1 Data cleaning

Missing cases were explored assessed thorough graphical analysis.

The minimum and the maximum values were also explored.

2 Methods

2.1 Instrument

self-administered questionnaire designed to assess severity and impact of chronic pain in dogs with osteoarthritis

3 Statistical analysis

Reliability analyses were performed by using the Cronbach’s alpha at the baseline, as well by the item-total correlation. The spearman correlation between all items at the first baseline and the second one an

4 Results

4.1 Attempt to replicate Brown et al. (2007) factor structure

CBPI was developed by Brown et al. (2007) by the study of the BPI, which is an instrument routinely used to provide a broad picture of the effect of chronic pain on human patients. They explored the psychometric properties of the CBPI within the responses of 70 owners of dogs with osteoarthritis and 50 typical dogs. They explored the data via PCA with Varimax rotation and concluded in favor of a two orthogonal dimensions model, in which the first accessed the severity of pain and the second its interference wit function. They also performed a test-retest procedure and compared the CBPI results with the results obtained by the Overall Quality-of-life (QOL). The authors found a Cronbach’s alpha of 0.92 for the total instrument, and 0.93 and 0.89 for the severity of pain and interference with function, respectively.

That said, following their recommendation, the first attempt of the present work was addressed to confirm the original model performing a CFA by defining features alike the original features. This analysis considered two orthogonal factors and used the Maximum Likelihood (ML) approach as the estimation method. The following image presents the conceptualization.

Results revealed a lack of fit; X2(35) = 834.429, p < 0.01, CFI = 0.830, TLI = 0.781, RMSEA = 0.262 [90 Percent CI = 0.223 0.302]. That said, the theoretical model was not confirmed by the data obtained empirically in this research. When situations like this one happen, one can explore the impact of modification indices or perform exploratory procedures to better understanding the data patterns.

4.2 Exploring the data

The frequency and proportions of each item level are plotted below grouped by the type of treatment (Carprofren and Placebo). All replies refer to the baseline measurement.

4.3 Factor analysis and Reliability exploration

Thus, regarding the original study of the CBPI, data from all dogs were used. The scree plot was computed by using the Parallel analysis (PA). PA provides a better method for evaluating the scree plot, once in addition to plotting the eigenvalues from the PCA, it generates random correlation matrices, analyzes them, and compare the resulting eigenvalues to the eigenvalues of the observed data.

The first The plot below displays the results considering the data obtained at the baseline of this research. The horizontal/x-axis presents the factor number, whereas the y-axis reports the eigenvalues (variance of the factors) computed by the original data (solid blue line) and the eigenvalue obtained by resampling. Factors should be retained if the eigenvalue from the observed data is higher than the one derived through simulation.

## 
## Note: parallel analysis suggests 1 factors.

Results suggested retaining only one component, which had eigenvalue of 7.62 from the raw data and 1.67 from simulated components. Consequently, a PCA with one dimension was modeled and the Table below reports the results. About 79% of the variance was explained by this component, which is higher than the original study, in which about 72% of the variance was accounted for by the two-factors model.

To assess the reliability of the data, the Cronbach alpha (internal consistence), spearman correlation between all items and the ICC (test-retest stability)were carried out. The Cronbach alpha was , suggesting the high reliability of the data, which is also seen by the correlation matrix plot (Figura 1). As the measure was used over time, the results gathered from the first two time-points are useful to test the stability of the results. We remind these time-points happened before the treatment procedures. The correlation between the first and the second baseline assessment was carried out through spearman Correlation Coefficient and the ICC was also computed.

