Psychometric properties of the German version of the Depressive and Anxious Avoidance in Prolonged Grief Questionnaire (DAAPGQ)

The Depressive and Anxious Avoidance in Prolonged Grief Questionnaire (DAAPGQ) was developed to measure depressive and anxious avoidance behaviors, which, according to cognitive-behavioral models, are supposed to play an important role in the development and maintenance of prolonged grief. The present study aimed to develop a German version of the DAAPGQ and evaluate its psychometric properties and validity within a representative sample of the German general population (N = 2531). The German-language DAAPGQ was developed using a forward-backward translation procedure. Then, a subsample of individuals who reported having lost a significant other (N = 1371) of a representative sample was assessed with the German DAAPGQ, along with information on sociodemographic characteristics, prolonged grief symptom severity (PG-13), general anxiety (GAD-2) and depression (PHQ-2). The factor structure of the DAAPGQ was evaluated using confirmatory factor analyses, reliability by calculating internal consistency on subscale level and convergent validity by correlations between DAAPQG subscale sores with PG-13, GAD-2 and PHQ-2 sum scores. As expected, a two-factor model with correlated latent variables showed good fit to the data, replicating findings from the original version. Internal consistency was high for both subscales (Cronbach’s α .86 and .95, respectively). Convergent validity was established by theoretically expected and statistically significant positive correlations of DAAPGQ subscales with symptom severity of prolonged grief, depression, and anxiety and negative correlations with time since loss. Furthermore, the addition of depressive and anxious avoidance significantly improved the prediction of prolonged grief symptom severity over sociodemographic and loss-related information. In sum, our results suggest that the German-language DAAPGQ is a reliable and valid measure of depressive and anxious avoidance and a useful tool to improve our knowledge on the role of avoidance in prolonged grief. We also provide descriptive data to improve the applicability of the DAAPGQ for individual diagnostics.

Introduction disorder (PTSD), whereas anxious avoidance was a mediator of the association between violent loss and PTSD [15].
A study investigating the role of negative cognitions and avoidance behavior in PGD symptoms, PTSD, anger, and revenge thoughts after homicide revealed that those who engage in depressive avoidance showed higher levels of PGD symptoms and PTSD, whereas anxious avoidance was associated with elevated revenge thoughts and feelings [16]. Additionally, a recent study revealed that depressive and anxious avoidance partially mediated the associations between PGD symptoms and worrying and rumination, suggesting that targeting both depressive and anxious avoidance could reduce rumination [17]. These results complement the findings of Eisma and colleagues, who found that avoidance behaviors mediated the link between grief rumination and PGD symptoms as well as depression [18].
Taken together, these results underline the assumption that avoidance behavior plays an important role in the development and persistence of PGD symptoms and other emotional distress after losing a loved one. However, all these studies were conducted in the Netherlands, and more international research is necessary. As a precondition for this goal, the present study aimed to develop a German version of the DAAPGQ, examine its psychometric properties and evaluate validity.
The original DAAPGQ was first applied in the context of an observational study in which the validation of the instrument was not the actual goal. The sample was therefore small. Nonetheless, the findings demonstrated factorial validity as well as convergent validity [14]. An empirically validated measure of grief-related avoidance is not only essential to support research. Such an instrument can also help clinicians identify patients at risk of developing PGD and assist therapists in individualized treatment planning and monitoring treatment progress.
The inclusion of PGD in the ICD-11 and the forthcoming DSM-5-TR further emphasizes the need to assess etiological factors that contribute to this disorder, such as grief-related avoidance. Moreover, since PGD must be explicitly considered with particular attention to cultural differences in the duration of symptoms and grief expression (Killikelly and Maercker, 2017), validated translations of questionnaires like the DAAPGQ are indispensable. We, therefore, aimed to provide a German translation of the DAAPGQ and extend the psychometric testing and validation. Concerning the factorial structure, we expected an acceptable model fit for a two-factor model comparable to the original version. Regarding convergent validity, we predicted the DAAPGQ would be positively associated with symptoms of PGD, depression, and anxiety and marginally decline under the influence of time and therefore show a small but negative correlation with time since loss. Associations between the DAAPGQ, PGD, depression and time since loss have already been investigated (as described above). The association between the DAAPGQ and anxiety, however, has not yet been examined. Given that PGD and anxiety symptoms have been shown to be low to moderately correlated [19][20][21], we would expect similar correlations between the DAAPGQ and anxiety. Anxiety and avoidance reinforce each other, which in turn can hinder the processing of grief-related information [22] and thus contribute to the development of PGD. We therefore expected at least low associations between depressive and anxious avoidance and anxiety. Additionally, we assumed that depressive and anxious avoidance would predict symptoms of PGD, even after controlling for sociodemographic and loss-related variables.

