A study is conducted to assess the relationship between the use of marijuana during pregnancy and adverse
Description
A study is conducted to assess the relationship between the use of marijuana during pregnancy and adverse
delivery outcomes, defined as major congenital malformations. The following variables are used in the
analysis.
Delivery outcome: major congenital malformation versus other delivery.
Risk factors:
1. Marijuana usage during pregnancy: yes or no
2. Race: White or non-white
3. SES categorized as: low, middle, or high
4. Maternal age
5. Any previous stillbirth: yes or no
a. Write down a model to evaluate this relationship including terms in the model for the confounding
factors and interactions between marijuana usage and each of the other factors. Be sure to state the
coding scheme you are using to represent the variables in the model.
b. Write down the odds ratio corresponding to the model in part (a) for the odds of malformation given
marijuana usage relative to the odds of malformation given no usage.
2. We want to assess the association between the development of heart disease (CHD) and the presence of an
abnormal ECG at entry into the study in a group of males. The following variables and codes are used.
Developed CHD: yes (1), no (0)
Abnormal ECG (X1 ): present (1), absent (0)
Hypertension (X2): present (1), absent (0)
Age in years (X3 )
High cholesterol (X4 ): present (1), absent (0)
Smoker (X5): yes (1), no (0)
The estimates of the β’s from a multiple logistic regression model for P(CHD = 1 | x) are shown below.
a. Determine the odds ratio for a subject with an abnormal ECG, hypertension, high cholesterol and is a
smoker compared to a subject without those characteristics of the same age. Interpret the OR.
b. Suppose a test was carried out for the hypothesis H0 : β3 = 0 in the above model and yielded a p-value of
0.25. The estimate of β1 without X3 in the model is 1.361. Would you use the model with or without X3?
Explain.
Variable ˆj
β
Abnormal ECG 0.262
Hypertension 0.650
Age 0.058
High cholesterol 0.150
Smoker 1.131
3. The following data set is adapted from a study to assess the relationship of several factors to low birth
weight. The study was carried out at a single medical center. Outcome of pregnancy was classified into
three groups: very low birth weight (< 2000 g), low birth weight (2000–2499 g) and normal (≥ 2500 g).
Several factors thought to affect birth weight were also collected. A total of 100 subjects are included in the
data set.
Variable Columns
1. Age of mother (yrs) 2-3
2. Weight of mother at last menstrual period (lbs) 5-7
3. Smoking status during pregnancy (1=yes, 0=no) 9
4. History of premature labor (Number of events) 11
5. History of hypertension (1=yes, 0=no) 13
6. Presence of uterine irritability (1=yes, 0=no) 15
7. Number of physician visits during the first trimester 17
8. Birth weight outcome (l=very low, 2=low, 3=normal) 19
The data set LBW.DAT and the SAS code is posted on Canvas.
a. Evaluate the relationships of variables 1 through 7 with birth weight outcome where the dependent
variable of interest is categorized as normal vs. low or very low. Assess each relationship adjusting for
all other variables. You will need to recode birth weight outcome as 0 for normal and 1 for very low or
low.
b. For each variable, the adjusted odds ratio, confidence interval and p-value should be recorded and
arranged in a table. In your table use a 5-year interval for maternal age and a 50lb interval maternal
weight. For variable(s) significantly related to birth weight, give an interpretation of the relationship(s)
stating the direction and magnitude.
c. Estimate the OR comparing a 28 year old mother who weighs 155lbs at her last menstrual period with
history of hypertension to a 33 year old mother who weighs 125lbs with no history of hypertension,
adjusting for all other variables. Interpret your estimate.
4. A study carried out at the University of Iowa examined potential risk factors for clinical outcome in patients
with a particular type of lymphoma. Multiple logistic regression models were fitted to assess the relationship
of the probability of complete response to several variables shown below.
Variables
Sex: 1=Female, 0=Male
Age (yrs): continuous
Symptoms: 1=A, 0=B
Marrow involvement: 1=No, 0=Yes
LDH: continuous on log10 scale
The regression coefficients and log likelihoods from fitting 4 models on 50 patients using various subsets of
the above variables are shown below.
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