linear regression

© 2012 by HealthCare Quality Improvement Solutions, LLC

HealthCare Quality Improvement Solutions


• The t-Test and Mann-Whitney Test are univariate methods

Analyze one factor at a time

The effect of all factors simultaneously is not revealed

Limits understanding of the underlying process generating performance

• Multivariate analysis

Analyzes multiple factors simultaneously

Provides a more comprehensive understanding of the underlying process generating performance

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0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

t-test Multiple Linear Regression

P-Value

Average Time to Primary PCI

RACE C_ARRIVAL_SHIFT m_ecg_lbb a_cardiology_consult


• Answers the question about whether the averages of a multi-category (more than two) factor or multiple factors are significantly different For example, if ethnicity is a factor thought to effect Door-

to-Balloon time in AMI patients The question could be formulated as:

– Is there a significant difference in average Door-to-Balloon time between caucasian, hispanic and asian ethnic groups?

• Multiple Linear Regression is used to answer this question by testing the hypotheses: H0: None of the comparisons are statistically significant

HA: At least one comparison is statistically significant And producing a P-Value for the tests

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• Questions can also be answered that involve multiple factors For example, a question could be formulated as:

– Is there a significant difference in average AMI fibrinolytic administration time among the following factors:

» Chest Pain,

» Hx Stroke,

» LBB,

» Hx Hypertension,

» Gender,

» Age,

» Day-of-Week,

» Shift?

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• Data type required: Response Variable

Continuous – Data that can assume any numerical value over a range of values – For example:

» Pneumonia Antibiotic Timing can be measured in:

Hours Minutes Seconds

Explanatory Variable Continuous variables can be used, but the focus of this module is on

using categorical variables Categorical

– Data that can be assigned to a group » For example:

Sex – male or female Ethnicity– Caucasian, African American, Asian


• Question:

Is there a significant difference in average Pneumonia Antibiotic Timing among the following factors:

Arrival shift ,

Emergent admission type?

• Null & Alternate Hypotheses:

H0: None of the comparisons are statistically significant

HA: At least one comparison is statistically significant

• Level of Significance:

0.05

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• This portion of the output depicts the P-Value associated with the Null & Alternate Hypotheses:




0.05

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Regression

Coefficients

t-Test

P-Value

Potential Factors (AKA, explanatory

variables)


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• The regression coefficients represent the effect of the explanatory variable on the average of the response variable; While holding the other explanatory variables constant.

• A negative coefficient indicates a reduction in the response variable

• A positive coefficient indicates an increase in the response variable


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• Interpretation of the Regression Coefficient depends on the format of the explanatory variable:

Explanatory variables that are binary (recorded as 0 and 1);

The Regression Coefficient represents the effect on the average of the response variable when the explanatory variable is 1 compared to when the explanatory variable is 0.

– For example: Pneumonia patients with an Emergency Admission receive the initial antibiotic on average 14.3 minutes faster than patients who are not an Emergency Admission.


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Explanatory variables that are recorded as indicator variables:

The Regression Coefficient represents the effect on the average of the response variable when the explanatory variable is 1 compared to the reference category.

For example:

Pneumonia patients that arrive on the evening shift (..Shift_2) receive the initial antibiotic on average 24.5 minutes slower than patients arriving on the day shift.

Pneumonia patients that arrive on the night shift (..Shift_3) receive the initial antibiotic on average 14.5 minutes slower than patients arriving on the day shift.


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• The P-Values are the result of conducting a t-Test on each explanatory variable

• What are the null and alternate hypotheses?

C_ADMISSION_TYPE_EMERGENCY

H0: emergency average = non-emergency average

HA: emergency average ≠ non-emergency average

C-ARRIVAL_SHIFT_2

H0: evening average = day average

HA: evening average ≠ day average

C-ARRIVAL_SHIFT_3

H0: night average = day average

HA: night average ≠ day average

Note how each indicator explanatory variable is compared to the reference category


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• What is the answer to the question:

Is there a significant difference in average Pneumonia Antibiotic Timing among the following factors:

Arrival shift ,

Emergent admission type?

• What are the quality improvement implications?

Yes


• Question:

Which of the following factors significantly effect average AMI Time To ECG: Age, Day of Week, ECG Technician, Chest Pain?

• Null & Alternate Hypotheses:




0.05

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• What is the answer to the question:

Which of the following factors significantly effect average AMI Time To ECG: Age, Day of Week, ECG Technician, Chest Pain?

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• What are the quality improvement implications?

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HealthCare Quality Improvement Solutions

Robert Sutter Contact Information

Email: [email protected] Website: https://sites.google.com/site/robertsutterrnmbamha/

mailto:[email protected]

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linear regression

Documents

average time

average door

day shift

nonemergency average

day average note

arrival shift

explanatory variable

significant ha