To assess the internal consistency of the questionnaire, we calculated Cronbach’s alpha coefficient (27). This coefficient measures the extent to which the items within each scale of the questionnaire are interrelated. A Cronbach’s alpha coefficient > 0.7 is generally considered acceptable, suggesting good internal consistency (28). We also estimated the McDonald’s omega coefficient (ω), for which a value > 0.70 was considered acceptable (29, 30).

Further, the matrix of item-scale and item-summary scale correlations were examined. We considered satisfactory if the item-own scale correlation and corrected item-total correlation was ≥ 0.30.

The reproducibility on the LTQL questionnaire was assessed though a test-retest study. The questionnaire of LTQL were send again via mail ten days after to 43 patients to answer again. In order to measure the agreement between the two wets of responses, the intraclass correlation coefficients (ICC) was calculated using a two-way mixed effects model. Values higher than 0.7 are considered acceptable (31).

To assess the structural validity of the questionnaire, different approaches were used. Firstly, we conducted EFA with promax rotation and CFA for categorical data to confirm the original structure put forth by the developers (16). This analysis aimed to determine if the 34 items in the questionnaire aligned with the proposed four-factor structure (domains), namely somatic concerns, philosophical/spiritual view of life, fitness and social support. Further, DIMTEST procedure was used to test the number of underlying factors in the questionnaire (32), and based on the results, the EFA and CFA were reconsidered. Secondly, we employed Rasch analysis to evaluate the unidimensionality and item functioning of each specific domain in the questionnaire. This analysis helps determine if the items within each dimension measure a single underlying construct effectively.

In the EFA, an item was considered to be in the factor if the factor loading and communality were ≥ 0.40 (33). In the CFA, we employed the robust weighted least squares estimator to estimate the model parameters. We calculated several fit indices to evaluate the goodness of fit of the model (34–37). The first fit index is the root mean square error of approximation (RMSEA), which provides a measure of how well the model fits the observed data. A RMSEA value < 0.08 is considered acceptable model fit and values < 0.06 are considered good model fit. The second set of fit indices includes the Tucker-Lewis Index (TLI) and Comparative Fit Index (CFI). Both indices assess the relative fit of the model by comparing it to a baseline model. Values > 0.95 indicate good model fit and values >0.90 indicate acceptable model fit. Further, we also examined the normed chi-square, considering values < 2 acceptable. However, because the chi-square test is sensitive to sample size, it was not used as a primary indicator of model fit. The standardized root mean square residual (SRMR) was also examined, for which a value < 0.08 was considered good fit. Additionally, we examined the factor loadings, which indicate the strength and direction of the relationships between the observed variables (items) and the underlying factors. Factor loadings ≥ 0.40 are generally considered acceptable, indicating that the items adequately reflect the factors they are intended to measure. Lagrange multiplier test, which identifies paths or covariances that should possibly be added to the model to improve the fit, was used when the model needed modification (36).

In the Rasch analysis, we utilized the polytomous Partial Credit Model due to the ordinal nature of the response scales in the questionnaire (38, 39), and it does not assume that the transition from category to category in the item is constant, allowing different probability of positive response from one category to another (40–42). We conducted separate analyses for each domain of the questionnaire to ensure that each domain was measuring a single underlying construct, which is a fundamental requirement in Rasch models (43). To assess unidimensionality, we employed two fit indices: the mean square information-weighted statistic (infit) and the outlier-sensitive statistic (outfit). Infit and outfit values between 0.6 and 1.4 are indicative of a good fit between the observed data and the model (44). We also conducted a principal component analysis (PCA) of the residuals to further evaluate unidimensionality. If the first domain was the only one with eigenvalues > 2, it would indicate that unidimensionality was not violated (45). To determine the position of items along the measured dimension, we examined the item separation index. This index provides an indication of the ability of the LTQL to discriminate between different levels of the measured construct. A value >2.0 is considered acceptable and comparable to a reliability of 0.80, suggesting that the items are effectively measuring distinct levels of the construct (43).

