BPD Bronchopulmonary Dysplasia by birth weight

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BPD (Bronchopulmonary Dysplasia) by birth weight
Proportion of BPD decreases with birthweight.
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Q Can we give a more precise functional form to
the relationship between the probability of
having BPD and birthweight?
Ans Yes, if exact birthweights rather than
birthweight categories are recorded.
By fitting a logistic regression model to the
dichotomous response BPD.
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Dichotomous Outcomes
BPD
No BPD
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Topic 18 Logistic regression
In linear regression, continuous Y
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Dichotomous Outcomes
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Logistic regression
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Plot of logistic
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Maximum likelihood estimation of the parameters
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Likelihood Ratio Test
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Logistic regression of BPD on birthweight Logit
estimates
Number of obs 223
W
62.42 (df1)
p value
0.0000 Log likelihood -111.86031
--------------------------------------------------
---------------------------------------
BPD Coef. Std. Err. z
Pgtz 95 Conf. Interval
-------------------------------------------------
--------------------------------------- birthwt
-.0042291 .0006409 -6.599 0.000
-.0054852 -.0029731 _cons 4.034291
.6957847 5.798 0.000 2.670578
5.398004 -----------------------------------------
-------------------------------------------------
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Logistic regression of BPD on birthweight Logit
estimates
Number of obs 223

W 62.42 (df1)
p
value 0.0000 Log likelihood
-111.86031 --------------------------------------
---------------------------------------- BPD
Odds Ratio Std. Err. z Pgtz
95 Conf. Interval ----------------------------
-------------------------------------------------
birthwt .9957798 .0006381 -6.599
0.000 .9945298 .9970313 -----------------
--------------------------------------------------
-----------
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Observed versus fitted