Procedures
A representative sample of the German population was drawn to be included in a cross-sectional survey between November 2017 and February 2018 based on a three-stage random sampling procedure: 1) random selection of 258 regional sample point areas, 2) random selection of target households within sample point areas based on a random-route procedure, 3) random selection of target persons within target households based on a Kish selection grid. Inclusion criteria for target persons were age equal or above 14 years, sufficient fluency in German language, and written informed consent. Random sampling and fieldwork were conducted by an independent market and social research agency (USUMA, Berlin, Germany). Target persons were approached without an appointment by one of 223 trained interviewers, up to four attempts were made to reach a target person. Potential participants received oral and written information about the study and provided informed consent. For target persons under the age of 18, additional parental informed consent was obtained. Sociodemographic information was collected in a face-to-face interview. Afterwards, participants filled out self-report measures on their own, and interviewers assisted in case of questions. The study and the procedures were approved by the local ethical review board (Leipzig University, Medical Faculty; AZ: 418/ 17-ek, 23.10.2017).

Participants
Of a total number of 5093 randomly selected target persons, 2531 (49.7%) could be included in the study. Reasons for non-response were that a) households could not be reached (n = 731, 14.4%), b) households refused to participate (n = 840, 16.5%), c) target persons could not be reached (n = 181, 3.6%), d) target persons refused to participate (n = 804, 15.8%). Six interviews were not applicable for analyses. Bias due to non-response was limited by household-(household size) and person-level (age, gender, place of residence according to federal state) weights. Of the 2531 individuals included in the study, 1371 (54.2%) reported having experienced the loss of a significant person.

Measures
The constructs used for the present study and described below were part of a larger thematically diverse set of self-report questionnaires implemented in the cross-sectional survey.
Sociodemographic information. Characteristics of the participant (age, gender, and education level) and characteristics of the deceased and the loss (e.g., relationship to the deceased, cause of death, time since death) were measured with a self-constructed questionnaire.
Depressive and Anxious Avoidance in Prolonged Grief Disorder (DAAPGQ). The DAAPGQ was developed to examine the role of depressive (DA) and anxious avoidance (AA) in PGD. The questionnaire contains nine items rated on an 8-point scale ranging from 1 = "not at all true for me" to 8 = "completely true for me." Five items were constructed to measure DA (range 5-40) and four items to measure AA (range 4-32). The first investigation revealed internal consistencies of .90 for the DA subscale and .74 for the AA subscale and both subscales were correlated with r = .77. [14]. The German Version of the DAAPGQ is provided within the S1 File. Two psychologists (JT and MN) independently translated the English version of the DAAPGQ into German. Both versions were compared for differences and merged by consensus into one German version. This version was then back translated by a native speaker. The back-translated version was then discussed with the original author (PB) for equivalence.
Symptoms of prolonged grief disorder. Symptoms of PGD were assessed using the German version of the PG-13 [6]. The PG-13 contains 13 items, 11 items assessing cognitive, behavioral, and emotional symptoms, rated on a 5-point Likert scale, and two items on duration and impairment that are to be answered "yes" or "no". The severity of PGD symptoms can be evaluated by summing the scores obtained from these 11 items, leading to a sum score range of 11-55. Higher scores indicate more severe grief symptoms. To meet the criteria for PGD symptoms according to Prigerson et al. [6], the participant had to experience separation distress (one out of two items scored with 4 or 5) and cognitive, emotional, and behavioral symptoms (five out of nine items scored with 4 or 5). Furthermore, the symptoms had to be elevated for at least six months (symptom duration � six months), and the participant must have significant impairment in social, occupational, or other important areas of functioning [6]. The PG-13 has been demonstrated to be reliable and valid [23]. Cronbach's alpha in the present study indicated excellent internal consistency for the PG-13 (α = .94).
Depressive and anxiety symptoms. The Patient Health Questionnaire-4 (PHQ-4) was used to assess core symptoms of depression (PHQ-2) and core symptoms of generalized anxiety disorder (GAD-2) with two items each. The four items are rated on a 4-point scale ranging from 0 (not at all) to 3 (nearly every day), leading to sum score ranges between 0 and 6 for both subscales. The PHQ-4 demonstrated good psychometric properties and serves as a screening instrument for depressive and anxiety disorders (PHQ-2 and GAD-2 � 3) [24]. Higher scores indicate higher degrees of depressive and anxiety symptoms [25]. The internal consistencies of the PHQ-4, PHQ-2 and the GAD-2 were good to acceptable in the present study (α = 0.87; α = 0.79; α = 0.80, respectively).

