Final answer:
The correct statement is that when a log odds ratio is greater than 0, it means that the odds ratio is greater than 1, indicating the event is more likely than its complement.
Step-by-step explanation:
The correct statement is: When a log odds ratio is greater than 0, it means that the odds ratio is greater than 1. This is because the logarithm of an odds ratio translates back to the actual odds ratio by taking the exponent of the log odds. If the log odds is positive, this exponentiation will result in an odds ratio greater than 1, indicating that the event is far more likely than its complement.
On the other hand, a negative log odds ratio implies that the odds ratio is less than 1, thus the event is far less likely than not occurring. If we consider the probability of success being greater than the probability of failure, that would correspond to an odds ratio greater than 1, which is not the scenario posed by a negative log odds ratio.
To summarize, in the context of epidemiology and public health, an odds ratio of 1 indicates no difference in risk, whereas ratios greater or less than 1 suggest higher or lower risk, respectively. The log odds being greater than 0 corresponds to an odds ratio greater than 1.