**2.3.2 Habits or modifying variables (Table 2)**

4. "Smoking habit" (SH). A nominal binary variable. Recorded whether or not the subject smoked.

5. "Noise outside work" (NOW). A nominal binary variable. Recorded whether or not noisy activities were undertaken outside of work.

6. "Hearing protection" (HP). A nominal binary variable. Recorded whether or not hearing protection was used.


#### Table 2. Habit variables

The events were defined based on the "degree of hearing alteration" variable, treating this as a nominal variable of binary response. Since in reality it is an ordinal variable with five modalities, it was necessary to transform the initial variable in such a way that the code (0)

Exploration Databases on Occupational Hearing Loss 197

makes it possible for both the response variable and the predictor variables to establish a strong dependence relationship with the single variable, thereby obtaining suitable variants of Cox's regression model for this particular case (Cox's regression with a time dependent variable). It is true that the character of this regression applied to the data is fundamentally explanatory as the prediction must be based on the most frequently recorded samples with

The steps that were followed to apply Cox's model (Hosmer & Lemeshow, 1999) were: (1) Ensuring that the events defined were Cox type events: i.e. they occurred only once and after the event occurred it was set permanently; (2) Checking the proportionality and consistency of the risks. A graph was used based on the projection of the survival functions (demonstrated and not demonstrated); (3) Assessing the high multicollinearity or interdependence. Those variables defined prior to the study, with a correlation of above 0.8, were eliminated; (4) Assessing the linearity of the quantitative variable (duration of exposure). A graph was used based on the projection of the duration of exposure of each individual with respect to their partial residual plot (calculated with respect to their age); (5) Assessing the existence of influencing observations. Delta-beta values were used. (Cook's distance applied to Cox's regression). Values above 1 were rejected; (6) To identify any possible confusion and interaction between variables, the method involving changing model coefficients was used; (7) The correlation between beta coefficients was used to assess the stability of each model; (8) The fit of the models was assessed using probability reasoning; (9) The model was validated indirectly as it was not possible to obtain another, different sample with which to assess this aspect. Validation of the latent structure was used,

obtained by the analysis of matches for each one of the two halves of the sample.

The Kaplan-Meyer method (K-M) was used to obtain the survival function of a particular event associated with the various covariables, and for the contrast of functions and their

Subsequently a Cox regression model was used, with the aim of explaining the relationships

To obtain the reliability functions the normal distribution model was used and for their contrast a U of Mann-Whitney and t-test was used. For this each one of the binary variables

The parametric model was only used as a descriptor of the variables and for testing certain controls, hypotheses and predictions, starting with the probability distributions: (1) Tests to establish controls (regarding the population percentage, with reference to one or more alterations, which must not be exceeded). The tests concern establishing a common "cut off point" for the modalities of the variable "degree of hearing alteration"; (2) Hypothesis tests (regarding the development of hearing alteration). These involve the analysis of the differences in probabilities based on a real value and a theoretical value. An individual with a particular duration of exposure experiences a degree of hearing alteration (real value). In turn, this individual, with that duration of exposure, could experience other degrees of

was transformed into another equivalent referring to duration of exposure.

the objective of ensuring the accuracy of the observations.

**3.1 Nonparametric reliability models** 

meaning the Log-Rank test was used.

**3.2 Parametric reliability models** 

between the variables.

represented the cases censored or in which the event did not occur, and the code (1) represented the event occurring. The system followed is represented in Table 3. This approach does not allow other reinterpretations of the type of censures to be used as they must necessarily be to the right because the exact decrease in the threshold is not available for each individual. Instead, only a diagnostic code is available, which did not allow us to define a specific decrease in dB and to relate this to the "duration of exposure" variable.


Table 3. Definition of events
