The field of chronic rhinosinusitis (CRS) has improved in the recent past in areas like treatment options, assessment of CRS severity, clinical outcomes and quality of life (QoL) of patients based on perceptions of patients and progress thereof [1].However, research gaps exist in terms of better comparisons, comparison of tools used, statistical tests on equality of disease severity or progress registered by one or a group of patients, etc. Large numbers of patients undergo endoscopic sinus surgeries(ESS) for treatment of CRS, a heterogenous inflammatory disease [2] resulting in impairments which affect QoL [3].  [4] observed about 33% patients do not achieve clinically important improvements in disease-specific outcomes following ESS. More accurate assessment and predictions of post-operative QoL is challenging. [5] opined that the manner in which CRS affect daily life of a patient is more important than CT scan results or presence or absence of a small polyp in an ethmoid cell. For patients with CRS, improvements in disease-specific QoL outcomes are complex and cannot be explained by surgical changes measured by endoscopic examination only [5] [6] observed that radiological severity, assessed by Lund-Mackay score (LMS), is weakly correlated with CRS severity as measured by Short Form 36 Health Survey (SF-36).[7] found that patients with CRS to have poor QoL are more likely than the persons without CRS. The computed tomography (CT) correlated significantly with the scores in the patient-based questionnaires only in the CRSwNP subgroup.Hence is the need to consider QoL instrumentfor capturing symptoms in greater detail which are moresensitive in detecting changes after therapeutic intervention [8]. However, it is important to choose a particular QoL instrument for assessment of therapeutic effects or comparison of two or moretherapeutic modalities on QoL. Major issues in empirical investigations to find relationships are two folds. The multidimensional toolsmay measure different dimensions with different number of items, response-categories,psychometric qualities and scores are not comparable. Moreover, the studies do not consider important methodological issues like meaningful additive aggregation of item scores or dimensions scores using distributions followed by them; use of techniques like regression, Principal component analysis (PCA), Factor analysis (FA), Analysis of variance (ANOVA) without checking theirs assumptions, find test reliability by Cronbach alpha ignoring assumptions of alpha or test-retest reliability ignoring difference in concepts like agreement and correlation, finding validity as correlation with a criterion scale which may assess different dimensions, etc. Comparison of two scales (Scale-1 and Scale-2) does not mean finding average score in Scale-1> or < average score in Scale-2 or find association between the scales. It is well known that scale with higher number of items and higher number of response-categories has higher mean, Standard deviation (SD), reliability and validity. We are interested in finding whether proportion of persons with a particular score in Scale-1 and Scale-2 are equal or not. In other words, we are talking of probability distributions of scores emerging from Scale-1 and Scale-2. Similar distribution of Scale-1 and Scale-2 scores (say normal distribution) will help to have meaningful arithmetic aggregation of item scores and statistical testing like equality of mean of the two scales, etc. The paper suggests transformations of raw scores to normally distributed scores keeping the same range of transformed item scores for better and meaningful comparisons of the scales along with estimation of relationship of CRS severity and QoL scales facilitating meaningful application of statistical analysis and inferences.

