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Creating a Propensity Score

The creation of a propensity score is based on a logistic regression with the dependent variable taking on the value of "1" if the individual is in the intervention group and "0" if the individual is in the comparison group, and with the potential confounders as the independent variables. The logistic regression is used to estimate the probability that, based on that individual�s potential confounders, that individual would be in the intervention or comparison group. Using the estimated coefficients from the logistic regression model and the measured potential confounders for an individual it is possible to calculate an estimated probability of being in the intervention group for each individual in the study. This estimated probability is called the propensity score for that individual.

The logistic regression determines the extent to which the potential confounders can predict whether an individual is in one group or the other, and provides an indication of the degree to which the groups are unbalanced on these confounders. The C-statistic from logistic regression provides a summary of the accuracy of the overall prediction based on the model and the coefficients for each of the independent variables provides an estimate of the effect of their independent effects.

Tables 1 and 2 contain the results of logistic regressions for Comparisons 1 and 2. For Comparison 1, a logistic regression model that contains no interaction results in a C-statistic of 0.875 indicating that the model can readily discriminate whether an individual is in the intervention or comparison group based on the potential confounders. This provides clear evidence that the groups are quite different in terms of these characteristics. The estimated odds ratio for the diagnosis of dementia is almost 18 indicating that this characteristic, even when one controls for other factors such as age and sex, is much more common in the intervention group than the comparison group. For Comparison 2, even a logistic regression with extensive interaction terms has a C-Statistic of 0.565 indicating that in this study the confounders are not very useful at discriminating between individuals with dementia who received atypical antipsyhcotics and those who received typical antipsyhoctics.

Propensity scores can be included as covariates in regression analyses, be used to define matches, or can be used to create strata. For the purposes of an example, the propensity scores were used to create strata. The results of the analysis of the association between hip fracture and atypical antipsychotic use within each of these strata are provided in a separate document.

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Table 1: Logistic regression for creation of propensity score
Comparison 1: Atypical users to non-users

Effect	Odds Ratio Estimate	Lower 95% CL	Upper 95% CL	Parameter Estimate	Standard Error	c statistic
Age, yrs	1.13	1.127	1.134	0.1227	0.00142	0.875
Age squared	0.992	0.992	0.992	-0.00804	0.000113
Male	1.082	1.054	1.111	0.0791	0.0135
Long acting benzodiazapine	1.505	1.406	1.611	0.4087	0.0347
Short acting benzodiazapine	3.691	3.599	3.786	1.306	0.0129
bisphosphonates	1.492	1.411	1.578	0.4	0.0285
oestrogen	1.022	0.968	1.079	0.0217	0.0277
alcoholism	2.039	1.921	2.164	0.7124	0.0305
Chronic Lung Disease (COPD)	1.063	1.033	1.093	0.0608	0.0145
Falls	1.286	1.228	1.347	0.2519	0.0235
Hyperparathyroidism	1.54	1.073	2.21	0.4319	0.1844
Hyperthyroidism	1.71	1.396	2.095	0.5365	0.1036
Obesity	0.905	0.843	0.971	-0.0998	0.036
Osteoporosis	1.031	0.984	1.08	0.0306	0.0236
Parkinsonism	2.554	2.44	2.674	0.9377	0.0233
Chronic renal failure	1.219	1.162	1.278	0.1977	0.0242
rheumatoid arthritis	0.88	0.833	0.93	-0.1278	0.0282
stroke	1.359	1.306	1.415	0.3071	0.0205
visual impairment	1.245	1.149	1.347	0.2188	0.0405
dementia	17.927	17.463	18.404	2.8863	0.0134

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Table 2: Logistic regression for creation of Propensity Score
Comparison 2: Atypical vs. Typical neuroleptics restricted to individuals with dementia

