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From |
"Visintainer, Paul" <Paul.Visintainer@baystatehealth.org> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Hosmer Lemeshow table incorrectly reported probabilities? |

Date |
Fri, 26 Aug 2011 10:21:22 -0400 |

<> Matthew, you can replicate the H-L cutpoints to see how it's generating the categories and the expected values: .sysuse auto Run a logistic and generate the predicted probabilities: .qui logistic foreign price trunk mpg .predict phat Create 5 groups (or 10 for the H-L test) of approximately equal size: .xtile group=phat, nq(5) Find the maximum predicted probability for each group (the cutpoint for each group) (I rounded this to match the H-L table output): .egen cutpoint=max(round(phat,.0001)), by(group) Generate the expected counts within groups (I rounded this to match the H-L table): .egen x=total(phat), by(group) .gen Exp_1=round(x,.1) Then, just tabulate your output and compare it to the H-L table: .estat gof, group(5) table .tab cutpoint // <-- "cutpoint" is given as "Prob" in the H-L table .tab Exp_1 Exp_0 is the difference between the group total and Exp_1. The whole thing looks like this: .sort phat .bys group: list phat foreign The H-L test is simply creating approximately equal groups of size n, then summing the predicted probabilities within each group to find the expected probability. The observed counts are compared to the expected counts. Paul ________________________________________________ Paul F. Visintainer, PhD Baystate Medical Center Springfield, MA 01199 -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Matthew Baldwin, MD Sent: Thursday, August 25, 2011 5:41 PM To: statalist@hsphsun2.harvard.edu Subject: st: Hosmer Lemeshow table incorrectly reported probabilities? Dear Statlisters, I created a logistic regression model that predicts mortality. I am examining the model's calibration, and the predicted probabilities for quintiles of risk seem to be incorrectly calculated using STATA. Using the code "gof, group(5), table" gives me the 5 groups used for the Hosmer-Lemeshow Chi squared test used to test model calibration and gives predicted probabilities (in this case, probability of death), observed and expected counts for both outcomes (deaths in this case), and totals for each group. However, the expected probabilities that the "estat gof, group(5) table" code in STATA gives are different from the expected probabilities I calculate from the expected counts in the table itself. I am confused about this: Logistic model for death2, goodness-of-fit test (Table collapsed on quantiles of estimated probabilities) +--------------------------------------------------------+ | Group | Prob | Obs_1 | Exp_1 | Obs_0 | Exp_0 | Total | |-------+--------+-------+-------+-------+-------+-------| | 1 | 0.0958 | 15 | 20.1 | 296 | 290.9 | 311 | | 2 | 0.1757 | 47 | 41.7 | 264 | 269.3 | 311 | | 3 | 0.3006 | 66 | 73.3 | 245 | 237.7 | 311 | | 4 | 0.4494 | 119 | 114.8 | 192 | 196.2 | 311 | | 5 | 0.9328 | 183 | 180.2 | 127 | 129.8 | 310 | +--------------------------------------------------------+ number of observations = 1554 number of groups = 5 Hosmer-Lemeshow chi2(3) = 3.46 Prob > chi2 = 0.3265 Here are my calculations for expected probabilities based on the table: x (expected mortality) y (observed mortality) 20.1/311 = 0.065 15/311 = 0.048 41.7/311 = 0.13 47/311 = 0.15 73.3/311 = 0.24 66/311 = 0.21 114.8/311 = 0.37 119/311 = 0.38 180.2/310 = 0.58 183/310 = 0.58 Can anyone explain how the expected probabilities in the table were derived? Is the "gof, group(x) table" function in STATA reporting incorrect expected probabilities? Thanks, Matthew Baldwin, MD Department of Pulmonary, Allergy, and Critical Care Medicine New York Presbyterian Hospital Columbia University College of Physicians and Surgeons * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ ---------------------------------------------------------------------- Please view our annual report at http://baystatehealth.org/annualreport CONFIDENTIALITY NOTICE: This e-mail communication and any attachments may contain confidential and privileged information for the use of the designated recipients named above. If you are not the intended recipient, you are hereby notified that you have received this communication in error and that any review, disclosure, dissemination, distribution or copying of it or its contents is prohibited. If you have received this communication in error, please reply to the sender immediately or by telephone at 413-794-0000 and destroy all copies of this communication and any attachments. For further information regarding Baystate Health's privacy policy, please visit our Internet site at http://baystatehealth.org. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Hosmer Lemeshow table incorrectly reported probabilities?***From:*"Matthew Baldwin, MD" <mrb45@columbia.edu>

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