The data are from a clinical trial comparing two drugs to treat lung function associated with chronic asthma. The severity of asthma is measured by a lung function test, where lower scores are better. These subjects were followed for 60 weeks at which time a lung function test is performed. If a subject drops below 3, they are in remission at that time (sustained remission is a separate question).
The following analysis is regarding the clinical trial of two drugs to treat lung function associated with chronic asthma. 220 patients were split into two different groups to assess the effectiveness of each drug's ability to improve the severity of asthma measured by a lung function test. Specifically, we are interested in whether there is a significant difference in lung score differences between each drug group. There were some indications of data issues. As indicated within the codebook the valid range for the Difference between Week 60 and Baseline Week 0 was between -6.00 to 3, upon cleaning, there were two data points that fell outside of the range, for the purpose of keeping the internal validity of the study, those two data points were removed from the final analysis. The overall sample size was N=220 patients but there was a considerable amount of missing data (n=28; 12.72%) in Week 60 Scores, Difference between Week 60 and 0, and overall Status. Descriptive statistics were conducted using frequencies and percentages for categorical data. Continuous data were summarized with means and standard deviations and/or medians with minimum and maximum values. Data analyses were conducted using JMP v.16 and were performed at an α=0.05 significance level. Overall, the average age of the sample was 16.06 ± 2.85 with more males (n=116; 52.72%) than females (n=104; 47.27%). The average Week 0 baseline score for the sample was 5.76 ± 1.09 with the median score coming out to 5.75, ranging from 2–8.56. At week 60 the average score for the sample was 3.22 ± 1.51 with a median score of 3.08, ranging between 0.16–7. By the end of the study, the overall difference between Week 60 and Baseline Week 0 was -2.47 ± 1.46 for the mean, and a median score difference of -2.69, ranging between -5.99 to 2. Additionally, after this difference was calculated, more participants were categorized as Active with their minimum Lung Function Score ≥ 3.0 (n=100; 52.08%) than Remission with their minimum Lung Function Score < 3.0 (n=92; 47.91).
Additionally, we examined the difference between Drug A and Drug B in their ability to treat lung functionality. The bivariate analyses consisted of the Likelihood Ratio chi-square for the categorical variables (i.e., sex and status), and independent t-tests for the continuous variables (i.e., age, week 0 scores, week 60 scores, and the Difference). Assumptions for both statistical tests were evaluated. The chi-squares’ expected frequencies for all categorical variables were met. Because the dependent variable is an interval-ratio variable, and we were examining the difference between two independent samples (i.e., Drug A and Drug B), the independent t-test was utilized to analyze the data. The normality assumption on the difference distribution for Drug A and separately for Drug B was assessed with histograms, Normal Quantile Plots, and the Shapiro-Wilk Tests. Week 0 Scores within Drug B indicated normality violations, given the large sample size for all groups the central limit theorem was invoked. For the equal variance assumption, the O’Brien, Brown-Forsythe, Levene, and Bartlett tests were used. Week 0 Scores, Week 60 Scores, and the Difference between Week 60 and Week 0 had unequal variance, thus, the T-Statistic for Unequal Variance was used. Participants who were in Drug A were more likely to be in remission (76.09 percent; χ2 = 77.89, p<0.0001), and, on average, participants in Drug A had a lower mean score than Drug B (2.14 ± 0.83 score compared to 4.09 ± 1.37, respectively; t(178.82)= 12.12, p <0.0001). This also carried into the difference in the score where participants in Drug A had a lower Difference Score than Drug B (-3.47 ± 0.84 score compared to -1,66 ± 1.35, respectively; t(176.67)= 128.49, p <0.0001). Overall, Drug A does appear to be associated in improving lung function. We next examined whether this bivariate relationship held under a multivariate model
I do believe that randomization was successful. Based on all of the variables that were not subjected to impact by the Drug Grouping such as Age, Sex, and Baseline Week 0 Scores, all P-Values recorded were not statistically significant. If randomization was not successful, I believe that these variables would have a significant P-Value recorded.
We were interested in whether participants in Drug A or Drug B showed different treatment effects in lung function scores between Baseline Week 0 and Week 60 controlling for age and sex. To analyze this research question, an ordinary least squares (OLS) multivariate regression analysis was used because the dependent variable was measured at the ratio, continuous scale and the research question of difference required us to control for two other variables. The OLS assumptions of normality, linearity, and homogeneity of variance were assessed with a scatterplot of the standardized residuals plotted against the standardized predicted values. In addition, the standardized residuals were plotted against each of the six predictor variables. Normality of the residuals was further assessed with a histogram, Normal Quantiles Plot, and the Shapiro-Wilk Test. Finally, multicollinearity was assessed with both a correlation and a review of the variance inflation factor (VIF) collinearity diagnostics. All assumptions were met, and no cases were identified as exerting any leverage or influence. The significant overall model (F(3,186)=40.62; p=<0.0001) suggests that at least one slope in the model is significant. Because JMP’s intercept is not correct, the intercept should not be interpreted. Overall, 39.58% of the variation in score difference is explained by Drug Group, sex, and age (R2=0.3958). The multivariate regression results are shown in Table 2. Participants who were within the Drug A group were associated with a lower mean lung function score of approximately 1.795, controlling for age and sex (B=-1.795, p<0.0001). Age and gender were not statistically significant predictors of lung functionality scores. This was apparent when evaluating which predictor was the strongest compared to age and sex. Based on the standardized coefficients which drug group a participant a part of was the strongest predictor in terms of lung functionality score with 0.611 as the coefficient. Additionally, the variance (R2=0.3958) indicates that important variables were excluded from the model. More research needs to be conducted to examine other variables related to lung functionality scores and drug groups.