item mean sd raw_alpha r.drop baseline_2 ICC PC1 h2
1 3.1 2.8 0.96 0.87 0.62 0.72 0.90 0.80
2 2.0 2.3 0.97 0.78 0.71 0.68 0.83 0.69
3 2.4 2.5 0.97 0.84 0.68 0.72 0.88 0.77
4 2.5 2.6 0.96 0.86 0.61 0.66 0.89 0.79
5 3.0 2.9 0.96 0.89 0.64 0.69 0.91 0.82
6 2.7 2.8 0.97 0.79 0.77 0.78 0.82 0.67
7 3.7 3.4 0.96 0.90 0.57 0.70 0.92 0.84
8 2.6 2.7 0.96 0.88 0.58 0.54 0.90 0.81
9 3.4 3.3 0.96 0.90 0.71 0.80 0.92 0.84
10 3.7 3.5 0.96 0.88 0.76 0.83 0.90 0.81

4.4 Known-groups

The known-groups validity was evaluated by comparing the results of the <pain scale?> between the disease-free participants and the clinically impaired ones. Known-groups method was one of the approaches of evaluating construct validity. A test is considered to exhibit known-groups validity if the test score could be used to discriminate between groups of participants with different features.

An independent t test was performed and its results revealed a significant difference between the two groups (t(39.09) - 12.34, p < 0.01). The plot below displays the results.

4.5 Cut-off

Medcalc

## 
## Call:
## optimal.cutpoints.default(X = "result", status = "disease", tag.healthy = 0, 
##     methods = "Youden", data = ., pop.prev = NULL, control = control.cutpoints(), 
##     ci.fit = FALSE, conf.level = 0.95, trace = FALSE)
## 
## Area under the ROC curve (AUC):  0.973 (0.937, 1.01) 
## 
## CRITERION: Youden
## Number of optimal cutoffs: 1
## 
##                   Estimate
## cutoff                3.00
## Se                    0.95
## Sp                    1.00
## PPV                   1.00
## NPV                   0.89
## DLR.Positive           Inf
## DLR.Negative          0.05
## FP                    0.00
## FN                    2.00
## Optimal criterion     0.95

## Press return for next page....

Check the power of the test

## 
##      One ROC curve power calculation 
## 
##          ncases = 40
##       ncontrols = 16
##             auc = 0.97
##       sig.level = 0.05
##           power = 1

4.6 Treatment over time

All dogs were measured over 3 time-points during the treatment protocol. To check differences within subjects and between groups, the data were modeled by a linear mixed model in accordance with the formula below:

\[y_i = b_0 + b_{0s} + b_1Group + b_2Time + b_3(Group \ x \ Time) + e_i\]

This model allows each subject start in different levels by adding a random intercept for each subject in this study, represented by \(b_{0s}\).

The results revealed a non-significant interaction between group and time (F(4, 452) = 0.89, p = 0.467), nor among groups (F(1, 38) = 0.238, p = 0.628). Contrasting with these results, the effect of the time was significant (F(4, 152) = 5.875, p < 0.01).

Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
factor(group) 41 41 1 38 0.24 0.63
factor(time) 4088 1022 4 152 5.88 0.00
factor(group):factor(time) 624 156 4 152 0.90 0.47

Post-hoc comparisons between time concluded significant differences between the baseline and week 4 (d = 11.246, SE = 2.95, df = 152, t = 3.809, p = 0.0020), baseline and week 6 (d = 9.489, SE = 2.95, df = 152, t = 3.214 , p = 0.01), baseline 2 and week 4 (d = 10.392, SE = 2.95, df = 152, t = 3.520, p = 0.0057), and baseline 2 and week 6 (d = 8.635, SE = 2.95, df = 152, t = 2.925, p = 0.0398). The table below reports the results

contrast estimate SE df t.ratio p.value
baseline - baseline 2 0.85 3 152 0.29 1.00
baseline - week 2 6.87 3 152 2.33 0.14
baseline - week 4 11.25 3 152 3.81 0.00
baseline - week 6 9.49 3 152 3.21 0.01
baseline 2 - week 2 6.01 3 152 2.04 0.25
baseline 2 - week 4 10.39 3 152 3.52 0.01
baseline 2 - week 6 8.64 3 152 2.92 0.03
week 2 - week 4 4.38 3 152 1.48 0.58
week 2 - week 6 2.62 3 152 0.89 0.90
week 4 - week 6 -1.76 3 152 -0.60 0.98

5 Discussion