Literature survey

Factors affecting QoL amongst CRS patients include:types (with nasal polyps (CRSwNPs) or without nasal polyps (CRSsNPs), symptom types, comorbidities, socio-bio-demographic factors like age, gender, behavioral factors including smoking habit, etc. [9] In a cohort study[10]investigated role of mucus cytokines in predicting postoperative outcomes using scores of 22-items SinoNasal Outcomes Test (SNOT-22) of patients who underwent ESS and found that Mucus cytokine profiles are helpful to identify CRS patients who are likely to obtain postoperative improvement after ESS. Major limitations of the cohort base investigation are (i) Data  may lack balance in baseline variables like age (>50 years or  50 years), gender (male or female), allergy status (Yes vs No), geographical and racial diversity, etc. and the derived results cannot be generalized,(ii) high degree of attrition of participants and extents of erosions are different for different subgroups formed with respect to age, gender and disease status, (iii) postoperative scores may affect impact due to acute disease exacerbationsof chronic rhinosinusitis (AECRS) which are distinct from baseline symptoms and need to be assessed independently while evaluating patients for CRS control [11](iv) diurnal fluctuations of cytokines may affect scores. In addition, missing data on the primary outcome creates problems in data analysis. Disease severity measured using imaging and the endoscopic grading system showed that patients with nasal polyps (NP) have more serious medicalcondition compared to CRS patients without polyps [12]. However, disease severity assessed through QoL tools, patients with polyps showed lighter disease burden than those without polyps [13]Empirically, several benefits of ESS have been found among patients with recurrent acute rhinosinusitis (RARS) like reduction in number of rhinosinusitis episodes, antibiotic courses, and missed workdays [14]; [15]. However, studies by [16] [17] show the opposite i.e. it increases disease-specific disorders and also general QoL in adults with RARS. [18] used PCA of item scores of SNOT-22 and found six independent  components of which  three are related to CRS-specific symptoms  called “nasal”, “extranasal rhinologic” and “olfactory/cough”; and the rest three are QoL related  impairments  “sleep disturbance,” “functional disturbance” and “emotional disturbance.” Explained variance by the components and factor loadings were different. However, impairments due to nasal obstruction, ear pain, ear fullness, and fatigue were included in the PCA. Moreover, PCA assumes normally distributed variables. Assigning equal importance to the items contradicts different factor loadings for items as observed from PCA. Responsiveness of an instrument aims at assessing changes over time and thus, requires repeated administrations of the instrument over the same sample at different time intervals during which the subject's health status may have undergone changes leading to disease progression or remission. However, there exists lack of consensus on the best method to quantify responsiveness [19]. [20] Suggested converting instrument scores to normally distribute scores (P-scores) and assess responsiveness of the instrument as percentage progress/deterioration of i-th patient in t-th time-period ( by  and also test effectiveness of treatments by : =  using paired t-test.  Out of 16 QoL instruments measuring sinusitis, [21] found that following three satisfy basic requirements of validity, reliability, and responsiveness:

• Chronic Sinusitis Survey (CSS),
• Rhinosinusitis Outcome Measure-31(RSOM-31),
• SNOT-16.

The CSS is a 6-item, duration-based monitor of CRS-specific outcomes. CSS measures sinusitis-specific symptoms and medications during the previous 8 weeks.Severity of symptoms is scored by 5-point items where 0: (none) to 4: (severe) and total CSS-scores range between 0 (worst)–100(best) where lower scores signify greater impact of disease on patients. [22] observed little association of the CSS scale scores with sinus CT findings.  RSOM-31 is a broad-based tool covering disease-specific rhinosinusitis and also general QoL measurements. 31-items of RSOM-31 are distributed overseven domains to measure symptom severity of patients in nasal, eye, ear, sleep, general, emotional, and functional problems. Two response scales: magnitude with 6-category response score and importance with 4-category response score are associated with each item and the product of the magnitude and importance scores is taken as the symptom-impact score.RSOM-31 was compacted into SNOT-22 to improve SNOT-16.  In 16-item Sinonasal outcome test 16 (SNOT-16),patients rate severity of their symptoms and the social/emotional consequences of their rhinosinusitis on 4-point scales (0 to 3). SNOT-16 scores, computed as mean of endorsed responses are negatively related to QoL i.e. higher SNOT-16 scores imply worse QoL and functional status. Scores of SNOT-16 were highly correlated with 7 of the 8 subscales of SF-36 [23]

Other QoL scales (Illustrative):

Rhinosinusitis Disability Index (RSDI) is a disease-specific health-related QoL instrument with 30 number of items, each in a 5-point scale (0 for “never” to 4 “always)for assessing impact of physical (11-items), functional(9-items), and emotional (10-items)dimensions of CRS. Total RSDI scores ranging between zero and 120 are obtained as sum of item scores [24].  Sinonasal outcome test 20 or 22: The RSOM-31 was reduced to a set of 20 items on nose, sinus, and general items to become the SNOT-20 and further addition of two other items to finalize the SNOT-22. The two additional items are related to nasal blockage and loss of sense of taste and smell, which were not included in SNOT-20. Scoring of SNOT-22 has been simplified. Total scores range between 0–120, with higher scores indicating a higher impact of disease [25]. Many generic QoL instruments are used for both pre- and postoperative studies in CRS. SF-36 is a popular generic QoL questionnaire containing K-point items where K= 2, 3, 5, 6. However, computation of total SF-36 score is not supported by the Manual of SF-36. Instead, two distinct concepts Physical Component Summary (PCS) and Mental Component Summary (MCS) are calculated requiring use of special algorithms. [26] gave an assumption-free method to find total SF-36 scores ( ) satisfying desired properties like normally distributed scores facilitating better comparison and computation of psychometric features like factorial validity and reliability.

