Distributional patterns of item responses and total scores on the PHQ-9 in the general population: data from the National Health and Nutrition Examination Survey

Data were drawn from the 2013–2014 NHANES. De-identified data from the NHANES are openly available for researchers [24]. The 2013–2014 NHANES includes a nationally representative sample of non-institutionalized civilian US citizens selected with a four-stage sample design [24]. The first stage comprised primary sampling units from a frame of all US counties. NHANES primary sampling units were selected with probabilities proportional to a measure of size. The second stage consisted of a sample of area segments. The sample was arranged to represent approximately equal sample sizes per primary sampling unit. The third stage of sample selection comprised dwelling units. In a given primary sampling unit, a list of all dwelling units was arranged, and a subsample of these was arranged to screen potentially sampled individuals. The subsampling rates were allocated to constitute a national, equal probability sample of households. The fourth stage comprised individuals within occupied dwelling units or households. A list of all eligible persons within a household was prepared, and a subsample of participants was selected based on their sociodemographic indicators. To correct for sampling bias, NHANES oversamples people aged 60 years or over, African Americans, Asians, and Hispanics. The survey consisted of an individual interview and a health examination. Written consent was obtained from participants. In the 2013–2014 NHANES, 14,332 individuals were selected, 10,175 completed the interview, and 9813 were examined.

Data from participants aged 18 years and older were drawn from the 2013–2014 NHANES. The sample consisted of 5924 respondents (ages 18–19 years, N = 336 [male: n = 154]; ages 20–29 years, N = 919 [male: n = 453]; ages 30–39 years, N = 961 [male: n = 461]; ages 40–49 years, N = 1007 [male: n = 464]; ages 50–59 years, N = 916 [male: n = 443]; ages 60–69 years, N = 2253 [male: n = 1155]; ages 70–79 years, N = 535 [male: n = 253]; ages 80 years and older, N = 332 [male: n = 153]). Among the 5924 respondents, 42% (N = 2491) were non-Hispanic white, 20.6% (N = 1223) were non-Hispanic black, 14.0% (N = 830) were Mexican, 11.4% (N = 675) were Asian, 8.8% (N = 523) were other Hispanic races, and 3.1% (N = 182) were other races, including multi-racial. Among 5588 respondents aged 20 years and older, the responses to the highest grade or level of education were as follows: less than 9th grade (7.9%, N = 439), 9–11th grade (13.7%, N = 765), high school graduate (22.5%, N = 1257), some college degree (30.8%, N = 1722), and college graduate or above (25.1%, N = 1400). The sociodemographic characteristics of the 2013–2014 NHANES samples are reported in detail elsewhere [24].

The present study is a secondary analysis of freely available data. Since the ethics committee of the Panasonic Health Center does not regard de-identified secondary data analysis as research on human subjects, the ethics committee of the Panasonic Health Center waived the need for formal ethical approval and ruled that no formal approval was required for the present study.

In the 2013–2014 NHANES, depressive symptoms were assessed using the PHQ-9. The nine items of the PHQ-9 reflect the nine criteria on which DSM-5 diagnoses of depressive disorders are based [25]. The PHQ-9 assesses the frequency of a variety of depressive symptoms within the past 2 weeks with 4-point response options: 0 = “not at all,” 1 = “several days,” 2 = “more than half the days,” and 3 = “nearly every day.” Total scores can range from 0 to 27.

First, we analyzed the distributions of the PHQ-9 item responses. Participants who did not respond to all PHQ-9 items (552 individuals) were excluded from the analysis. The non-response rate for each item (e.g., “refused,” “don’t know,” or “missing” to each item) was 8.98% (N = 532) for “anhedonia,” 9.00% (N = 533) for “depressed mood,” 8.93% (N = 529) for “sleep problems,” 8.93% (N = 529) for “low energy,” 8.95% (N = 530) for “appetite change,” 9.00% (N = 533) for “low self-esteem,” 8.98% (N = 532) for “concentration difficulties,” 8.98% (N = 532) for “psychomotor agitation or retardation,” and 9.00% (N = 533) for “suicidal ideation.” The final sample for the item response analysis comprised 5372 individuals.

Item response rates were calculated for all nine items. According to previous studies, all ratios of the degree adverb option to the adjacent degree adverb option are similar among depressive symptom items [12, 15]. Thus, the ratios of “more than half the days” to “several days” and “nearly every day” to “more than half the days” were calculated for all nine items. To evaluate the complex pattern of item responses, item responses were analyzed with histograms using normal and log-normal scales. According to the mathematical model of item responses in the previous study, if the ratios of the degree adverb option to the adjacent degree adverb option are similar among all items, all lines for the nine items will follow a parallel pattern on a log-normal scale [12]. As the pattern of item responses was different according to the response options, unitary regression analysis was not appropriate for the pattern analysis.

