Poisson regression
Poisson regression is a statistical technique used to model count data, where the outcome variable represents the number of occurrences of an event within a fixed period of time or space. It assumes that these events follow a Poisson distribution, ________ _______ _______ _______ __________ ________ ___ ___ ________ ____ ______.
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Polytomous logistic models
A random sample of 250 patients was selected and their workout timing and diabetes status were recorded. The following table shows the workout timing and severity of diabetes:
| Workout (in minutes) | Severity of diabetes status | |||||||||
| Low | Moderate | High | ||||||||
| 0 −15 | 06 | 27 | 19 | |||||||
| 15 to 30 | 08 | 36 | 17 | |||||||
| 30 to 45 | 21 | 45 | 33 | |||||||
| ≥ 45 | 14 | 18 | 06 | |||||||
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 | |||
as the initial values of the parameters (solve only for one Iteration).
Explain the assumptions underlying multiple linear regression model.
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 loglog .
Poisson regression
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 |