Poisson regression
Poisson regression is a statistical method used to model the relationship between a count variable and one or more predictor variables. It is a type of generalized linear model that is particularly useful for analyzing count data, such as the number of accidents on a road per day, the number of ______ ______ _____ ________ ______ ____ _______.
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The following data on diagnosis of coronary heart disease (where 0 indicating absence and 1 indicating presence), serum cholesterol (in mg/dl), resting blood pressure (in mmHg) and weight (in kg) were obtained for 80 patients to explore the relationship of coronary heart disease with cholesterol and weight.
| S. No. | Serum Cholesterol (mg/dl) | Weight (kg) | Number of Patients having CHD | Total Number of Patients | |||
| 1 | 420 | 60 | 10 | 20 | |||
| 2 | 450 | 68 | 15 | 30 | |||
| 3 | 400 | 54 | 4 | 15 | |||
| 4 | 510 | 74 | 2 | 10 | |||
| 5 | 480 | 62 | 1 | 5 | |||
(i) Fit a multiple logistic model for the dependence of coronary heart disease on the average serum cholesterol and weight considering and
as the initial values of the parameters (solve only for one Iteration). (ii) Test the significance of the fitted model using Hosmer-Lemeshow test at 5% level of significance.
Polytomous logistic models
Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.
Describe censoring and differentiate between different types of censoring with the help of examples which are not considered in Block 4 of MSTE-004.
State whether the following statements are True or False. Give reason in support of your answer:
(a) The value of sensitivity of the following results of a diagnostic test is 0.85.
| Disease | Test result | Total | |||
| + | – | ||||
| Present | 170 | 30 | 200 | ||
| Absent | 20 | 280 | 300 | ||
| Lung Cancer | No Lung Cancer | Total | ||||||
| Smokers | 100 | 1220 | 1320 | |||||
| Non-smokers | 50 | 2260 | 2310 | |||||
(c) The logit link function is .
(d) We define three indicator/dummy variables for a regressor variable with three categories.
(e) Left censoring occurs whenever the exact time of occurrence of an event is not known.
A study was conducted on 185 patients aged more than 45 years which are followed until the time of death or up to 10 years, whichever comes first. The patients have different covariates: age, gender (male/female), systolic blood pressure, smoking (yes/no), total serum cholesterol and diabetes (yes/no). The objective of this study is to determine which covariate influences the survival time. An analysis is conducted to investigate differences in all-cause mortality between men and women participating in the study. Suppose we obtain the following results after applying the Cox regression hazard model analyses:
| Risk Factor | Parameter Estimate | SE | ||||
| Age | 0.150 | 0.010 | ||||
| Gender | 0.450 | 0.150 | ||||
| Systolic Blood Pressure | 0.015 | 0.008 | ||||
| Smoking | 0.650 | 0.170 | ||||
| Total Serum Cholesterol | 0.002 | 0.004 | ||||
| Diabetes | -0.350 | 0.250 | ||||
Explain the assumptions underlying multiple linear regression model.