Deck 6: Count Data

Question 1

Suppose the event rate of cavity per child-tooth is 0.6. If a child has 3 teeth, how many cavities are likely to be observed in this child? Explain.

Answer 1

It is likely to observe 0.6*3=1.8~2 cavities in this child's mouth

Question 2

Fill in the age-specific rates and calculate the age-adjusted rate based on them.

Answer 2

The age-specific rates are 0.05, 0.04, and 0.08 for age group <30, 30-30, and >50, respectively. The age-adjusted rate is 0.05*0.22+0.04*0.44+0.08*0.33=0.034or 3.4 per 100 persons.

Question 3

Choose the appropriate summary statistic (mean, event rate, or proportion) for the following scenarios. Explain why it is appropriate and how it could be applied.
a.Data on farm injuries are collected over a 10-year period. Describe the number of farm injuries per year that require hospitalization.
b.Data were collected at a sleep clinic to better understand the variables associated with waking during the night. Describe the number of patients who wake up more than once in a night.
c.Surveys were used to investigate smoking patterns in a group of osteoporotic women. At baseline, participants who currently smoked were asked to provide the average number of cigarettes smoked in a day. Describe the average number of cigarettes smoked per day.

Answer 3

a.Event rate. The numerator of the event rate is the total number of farm injuries requiring hospitalizations during the time period. The denominator is the total number of farmers at risk-requires an estimate of the number of farmers at risk for each year of observation. If this is not available, an "average" number of farmers for a year can be multiplied by 10. The event rate is appropriate because farmers could be injured multiple times.
b.Proportion. Number of patients waking up more than once per night/total number of patients in the study. Patients either wake up more than once per night or not.
c.Mean=sum of the average number of cigarettes smoked per day/total number of participants.

Question 4

Consider your own area of research. Provide an example where it would be appropriate to use Poisson regression. Defend your answer.

Question 5

When the event rate is of interest, which of the following equations represents the Poisson regression model? (µ=true mean count of events, t=subject years)

A) µ/t =α+β₁x₁+β₂x₂+ · · · +βK^xK
B) µ-t =α+β₁x₁+β₂x₂+ · · · +βK^xK
C) logit(µ/t) =(α+β₁x₁+β₂x₂+ · · · +βK^xK)
D) ln(µ) =α+β₁x₁+β₂x₂+ · · · +βK^xK + ln(t)

Question 6

Age-adjusted event rates are used to

A) Correct event rates for measurement errors in age.
B) Determine an event rate for each age group.
C) Compare event rates for different populations.
D) Compare event rates of the same age group.

Question 7

A pharmaceutical company was mandated by the FDA to conduct a long-term safety study to investigate the rate of seizures for patients who used drug AA. Patients with any exposure to the drug were observed for a 5-year period. A Poisson regression analysis was done to determine the relationship of race and time on drug (days) on seizure rates. Provide a summary of the results for the report to the FDA.

Question 8

Which of the following equations represents the Poisson regression model? (µ=true mean count of events)

A) µ =a+b1x1+b2x2+ · · · +bKxK
B) ln(µ)=a+b1x1+b2x2+ · · · +bKxK
C) logit(µ)=a+b1x1+b2x2+ · · · +bKxK
D) exp(µ)=a+b1x1+b2x2+ · · · +bKxK

Question 9

Consider a Poisson regression model ln(µ/t)=a+b?(female)+ b?(age), where the outcome variable is the number of motorcycle accidents during the past 10 years. Using data from a national injury surveillance system, the following table results from performing the Poisson regression:
a. Compute an estimate for the adjusted rate ratio associated with gender.
b. Provide a 95% CI for the adjusted rate ratio.
c. Using the answers from (a) and (b), provide a summary conclusion.

Question 10

The association between birth defects and smoking during pregnancy is investigated in a low SES population. Vital statistics records were used to determine the number of pregnancies that resulted in birth defects. Suppose that 4 birth defects were observed in a total of 2050 pregnancies. What would be the birth defect rate? What is the event rate per 1000 pregnancies?

Question 11

Which of the following should be considered as a count variable?

A) birth weight
B) number of hours worked
C) blood pressure
D) employment status

Question 12

Which of the following does NOT characterize the Poisson regression model?

A) It utilizes least squares method to estimate parameters.
B) It can be used to model count response variables.
C) It can be used to model rate data.
D) It assumes that the mean and the variance of the outcome are the same.

Question 13

A study was performed to investigate disease relapses between two groups of Crohn's disease patients. All subjects entered the study with the disease under control. Suppose 18 patients in group A experienced relapses, and only 5 patients in group B experienced relapses. Why would it be incorrect to say that patients in group A have higher risks of relapse than those in group B? What information do we need to make a justified comparison?

Question 14

Define overdispersion. What are the consequences of overdispersion?

Question 15

Consider a study where the goal is to determine the association between lung cancer and crystalline silica exposures adjusting for other risk factors. When the p-value associated with age is 0.4532, the researcher decided to keep age in the model. Why?

Question 16

A study is conducted to investigate the incidence of second myocardial infarction (MI). After having the first MI, 40 subjects are followed. With the exception of three patients, all subjects were observed for 10 years. The three exceptions contributed 1.5, 5.3, and 7.5 years. What are the total person-years in the study? If there were 3 events during this study, what is the event rate?

Question 17

Provide an example when it would be more appropriate to use negative binomial regression instead of Poisson regression to investigate a relationship between an outcome and an explanatory variable(s). Explain.

Question 18

A law enforcement database was used to collect the number of driving under the influence (DUI) and alcohol-related incidents as well as the number of motor vehicle crashes for each county in the region. Counties were ranked according to alcohol experiences (none/sparse, low, moderate, high). A Poisson regression was used to investigate the relationship between the number of motor vehicle crashes and the alcohol ranking. The results of a Poisson regression indicated that counties in the high alcohol ranking had a 40% increase in the rate of motor vehicle crashes. However, when the analysis was repeated and additional variables (rural/urban, percentage of population between 16 and 25) were included in the model, the difference in the rate of crashes was no longer significant. What could explain this scenario?

Question 19

The objective of a study is to determine the surgery mortality rate. It was well speculated that age is a confounder. Thus, the investigator would like to estimate the death rate by controlling for age effect. Explain which methods, age-adjusted rates or Poisson regression with age adjustment, would you use? Explain and justify your choice.

Question 20

What techniques can be used to detect overdispersion?