A Practical Approach to Analyzing Healthcare Data, Fourth EditionChapter 4, Analyzing Categorical Variables

Susan White, PhD, RHIA, CHDA

ahima.org

Learning Objectives

Compare and contrast rates and proportions commonly used in healthcare

Relate the rates and proportions to the appropriate statistical methods

Illustrate commonly used descriptive and inferential statistics

ahima.org

Categorical Variables

Data elements that represent categories

Nominal (no natural order)

Ordinal (ordered)

Healthcare Examples

Gender

Discharge status

Dead/Alive

ahima.org

Rates and Proportions

Commonly used in healthcare

Mortality rates

Infection rates

Complication rates

Readmission rates

Must understand the numerator and denominator of each rate

Numerator – count of subjects that meet the criteria to be measured

Denominator – count of subjects that could meet the criteria to be measured

Example – 30 day readmission rate for COPD

Numerator – patients discharged with a principal diagnosis of COPD and readmitted within 30 days

Denominator – patients discharged with a principal diagnosis of COPD

Be aware of any exclusion criteria

Adults only?

Gender specific rates

Immune-compromised patients

ahima.org

Census Statistics

Inpatient census

Number of patients in the facility at a set point in time

Typically measured at midnight

Daily inpatient census

Number of patients in the facility at a set point in time plus any patients that were both admitted and discharged during that day

Resources are expended to treat patients that are admitted and discharged on the same day

May be a more relevant statistic that inpatient census for monitoring resource consumption

Inpatient service day

Inpatient service day for a particular day is equal to the daily inpatient census that that day

Average daily inpatient census

The number of inpatient service days averaged over a set time period.

Formula:

ahima.org

Example 1

The hospital inpatient census at midnight on January 15th is 102. Fifteen patients are admitted, three patients are discharged and one patient is admitted and subsequently dies on January 16th.

What is the inpatient census for January 16th?

102 + 15 – 3 = 114

How many inpatient service days were provided on January 16th?

102 + 15 – 3 + 1 = 115

(Note that the one patient admitted and discharged on the same day is included in the inpatient service days, but not present for the January 16th inpatient census count.)

ahima.org

Example 2

If the number of inpatient service days for the first calendar quarter of 2015 was 9,015, what was the average daily inpatient census for the quarter (round to the nearest 0.1 of a day)?

Step 1: Find number of days in period. First calendar quarter is January (31 days), February (28 days), March (31 days). Number of days = 31 + 28 + 31 = 90

Step 2: Divide the [inpatient service days] by the [number of days] in the period. 9015/90 = 100.2 days

ahima.org

Utilization Rates

Cesarean section rate:

Number of c-sections performed divided by number of deliveries

Note the denominator is the number of deliveries (not mothers) and includes both c-section and vaginal births

Inpatient occupancy rate

Inpatient service days divided by the number of bed days in the period

The number of bed days is the number of beds available for each day in the period measured

If the number of beds changes during the period, then that change must be reflected in the number of bed days.

Mortality Rates

Gross mortality rate – number of patients that died divided by the number of patients discharged during the period

Net mortality rate: number of patients that died at least 48 hours after admission divided by the number of patients discharges during the period

The net rate excludes patients that died within 48 hours of admission from the numerator.

Autopsy Rates

Gross autopsy rate – number of autopsies performed divided by the number of patients that died while in the hospital during a period

Net autopsy rate – number of autopsies performed divided by the number of bodies available for autopsy

The net rate excludes bodies that might be taken to the coroner for investigations from the denominator.

ahima.org

Example 3

If the number of inpatient service days for the first calendar quarter of 2015 was 9,015 and the facility had 120 beds available until closing 20 beds on March 1st, what was the inpatient bed occupancy rate for the quarter (round to the nearest 0.1)?

Step 1: Find the number of bed days.

Step 2: Divide inpatient service days by number of bed days:

9015/10180 = 0.886 or 88.6%

Month	Beds Available	Days	Bed Days
January	120	31	3,720
February	120	28	3,360
March	100	31	3,100
Total			10,180

ahima.org

Example 4

AMC Hospital discharged 256 patients during November. Ten of those patients died and 2 died on the same day as they were admitted. What are the gross and net mortality rates for AMC Hospital (round to the nearest 0.1 of a percent)?