After confirming that the item of suicidal ideation followed the characteristic patterns observed in depressive symptom items, we analyzed the distribution of the PHQ-9 total scores. The pattern of total score distribution was analyzed by graphical analysis. Since an exponential pattern shows a linear pattern with a log-normal scale, a log-normal scale enables us to detect the extent of an exponential pattern. The least square method was used in regression analysis. Data were analyzed using JMP software, version 11 (SAS Institute Inc., Cary, NC, USA).

Table 1 displays the item responses of the PHQ-9. The item responses for all nine items showed a similar pattern, with the frequencies being the highest for “not at all,” decreasing from “not at all” to “more than half the days,” and being the lowest for “more than half the days” or “nearly every day.” Regarding item 9 (suicidal ideation), the percentages of item responses for “not at all,” “several days,” “more than half the days,” and “nearly every day” were 96.6, 2.3, 0.6, and 0.6%, respectively. There were no exceptions to this pattern. The ratios of “more than half the days” to “several days” (0.23 to 0.36) were smaller than those of “nearly every day” to “more than half the days” (0.77 to 1.42).

To compare the complex pattern of the item responses, we plotted all item responses on the same chart (Fig. 2). The item responses of the all items exhibited a same mathematical distribution, which showed different types of patterns with “several days” forming a boundary (Fig. 2a). Between “not at all” and “several days,” as pointed by the red arrow in Fig. 2a, the lines for the nine items crossed at a single point. On the other hand, between “several days” and “nearly every day,” lines for the nine items appeared to barely cross each other.

Using a log-normal scale, lines of the item responses showed a parallel pattern between “several days” and “nearly every day” (Fig. 2b). The gradient of the linear pattern of item responses moved downward from “several days” to “more than half the days” (blue arrow) and horizontally from “more than half the days” to “nearly every day” (red arrow). These observations are consistent with the ratios of “more than half the days” to “several days” (0.23 to 0.36) being smaller compared to those of “nearly every day” to “more than half the days” (0.77 to 1.42). The degree of parallelism of the nine lines represents the similarity of the ratios of “more than half the days” to “several days,” and “nearly every day” to “more than half the days” among the nine items. Although the line for Item 9 was a little away from the other lines, it was almost parallel to those of other depressive symptom items.

Figure 3a depicts the total score distribution of the PHQ-9. The total score distribution was right-skewed, and the frequency of the zero score was 31.9%. Using the log-normal scale, the total score distribution showed a linear pattern, suggesting that the total PHQ-9 scores approximated an exponential pattern (Fig. 3b). As indicated by the arrow, the total score distribution exhibited slightly higher frequencies compared to those predicted from the exponential pattern at the lower end of the distributions.

A regression curve for the exponential model was calculated from 0 to 25 points (y = 0.20e^-0.211x, R² = 0.98). The independent variable (x) was the total score, and the dependent variable (y) was the percentage of participants. R² was the coefficient of determination. The analysis indicated a high coefficient of determination, confirming that an exponential distribution was a good fit to the total PHQ-9 scores.

The item responses on the PHQ-9 exhibited the same mathematical pattern as the other depression screening scales, such as the CES-D and K6 [12, 15]. The pattern of the item responses was characterized by crossing at a single point between “not at all” and “several days” and a parallel pattern from “several days” to “nearly every day” on a log-normal scale. As noted in the Introduction, the characteristics of such an item response pattern could be explained mathematically [12]. If the ratios of “more than half the days” to “several days” and “nearly every day” to “more than half the days” are similar among all items, the lines for item responses exhibit the characteristic pattern [12]. In fact, the ratio of “more than half the days” to “several days” and “nearly every day” to “more than half the days” were similar among all the items. Further research is needed to clarify how the ratios of the adjacent degree adverb options on depression screening scales are similar among all items.

In the present study, the average ratios of “several days” to “more than half the days” (0.29) and “more than half the days” to “nearly every day” (1.00) differed according to the level of item responses (Table 1). According to the finding that boundary curves of each depressive symptom score in the distribution of total depressive symptom scores approximate an exponential pattern [26], the probability of each degree adverb option reflects the “distance” for each degree adverb option. Thus, it is suggested that the distance of “more than half the days” is approximately equal to that of “nearly every day” and one-third of that of “several days.”