Statistical analysis
All statistical analyses were conducted using the Statistical Package for Social Sciences, version 25 (IBM1 SPSS1), including the software Analysis of Moment Structures, version 25 (IBM1 SPSS1 Amos). The significance level was set to α = .05.
Item analyses. We examined the item descriptives, item difficulties (in %) using the for- x i = mean of item i; min(x i ) = minimal value on item i; max(x i ) = maximum value on item i), corrected item-total-correlations, and percentages of missing values.
Reliability. Scale reliability was determined via internal consistency. Internal consistency was calculated using Cronbach's α with α � .70 indicating acceptable reliability. Mean interitem correlations were calculated as an indicator of subscale homogeneity.
Construct validity. Factor analysis. The internal factor structure of the DAAPGQ as an indicator of construct validity was assessed with confirmatory factor analysis (CFA) based on structure equation modeling using the software AMOS, version 25. We predicted a two-factor model with two correlated latent variables (DA and AA). As the χ2-test as a global measure for the model fit is largely influenced by sample size, the following close fit indices and corresponding cut-off criteria were additionally used to evaluate the model fit: (1) [26,27]. As the original model assuming two correlated factors and uncorrelated errors showed only partially acceptable fit to the data, minor modifications to the model were necessary. Therefore, the total sample was split into two random samples using the SPSS 25 random selection procedure. Model modifications, guided by an inspection of modification indices and only included if they were theoretically plausible, were performed in the first split-half sample and the final model was then cross-validated in the second split-half sample.
Convergent validity. Convergent validity was assessed as an indicator of construct validity by calculating Pearson's correlation coefficients between subscales of the DAAPGQ and theoretically related constructs, i.e. PGD symptoms (PG-13) and depressive and anxiety symptoms (PHQ-4). We predicted both subscales DA and AA to be positively correlated with these measures. Furthermore, we predicted that DA and AA would marginally diminish over time and therefore negatively correlate with time since loss.
Additionally, a hierarchical regression analysis was performed to further establish construct validity. We expected that DA and AA would predict symptoms of PGD, even after controlling for sociodemographic variables, variables related to the loss, and the relationship to the deceased. Only participants who fulfilled the ICD-11 time criterion (time since loss �6 months) were included in this analysis. Four blocks of independent variables were entered hierarchically in order of their point in time related to the loss (pre-loss, loss, peri-loss): sociodemographic variables (age, gender); variables related to the loss (time since loss, number of losses, cause of death); relationship to the deceased; and DA and AA. Dummy variables were generated for the categorical variables cause of death and relationship to the deceased. Reference groups were anticipated natural death (e.g., illness) and losing a parent, respectively. The categories of accident, suicide, and violent death were grouped into sudden violent death. The variance inflation factor was calculated for the diagnosis of multicollinearity. Values above 5 were considered as an indication of multicollinearity [28].

Participant and loss-related characteristics
A total of 1371 (54.2%) individuals reported having experienced a major bereavement. Table 1 gives an overview of the demographic characteristics of the bereaved sample. Loss-related characteristics are displayed in Table 2. Bereaved individuals were aged between 14 and 93 years (M = 54.56, SD = 17.28). About 59% were women, about 56% were living with a partner, and the great majority (97.1%) reported German nationality ( Table 1). The time since the loss of the significant person ranged between 0 and 976 months (M = 128.14, SD = 138.11). About 40% indicated the time since the loss to be greater than 10 years. The majority (46.6%) reported to have lost a parent, and sudden natural death was reported most frequently (44.7%) as the cause of death (Table 2). According to the diagnostic algorithm of the PG-13, 3.3% (n = 45) met the criteria for clinically relevant PGD symptoms. Those with relevant PGD symptoms were mostly female (71%; n = 32), mean age was 61.09 (SD = 18.80), mean time since loss was 69.91 months (range: 7-456 months, SD = 100.31). About half of them reported to have lost a partner (n = 23), and a quarter lost a parent (n = 11), 9% lost their child (n = 4). The most frequently indicated cause of death was a disease (n = 21), followed by sudden natural deaths (n = 16).

