%

The logit for comparing (no MEBt or MEBt I) with MEBt ≥II, (using α₂):

= 3.2009 - (0.3421*1) - (0.0148*65)

= 3.2009 – 0.3421 – 0.962

= 1.8968

The odds of a 65-year-old female having no MEBt or MEBt I are e^1.8968 which = 6.66 times the odds of having MEBt ≥II.

The probability of a 65 year old female having MEBt ≥II

= 1-[the probability of having either no MEBt or MEBt I]:

= 1-[ e^1.8968 / (1+ e^1.8968)]

= 1-[6.66 / 7.66]

= 1-87%

=13%.

Therefore, the probabilities of each of the three outcomes for a 65-year-old female are: no MEBt (77%), MEBt I (10%) and MEBt ≥II (13%), total=100%.