Logistic regression

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  • Use this as an introduction to logistic regression using the transition from the chi-square test. Note that the chi-square test performs an overall hypothesis test of whether physician proportion of VTE prophylaxis, but it does not tell you which physicians are necessarily significantly different.Ask the question about whether physician 8 is significantly different than physician 3In this example, physician 3 was chosen as the reference physician since they have the highest rate. You can choose any physician you like, but I suggest choosing the highest for comparison.Logistic regression not only performs an overall test of hypothesis about whether all the proportions are equal, but it conducts a hypothesis test of each variable (physician in this case) and produces a p-value. Therefore, you are able to ascertain which physicians are significantly different from the reference physician. Used the Surgical_VTE.MPJ dataset for this example.
  • Note that chi-square response variable is not necessarily limited to a binary variable.Minimum sample size rule of thumb is 10 observations per explanatory variable in the model.
  • The null hypothesis states that none of the explanatory variables have a statistically significant effect on the response variable
  • The mean response of the binary logistic regression model is the probability that Y=1 (Neter page 568). Or put another way it represents the proportion of observations (patients) that have the outcome of interest (Hosmer/Lemeshow page 20)Odds Ratio = eB1. e = exponentiate (2.718) the coefficient
  • It is a measure of association. It quantifies how much more likely (>1) or unlikely (<1) it is for the outcome to be present among those with x=1 than among those with x=0.The odds ratio = eCoef and ln (odds ratio) = Coef: when the independent variable is coded as 0 and 1.The odds ratio confidence intervals are derived as Coef ± 1.96(SE Coef) then exponentiate (eCoef) the end points.e = 2.71828183
  • The reference category has an odds ratio of 1 (HosmerLemeshow page 57).
  • The class should perform the data screening prior to conducting the analysis.Note that in the previous analysis we discovered that receiving and interpreting an initial ecg with 10 minutes significantly improved the chance of receiving a thrombolytic within 30 minutes. So the question becomes: what factors effect time to initial ECG?The QI team now can begin to analyze factors that effect whether an initial ecg is conducted and evaluated within 10 minutes.
  • Potentially hook up to one person’s computer and review results. Shift 3 actually has a univariate higher proportion, but the odds ratio is <1 in a multivariate environment. If you conduct the analysis with shift as one variable, the shift 1 and 2 have odds ratios <1, but when add other variables it changes – especially with the addition of the dedicated ecg tech variable. Implying that use of the ecg tech may be inconsistent across shifts.Ask attendees to explain parts of the output. The overall null hypothesis is rejected. Overall the model fits the data.QI Implications: Investigate the following: Why is there a difference in sex and race? Why doesn’t the ecg protocol have a significant impact on ecg within 10 minutes? Why don’t patients with chest pain have a significant impact on getting an ecg within 10 minutes?Looks like need to use dedicated ecg tech more consistently and review and or revise the protocol and train clinicians on the protocol. Understand either if the protocol is not being used or if it being used incorrectly.
  • Potentially hook up to one person’s computer and review results. Shift 3 actually has a univariate higher proportion, but the odds ratio is <1 in a multivariate environment. If you conduct the analysis with shift as one variable, the shift 1 and 2 have odds ratios <1, but when add other variables it changes – especially with the addition of the dedicated ecg tech variable. Implying that use of the ecg tech may be inconsistent across shifts.Ask attendees to explain parts of the output. The overall null hypothesis is rejected.QI Implications: Investigate the following: Why is there a difference in sex and race? Why doesn’t the ecg protocol have a significant impact on ecg within 10 minutes? Why don’t patients with chest pain have a significant impact on getting an ecg within 10 minutes?Looks like need to use dedicated ecg tech more consistently and review and or revise the protocol and train clinicians on the protocol. Understand either if the protocol is not being used or if it being used incorrectly.
  • Logistic regression