Item analyses
The item characteristics of the German version of the DAAPGQ are displayed in Table 3. Item means on the eight-point response scale (range 1-8) ranged from 1.79 (item 3) to 3.01 (item 9). All items were positively skewed. Skewness ranged from 0.76 (item 9) to 2.22 (item 3). Seven items showed a positive and two items (8, 9) a negative kurtosis. Kurtosis ranged from -0.70 (item 9) to 4.39 (item 3). Item difficulties ranged between 13.19% (item 3) and 33.51% (item 9), indicating a low to medium probability of scores > 1 ('not at all true for me'). Corrected item-total-correlations were high (0.60 � r it � 0.79), indicating an adequate discriminatory power. The percentage of missing values was low (� 0.95%) for all items.

Internal factor structure
CFAs were performed for cases with complete data in the DAAPGQ, resulting in a total sample of N = 1345. The original model assuming a two-factor model with uncorrelated errors in the total sample showed contradictory findings. While some indices indicated an acceptable fit to the data (CFI = .970, TLI = .958; SRMR = .057) the inspection of the RMSEA (RMSEA = .096, 90%CI: .087,.105) and the χ2-test (χ2 = 349.401, p > .001) indicated poor model fit. Therefore, minor model modifications were performed in the first split-half sample (n = 672). The final model, allowing for correlations of unique variances between two items from the depressive avoidances scale (items 3 and 4, items 4 and 5) as well as between two items from the anxious avoidance scale (items 6 and 8, items 7 and 9), showed a good fit to the data in the first splithalf sample (χ2 = 95.529, p < .001; CFI = .987; TLI = .978; RMSEA = .071, 90%CI: .056,.085; SRMR = .023). These correlations were considered theoretically plausible due to similarities of the wording in these items and the overlaps in content, which may display a non-random measurement error. The cross-validation in the second split-half sample (N = 673) confirmed the good fit to the data (χ2 = 101.601, p < .001; CFI = .985; TLI = .976; RMSEA = .073, 90%CI: .059,.088; SRMR = .034). Because the χ2-test is strongly influenced by sample size, we did not take it into account as a global measure of model fit. Table 4 presents the descriptive data for both subscales for the total sample and participants with and without PGD symptoms, according to the diagnostic algorithm of the PG-13. In the  Table 3. Psychometric properties of the DAAPGQ items.

M SD Skew Kurt p i (%) r it % missings
Depressive Avoidance total sample, both subscales were positively skewed. The kurtosis for DA was also positive, for AA slightly negative. Cronbach's α was .95 for DA, and .86 for AA. Mean inter-item correlations were .81 for DA and .61 for AA. A significant correlation between the two subscales was found, with r = .55 (p < .001).

Convergent validity
As expected, the subscales of the DAAPGQ were significantly correlated with symptoms of prolonged grief, depression, and anxiety and negatively with time since loss. All correlations are presented in Table 5. The highest positive correlation was found between the DA subscale and the PG-13 with r = .739, the lowest between AA and time since loss (r = -.204).
Furthermore, the results of the regression analysis demonstrate that DA and AA predict symptoms of PGD, even after controlling for sociodemographic variables, variables related to the loss, and the relationship to the deceased. The results are summarized in Table 6. The sociodemographic variables in step 1 explained 2.9% of the variance. Entering variables related to the loss (step 2) increased the explained variance to 9.6%. The third step (relationship to the deceased) led to an explained variance of 19.6%. DA and AA were entered in the last step, improving the model with changes in R 2 of 39.8%. The final model explained 59.4% of variance (F (11,1156) = 153.744, p < .001), which can be considered a large effect size, according to Cohen [29].
All VIF values were below 5, which means there was no indication of multicollinearity. The standardized regression coefficient showed that DA and AA provided a significant contribution to symptoms of PGD. More DA (ß = .61, p < .001), and more AA (ß = .18, p < .001) were associated with higher levels of prolonged grief symptoms.