In order to assess local dependency, we examined the residual correlations between items within a domain of the questionnaire. The effect size of the model fit, MADaQ3, was provided as a summary measure of all pairs of Yen’s Q3 residual correlations. Values closed to 0 support the assumption of local independence (46). Identifying local dependency helps ensure that the items are measuring distinct aspects of the construct and are not overly redundant. We also examined the functioning of the rating scale categories for each item. It is important to have a clear and progressive level of difficulty across the response categories, indicating that higher response options correspond to higher levels of the underlying construct (43). If the response categories were found to be disordered, meaning that higher response options did not consistently reflect increases in the construct. The item-person map for each domain was also provided, in which both individuals and items are presented in the same logit scale. To detect differential item functioning (DIF), which occurs when different groups within the sample respond differently to individual items (38), we compared different levels of the trait bases on age group (< 65 vs. ≥ 65 years). Age can influence how a person faces and adapts their experiences and emotional aspects regarding BC survivorship. We used the Mantel-Haenszel test considering a statistically significant at P<0.05 to indicate noticeable DIF (47) and the following cut-off points: if |DIF| ≥ 0.43 logits, it is considered slightly to moderate DIF; and if |DIF| ≥ 0.64 logits, we considered moderate to large DIF (48).

In addition, we have explored the careless responding by means of the standardized log-likelihood (l_z), which is a person-fit statistic based on item response theory that quantifies the discrepancy between the expected and empirical likelihood for each individual (49–51), and it is useful to detect unexpected responses. The l_z statistic asymptotically follows a standard normal distribution, and we used the theoretical cutoff of -2.326 (one-tailed significance test with α = 0.01). That is, a response pattern would be flagged if l_z is less than -2.326.

Finally, a CFA was performed considering the items that fitted the Rasch model, in order to compare the results of the structural validity once the misfitting items had been excluded.

To assess the convergent validity of the LTQL questionnaire, we used Spearman’s Correlation coefficient to examine the relationships between LTQL domains and other validated questionnaires, such as QLACS (18), EORTC-QLQ-BR23 (19), HADS (20). We hypothesized that LTQL total score should have negative high correlations with other total scores of other QoL measures such as QLACS and EORTC-QLQ-BR23 and with other emotional measures such as HADS anxiety and depression. On the other hand, we hypothesized that somatic concerns domain of the LTQL should have a negative high correlation with certain domains of QLACS (fatigue, cognitive problems, negative feelings, sexual problems, pain, appearance concerns, distress recurrence) and domains of HADS (depression and anxiety). We have been unable to study convergent validity for the other LTQL domains (philosophical/spiritual view of life, fitness, and social support) due to the lack of adequate dimensions or scales in our study. We considered convergent validity as moderate when 0.3<r<0.49 and high if r≥0.50 (52).

Known-groups validity of the LTQL was examined by comparing the LTQL total score and domain scores among groups based on the type of treatment (yes/no lumpectomy, yes/no mastectomy, etc.). For this analysis, we used t-test or non-parametric Wilcoxon tests. We hypothesized that patients who had more aggressive treatment would have lower LTQL. Furthermore, to assess the magnitude of group differences, the effect size was calculated as the mean difference divided by the pooled standard deviation. Cohen’s benchmarks were used to classify the magnitude of effect sizes: <0.20 being considered not significant; 0.20 to 0.49 small, 0.50 to 0.79 moderate, and ≥0.80 large (53).

All effects were considered statistically significant at P<0.05. The statistical analyses were performed with IBM SPSS Statistics for Macintosh (Version 25.0 macOS 10.12.x (Sierra); IBM), SAS for Windows (Version 9.4; SAS Institute Inc., Cary, NC, USA, 2016), Mplus (Version 6.1; Muthén & Muthén, 1998-2010), Winsteps (Version 3.71.0.1; John M. Linacre, 2011), and RStudio (Version 1.4.1106; © 2009-2021 RStudio, PBC). The R package EFA.dimensions version 0.1.8.1 (Brian P. O’Connor, 2023) was used for the DIMETEST procedure and the R package PerFit version 1.4.6 (Jorge N. Tendeiro, 2021) for the l_z person-fit statistic to explore careless responding.

