Exposure to Missile Alarms as a Measure of Missile Attacks and PTSD Symptoms
The ANOVA analysis, focusing on a dichotomous variable labelled 'PTSD Binary' concerning the number of missile alarms, provides significant insights into the correlation between missile alarm exposure and the likelihood of PTSD. The analysis revealed an F-statistic of approximately 8.12 and a p-value of 0.0046. This F-statistic indicates notable variance in the number of missile alarms experienced by individuals across different groups, signifying varied exposure levels to potentially traumatic events. Importantly, the precise p-value, which is significantly less than the conventional threshold of 0.05, robustly suggests that these differences are statistically significant.
This finding is pivotal as it implies that individuals exposed to a higher frequency of missile alarms are more likely to be classified as suffering from PTSD. In essence, there appears to be a stronger correlation between a higher exposure to missile alarms, as a proxy to the number of missile attacks in the residential area, and the likelihood of developing PTSD.
In order to try and estimate as accurately as possible the relationship between the number of missile alarms in the respondent's place of residence, as a measure of the intensity of exposure to missile attack events, and the score in the PCL-5 test as a measure of the severity of PTSD symptoms, various models were examined. Both linear and non-linear models were tested for their fit in describing the findings.
In the presented analysis in
Figure 5, a linear regression model is employed to elucidate the relationship between the frequency of missile alarm exposure in a respondent's residential area and the severity of post-traumatic stress disorder (PTSD) symptoms, as quantified by the PCL-5 test scores. The PCL-5 score, serving as the dependent variable, is a recognized metric for evaluating the intensity of PTSD symptoms, with higher scores indicative of greater symptom severity. The independent variable, the number of missile alarms, is utilized as a surrogate measure for the respondent's exposure level to missile attacks. The resultant regression plot, accentuated with a red trend line, delineates a discernible linear association between these two variables. The R-squared value, prominently displayed on the plot, conveys the extent of variance in PTSD symptomatology that can be ascribed to variations in missile alarm exposure.
The statistical findings from the simple linear regression analysis revealed a notable relationship between the number of missile alarms in a respondent's residential area and their PCL-5 test score, which assesses the severity of post-traumatic stress disorder (PTSD) symptoms. The regression model, based on observational data, demonstrates a linear correlation, where an increase in the number of alarms is associated with a higher PCL-5 score. This suggests that greater exposure to missile alarms, indicative of potential exposure to traumatic events, corresponds to more severe PTSD symptoms. The R-squared value indicates the proportion of variance in the PCL-5 scores that can be explained by the number of alarms. While this correlation is statistically significant, it is important to note that it does not imply causation. Other factors not accounted for in this model might also influence PTSD severity.
In the conducted analysis presented in
Figure 6, a logarithmic transformation was applied to the variable representing the number of missile alarms to examine its correlation with the severity of post-traumatic stress disorder (PTSD) symptoms, as measured by the PCL-5 score. This methodological approach, diverging from the standard linear regression analysis, addresses potential non-linear relationships and skewness in the data. Logarithmic transformations are particularly beneficial when variables exhibit a broad range or when the relationship between variables is multiplicative.
The application of this transformation yielded a linear correlation between the log-transformed missile alarm counts and PCL-5 scores, suggesting a significant proportion of the variance in PTSD symptom severity is explainable by these transformed alarm counts. This indicates a potentially more robust relationship than what might be inferred from the untransformed data. The analysis reveals two key insights: firstly, the persistence of a statistical correlation between missile alarm exposure and PTSD severity, consistent with initial linear observations. Secondly, and perhaps more critically, the relationship appears to exhibit a logarithmic pattern. This implies that increments in alarm exposure, particularly at lower ranges, are associated with a more pronounced impact on PTSD symptom severity compared to higher ranges.
Moving beyond linear models, we explored a variety of non-linear modeling approaches in an effort to best describe the relationship between the variables. Ultimately, we implemented a quadratic polynomial regression model, which emerged as the most suitable for capturing the potential non-linear dynamics, as depicted in
Figure 7. This model, a deviation from previous linear approaches, revealed an increased explanatory power, as demonstrated by a higher R-squared value. The quadratic model suggests a positive correlation between the frequency of missile alarms and the severity of PTSD symptoms up to a certain point, beyond which the impact of additional alarms appears to plateau or diminish significantly.
The model indicates that initially, as the number of missile alarms increases, there is a corresponding increase in PTSD symptom severity. However, this trend reaches a threshold, beyond which further exposure to missile alarms does not continue to escalate PTSD symptoms at the same rate. This point of inflection, where the rate of change in PTSD severity begins to level off, is a critical finding of the analysis. It suggests a possible saturation effect or a coping mechanism, where individuals exposed to a high number of alarms might not experience a proportional increase in symptom severity.
The exact point of this transition, as identified by the model, occurs at the vertex of the quadratic curve (124.88 rocket alarms at 20.88 PCL-5 points). This vertex represents the number of alarms beyond which additional exposures have a markedly reduced impact on PTSD severity. The quadratic model has the lowest Mean Squared Error (MSE) and the highest R-squared (R²) value, suggesting it provides the best fit among the three for explaining the relationship between the Total PCL-5 Score and the number of rocket alarms.
Non-parametric models, such as the Locally Weighted Scatterplot Smoothing (LOWESS) model, are valuable analytical tools in statistics, especially when the relationship between variables does not conform to a specific parametric form. Unlike parametric models that presuppose a certain functional relationship (like linear or polynomial), non-parametric models are more flexible and can adapt to the shape of the data, making them ideal for exploring complex and nuanced relationships.
