Measurement problems in Drug Addiction and Quality of Life

Studies of substance abuse involve both categorical variables and also count data which violate assumptions of normality required for parametric statistical analysis. Clustering of individuals, non-availability of repeated measurements, significant missing data, biased samples, methodological problems of questionnaires covering dimensions of drug addiction, use of statistical analysis without verification of assumptions of such techniques, etc. aggravates the problem. Primary data on drug addiction (substance use disorder) are mostly taken from websites of United Nations Office on Drugs and Crime (UNODC), World Health Organization (WHO), Institute for Health Metrics and Evaluation, Alberta Gambling Research Institute, etc. Data collected from clusters like schools, clinics, communities, etc. may violate assumption of independent observations [1]. Moreover, residuals of fitted regression equation with binary dependent variable may not satisfy the assumptions of regression.

Individuals with substance use disorder also suffer from mental disorders [2]. However, reasons of such co- occurrence are not clear. As per old estimates, 30% to 60% of patients seeking treatment for alcohol addiction meet Posttraumatic Stress Disorder (PTSD) criteria and one third of individuals with experience of PTSD experienced alcohol dependence [3]. Similar co-occurrence of schizophrenia and marijuana addiction was reported [4]. Overlapping symptoms shown by mental disorders and substance use disorders create difficulties. For example, common symptoms of schizophrenia like paranoia, hallucinations, delusions, are also shown by persons who use methamphetamine for a long time. Data structure of Quality of Life (QoL) is more or less similar to that of drug addiction data in terms of variables in ordinal level. QoL involves self-reported scales where subjects indicate their perceptions about their physical and mental health and also non-health aspects such as sociocultural conditions like social and professional roles in being productive and others. While sustenance alone may have little effect on QoL [5], gain on QoL may accrue gradually with increasing length of abstinence exceeding the initial six months [6].

Scales used in substance abuse research, QoL containing K-point items and are not comparable because of different number of dimensions covered, different number of items, different values of K, scoring methods, etc. which give rise to different unknown distributions of scale scores and score ranges. Moreover, such scales suffer from methodological limitations. From the angel of probability distribution, scores of two items X + Y = Z requires similar distribution of X and Y and knowledge of distribution of Z so as to find for discrete case and for continuous case. Comparison of two scales does not mean finding Average^Scale−1 > or < Average^Sacle−2 or to find correlation between the scale scores. However, concept of comparability is different from correlation and may demand that for any given score x₀ of Scale-1, one can find corresponding score y₀ of Scale-2 and vice versa, similar rank orderings by the scales, even if the scales have different formats. For example, X and are quite comparable despite for X: 1, 2, 3,.…30.

The paper addresses methodological problems in analysis of drug addiction data and data on quality of life of persons with and suggests transforming raw item scores to equidistant scores and further transformations to normally distributed scores for meaningful arithmetic aggregation reflecting current status satisfying desired properties and facilitating parametric statistical analysis and inferences along with better estimation of reliability, validity and evaluates QoL for drug addicts.

A large number of factors associated with drug addiction and decision of substance use have been found. An illustrative list includes family-related factors and quality relationships among family members [7], influence of companions and peers [8], lower socioeconomic status [9], etc. Intra-class correlation approach has been used to evaluate cluster-based dependency data [10]. Substance Use Risk Profile Scale (SURPS) [11] is popular instrument to assess four personality risk factors for substance misuse where 23 items are distributed over four sub-classes or dimensions: Impulsivity (5 items), Sensation Seeking (6 items), Anxiety Sensitivity (5 items), and Hopelessness (7 items). Each item is in 4-point scale from 1 (strongly disagree) to 4 (strongly agree). All but one item in the Hopelessness subscale were reverse scored. The four dimensions showed different levels of association for different classes of drugs.

Attempts have been made to evaluate QoL for persons suffering from Substance Use Disorder (SUD) using generic instruments like WHO Quality of Life Assessment-BREF (WHOQOL-BREF), 36- Item Short Form Health Survey questionnaire (SF-36), etc. and also specific tool like Injection Drug User Quality of Life Scale (IDUQOL) for injection drug users, Drug Users Quality of Life Scale (DUQOL) for drug users who do not inject drugs, etc. for assessment of chronic nature of substance dependence, impairments or disorders [12]. DUQOL aims at measuring perceptions of drug users about their QoL in a structured questionnaire and also detect changes in QoL due to various interventions [12].

