Question

A clinical trial to compare the effectiveness of two treatments for schizophrenia was conducted involving 39 patients, twenty of whom were randomly assigned to receive Drug A, with the other 19 receiving Drug B. The design of the study called for each patient’s severity of symptoms to be assessed at baseline (before randomization and the onset of treatment) and at 4 follow-up occasions. Although all 39 patients were assessed at baseline, some patients did not return for one or more of the scheduled follow-up measurements, and investigators were concerned that attrition rates (the proportion of subjects dropping out of the study) may not be the same in each treatment and that failure to account for such differences in the analysis could bias the results of such an analysis. Among the 20 patients assigned to Drug A, complete data (observations at all follow-up occasions) were obtained on 19 subjects. Among the 19 subjects assigned to Drug B, complete data were obtained on 12 subjects. Use R coding to help answer the questions.

I. Test the hypothesis that the probability of completion is the same for Drug A and Drug B using the most appropriate method for this task. Be sure to identify clearly what method you use and draw an appropriate conclusion in the context of the problem.

II. Compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B. Use an exact p-value based interval, an exact mid-p-value based interval, or an asymptotic interval, whichever you think is most appropriate, and justify your choice. Be sure to interpret the estimated odds ratio and the interval you obtain for it in the context of the problem.

III. Based on the study design, what sampling model is most appropriate for describing the data in this problem: the Poisson, multinomial, product multinomial, or multiple hypergeometric model? What sampling model are your inferences in parts (I) and (II) based on?

Answer 1

To test the hypothesis that the probability of completion is the same for Drug A and Drug B, you can use a chi-square test for independence. To compute a 90% confidence interval for the odds ratio, use the log odds ratio and its standard error. The most appropriate sampling model for this problem is the multiple hypergeometric model.

Step-by-step explanation:

In order to test the hypothesis that the probability of completion is the same for Drug A and Drug B, you can use a chi-square test for independence. This test will determine if there is a significant association between the completion rates of the two drugs. Calculate the observed and expected frequencies for each drug, then use these values to calculate the chi-square test statistic. With the chi-square test statistic, you can determine the p-value and compare it to the predetermined significance level.

To compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B, you can use the log odds ratio and its standard error. Calculate the log odds ratio by taking the natural logarithm of the odds ratio. Then compute the standard error using the formula: (1 / √a) + (1 / √b), where a is the number of patients completing the study in group A and b is the number of patients completing the study in group B. Finally, use the log odds ratio and standard error to calculate the upper and lower bounds of the confidence interval using the formula: log odds ratio ± (critical value * standard error).

The most appropriate sampling model for describing the data in this problem is the multiple hypergeometric model. This model takes into account the random assignment of patients to either Drug A or Drug B, as well as the attrition rates and incomplete data for certain patients. The data in parts (I) and (II) are based on this multiple hypergeometric model as the sampling model.