The threshold bias model: a mathematical model for the nomothetic approach of suicide

Abstract

Background: Comparative and predictive analyses of suicide data from different countries are difficult to perform due to varying approaches and the lack of comparative parameters.

Methodology/principal findings: A simple model (the Threshold Bias Model) was tested for comparative and predictive analyses of suicide rates by age. The model comprises of a six parameter distribution that was applied to the USA suicide rates by age for the years 2001 and 2002. Posteriorly, linear extrapolations are performed of the parameter values previously obtained for these years in order to estimate the values corresponding to the year 2003. The calculated distributions agreed reasonably well with the aggregate data. The model was also used to determine the age above which suicide rates become statistically observable in USA, Brazil and Sri Lanka.

Conclusions/significance: The Threshold Bias Model has considerable potential applications in demographic studies of suicide. Moreover, since the model can be used to predict the evolution of suicide rates based on information extracted from past data, it will be of great interest to suicidologists and other researchers in the field of mental health.

Figure 1. Suicide rates by age and gender in USA referring to the years 2001 and 2002.

The data points marked with circles represent the average rate (considering both genders). The curves shown in continuous lines were obtained by fitting the Equation 5 over the aggregate data. Dashed and dotted curves define, respectively, the prediction bands and the confidence bands calculated for 95% confidence intervals.

Figure 2. Suicide rates by age in USA averaged for both genders referring to the year 2003.

(a) Linear extrapolations of parameter values obtained for the years 2001 and 2002 in order to estimate their values for 2003. (b) Prediction curve (continuous line) and the prediction bands (dashed lines) for the year 2003.

Figure 3. Semi-log graph of suicide rates by age.

The curves shown as continuous lines were obtained by using the Equation 5 to fit the aggregate data from Sri Lanka (1999, males), USA (2002, males) and Brazil (2002, males and females). Note the tendency towards the same average critical age.

Figure 4. Suicide rates by age, gender and method in the USA in the quadrennium 1999-2002.

This figure is a graphic representation of data sets reported in reference (Table 17). While the male suicide rates are strongly related to firearms, female rates are not clearly associated with a specific suicide method.

Figure 5. Influence of main TBM parameters on the obtained curve shapes.

Distributions calculated for: (a) Increasing threshold parameter, apex constant fixed; (b) Increasing apex constant, threshold parameter fixed and (c) constant product between these two parameters. The curve marked with an asterisk in (a) is the Weibull distribution.