The Cronbach’s alpha and McDonald’s omega coefficients are shown in Table 2 and they were above 0.7 in all domains and the summary scale, supporting the internal consistency. As can be seen in Table 3 , in LTQL domains, all corrected item-domain and item-summary scale correlations were above 0.30, with similar values in item-domain correlation (range: 0.38 to 0.82) and in the item-summary scale correlations (range: 0.36 to 0.82). Missing data was 0% in all items.

Considering test-retest reliability, range from 0.72 to 0.96 ( Table 2 ) in the domains scales.

The EFA provided factor loadings ranging from 0.41 to 0.91, exceeding the benchmark of 0.40 ( Table 3 ). The item 34 showed high factor loadings in both “Somatic concern” and “Fitness” domains. The communality values were also higher than 0.40 for most items, except for items 7, 11, 32, 2, and 31, which were higher than 0.30, and item 30 with communality of 0.25. The percentage of variance explained by the four factors was 51.40%. The results of the CFA for the four factors (domains) model provided acceptable fit indices ( Figure 1 ). Based on the Lagrange multiplier test, covariances between the errors of the following three pair of items were considered to improve the model fit: items 34 and 15, items 34 and 29, and items 34 and 21. We have already seen in EFA results that item 34 had a very high factor loading in the Fitness domain to which items 15, 29 and 21 belong. For this CFA ( Figure 1 ) the RMSEA value was 0.077, less than 0.80, and both TLI and CFI, 0.901 and 0.909 respectively, were higher than the threshold of 0.90, just above the threshold to consider an acceptable model fit. The normed chi-square was 3.01, exceeding the threshold of 2, and the SRMR was 0.102, exceeding the threshold of 0.08. Further, all domain loading was above 0.40, ranging from 0.42 to 0.94, and were statistically significant (P<0.0001).

The DIMTEST procedure suggested five factors, instead of four. Therefore, the EFA was explored considering five factors ( Supplementary Table S1 ). Results were similar with the main difference that the “Philosophical/Spiritual view of life” domain is divided into two factors: items 3, 10, 13, 16 and 26, on the one hand (domain 2A with items related to post-cancer growth), and items 2, 9, 18, 20, 27 and 30, on the other hand (domain 2B with items related to spiritual guidance). Besides, the item 34 also showed high factor loadings in both “Somatic concern” and “Fitness” domains, and the communality values were lower than 0.40 for items 7, 11, 32 and 31, although higher than 0.30, except for item 30 with communality of 0.26. The percentage of variance explained by the five factors increased to 56.42%. The results of the CFA for the five factors model provided slightly better fit indices ( Supplementary Table S1 ). The RMSEA value was 0.068, the TLI and CFI were 0.924 and 0.930, respectively, the normed chi-square was 2.55, and the SRMR was 0.089. Further, all domain loading was above 0.40, ranging from 0.42 to 0.93, and were statistically significant (P<0.0001).The results of the Rasch analyses for each domain are shown in Table 4 . Regarding the Somatic Concerns domain, four items showed misfit (items 11, 23, 32 and 34) and were thus removed from the scale. In the Philosophical/Spiritual View of Life domain only one item showed misfit and was removed (item 30). The same applies to the Social Support domain, with one item removed (item 31) due to misfit. After removing those items, the rest of the items conforming each domain supported the unidimensionality with infit and outfit statistics between 0.6 and 1.4. The PCA of the residuals did not yield additional factors with eigenvalues higher than 2 in any of the four domains, and therefore the unidimensionality was also supported. The item separation indexes were high for all domains, ranging from 3.94 for the Social Support domain to 9.56 for the Fitness domain, indicating reliability higher than 0.80. The functioning of the rating scale categories was also adequate in all item of all domains, except in item 20, in which the first two categories were found disordered, although with a minimal difference ( Supplementary Table S2 ). The item and person location for each domain are shown in Figure 2 . Regarding local independence, MADaQ3 effect sizes ranged from 0.091 in Fitness domain to 0.227 in Philosophical/Spiritual view of life domain. Besides, regarding DIF between age groups analysis, although we found two items from the Philosophical/Spiritual View of Life domain (items 3 and 20) with significant DIF, the magnitude of the difference was lower than the threshold of 0.43, and therefore, we did not considered relevant ( Supplementary Table S3 ).

