Participants

A total of 863 patients participated in this study. In this sample, 473 (55%) were male and 390 (45%) female. Mean age was 65.4 years old (SD = 10.7). Most were married or partnered (67%), had a primary level of education (48%), and half of the participants' employment status was retired or unemployed. As for clinical characteristics, the most common tumors were thorax (32%), digest (40%), and others (28%). Adenocarcinoma histology was the most frequent (63%) and most cancers were stage IV (80%). The most widely used treatment was chemotherapy (53%), immunotherapy (7%), and targeted drugs (5%). Estimated survival was less than 18 months in 45% of the sample (see Table 1).

Instruments

Socio-demographic characteristics were collected using a standardized self-report form. Clinical variables related to cancer and antineoplastic treatment were obtained by the medical oncologist from the patients´medical records.

The ^{Herth Hope Index (HHI) (Herth, 1992}) measures various dimensions of hope using a 4-point Likert scale that ranges from 1 (strongly disagree) to 4 (strongly agree) with items #3 and #6 reverse-coded, we used the Spanish version of HHI (^{Sánchez-Teruel et al., 2020}). The original english version has three factors: (a) temporality and future that appraises thoughts (sum of items 1, 2, 6, and 11); (b) positive readiness and expectancy dimension (sum of items 4, 7, 10, and 12), and (c) interconnectedness (sum of items 3, 5, 8, and 9). The scale has a global score of 12 to 48, as well as single-item scores from 1 to 4 (^{Herth, 1992}). Higher scores denote greater hope. The estimated internal consistency coefficient for the original scale was .97 (^{Herth, 1992}); in a Spanish sample, the cronbach's α was .97 (^{Sánchez-Teruel et al., 2020}).

The Brief Resilient Coping Scale (BRCS) is a unidimensional outcome measure consisting of 4-item (^{Sinclair & Wallston, 2004}) designed to assess an individual's ability to adapt to stress and adversity, commonly referred to as resilience. Items are scored from 1-5; 1 equal “strongly disagree” and 5 means “strongly agree”. The sum score ranges from 4 to 20; the higher the score, the more resilient the coping strategy. The internal consistency of the BCRS scores in a sample of Spanish cancer patients was (ω = .86) (^{Calderon et al., 2022}).

Spiritual well-being scale was appraised by the validated Spanish version of the Functional Assessment of Chronic Illness Therapy-Spiritual Well-Being Scale (FACIT-Sp) (^{Jimenez-Fonseca et al., 2018}; ^{Peterman et al., 2002}). This instrument consists of 12 items scored on a five-point scale and contains two subscales, meaning/ peace and faith. The sum yields the index of spiritual well-being. The higher the score, the greater the person's wellbeing. Reliability for the scale scores was between .85 - .86 in the Spanish sample (^{Jimenez-Fonseca et al., 2018}).

Procedure

A prospective, multi-institutional, observational study was conducted across 15 tertiary referral hospitals in Spain from February 2020 to November 2022 (for more detail, see (^{Velasco-Durantez et al., 2023}). Funded by the Bioethics group of the Spanish Society of Medical Oncology (SEOM), the study was approved by ethics committees and by the Spanish Agency of Medicines and Medical Devices (AEMPS; ID: ES14042015). Participants were ≥18 years with resected, histologically-confirmed, advanced cancer not eligible for surgery/ therapy. Data collection was similar across hospitals and data relating to the participants were obtained from the institutions where they received treatment. Participation was voluntary, anonymous, and in no way impacted patient care. Those who agreed to participate signed the consent form and received instructions on how to complete the written questionnaires. Participants filled out the questionnaires at home and returned them to the auxiliary staff during the next visit. Data collection procedures were consistent across all hospitals, with participants data obtained from their respective treating institutions. Data were collected and updated by the attending medical oncologist through a web-based platform (https://www.neoetic.es).