Here, subjects classify each chosen area as “important” or “unimportant”. Summative scores are taken giving equal importance to items and three average scores are computed viz. total DUQOL for important and for areas that are not important DUQOLNot . Higher value of DUQOLTotal Total implies better QoL. QoL scales in the context of drug dependence have been reviewed [13]. Another QoL scale for patients with drug addiction/ dependence (QOL-DA) with 40 number of 5-point items (1 to 5) was developed [14]. Validity of domains of QOL-DA were found as correlation with SF-36 and WHOQOL-100 as criterion scales and responsiveness of the scale i.e. change of QOL-DA score between pre- and post-detoxification was tested by t-test. However, t-test requires normal distribution of the variable.

The generic and SUD specific tools are self-reported questionnaires with floor and ceiling effects, cover different dimensions and contain different number of items in K-point scale, K = 2, 3, 4, 5, …and so on. Different scoring methods adopted by the scales give rise to different score ranges and unknown distributions of scale scores and are not comparable. The Manual of SF-36 (http:// www.webcitation.org/6cfeefPkf) does not permit computation of total score for an individual. Different features of two generic QoL scales being used in the context of substance use are as follows:
A. SF- 36: Total 36 items and 8 dimensions; item levels (K) where K= 2, 3, 5, 6, 7. Response 1 to a Binary item is recorded as 0 and response 2 is recorded as 100; score ranges of items are different and some items need reverse scoring. However, original item scores are rescaled to range between 0 to100. Subscale-wise reliability, validity, etc., are obtained but not for the entire scale.
B. WHOQOL-BREF [15]: Total 26-items are non-uniformly distributed over five dimensions. While “Environmental health” contains 8 items (maximum), the “General health” contains only 2 items (minimum). However, each item is in 5-point format. Method of scoring dimensions are not uniform. But dimension scores are transformed by linear transformation to range between 0 to 100.

Major limitations

Major limitations of the above said ordinal K-point scales K= 2, 3, 4, 5, 6, 7, etc. are:
a) Item scores are not equidistant. For example, latent distant between successive levels of DUQOL like Very dissatisfied & moderately dissatisfied (D12)≠ Moderately dissatisfied & slightly dissatisfied (D23) ≠ Slightly dissatisfied & Neutral (D34) ≠ Neutral & Slightly satisfied (D45) ≠ Slightly satisfied & moderately satisfied (D56) ≠ Moderately satisfied & very satisfied (D67). Non-satisfaction of equidistant property fails to make meaningful arithmetic aggregation and could be meaningless [16].
b) Equal importance to the items of DUQOL contradicts different values of inter-item correlations which ranged between 0.583 to - 0.024 and different values of item-total correlations (0.778 for 6^th item and 0.242 for the 2^nd item) [17].
c) The scales differ with respect to length, width giving rise to non-uniform score ranges and unknown distributions of scale scores. For example, mean, variance, reliability, validity, are different for different K-point scales for K= 2, 3, 5, 6 of SF-36 [18].
Thus, scores obtained from the scales are not comparable. d) Different responses to different items can generate tied scores for several respondents which results in reduces discriminating power of scale.

One remedy is to transform scores of each item to equidistant scores which can be normalized and further transformed to range between 1 and 100 (say) facilitating meaningful addition to get normally distributed sub-scale scores and scale scores enabling parametric statistical techniques. Such normally distributed scale scores avoid various tests of normality with limitations. For example, major limitations of Shapiro-Wilk test are: (i) sensitive to sample size i.e. the test is more likely to reject the null hypothesis of normality as the sample size increase (ii) does not provide information on extent and nature of deviations from normality.

Suggested method

Chakrabartty SN [19] gave a method for transforming raw item scores to equidistant scores where anchor values are taken as 1, 2, 3, 4, 5, and so on, and ensuring each item is positively related to the traits being measured. The method is briefly discussed below for 5-point items:

Consider the data matrix of raw scores (X_ij) of order n × m where n denotes number of individuals answering the scale and m denotes number of items of the scale. The general element X_ij of the matrix denotes raw score achieved in the j-th item by the i-th individual. Clearly Monotonic and equidistant scores can be obtained by considering different weights W_ij > 0 to j-th level of i-th item following the steps given below.

