Discuss,is there any difference between the centers in level of engagement in the trial and is this affected by the gender of patients.

you are part of an international team setting out to explore possible effects of a new medication on treatment resistant trichotillomania (TTM) patients. Before a full scale randomized placebo-controlled trial can be authorized, an open-label trial has been performed (i.e., everyone receives the medication). Participating patients have been followed up on a monthly basis for three months and assessed for symptom severity.
The medication has been given to patients in different centers around the world including: 1 London 2 New York 3 Rio 4 New Delhi
Your team has created a file of all participants in the study, consisting of: 1. Gender (1=Male; 2=Female) 2. Sociology-economic status (1=low up to 4=high) 3. Clinic location (1=London ; 2=New York ; 3=Rio; 4=New Delhi) 4. Behavioral Therapy (1= patient also receives behavioral therapy ; 2= patient does not receive behavioral therapy) 5-8: Symptom severity at times 0 (baseline), 1 (after 1 month), 2 (after 2 months) and 3 (after 3 months). Note lower scores indicate worse severity. 9. Engagement as judged by treatment team. Higher scores indicate higher engagement levels. 10. Satisfaction at the end of therapy. Higher scores indicate higher satisfaction levels.
As the person with the most solid statistical expertise in the team, you have been asked to compile a report that will answer your collaborators queries.
For each query, please provide four, clearly marked, separate sections:
a. A description of the analysis process you have decided to implement (similar to what would be found in the methods section of a research paper). In addition, please support your proposed analysis with a justification (e.g., why this statistical procedure is appropriate and/or whether steps were required to address any problems with data quality).
b. A summary of the analyses and findings as would be found in the results section of a research paper (in APA style). In some cases, follow-up analyses may be appropriate. If so, it is up to you to choose which follow-up analyses, but please provide a brief rationale justifying your choice (1-2 sentences).
c. Suitable descriptive statistics to enable the reader to understand the findings and conclusions [you will be assessed on accuracy but also clarity so please ensure these are communicated clearly to the reader, be it in text, table or graph format]. Note, if appropriate, you can combine sections b and c though please justify.
d. A conclusion communicating to your reader how the analysis has addressed the query with a brief discussion of possible implications/recommendations.
The queries are:
1. Your boss is concerned with the expenses of maintaining trained therapists. Your colleague, Michael (in charge of representing the therapists), claims they contribute to the level of engagement of patients in the trial. Does having a therapist present make a difference for judged level of engagement?
2. Your colleague is concerned that socioeconomic status may be playing a role in reported levels of satisfaction. Is there a difference in satisfaction levels between those patients with the lowest versus those with the highest SES?
3. Ultimately, everyone wants to know: did the medication have any effect on symptom severity? (i.e., is there a difference in symptom severity at the different time points?).
4. Is there any difference between the centers in level of engagement in the trial and is this affected by the gender of patients (i.e., is level of engagement the same for female and male patients across the different locations?). Provide the full analysis.

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