Data Analysis

Analyses were performed sequentially in keeping with the afore-mentioned purposes. First, exploratory factor-analytic solutions intended to ascertain the dimensionality and structure of the HHI scores were fitted using the FACTOR software (^{Ferrando & Lorenzo-Seva, 2017}) following a double cross-validation schema. Second, because a clear, stable structure was detected, a restricted confirmatory factor-analytic solution (CFA) was fitted in the entire sample with the Mplus software (^{Muthén & Muthén, 2012}). To conduct both exploratory and confirmatory factor analyses, we divided the sample into two halves using Solomon method (^{Lorenzo-Seva, 2022}). This method aims to split the sample into two halves, generating two subsamples with equivalent levels of common variance. All the structural solutions at the item level were fitted using robust unweighted least squares estimation. In the EFA solutions, an empirical robust test statistic called LOSEFER, which corrects moments up to the fourth order was used (^{Lorenzo-Seva & Ferrando, 2023}). In assessing model fit and appropriateness, we considered indices from three groups that examined different facets of fit: absolute fit (GFI and RMSR), relative fit concerning degrees of freedom (RMSEA), and comparative fit (CFI). These indices were chosen from all available options to provide a comprehensive evaluation. As for reference values, GFI and CFI values ≥ .95 are indicative of good model fit (^{Schermelleh-Engel et al., 2003}), whereas SRMR values ≤ .08 and RMSEA values ≤ .06 are deemed indicative of satisfactory fit. In the EFA solutions, the adequacy of matrix correlation to be factor analyzed, Kaiser-Meyer-Olkin (KMO) test for sampling adequacy was computed. Normed-MSA indices were also examined to determine if any item failed to share enough communality with the entire set of items: values below .50 suggest that the item does not measure the same domain as the remaining items in the pool and, hence, should be removed (^{Lorenzo-Seva & Ferrando, 2021}). Optimal Implementation of Parallel Analysis was computed to assess the advised number of factors to be extracted (^{Timmerman & Lorenzo-Seva, 2011}). The following indices were used to judge essential unidimensionality: Explained Common Variance (ECV) and Mean of Item Residual Absolute Loadings (MIREAL). ECV values > .85 and MIREAL < .30 suggest that the data can be treated as fundamentally unidimensional (^{Ferrando & Lorenzo-Seva, 2018}). To study the replicability of the factor structure obtained in the first Solomon subsample, a CFA was carried out on the second Solomon subsample using the procedure and criteria described thus far. To determine whether there were pairs of items with correlated errors, we computed Robust Absolute Residuals (RAR), Robust Anti-Image-Based Partial Correlation (RAIPC), EREC, and ENIDE (^{Ferrando et al., 2022}). Finally, as both previous analyses led to the same conclusions, the common CFA solution was fitted to the total sample to use all the information available from the data. The CFA parameterization was used to gauge measurement invariance, whereas the corresponding IRT parameterization was applied to exam appraise the functioning of the items and the properties of the test scores. Measurement invariance was evaluated by fitting the prescribed CFA solution in groups defined by gender (two groups), age (three group levels), tumor site (three groups), and expected survival (two groups). All the analyses sought to test for the strong or scalar invariance. If this condition is attained, it can be assumed that the HHI items function with the same measurement properties in all the groups considered and, that mean group differences in the HHI scores can therefore be validly interpreted as reflecting ‘true' group differences. Item functioning was assessed using: (a) the item discriminating power and (b) the boundary category thresholds. As for the scores, we considered IRT-based scores and gauged their conditional and marginal reliability. The behavior of the simple raw scores as a ‘proxy' for the IRT scores was also appraised. Finally, evidence of convergent validity was obtained by fitting a structural equation model in which the ‘internal' CFA solution was extended to include the BCRS and FACIT scores to the data as external variables.

Descriptive Statistics and Structure Assessment of HHI

Descriptive statistics of the HHI can be found in Table 2. Item scores ranged from 1.40 (item 3) to 3.68 (item 12). HHI item score distributions were unimodal and asymmetrical (negatively skewed), thereby indicating that most of the values were concentrated at the highest end of the response scale. Therefore, all the structural models used categorical-variable methodology, treating the item scores as ordered-categorical. Nevertheless, some distortions can be expected at the scoring level (see below).