Step-I: Find frequency of ach level of an item. Denote the maximum frequency by fmax and the minimum frequency by f_min .

Step-II: Assign initial positive weights W₁, W₂ , W₃ , W₄ and W₅ to the response-categories so that W_1>, 2W_2> , 3W_3> , 4W_4> , 5W_5> form an arithmetic progression. This will ensure satisfaction of equidistant property, since common difference say β for p = 2, 3, 4, 5

The above initial weights can be converted to final weights so that and Constant. Item-wise equidistant scores (E) can be standardized by and further transformed to proposed scale score (δ ) by so that and δ_i follows . Dimension score (D_i) is taken as sum of relevant δ_i ’s and scale score (δ ) = Σ D_i .Here, δ ~ normal , enabling undertaking of parametric statistical analysis.

Normally distributed δ_i score of i-th individual obtained from a chosen scale to measure substance use disorder (SUD) reflect intensity or severity of SUD of that individual. Following similar steps, several dimensions of chosen QoL scale can be aggregated to get normally distributed QoL_i score to reflect overall QoL status of the i-th individual.

Properties and benefits

δ -scores and QoL scores can be computed by combining several scales, irrespective of their formats and correlations among the scales. Parameters of normally distributed δ -scores and QoL scores can be found from data since it is obtained as convolution of distributions of item scores which again follow normal distribution. Properties satisfied by δ -scores and QoL scores are given below the following desired properties:
A. Continuous and monotonically increasing
B. Zero value of E-scores occurs if and only if f_ij = 0 for j-th level of i-th item.
C. Avoid skew and outliers and give unique ranks to the individuals.
D. The dimensions of SUD or QoL can be ranked with respect to relative importance given by respectively.
E. Progress/deterioration of SUD of i-th person in successive time-periods can be assessed by which reflects responsiveness of the scale and also effectiveness of adopted treatment plans and interventions. Progress in terms of QoL can be assessed similarly. For a group of persons suffering from substance use disorder (SUD), progress is indicated if Similarly, percentage improvement in QoL in successive time periods is given by Dimension(s) showing deteriorations are critical and require initiation of necessary corrective interventions.
F. Path of progress/deterioration of one or a sample of persons with SUD over time can be compared using longitudinal data. A decreasing graph of it δ and time (t) implies progress registered by the i-th patient and an increasing graph implies the reverse. Such plot is akin to hazard function of survival. For QoL, increasing graph indicates progress. Significance of progress of δ can be tested by by x2 test.
G. Normality of δ -scores and QoL scores facilitate estimation of population mean and population variance from a representative unbiased sample drawn by probability-based sampling technique. Statistical tests of equality of mean and variance of addiction scores or QoL scores for two groups or a single group at different time periods like H₀ :μ₂ or H_0: H₀ :σ₁² =σ₂² using cross-sectional or longitudinal data can be undertaken.
H. Normality of δ -scores or QoL scores enable testing statistical hypothesis across demographic variables like gender, age, income levels, educational attainments, etc. by t-ratios or ANOVA.
I. Question arises whether cut-off scores of two scales are equivalent. If scores of each scale are transformed to normally distributed scores, equivalent scores of the two scales can be found by solving so that area of the curve f (x) for Scale-1 up to x0 = area of the curve g ( y) for Scale-2 up to y₀ [20] solved the equation using N(0,1) table, even if scales are of different formats or contain different dimensions.
J. A sample of individuals can be classified into K number of mutually exclusive classes based on S-scores with normal pdf by Davies-Bouldin Index (DBI) [21] based on within-cluster and between-cluster distances reflecting classification efficiency in terms of lower value of DBI and is computed by

C_i: Centroid i.e. mean of the i-th class n_i : number of individuals in the i-th class.

The lowest DBI value in the plot of DBI and number of clusters gives optimal number of clusters. Fixing K=2 and obtaining data from normal and persons with SUD, an optimal cut-off score of δ -scale can be explored. However, the results need to be verified with clinical observations.

