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Figure 6.5: Mean mortality rate estimates by year and port. Bars represent 95 confidence intervals.
The above plot was generated from an interaction term involving yearport that was added to the statistical model. It demonstrates that in any given year, there is variability between ports with
respect to average annual mortality rate. Voyages that included sheep loaded from Portland had the highest annual mortality rate in four of the six years and the lowest annual mortality rate in the two
remaining years. It is also useful to note that voyages containing only sheep from Fremantle only had the lowest annual mortality rate in one year and in all remaining years were in the middle.
6.2 Odds of reportable mortality events
The dataset was inspected against the reports from mortality investigations involving sheep voyages and the 13 voyages relating to the mortality investigations were identified.
A binary variable was then developed to apply case-control coding to voyages: 0=control = those voyages that did not involve any reportable mortality event for sheep
n=264 1 = case = those voyages that incorporated one or more consignments that involved a
reportable mortality event n=13 .5
1 1.
5 2
Mo rt
a lit
y ra te
d e
a th
s p e
r 1 sh
e e
p
2006 2007
2008 2009
2010 2011
Year Portland
Adelaide Fremantle
Mean mortality rate by year and port
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All other variables were coded as indicated above. The binary outcome variable was then used as the outcome in a logistic regression model to look for
factors that may be associated with the odds of a reportable mortality event. Because there were only 13 case voyages, there were more numeric problems in fitting the
statistical model to this particular outcome. Case voyages only occurred in some months and only in some years and not for all exporters and therefore it was not possible to derive as much detail as for
the negative binomial analyses described above. However, the findings are valid and are useful.
It was not possible to incorporate exporter or any interaction in the final model. The results from the final model are presented below as odds ratios OR.
Table 6.4: Results from multivariable logistic regression analysis. OR=odds ratio, se=standard error, z=z-statistic, CI=confidence interval.
95 CI Variable Level
OR se
z p-
value lower upper Year 2006 reference
2007 7.94 8.58 1.92 0.055 0.96 65.95
2008 1 empty 2009 0.53
0.73 -0.46
0.6 0.04 7.91
2010 2.14 2.40 0.68 0.5 0.24 19.30 2011 0.40
0.55 -0.66
0.5 0.03 6.08
Month 1 1
empty 2 1
empty 3 1
empty 4 1
empty 5 reference
6 5.38 7.49 1.21 0.2 0.35 82.21
7 1.00 1.66
0.9 0.04
25.89
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8 3.68 4.94 0.97 0.3 0.27 51.03
9 1.07 1.79 0.04 0.9 0.04 28.40
10 0.54 0.88
-0.38 0.7
0.02 12.95
11 1 empty
12 1 empty
Port Fremantle reference
Portland 9.15 7.46 2.72 0.007
1.85 45.23 Adelaide 0.85 1.14 -0.12 0.9
0.06 11.77 Intercept
0.01 0.02
-2.75 0.006 0.00
0.29
Odds ratios OR provide a measure of the strength of association relative to the reference level for that particular variable. Examples of the interpretation of the above results are provided below.
A case voyage is a voyage that has a reportable mortality event. Odds ratios provide a measure of the likelihood of a case voyage occurring, expressed as the odds. When the OR is greater than one
then the factor is associated with an increased odds or likelihood of the event happening.
It is also important to look at the p-values to determine if the comparison is statistically significant. Most of the comparisons in this model are not statistically significant and this reflects the small
number of cases.
There was a 7.94 increase in the odds of a mortality event occurring in 2007 compared to 2006. In contrast the odds of a case occurring in 2011 was greatly reduced compared to 2006 OR=0.4. If
the odds of an event was reduced by a multiple of 0.4, this is the same as a 1-0.4=0.6 or 60 reduction in odds. Notice that none of the years were statistically different.
The two months with the highest odds of a mortality event occurring were June and August compared with May. Again there was no statistical difference between months of the year.
Those voyages containing sheep loaded in Portland had a 9-fold higher odds of a reportable mortality event compared to voyages containing only sheep loaded in Fremantle. This difference
was statistically significant p=0.007. There was no difference in odds of a reportable mortality event between Fremantle and Adelaide p=0.9.
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In summary, the logistic regression model is of limited use because of the small number of case voyages. Caution should be applied to avoid over interpretation of the findings.
Nontheless, the most substantive finding of this analysis is that there appears to be an increased risk of mortality events for voyages containing sheep that were loaded at Portland. This finding is
consistent with the findings from the negative binomial modelling discussed in the previous section.
While some caution is advised, the findings also suggest that there is little difference between sheep loaded in Adelaide and sheep loaded in Fremantle with respect to the risk of a reportable mortality
event.
6.3 Results of statistical analyses in context
