Chapter 19

Other Useful Kinds of Regression

IN THIS CHAPTER

Using Poisson regression to analyze counts and event rates

Getting a grip on nonlinear regression

Smoothing data without making any assumptions

This chapter covers regression approaches you’re likely to encounter in biostatistical work that are not

covered in other chapters. They’re not quite as common as straight-line regression, multiple

regression, and logistic regression (described in Chapters 16, 17, and 18, respectively), but you

should be aware of them. We don’t go into a lot of detail, but we describe what they are, the

circumstances under which you may want to use them, how to execute the models and interpret the

output, and special situations you may encounter with these models.

Note: We also don’t cover survival regression in this chapter, even though it’s one of the most

important kinds of regression analysis in biostatistics. Survival analysis is the theme of Part 6 of this

book, and is the topic of Chapter 23.

Analyzing Counts and Rates with Poisson

Regression

Statisticians often have to analyze outcomes consisting of the number of occurrences of an event over

some interval of time, such as the number of fatal highway accidents in a city in a year. If the

occurrences seem to be getting more common as time goes on, you may want to perform a regression

analysis to see whether the upward trend is statistically significant (meaning not due to natural random

fluctuations). If it is, you may want to create an estimate of the annual rate of increase, including a

standard error (SE) and confidence interval (CI).

Some analysts use ordinary least-squares regression as described in Chapter 16 on such data, but event

counts don’t really meet the least-squares assumptions, so the approach is not technically correct.

Event counts aren’t well-approximated as continuous, normally-distributed data unless the counts are

very large. Also, their variability is neither constant nor proportional to the counts themselves. So

straight-line or multiple least-squares regression is not the best choice for event count data.

Because independent random events like highway accidents should follow a Poisson distribution (see

Chapter 24), they should be analyzed by a kind of regression designed for Poisson outcomes. And —

surprise, surprise — this type of specialized regression is called Poisson regression.

Introducing the generalized linear model

Most statistical software packages don’t offer a command or function explicitly called Poisson

regression. Instead, they offer a more general regression technique called the generalized linear