Normality of S-scores or QoL-scores enable undertaking of analysis like

Computation of correlation between SUD and QoL indicating association between them. Patients with SUD usually have lower QoL. This is in line with patients with mental disorders. Major influencing factors of lower QoL of drug abusers were gender, mode of drug abuse, and family atmosphere [22]. Thus, r_SUD,QoL is likely to be negative.

Finding empirical relationship say regression equation of SUD measured by δ -scores on different dimensions of QoL where the coefficient β_i may indicate relative importance of the i-th dimension of QoL. Stepwise regression method is preferred to have a set of QoL dimensions for prediction of the dependent variable. Similar regression equation of QoL-scores on dimensions of SUD can be fitted.

The dependent variable in substance abuse research may be binary like whether a participant took drugs in the last month or not, better method is Logistic Regression (LR) which is of the following form for k-independent variables

where π : probability of success and (1−π ) : probability of failure. 0 ≤π ≤1< /p>

β₀: Constant

β_i regression coefficients of i-th independent variables

Here, is odd ratio of success.

Test of significance of β_m i.e. H₀ : β_m = 0 against H₁:β_m ≠ 0 is undertaken using Wald test by

For simultaneous evaluations of effects of various levels of clustered data in substance abuse prevention and cross-site evaluation of community partnerships, multilevel analysis have been used [24]. For cluster data, empirical relationships between i-th individual and j-th school may be given by:

Non-satisfaction of normality assumption of error terms and μ_1j introduce bias into standard errors at both levels and affects validity of hypothesis tests. Multilevel models can be extended to evaluate effects at third order cross-levels School X Individual X Classroom. However, multilevel analysis is not without limitations. Weakened causal inference without randomization is one such limitation. In reality, situations are there where randomization may not be possible [25].

Predictors across demographic and socio-economic subgroups like (gender, income, socioeconomic status, etc.) differ. Covariance Structure Analysis (CSA) may help testing equality or invariance of effects across groups, and comparing the model with and without parameters freed across groups. However, prior checking of multivariate normal distribution is needed for CSA.

Different methods of finding reliability deviating from theoretical definition of reliability give different values of reliability (rtt). Avoiding verification of assumptions of Cronbach’s alpha, theoretical reliability (rtt(Theoretical)) can be found by

where N: sample size and r_gh. : correlation between g-th and h-th sub-tests [26]. A pre-requisite of the method is to dichotomize the test in two parallel sub-tests.

Normally distributed δ -scores helps to test whether sub-test scores are parallel by testing by t-test and by F-test or by testing equality of regression lines of and where by ANOVA or by Mahalanobis where for the i-th item.

For a multidimensional scale, Factorial validity indicates validity of the main factor for which the test was developed and is computed [27]. Factorial validity of δ -scores avoids selection of criterion scale with similar factor structure and administration of two scales.

Selection of measurable indicators is important for measuring SUD and QoL. The proposed S-scores and QoL scores can be found by arithmetic aggregation of all relevant causes and intensities. Normality of δ -scores or QoL scores offer significant benefits including testing of statistical hypothesis across demographic variables by t-ratios, ANOVA, F-test, etc. Ranking of the factors, quantification of responsiveness of scales, comparison of progress/ deterioration path of different types of SUD through longitudinal data and better measures of reliability and validity adds to the benefits.

Association between δ -scores and QoL scores can be found by simple correlation or by multiple correlation of QoL scores as dependent variable and dimension scores of SUD as set of independent variables or as canonical correlation between dimensions of δ -scores and dimensions of QoL. Optimal cut-off score of δ -scores can be explored by fixing K=2 (normal persons and persons with SUD) in Davies-Bouldin Index.

Analysis incorporating categorical dependent variables for drug use can be undertaken by multilevel analysis or by Covariance structure analysis.

The paper is an improvement of assessment of SUD and QoL with benefits of parametric analysis. Normally distributed δ -scores and QoL scores may balance the supply and demand sides of SUD. Future studies may be undertaken for improvements of the methods described in this paper with emphasis on robustness of measurements considering among others effectiveness of social support programmes among patients with SUD on their QoL based on primary as well as secondary data in substance abuse research available from various national data sets like National Center for Health Statistics [28], Cochran Controlled Trials Register [29], National Institute of Health [30], etc.