Effect	Parameter Estimate	Standard Error	Odds Ratio Estimate	Lower 95% CL	Upper 95% CL	c statistic
Age, yrs	-0.00274	0.00256	0.997	0.992	1.002	0.565
Age squared (age2)	-0.00131	0.000258	0.999	0.998	0.999
Male	0.8128	0.2389	2.254	1.411	3.6
Long acting benzodiazepine (LAB)	-0.5486	0.6065	0.578	0.176	1.897
Short acting benzodiazepine (SAB)	-0.5528	0.2215	0.575	0.373	0.888
bisphosphonate	0.6685	0.6717	1.951	0.523	7.278
oestrogen	1.6924	0.5576	5.433	1.821	16.205
alcoholism	-0.2528	0.4497	0.777	0.322	1.875
Chronic Lung Disease (COPD)	-0.4181	0.2573	0.658	0.398	1.09
Falls	-0.0866	0.3803	0.917	0.435	1.932
Obesity	0.0908	0.6722	1.095	0.293	4.089
Osteoporosis	0.0925	0.4567	1.097	0.448	2.685
Parkinsonism	0.5631	0.3663	1.756	0.857	3.6
Chronic renal failure (CRF)	-0.8932	0.4225	0.409	0.179	0.937
rheumatoid arthritis	0.2148	0.5273	1.24	0.441	3.485
stroke	-0.1779	0.3334	0.837	0.435	1.609
Visual impairment	-2.9099	0.8644	0.054	0.01	0.297
Interaction age male	-0.0104	0.00295	0.99	0.984	0.995
interaction age LAB	0.00304	0.00748	1.003	0.988	1.018
Interaction age SAB	0.00629	0.00273	1.006	1.001	1.012
Interaction age bisphosphonate	0.00785	0.00833	1.008	0.992	1.024
Interaction age oestrogen	-0.0166	0.00696	0.984	0.97	0.997
Interaction age alcoholism	0.00174	0.00549	1.002	0.991	1.013
Interaction age COPD	0.00622	0.00316	1.006	1	1.013
Interaction age falls	0.000248	0.00467	1	0.991	1.009
Interaction age obesity	-0.00469	0.00829	0.995	0.979	1.012
Interaction age osteoporosis	0.000791	0.00565	1.001	0.99	1.012
Interaction age Parkinsonism	-0.00778	0.00451	0.992	0.984	1.001
Interaction age CRF	0.0122	0.00518	1.012	1.002	1.023
Interaction age rheumatoid arthritis	-0.00524	0.00652	0.995	0.982	1.008
Interaction age stroke	0.00182	0.00407	1.002	0.994	1.01
Interaction age visual impairment	0.0357	0.0105	1.036	1.015	1.058
Interaction male age2	0.00128	0.000318	1.001	1.001	1.002
Interaction male LAB	-0.1816	0.1116	0.834	0.67	1.038
Interaction male SAB	-0.0331	0.0376	0.967	0.899	1.041
Interaction male bisphosphonate	-0.0421	0.1593	0.959	0.702	1.31
Interaction male alcoholism	-0.0466	0.0752	0.954	0.824	1.106
Interaction male COPD	-0.1126	0.043	0.893	0.821	0.972
Interaction male falls	0.0991	0.0607	1.104	0.98	1.244
Interaction male obesity	0.0854	0.1227	1.089	0.856	1.385
Interaction male osteoporosis	0.0344	0.0937	1.035	0.861	1.243
Interaction male Parkinsonism	0.1239	0.0612	1.132	1.004	1.276
Interaction male CRF	-0.024	0.0682	0.976	0.854	1.116
Interaction male rheumatoid arthritis	0.0561	0.0904	1.058	0.886	1.263
Interaction male stroke	-0.0648	0.0538	0.937	0.844	1.041
Interaction male visual impairment	-0.0801	0.1134	0.923	0.739	1.153
Interaction age2 LAB	0.000111	0.000879	1	0.998	1.002
Interaction age2 SAB	0.000288	0.000288	1	1	1.001
Interaction age2 bisphosphonates	-0.00066	0.000907	0.999	0.998	1.001
Interaction age2 oestrogen	0.000726	0.000806	1.001	0.999	1.002
Interaction age2 alcoholism	0.00079	0.000631	1.001	1	1.002
Interaction age2 COPD	-0.00036	0.000341	1	0.999	1
Interaction age2 falls	-0.00027	0.000456	1	0.999	1.001
Interaction age2 obesity	0.000829	0.000977	1.001	0.999	1.003
Interaction age2 osteoporosis	-0.00011	0.000585	1	0.999	1.001
Interaction age2 Parkinsonism	9.14E-06	0.000539	1	0.999	1.001
Interaction age2 CRF	-0.00085	0.000562	0.999	0.998	1
Interaction age2 rheumatoid arthritis	0.000359	0.000703	1	0.999	1.002
Interaction age2 stroke	-0.00006	0.000448	1	0.999	1.001
Interaction age2_visual impairment	-0.00121	0.000892	0.999	0.997	1.001