Exploratory Factor Analyses

The inter-item polychoric correlation matrix had good properties KMO = .906. Normed-MSA for items ranged from .635 to .962. These outcomes indicated that the correlation matrix is well suited for factorial analysis. For items 3 and 6, however, the estimates did not significantly differ from the threshold value of .5.

Parallel analyses revealed that a single dimension accounted for 61.6% of the common variance and suggested a single factor to be extracted. However, the essential unidimensionality index values were ECV = .838, and MIREAL = .257. The values of the indices are close but slightly below the threshold values for essential dimensionality.

We also inspected the corresponding indices at the item level: items 3 and 6 showed values close to zero. The unidimensional factor analysis solution yielded acceptable goodness-of-fit levels: RMSEA = .051, CFI = .991, GFI = .986, and RMSR = .069. The communality of items to this single factor were < .20, except for items 3 and 6. These outcomes also point toward a single dimension underlying the dataset, except for the contributions of items 3 and 6.

To inspect pairs of items that might have correlated errors, we computed four indices (RAR, RAIPC, EREC, and ENIDE), all coincided in pointing toward two pairs of items as plausibly having correlated errors. The suspicious pairs were 1 and 2 and 11 and 12. Failure to factor in these redundancies could distort the results; consequently, we addressed them (see below). As the EFA solution cross-validated well in both samples, our final conclusions were that: (1) a single factor model was acceptable; (2) items 3 and 6 did not contribute to this factor and could be eliminated from the set of items, and (3) two pairs of items with correlated errors were present in the data, see Table 3.

Confirmatory and Multiple Group Analyses

The total group CFA solution and the multiple-group solutions specified above had excellent fit, which provides ample support about the tenability of the strong invariance hypothesis. On the basis of this invariance, mean group differences in the HHI construct can be meaningfully interpreted. However, results in Table 4 reveal that no significant mean group differences appear in any case. In our view, these results reflect a “ceiling” effect anticipated above: the reported levels of Hope are so consistently high in general, that there is no room for strong group differences to emerge.

IRT Item and Score Properties and Measurement Accuracy

Columns 2-5 in Table 4 show the item parameter estimates in IRT metric. Commensurate with the factorial loadings, discriminations rate high for a personality test which again, evidences the strong internal consistency of the scale, but also, possibly, certain content redundancy. The category parameters tend to be all negative, thereby indicating item “easiness” in the sense that, only a moderate level of hope is required to endorse the highest response category.

As for the score properties, two types of scores were computed based on the solution in Table 4: EAP factor score estimates (^{Ferrando & Lorenzo-Seva, 2016}) and the usual simple sum scores. For the EAP scores, the marginal reliability estimate was .87. The conditional reliability (information) curve is presented in Figure 1 and is clear: the EAP scores demonstrate good accuracy to measure the low and medium trait levels with precision, but are unreliable at the upper end of the scale. Thus, the HHI would be a good instrument to detect individuals with low levels of hope, but would be less suitable for differentiating among those (the majority) that report high levels.

Figure 1. The Reliability (Conditional) Estimates as a Function of Trait Level 

As for the raw or sum scores, the omega reliability estimate was .88, which again is acceptable for this relatively short test. The estimated fidelity coefficient was .97. These results indicate that the sum scores can be used as good proxies for measuring the Hope dimension. However, if the HHI scores are to be used for high stake testing or to establish cut-off values, then the IRT-EAP scores are preferable.

External Validity Evidence

The CFA solution above was extended to include four relevant external variables and fitted the data quite well: GFI = .982, RMSEA = .027, and NNFI = .970. All the standardized validity coefficients relating the hope construct to the external variables were statistically significant: resilience (β = .26), spiritually well-being (β = .29), meaning/ peace (β = .73), and faith (β = .44).