    1. 1. HealthCare Quality Improvement Solutions© 2012 by HealthCare Quality Improvement Solutions, LLC
    2. 2. • Answers the question about whether the proportions of multiple factors are significantly different  For example, a question could be formulated as: – Is there a significant difference in the proportion of AMI patients receiving Primary PCI within 90 minutes of hospital arrival among the following factors: » Gender, » Race, » Arrival Shift, » Arrival Day of Week, » Chest Pain, » Left Bundle Branch Block? • Logistic 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 2© 2012 by HealthCare Quality Improvement Solutions, LLC
    3. 3. 3© 2012 by HealthCare Quality Improvement Solutions, LLC
    4. 4. • Data type required  Response Variable  Categorical (Binary) – Data that is classified into two mutually exclusive categories » For example:  Primary PCI Received Within 90 Minutes of Hospital Arrival: Yes vs. No  Beta Blocker on Arrival: Yes vs. No  ACEI or ARB at Discharge: Yes vs. No  Explanatory Variable  Continuous variables can be used, but the focus of this modulte is on using categorical variables  Categorical – Data that is classified into mutually exclusive categories » For example:  Gender – male or female  Ethnicity– hispanic, asian, caucasian  Discharge Status – Home, SNF, Nursing Home, Expired 4© 2012 by HealthCare Quality Improvement Solutions, LLC
    5. 5. • Assumptions:  Patients are selected randomly  The factor categories are independent  The outcome of one factor category has no influence on the outcome of the other factor category 5© 2012 by HealthCare Quality Improvement Solutions, LLC
    6. 6. • Question:  Is there a significant difference in the proportion of AMI patients receiving Fibrinolytic Therapy within 30 minutes of hospital arrival among the following factors:  Arrival Shift,  Initial ECG within 10 minutes? • Null & Alternate Hypotheses:  H0: None of the comparisons are statistically significant  HA: At least one comparison is statistically significant • Level of Significance:  0.05 6© 2012 by HealthCare Quality Improvement Solutions, LLC
    7. 7. 7© 2012 by HealthCare Quality Improvement Solutions, LLC
    8. 8. • This portion of the output depicts the P-Value associated with the Null & Alternate Hypotheses:  H0: None of the comparisons are statistically significant  HA: At least one comparison is statistically significant • Level of Significance:  0.05 8© 2012 by HealthCare Quality Improvement Solutions, LLC
    9. 9. P-Value • What is the answer to the question:  Is there a significant difference in the proportion of AMI patients receiving Fibrinolytic Therapy within 30 minutes of hospital arrival among the following factors:  Arrival Shift,  Initial ECG within 10 minutes? • Level of Significance:  0.05 • What are the quality improvement implications? 9© 2012 by HealthCare Quality Improvement Solutions, LLC
    10. 10. • For binary explanatory variables the Odds Ratio represents the likelihood of experiencing the outcome when the explanatory variable is present (Code 1) compared to when it is absent (Code 0) • For example,  Patients that receive an initial ECG within 10 minutes (Code 1) are 4.23 times more likely to receive Fibrinolytic Therapy within 30 minutes compared to patients who do not receive an initial ECG within 10 minutes (Code 0)  While holding the other explanatory variables constant 10© 2012 by HealthCare Quality Improvement Solutions, LLC
    11. 11. • For indicator variables the Odds Ratio represents the likelihood of experiencing the outcome when the explanatory variable is present compared to the reference category - which has an Odds Ratio of 1.00 • For example,  Patients that arrive on the evening shift (C_ARRIVAL_SHIFT_2) are only 0.11 times as likely to receive Fibrinolytic Therapy within 30 minutes compared patients that arrive on the day shift  While holding the other explanatory variables constant • When interpreting indicator variables the comparison is to the reference category  For Arrival Shift the reference category is the day shift (C_ARRIVAL_SHIFT_1) 11© 2012 by HealthCare Quality Improvement Solutions, LLC
    12. 12. • Question:  Which of the following factors significantly impact receiving an initial ECG within 10 minutes:  Sex, Race, Arrival Shift, Dedicated ECG Technician, ECG Protocol, Patients presenting with chest pain? • Null & Alternate Hypotheses:  H0: None of the factors are statistically significant  HA: At least one factor is statistically significant • Level of Significance:  0.05 12© 2012 by HealthCare Quality Improvement Solutions, LLC
    13. 13. • Null & Alternate Hypotheses:  H0: None of the factors are statistically significant  HA: At least one factor is statistically significant • Which hypothesis do you accept? 13© 2012 by HealthCare Quality Improvement Solutions, LLC
    14. 14. • What is the answer to the question:  Which of the following factors significantly impact receiving an initial ECG within 10 minutes:  Sex, Race, Arrival Shift, Dedicated ECG Technician, ECG Protocol, Patients presenting with chest pain? • What are the quality improvement implications? 14© 2012 by HealthCare Quality Improvement Solutions, LLC
    15. 15. HealthCare Quality Improvement Solutions Robert Sutter Contact Information Email: rdsutterjr@gmail.com Website: https://sites.google.com/site/robertsutterrnmbamha/© 2012 by HealthCare Quality Improvement Solutions, LLC

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