The results of this study show that the response to item 9 exhibited the same pattern as the responses to the other eight depressive symptom items, suggesting that suicidal ideation shares a common mechanism with the other eight depressive symptoms. From a neuroscientific standpoint, the common mechanism of depressive symptoms is comprehensible. Many researchers have suggested that specific neural regions constitute a final common pathway for depressive symptoms [27, 28], suggesting that all depressive symptoms are influenced by the activity of this final common pathway.

Although the response to item 9 can identify individuals at an increased risk of suicide ideation, screening a given individual’s suicide attempt possibility is another question. In general, it is not easy to predict individual patient-level suicide [23]. Simon et al. reported that the risk of a non-fatal or fatal suicide attempt over 1 year increases from about 0.4% among outpatients reporting suicidal ideation of “not at all” to 4% among those reporting suicidal ideation “nearly every day” [29]. Of note, although the outpatients reporting suicidal ideation “nearly every day” have a 10 times higher risk of a non-fatal or fatal suicide attempt than those reporting suicidal ideation “not at all,” 96% of outpatients reporting suicidal ideation “nearly every day” do not commit suicide over 1 year, indicating the difficulty in screening for potential suicidality [22, 23, 29]. We can use responses to item 9 as a predictor of individual patient-level suicide but making an accurate prediction/representation of suicidality is not possible. The low specificity of item 9 to screen for acute suicide could be partly explained how the item is worded [30]. Item 9 consists of two parts: thoughts of being better off dead and thoughts of hurting oneself in some way. However, most patients who endorse item 9 appear to be agreeing with the first part only [31, 32]. Consequently, although the response to item 9 has the potential to identify individuals at increased risk of suicide, further procedures would be necessary to assess the actual risk of suicide in individuals endorsing Item 9.

Our findings indicate that the total PHQ-9 score from the NHANES data exhibits an exponential pattern except at the lower end of the distribution. These findings are consistent with results of other nationally representative surveys that the K6, CIS-R, and CES-D in the USA, England, and Japan, respectively [15, 17, 18]. Previous research demonstrated that the response rate of the negative adverb option (“not at all”) plays an important role in predicting the non-exponential pattern at the lower end of the distribution [13, 33]. Specifically, at the lower end of the distribution, the sum of the item scores with a high rate for the negative adverb option showed higher scores in comparison with those expected from the exponential pattern. Conversely, the sum of item scores with a low rate for the negative adverb option showed lower scores. Actually, according to our calculations, the average probability of “not at all” in the present study (76.3%) was higher than that of the MIDUS data (61.8%), which represented an exponential distribution for the whole extent of total scores [15].

There are limitations to this study. Though we investigated whether item responses and total item scores on the PHQ-9 followed characteristic patterns observed in other studies, we did not evaluate the fitness of other mathematical models. Given that item responses and total item scores showed exponential-related patterns, we could not propose other mathematical models. Future research might seek to investigate the comparative fit of other models to the NHANES data. Additionally, although we assessed the similarity of the pattern of item responses through graphical analysis, the similarity of the pattern was not quantified due to the complexity of the pattern. A simple and unitary pattern allows for applying existing distribution models (Gaussian models, exponential models, etc.) and calculating the goodness of fit through unitary regression models. Conversely, in the case of such a complex pattern, these procedures are difficult. Further research is needed to develop a quantification method of the similarities between the complex patterns.

However, our study has methodological advantages. Although the method of the present study was simple (visualization with histograms), it enabled the identification of a complex pattern of item responses. Graphical analysis is essential for exploratory data analysis of complex models [34, 35]. In addition, as noted in the Introduction, using data from the NHANES ensured a large sample size with limited selection bias. Moreover, since all data were publicly available, researchers can easily review the present findings using the raw data.

In the end, evidence that item responses and total scores on the PHQ-9, CES-D, and K6 follow the same mathematical patterns will shed light on the process of depressive symptomatology. In general, depressive symptoms are measured with depression screening scales and these total scores are clinically used as an index of depression severity. To support such procedures, all depression symptoms must constitute a single latent trait [36]. However, previous studies using factor analysis contradict regarding the number of latent traits in depression screening scales [19]. The findings of this research could complement those of previous studies. Based on the same mathematical pattern of item responses among all nine items, all depressive symptoms may share a common pathway. Further research should be carried out to clarify the mechanism of the mathematical patterns in depression rating scales in the general population. Moreover, much of the research up to now has been limited to the data from Japan, the US, and the UK. The degree to which these results generalize to other countries is unclear and, therefore, warrants examination.