# Supplement to Stratified Regression Chapter

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## Assignment

Question 1: Estimate mortality rate in 6 months for lung cancer patients with various common comorbidities.  Data► SQL► Jehanzeb's Solution► Video►

• Use SQL to construct case/control comparisons for each comorbidity of lung cancer.
• Use SQL to estimate the intercept for parameters of the multiplicative function form.
• Report the mortality rate for patients who just have lung cancer and no other comorbidities.
• Provide the equation that calculates the risk for combination of lung cancer and its comorbidities.
• Select 3 comorbidities and calculate the prognosis of a patient with a combination of 3 comorbidities and lung cancer.

Question 2: Many patients, at end of life, experience disabilities. In fact, disabilities are often used to anticipate end of life. The attached data show the disabilities residents of veteran administration nursing homes have experienced.  Estimate how various disabilities predict mortality in 6 months.  The data do not have headers.  The variables are listed in the following order: ID, age, gender (M for male, F for Female), number of assessments completed on the person, number of days followed, days since first assessment, days to last assessment, unable to eat, unable to transfer, unable to groom, unable to toilet, unable to bathe, unable to walk, unable to dress, unable to bowel, unable to urine, dead (1) or alive (0), and assessment number.  The following table should assist in organizing the data.

 ID Age Sex tAssess Followed DaysFirst DaysLast uEat uSit uGroom uToilet uBathe uWalk uDress uBowel uUrine Alive AssessID 1 66 M 9 915 0 915 0 0 0 0 0 1 0 0 0 0 1 1 66 M 9 915 7 908 0 0 0 0 0 1 0 0 0 0 2 1 66 M 9 915 18 897 0 0 0 0 0 1 0 0 0 0 3 1 66 M 9 915 238 677 0 0 0 0 0 1 0 0 0 0 4

• Clean the data using the following steps: The age at death is given as a row of data.  For each assessment calcualte if the patient dies in 6 months from the assessment.  If the patient never dies assume not dead in 6 months.  At death assume that the patient has all disabilities, as is the data indicates no disabilities at death.  Drop last assessment as no outcomes can be calculated from last assessment. Assume age of assessment is age at first assessment (given as the second variable) plus days to assessment/365.  Residents with negative age should be dropped because of date of birth errors.  Residents 100 or more years should be dropped because of small sample.  Note that the analysis is done at assessment level and not at patient level.  Data► Clean►
• Predict from the patient's assessments (i.e. their age, gender, and disabilities at time of assessment) if the patient is likely to die in the next 6 months and may be a candidate for hospice care.  Do not use regression in these analysis and estimate the parameters using SQL. SQL► Answer►
• Calculate the k constant for the multiplicative model using SQL.  SQL►
Generate possible k values and see which one of the k values satisfy the equation:

• Use the model you have developed to predict the probability of mortality for a 75 year old resident with urine, bowel, and toilet disabilities.  Enter the case description into a table called RecentCases, using Create Table and Insert Value commands.  Then use this table to predict the probability of mortality for this resident.  SQL►
Make sure that the probability of mortality is adjusted to range between minimum amd maximum probabilities for different strata.  Stratfied regression provides a transformed probability that should be adjusted to estimate the actual probability using this formula:

Where Max is the maximum and Min is the minimum probabilities for each strata.