**3. Methods**

The way of initially tackling the analysis of the data was by defining the survival functions. The main focus of this study was to identify the patterns of hearing alteration over time, related to the environmental conditions to which the individuals were exposed and their "habits". Once the survival functions were defined and examined, the data was analysed using various regression analysis techniques to identify the most suitable method.

The starting point was one quantitative variable with the remaining variables being qualitative. We are in a limiting case when applying regression theory to the data, that as indicated by Martín & Paz (2007).

Due to reason stated above the number of useful regression models was limited. Linear regression models require at least two quantitative variables. Models based on the discriminating function require the normal distribution of variables, an aspect which in this case was not satisfied as the only category contrasting with the rest (healthy) did not follow a normal distribution. The remaining categories of this variable are self-contained and as a consequence they cannot be analysed using this technique. Multivariate analysis of variance is not an alternative to discriminant analysis as it also requires at least two quantitative variables.

Specific regression techniques for the analysis of quantitative variables also present problems. Thus, logistic regression with nominal binary or polytomous response (Silva & Barroso, 2004), does not allow the quantitative variable (taken as independent) to be correlated with the others variables. Ordinal regression (Greenland, 1994) is not operational either as it is an extension of the above.

The most ideal model for the analysis of this situation is Cox's regression model, which makes it possible to work with only one quantitative variable (Cox & Snell, 1989). It also

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.

(H)

(H+IAT)

The way of initially tackling the analysis of the data was by defining the survival functions. The main focus of this study was to identify the patterns of hearing alteration over time, related to the environmental conditions to which the individuals were exposed and their "habits". Once the survival functions were defined and examined, the data was analysed

The starting point was one quantitative variable with the remaining variables being qualitative. We are in a limiting case when applying regression theory to the data, that as

Due to reason stated above the number of useful regression models was limited. Linear regression models require at least two quantitative variables. Models based on the discriminating function require the normal distribution of variables, an aspect which in this case was not satisfied as the only category contrasting with the rest (healthy) did not follow a normal distribution. The remaining categories of this variable are self-contained and as a consequence they cannot be analysed using this technique. Multivariate analysis of variance is not an alternative to discriminant analysis as it also requires at least two quantitative

Specific regression techniques for the analysis of quantitative variables also present problems. Thus, logistic regression with nominal binary or polytomous response (Silva & Barroso, 2004), does not allow the quantitative variable (taken as independent) to be correlated with the others variables. Ordinal regression (Greenland, 1994) is not operational

The most ideal model for the analysis of this situation is Cox's regression model, which makes it possible to work with only one quantitative variable (Cox & Snell, 1989). It also

using various regression analysis techniques to identify the most suitable method.

**Event 1**:

**Event 2**:

**Event 3**:

**3. Methods** 

variables.

Healthy (code 0) Altered (code 1)

Recovered (code 0) Not recovered (code 1)

No falls in conversational freq. (code 0) With falls in conversational freq. (code 1)

Table 3. Definition of events

indicated by Martín & Paz (2007).

either as it is an extension of the above.

Events Modalities ¿Event of Cox?

(IAT+AAT+MH+AH)

(AAT+MH+AH)

(H+IAT+AAT) (MH+AH)

YES

YES

YES

Temporary effect (IAT) treated as permanent

Permanent effect

Permanent effect

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 objective of ensuring the accuracy of the observations.

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.
