1 chapter 16 logistic regression analysis. 2 content logistic regression conditional logistic...

Chapter 16 logistic RegressionAnalysis

ContentLogistic regression Conditional logistic regression Application

Purpose: Work out the equations for logistic regression which are used to estimate the dependent variable (outcome factor) from the independent variables (risk factors). Logistic regression is a kind of nonlinear regression.Data: 1.The dependent variable is a binary categorical variable that has two values such as "yes" and "no. 2.All of the independent variables, at least, most of which should be categories. Of course, some of them can be numerical variable. The categorical variable should be quantified.

Implication: Logistic regression can be used to study the quantitative relations between the happening of some diseases or phenomena and many risk factors. There are some demerits to use test (or u test ): 1. can only study one risk factor. 2. can only educe the qualitative conclusion.

Category:1.Between-subjects (non-conditional) logistic regression equation2. Paired (conditional) logistic regression equation

1 logistic regression non-conditional logistic regression

I Basic ConceptionThe probability of positive outcome under the function of m independent variables can be marked like this:

If: Regression modelProbability: P01logitP Scale:
While
is the constant term
is the coefficient of regression
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1
0.01799
0.01889
0.01984
0.02084
0.02188
0.02298
0.02413
0.02533
0.0266
0.02792
0.02931
0.03077
0.0323
0.0339
0.03557
0.03733
0.03917
0.04109
0.04311
0.04522
0.04743
0.04974
0.05215
0.05468
0.05732
0.06009
0.06297
0.06599
0.06914
0.07243
0.07586
0.07944
0.08317
0.08707
0.09112
0.09535
0.09975
0.10433
0.1091
0.11405
0.1192
0.12455
0.13011
0.13587
0.14185
0.14805
0.15447
0.16111
0.16798
0.17509
0.18243
0.19
0.19782
0.20587
0.21417
0.2227
0.23148
0.24049
0.24974
0.25923
0.26894
0.27888
0.28905
0.29943
0.31003
0.32082
0.33181
0.34299
0.35434
0.36586
0.37754
0.38936
0.40131
0.41338
0.42556
0.43782
0.45017
0.46257
0.47502
0.4875
0.5
0.5125
0.52498
0.53743
0.54983
0.56218
0.57444
0.58662
0.59869
0.61064
0.62246
0.63414
0.64566
0.65701
0.66819
0.67918
0.68997
0.70057
0.71095
0.72112
0.73106
0.74077
0.75026
0.75951
0.76852
0.7773
0.78583
0.79413
0.80218
0.81
0.81757
0.82491
0.83202
0.83889
0.84553
0.85195
0.85815
0.86413
0.86989
0.87545
0.8808
0.88595
0.8909
0.89567
0.90025
0.90465
0.90888
0.91293
0.91683
0.92056
0.92414
0.92757
0.93086
0.93401
0.93703
0.93991
0.94268
0.94532
0.94785
0.95026
0.95257
0.95478
0.95689
0.95891
0.96083
0.96267
0.96443
0.9661
0.9677
0.96923
0.97069
0.97208
0.9734
0.97467
0.97587
0.97702
0.97812
0.97916
0.98016
0.98111
0.98201
1
0.5
P
Z
Sheet1
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-3.90.01984
-3.850.02084
-3.80.02188
-3.750.02298
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-3.60.0266
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-3.40.0323
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-3.30.03557
-3.250.03733
-3.20.03917
-3.150.04109
-3.10.04311
-3.050.04522
-30.04743
-2.950.04974
-2.90.05215
-2.850.05468
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-2.750.06009
-2.70.06297
-2.650.06599
-2.60.06914
-2.550.07243
-2.50.07586
-2.450.07944
-2.40.08317
-2.350.08707
-2.30.09112
-2.250.09535
-2.20.09975
-2.150.10433
-2.10.1091
-2.050.11405
-20.1192
-1.950.12455
-1.90.13011
-1.850.13587
-1.80.14185
-1.750.14805
-1.70.15447
-1.650.16111
-1.60.16798
-1.550.17509
-1.50.18243
-1.450.19
-1.40.19782
-1.350.20587
-1.30.21417
-1.250.2227
-1.20.23148
-1.150.24049
-1.10.24974
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-10.26894
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-0.90.28905
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-0.70.33181
-0.650.34299
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-0.550.36586
-0.50.37754
-0.450.38936
-0.40.40131
-0.350.41338
-0.30.42556
-0.250.43782
-0.20.45017
-0.150.46257
-0.10.47502
-0.050.4875
00.5
0.050.5125
0.10.52498
0.150.53743
0.20.54983
0.250.56218
0.30.57444
0.350.58662
0.40.59869
0.450.61064
0.50.62246
0.550.63414
0.60.64566
0.650.65701
0.70.66819
0.750.67918
0.80.68997
0.850.70057
0.90.71095
0.950.72112
10.73106
1.050.74077
1.10.75026
1.150.75951
1.20.76852
1.250.7773
1.30.78583
1.350.79413
1.40.80218
1.450.81
1.50.81757
1.550.82491
1.60.83202
1.650.83889
1.70.84553
1.750.85195
1.80.85815
1.850.86413
1.90.86989
1.950.87545
20.8808
2.050.88595
2.10.8909
2.150.89567
2.20.90025
2.250.90465
2.30.90888
2.350.91293
2.40.91683
2.450.92056
2.50.92414
2.550.92757
2.60.93086
2.650.93401
2.70.93703
2.750.93991
2.80.94268
2.850.94532
2.90.94785
2.950.95026
30.95257
3.050.95478
3.10.95689
3.150.95891
3.20.96083
3.250.96267
3.30.96443
3.350.9661
3.40.9677
3.450.96923
3.50.97069
3.550.97208
3.60.9734
3.650.97467
3.70.97587
3.750.97702
3.80.97812
3.850.97916
3.90.98016
3.950.98111
40.98201
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Sheet3

The meaning of model parameter By constant we mean the natural logarithm of likelihood ratio between happening and non-happening when exposure dose is zero. By regression coefficient we mean the change of logitP when the independent variable changes by one unit.

The statistical indicator--odds ratio which is used to measure the function of risk factor in the epidemiology ,the formula of computation is: Odds ratio (OR)
In the formula ,
is the incidence of a disease when
is
,and
is the incidence of a disease when
is
.
is called odds ratio when many variables had been adjusted, it show the function of the risk factors without the influence of the other independent variables.
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_1208683399.unknown
_1208683450.unknown
_1208683486.unknown
_1208683415.unknown
_1208683343.unknown
_1077608162.unknown

The relationship with logistic P
Comparing the conditions of disease when one risk factor has two different exposure levels (
,
), the natural logarithm of Odds Ratio is:
_1077608069.unknown
_1077608080.unknown

We often think that
is an ineffective parameter, because there is no relationship between
and
.
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_1208781372.unknown
_1208781297.unknown

II the parametric estimation of logistic regression model parametric estimation Theorythe estimation of likelihood
_1077608381.unknown
_1079443675.unknown
_1081064387.unknown
_1077608256.unknown

2.Estimation of OR It can show the OR of two different levels c1c0 of one factor.
_1077608162.unknown
_1077608169.unknown
If the independent variable
only has two levelsthe exposur

1 chapter 16 logistic regression analysis. 2 content logistic regression conditional logistic...

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kind of nonlinear regression

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p01logitp scale

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