Discussion
The DAAPGQ measures avoidance behavior after the loss of a loved one and consists of the subscales depressive and anxious avoidance. This study aimed to provide a German version of the DAAPGQ and evaluate its psychometric properties and validity in a large sample of bereaved individuals drawn from a representative sample of the German general population. We also provide descriptive data on DAAPGQ scales which may help users of the DAAPGQ interpret their findings in relation to this normative representative sample. The percentage of missing values in DAAPGQ items was very low (� 0.95%), indicating that the items were very well accepted by the study participants. Item descriptives showed that item distributions were positively skewed for both subscales, and corrected item-total correlations were high. Item difficulties were medium to high (range: 13.19-33.51%). Especially the items tapping depressive avoidance were rather difficult. When interpreting this fact, it is important to keep in mind that the questionnaire focuses on DA and AA in PGD and that both are correlates of PGD symptoms [14]. It is therefore plausible that some items are more relevant to a minority of bereaved experiencing a more persisting and disabling grief reaction. This is illustrated by our findings that participants with PGD symptoms reported much higher levels of DA and AA than participants without PGD symptoms. The more difficult items may have discriminatory power between people with and without PGD symptoms. In addition, the internal consistencies of the subscales of the DAAPGQ were good to excellent in this study and comparable to internal consistencies found for the original version in other studies [e.g., 15,16].
With regard to the factorial validity and internal factor structure of the DAAPGQ, our study replicated the findings by Boelen and Van Den Bout [14], supporting a two-factor model Table 6. Results of hierarchical regression for predictors of PGD symptoms (n = 1168).
Step 1 Step 2 Step 3 Step 4 with two distinct but correlated factors. To improve the model fit, we allowed for correlated error-terms for two items of each subscale. We consider these correlations theoretically plausible due to the overlaps in content and similarities of the wording in these items, which may display a non-random measurement error. This result supports the distinction of depressive and anxious avoidance in the cognitive-behavioral model of PGD symptoms [9,14]. The validity of the DAAPGQ was further supported by this study. As expected, the subscales DA and AA only slightly diminished over time, as evidenced by the negative but mild correlation with time since the loss. This indicates that avoidance tendencies once manifested remain somewhat stable over time, which may contribute to the development of PGD. This result also replicates the findings by Boelen and Van Den Bout [14].
Additionally, both DA and AA were significantly and positively correlated to symptoms of PGD, depression, and anxiety. This is consistent with previous research and theoretical considerations that regard avoidance as a mechanism that fosters and maintains PGD symptoms [9]. Furthermore, PGD symptoms, in turn, are also associated with anxiety and depression [30]. Since DA and AA are thought to contribute to the development of PGD, we hypothesized that both should also correlate with depression and anxiety. Furthermore, avoidance behavior has been found a key mechanism in the maintenance of both depression and anxiety [31,32].
The results of the regression analysis further demonstrated that both DA and AA predict symptoms of PGD. This association remains, even after controlling for sociodemographic variables, variables related to the loss and the relationship to the deceased. DA and AA explain almost 40% of the variance, which is a large proportion, underlining the importance of avoidance as an independent mechanism. All these results provide evidence for the validity of the DAAPGQ.
A major strength of this study is the large representative sample of the German general population, which extends the findings from Boelen and Van Den Bout [14] to a representative sample. This allows for the provision of normative descriptive data, which may help future users of the DAAPGQ interpret their findings in relation to our data and improve the applicability of the DAAPGQ with regard to individual diagnostics.
Major limitations are the cross-sectional design and the lack of data on retest-reliability and sensitivity to change, which is of particular importance when using the DAAPGQ in intervention studies. Furthermore, only a limited number of constructs were used to calculate construct validity, and no other measures of loss-related avoidance or general avoidance such as the Acceptance and Action Questionnaire-II [AAQ-II, 33] were applied to evaluate convergent validity. Lastly, we used the PG-13 to assess PGD symptoms. Even though it is one of the most widely used and well-established instruments for assessing PGD symptoms, its items do not assess all of the current PGD criteria included in the ICD-11 (nor the DSM-5-TR). At the time of assessment, there was no tool available capturing all the PGD ICD-11 criteria [23]. Thus, we recommend future research to assess PGD according to the latest ICD-11 criteria to provide more accurate normative, descriptive data of the DAAPGQ.

Implications and conclusion
Despite these limitations, we can conclude that the DAAPGQ demonstrated good psychometric properties, and factorial and construct validity were established. Thus, the DAAPGQ can be considered a reliable and valid tool to assess grief-related avoidance after losing a loved one. We, therefore, recommend the use of the German version in German-speaking countries. As prior study results suggest, reducing DA and AA should be central within psychological interventions for persistent distress following the loss of a loved one [14,15]. Targeted interventions adapted to the needs of the bereaved might be most efficacious. Thus, more knowledge on the isolated effectiveness of interventions targeting DA and AA might be beneficial. There is already preliminary evidence that interventions targeting DA are effective [34]. The DAAPGQ could also serve as a tool to assess treatment progress by monitoring the scores during the course of treatment. For this, however, the sensitivity to change of the DAAPGQ should be investigated first, which we recommend for future research. As the DAAPGQ is short with only nine items, it should be easy to implement within efficacy or effectiveness research of grief therapy.