We also performed the Rasch analysis for the two subscales of the “Philosophical/Spiritual view of life” suggested by the five-factor EFA solution ( Supplementary Table S4 ). The results were similar to those found for the “Philosophical/Spiritual view of life” total domain, except that the functioning of the rating scale categories of item 20 was adequate and the item 20 did not present DIF by age group. However, we found significant DIF in items 3 and 26, with values slightly higher than the threshold of 0.43 to consider not relevant, although lower than 0.64 ( Supplementary Table S4 ). Regarding local independence, MADaQ3 effect sizes were much lower, 0.074 and 0.054, respectively.

Regarding the careless responding examination for each domain, the respondents with critical l_z values were minimal, ranging from 1.18% of the participants (4 patients) in the Fitness domain to 3.82% (13 patients) in the Philosophical/Spiritual view of life domain, with l_z values very closed to the threshold of -2.326. Further, when we analyzed the careless responding in the two subscales of the Philosophical/Spiritual view of life domain proposed by EFA, the careless respondents were even lower (0.58% and 0.88%, respectively). Therefore, we concluded that careless responding was not relevant.

The results of the CFA for the four factors after excluding the six misfitting items, provided acceptable fit indices. The RMSEA value was 0.080 (90% CI, 0.075 – 0.086), and both TLI and CFI, 0.915 and 0.924 respectively, were higher than the threshold of 0.90, just above the threshold to consider an acceptable model fit. The normed chi-square was 3.19, exceeding the threshold of 2, and the SRMR was 0.097. Further, all domain loadings were above 0.40, ranging from 0.52 to 0.93, and were statistically significant (P<0.0001).

The results of the CFA for the five-factor structure, after excluding the six misfitting items, shown slightly better results. The RMSEA value was 0.066 (90% CI, 0.061 – 0.072), and both TLI and CFI, 0.95 and 0.94 respectively, almost reach the threshold of 0.95 to be considered satisfactory fit. The normed chi-square was 2.49, exceeding the threshold of 2, the SRMR was 0.080, and factor loadings ranged from 0.59 to 0.93.

Table 5 shows results on the convergent validity analysis. As we hypothesized, LTQL total score was negatively correlated with the total score of other QoL scales, such as QLACS (r=-0.39) and EORTC-QLQ-BR23 (r=-0.50), and with other emotional measures such as HADS anxiety (r=-0.45) and HADS depression (r=-0.57).

Regarding the somatic concerns domain of the LTQL was negatively correlated with certain domains of QLACS, such as fatigue (r=-0.54), cognitive problems (r=-0.55), negative feelings (r=-0.50), sexual problems (r=-0.54), pain (r=-0.74), appearance concerns (r=-0.68), distress recurrence (r=-0.61), domains of HADS, such as depression (r=-0.51) and anxiety (r=-0.50), and EORT-QOL-BR23 (r=-0.70).

Known-groups validity was evaluated across all domains, revealing statistically significant differences solely within domain 1 (somatic concerns). Patients who underwent with Lumpectomy demonstrated higher scores in somatic concerns (t=-2.02, p=0.044) and did those who did not undergo mastectomy (t=2.314, p=0.021). Conversely, no statistical significant differences (p>0.05) were observed between domains of LTQL and various other treatment types, including sentinel node extraction, axillary lymph node dissection, plastic reconstructive surgery, absence of surgical radiotherapy, chemotherapy before or after surgery, hormonal therapy, hormonal therapy before and/or after surgery, targeted therapy, or molecular therapy, or the use of external breast prostheses.