Gross mortality rate

= 12/256 = 0.047 = 4.7%

Net mortality rate

= (12 – 2)/256 = 0.039 = 3.9%

ahima.org

Example 5

AMC Hospital discharged 256 patients during November. Ten of those patients died and 2 died on the same day as they were admitted. Four bodies were autopsied. One body was transferred to the coroner’s office for a criminal investigation. What are the gross and net autopsy rates for AMC Hospital (round to the nearest 0.1 of a percent)?

Gross autopsy rate

= 4/12 = 0.333 = 33.3%

Net autopsy rate

= 4/(12-1) = 4/11 = 0.364 = 36.4%

ahima.org

Census/Utilization Rates

ahima.org

Population Health and Epidemiology Rates

Epidemiology – study of patterns in disease occurrence and spread

Incidence rate –

Number of new cases of a disease divided by the population at risk for acquiring the disease

Prevalence rate –

Number of cases of the disease (both new and existing) divided by the population at risk for acquiring the disease

Point prevalence – prevalence of a disease at a particular point in time

Period prevalence – prevalence of a disease during a time period (month, year, etc.)

ahima.org

Example 6

The Department of Health in Center City is interesting in determining the effectiveness of the flu vaccine. They determined that there were 100 new flu cases during the month of January. The population of Center City was 15,000 during that month. What is the incidence rate of flu for Center City in January?

Incidence rate = 6.7 per 1,000

ahima.org

Example 7

The officials in Center City wanted to further study the impact of the flu on the population. There were 54 residents with the flu on January 31st and 10 residents with the flu on January 1st. Use this data and the fact that there were 100 new cases during the month of January to determine the point prevalence for January 31st and the period prevalence for the month of January.

(Note that period prevalence includes anyone with the disease during the period. Since 10 residents were sick with he flu on Jan 1st, they are included in the numerator of the period prevalence for January).

ahima.org

Descriptive Statistics: Proportions

Each subject either has or does not have the attribute to be counted (dead/alive, success/failure, yes/no)

Recode each observation as a binary variable (two values):

If attribute is present = 1

If attribute is not present = 0

The mean of the 0s and 1s is the proportion of subjects with the attribute

Simple example:

What proportion of patients are female?

Patient genders: M, M, F, F, M

Recode F = 1; M = 0

Recoded gender data: 0, 0, 1, 1, 0

Mean = 2/5 = 0.4 or 40% of patients are female

ahima.org

Descriptive Statistics

Frequency distribution

Appropriate for both nominal and ordinal categorical data

Typically the counts and percentages for each category are presented

ahima.org

Charts or Graphs

Since this subset of CPT codes is ordinal, the bar chart is a better representation.

Pie charts are a good choice for nominal data.

ahima.org

Contingency Tables

Used to display and analyze the relationship between two categorical variables

Notice in table below:

20/32 = 62.5% of female patients were discharged home

10/24 = 41.7% of male patients were discharged home

Is this just a random occurrence or is this evidence that there is a significant relationship between gender and being discharged to home?

A hypothesis test may be used to answer that question

ahima.org

Ranks and Percentiles

Ranks and percentile may be used to describe ordinal data

Ranks – the position of a value after the sample is ordered using order of magnitude – usually ascending (increasing) order

Percentile

AKA percentile rank

Points that divide the sample into 100 equal parts

Important percentile ranks:

25th percentile

AKA first quartile

25% of the values in the sample are less than the 25th percentile

50th percentile

AKA median or second quartile

50% of the values in the sample are less than the 50th percentile (50% are also greater)

75th percentile

AKA 3rd quartile

75% of the values in the sample are less than the 75th percentile

ahima.org

Inferential StatisticsHypothesis Testing Basics

Hypothesis test – statistical technique used to determine if the evidence (values) present in a random sample is strong enough to make a conclusion about the population

Null hypothesis (Ho) – status quo, requires no action

Example: Ho for Table 4.3 is that there is no relationship between gender and discharge to home

Alternative hypothesis (H1 or Ha) – complement of the null hypothesis, often referred to as the research hypothesis

Example: H1 for Table 4.3 is that there is a relationship between gender and discharge to home

Data is gathered from a random sample of a population to determine if the null hypotheses can be rejected

ahima.org

Hypothesis Testing Basics

Test statistic –

A statistic that is calculated to determine if the data values support

Must be compared to a known probability distribution to determine the making an error in deciding whether or not to reject the null hypothesis.