The LOWESS model I initially presented is a prime example of a non-parametric approach. It creates a smooth curve through the dataset, allowing for the visualization of potential patterns and trends that might not be apparent or accurately captured by traditional parametric models. In the context of our analysis, the LOWESS model was applied to explore the relationship between the number of missile alarms in a respondent's residential area and the severity of their PTSD symptoms, as measured by PCL-5 scores.
The results of the LOWESS analysis (
Figure 8) revealed a nuanced, possibly non-linear relationship between these two variables. The smoothed curve indicated an initial increase in PTSD symptom severity with an increasing number of alarms, followed by a leveling off or potential decrease beyond a certain point. This pattern suggests a complex dynamic where initial exposure to missile alarms might significantly impact PTSD symptoms, but this impact might plateau or change beyond a certain level of exposure. These findings highlight the utility of non-parametric models in capturing the subtleties inherent in real-world data.
The subsequent sections of the article will investigate additional socioeconomic factors that correlate with PTSD, aiming to provide a more holistic understanding of the factors contributing to its development.
Socioeconomic Status and PTSD Symptoms
To examine the relationship between socio-economic factors and the prevalence of PTSD symptoms, we applied both simple probit and OLS models. The probit models use a binary dependent variable to classify individuals as either exhibiting PTSD symptoms (1) or not (0), thereby assessing the likelihood of clinical-level manifestation of PTSD symptoms based on socio-economic factors. Furthermore, our OLS models, which utilize the PCL-5 Score Variable, delve deeper into this relationship. These models collectively aim to explore how socio-economic status correlation with the probability of experiencing PTSD symptoms. The results of these models are presented in
Table 2 and
Table 3.
By employing single-variable models, we could isolate each socioeconomic factor to determine its specific impact on PTSD symptoms likelihood. Our analysis indicates that individuals with higher levels of education and income, as well as those who are married and those with more children, have a significantly lower probability of experiencing PTSD symptoms. Moreover, there's a negative correlation—statistically significant—between the socio-economic status of an individual's residence area and the probability of developing PTSD symptoms. Both probit and OLS models corroborate these findings, with the OLS models demonstrating greater robustness.
Analysis of
Table 1 reveals marked differences in age, income, education, and number of children between the two studied groups. To explore how these demographics, along with the frequency of missile alarms, relate to PTSD symptoms, we employed multivariate probit models. These models use a binary dependent variable based on DSM-5 criteria, representing clinical (1) or non-clinical (0) levels of PTSD symptoms, where '0' indicates symptoms below the clinical threshold. This dichotomous approach, detailed in
Table 4, aligns with professional clinical standards for accurately identifying clinical PTSD, as measured by the PCL-5 test. The models aim to rigorously analyze the interplay between PCL-5 test outcomes and various factors, including missile alarm frequency, age, education, and other relevant controls. The primary objective is to discern and comprehend the variables most strongly correlated with the PCL-5 test results.
Our analysis demonstrated a statistically significant positive correlation between the frequency of rocket alarms in a residential area and the probability of manifesting PTSD symptoms (p<0.01 across all tested models, models 1-4). When employing the categorical area variable as a substitute for the number of alarms (models 5 and 6), it became evident that regions situated at greater distances from the Gaza Strip were less likely to fall into the PTSD category. Although the distance from the Gaza Strip and the number of missile attacks are inversely related, in most cases, the frequency of sirens serves as a more precise predictor of missile attacks than mere geographical proximity to the Gaza Strip. This is likely due to the variable intensity of rocket fire targeting different areas, making siren activations a more reliable gauge of missile threat.
In the majority of the models where age was included as a variable, except model 3, we observed a statistically significant negative correlation between age and the probability of developing PTSD symptoms. This implies that the likelihood of experiencing PTSD symptoms diminishes as age increases. This finding is in congruence with existing academic literature, notably, the study conducted by Kongshøj and Berntsen (2022), which similarly identified a decrease in the propensity for PTSD symptoms with advancing age.
Our data also underscore the influential roles of education and income in determining an individual's risk of falling into the PTSD category. According to our models, individuals with higher educational attainment (models 3 and 5) and greater income levels (models 4 and 6) were generally less prone to PTSD symptoms. These findings are consistent with what is described in the literature review. Due to the high correlation between education and income, it was not feasible to include both variables in a single model without affecting its accuracy. The inclusion of additional variables did not improve the model's predictive power. These findings correspond to previous research on the subject, particularly in the context of the impact of education level on the tendency to develop PTSD and the income effect on the subject.
The number of children under 18 years of age per respondent demonstrates a statistically significant inverse correlation with the likelihood of experiencing post-traumatic stress symptoms that surpass diagnostic levels. Specifically, a higher number of children is associated with a reduced probability of exhibiting symptoms at a clinically significant level. When this analysis was broadened to include all children, regardless of their age, similar trends were observed. However, this more inclusive count of children slightly improved the variable's explanatory strength, thereby augmenting the overall diagnostic robustness of the model.
Table 5 introduces a Multivariate Ordinary Least Squares (OLS) Regression Analysis, aimed at delving into the factors that influence the severity of PTSD, as quantified by the PCL-5 scores. This approach extends beyond the scope of the probit models, employing the overall PCL-5 test score as the dependent variable. Although the PCL-5 test is not the principal diagnostic tool, it is recognized in the literature as a valid metric for assessing PTSD severity. The strength of using the PCL-5 score lies in its continuous nature, offering a nuanced range of scores instead of a binary categorization. This feature brings a higher level of specificity and granularity to the assessment, thereby enhancing the explanatory capability of the analysis, which is observed to be more substantial than that of the probit models.
The results of the OLS model were consistent with those from the probit model, exhibiting similar directional trends. However, the OLS model displayed greater strength, particularly in terms of the statistical significance of its explanatory variables and a higher R^2, indicating a greater proportion of variance explained.