Proposed method:

Method proposed by [27-28] to transform multidimensional scale to follow normal distribution involves the following stages:

• Ensure uniformity in directions of scales so that higher score indicatesimproved QoL
• For meaningful addition of ordinal scores, item scores are converted to equidistant scores (E-scores) as weighted sum where weights are obtained from frequency of response-categories of items. The weights are different for different response-categories of different items.
• Standardize E-scores to Z-scores following N(0,1)
• Transform Z-scores to proposed scores (P-scores) so that P-score of each item lies between I and 100. This is independent of number of respose-categories in items.
• Obtain dimension scores as sum of P-scores of items relevant for the dimension and scale scores as convolution of dimension scores or equivalently as convolution of item scores.

Scale scores and dimension scores follow normal distributions and parameters of distributions can be obtained from the data.

Major benefits of P-scores are:

• Data structure is not changed much
• Reflects position of individuals by monotonically increasing continuous variables
• Finding relative importance of the dimensions as change in scale score due to small change in score of a dimension (elasticity) and ranking of dimensions with respect to elasticity.
• Quantifies progress registered by one or a sample of individuals across time i.e. responsiveness by and plotting of progress path across time.
• Possible to undertake testing hypothesis like or  for longitudinal data and also for snap-shot data by t-tests and  by  
• Test effectiveness of treatments by : = using paired t-test since pre- and post-operation groups are not independent.
• Finding equivalent cut-off scores and for two scales X and Yrespectivelyby solvingthe equation  using normal probability table for a known value of  where  and  denote respectively normal density function of P-scores for Scale X and Scale Y. Finding equivalent score-combinations is possible even if the scales have different number of items or dimensions
• Test reliability as per theoretical definition by dichotomizing a test in two parallel subtests (g-th and h-th) and test which is equivalent to test   by F-test.
• To find the validity by Factorial Validity expressed as ratio of the first eigenvalue ( ) to the sum of all eigenvalues i.e. Factorial Validity = .  Factorial validity considers the main factor for which the scale was developed.  It avoids problem of selecting criterion scale where dimensions are similar to the dimensions covered by the scale in question.

Major limitations of QoL scales using summative Likert scores can be avoided by the proposed method generating continuous, monotonic, normally distributed scores and facilitating inferences like estimation of population mean (μ), variance (σ^2), confidence interval of μ,  testing statistical hypothesis like H_0: μ_1=μ_2 or H_0: σ_1^2=σ_2^2 etc. In addition, it can assess progress/deterioration by a patient or a group of patients between two successive time periods, reflecting responsiveness of the scale and effectiveness of a treatment plan. Equivalent score combinations (x_(0,) y_0)were found where area under curve f(x) up to x_0= area of the curve g(y) up to y_0 where f(x) andg(y)represent respectively normal pdf of X and Y. Method described to obtain test reliability as per the theoretical definition.  Normally distributed P-scores can be used to test H_0: r_tt=(S_T^2)/(S_X^2 )=1⇔H_0: σ_X^2=σ_T^2  against H_1: σ_X^2>σ_T^2by F-test. A simple measure of validity of a multidimensional QoL scale is proposed as the ratio of the first eigenvalue to the sum of all eigenvalues. The proposed measures improve quality of measurements of QOL scale, facilitate meaningful comparisons across groups and time and are critically relevant to policy makers and researchers in social and medical sciences.

Proposed method of transforming raw Likert scores to continuous, monotonic scores following normal distribution helps to avoid major limitations and undertake analysis under parametric set up. Suggested integration of several QoL scales has clear theoretical advantages. Assumption-free measures of reliability, validity, etc. may be used while comparing comprehensively areas of multidimensional QoL scales. Future studies with multi-data sets involving more than one QoL scales are suggested along with issues relating to psychometric properties of the proposed transformation.

Declaration

Acknowledgement: Nil

Funding details: No funds, grants, or other support was received Conflicts of interest: The author has no conflicts of interest to declare

Availability of data and material: Nil (The paper used no data)

Authors' contributions: Sole Author and contributed in each of the stages of preparation of the manuscript fromConceptualization, Methodology and Writing

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