Type I error – incorrectly rejecting the null hypothesis when it is true

The alpha level or acceptable level of this error is set by the analyst prior to the start of the analysis of the data

The p-value is the smallest alpha level for which the null hypothesis would be rejected

If the p-value is smaller than the pre-set alpha level, then there is sufficient evidence to reject the null hypothesis

Type II error – incorrectly NOT rejecting the null hypothesis when it is false

this error may be controlled by the type of hypothesis test and the sample size used in the study

ahima.org

Hypothesis Testing Steps

Determine the null and alternative hypotheses

Set the acceptable type I error or alpha level

Select the appropriate test statistic

Compare the test statistic to a critical value based on the alpha level and the distribution of the test statistic

Reject the null hypothesis if the test statistic is more extreme than the critical value. If not, do not reject the null hypothesis.

ahima.org

Inferential Statistics:Proportions

Used to determine if a population proportion is higher or lower than a standard

May be interested in a one or two sided hypothesis

Two sided alternative: important to know if population of interest is higher or lower than standard

One sided alternative: only concerned about higher or lower, not both

Two sided

One sided

ahima.org

One-sample Z-test for proportions

Reject Ho

Reject null hypothesis when Z is extreme

ahima.org

Example: One-sample Z-test for proportions

Follow 5 basic steps in hypothesis testing:

1. Determine the null and alternative hypotheses:

Null hypothesis (Ho): p = 85 percent or 0.85

Alternative hypothesis (Ha): p ≠ 0.85

2. Set the acceptable type I error or alpha level

The company leaders are willing to accept a five percent error rate. Alpha = 0.05

3. Select the appropriate test statistic

Z is the appropriate test statistic

ahima.org

Example: One-sample Z-test for proportions (continued)

4. Compare the test statistic to a critical value based on alpha and the distribution of the test statistic

5. Reject the null hypothesis if the calculated test statistic is more extreme than the critical value. If not, then do not reject the null hypothesis

Since Ha is a two sided alternative (≠) we select the critical value associated with the alpha level divided by two. We want to protect against both higher and lower alternatives. We reject Ho if Z > 1.960 or Z < −1.960. Z = −1.36 is not less than −1.960, therefore do not reject the null hypothesis

Conclusion: The observed 70% rate from the sample of 10 employees is not sufficient evidence to reject the null hypothesis

ahima.org

Example: One-sample Z-test for proportions (continued)

ahima.org

Confidence Interval for Proportions

Confidence interval: a range of values based on a sample that contains a population value with a set level of confidence.

Common in political surveys

President’s approval rating is 60% +/- 5%

AKA margin of error (+/-5%)

The width of a confidence interval is a function of the proportion value and the sample size

Widest confidence interval (large margin of error) when p = 50%

Larger sample side results in a narrower confidence interval for a proportion

1.96 for 95% confidence interval

ahima.org

Example: Confidence Interval for Proportions

Conclusion: Based on the sample, we are 95% sure that the range 42% and 98% covers the true vaccination rate.

ahima.org

Two-sample Z-test for Proportions

Used to determine if the proportion for a particular attribute is higher or lower when comparing two populations

Is the mortality rate as Hospital A higher or lower than that in Hospital B?

May be a one-sided or two-sided test depending the desire to determine which population is higher or lower

ahima.org

Two-sample Z-test for Proportions

If Z > standard normal critical value at α/2, or Z < -(standard normal critical value at α/2), then reject Ho

Difference in sample proportions divided by standard error

Overall proportion when two samples are pooled together

ahima.org

Example: Two-sample Z-test for Proportions

Is the mortality rate for MS-DRG 292 (p1) different from that in MS-DRG 293 (p2)?

AC21620-Chapter4.pptx

image3.jpg

image4.png

image5.png

image6.png

image9.png

image7.png

image8.png

image10.png

image11.png

image12.png

image13.png

image14.png

image15.png

image16.png

image17.png

image18.png

image19.png

image20.png

image21.png

image22.png

image23.png

image24.png

image25.png

image26.png

image1.jpg

image2.jpg