Impact of missing data mechanism on the estimate of change: a case study on cognitive function and polypharmacy among older persons

Figures & data

Figure 1 Flow diagram of the participants.

Table 1 Sample characteristics

Characteristic			Min	Max	N
Females, n (%)	548	(70)			781
Mean age* ± SD (Median)	81.7	±5.0 years (80.4)	75	98	781
Mean MMSE score ± SD (Median)
2004	24.6	±6.8 points (27.0)	0	30	770
2005	24.4	±7.3 points (27.0)	0	30	713
2006	23.9	±7.8 points (27.0)	0	30	657
2007	23.6	±8.0 points (26.0)	0	30	607
Mean number of drugs ± SD (Median)
2004	6.4	±3.8 drugs (6.0)	0	23	781
2005	6.9	±3.8 drugs (6.0)	0	23	717
2006	7.1	±3.7 drugs (7.0)	0	20	657
2007	7.1	±3.7 drugs (7.0)	0	20	609

Note:

* At the baseline examination, 2004.

Abbreviations: MMSE, Mini-Mental State Examination; SD, standard deviation; N, number of observations; Min, minimum; Max, maximum.

Figure 2 Latent growth curve model for Mini-Mental State Examination (MMSE) score under non-ignorable missing data assumption (Model 3).

Table 2 Fitted latent growth curve (LGC) models with or without explicit models for dropout under different missing data assumptions

Outcome in LGC model	Model	Missing data assumption	Explicit dropout model	Predictors in dropout model
MMSE	1	MAR	No	na
	2	MAR	Yes	Previous MMSE
	3	MNAR	Yes	Previous and current MMSE
	4	MNAR	Yes	Current MMSE
	5	MNAR	Yes	Previous and current MMSE, age, and sex
Number of drugs	6	MAR	No	na
	7	MAR	Yes	Previous number of drugs
	8	MNAR	Yes	Previous and current number of drugs
	9	MNAR	Yes	Current number of drugs
	10	MNAR	Yes	Previous and current number of drugs, age, and sex

Abbreviations: MMSE, Mini-Mental State Examination; MAR, missing at random; MNAR, missing not at random; na, not applicable.

Table 3 Estimation results from latent growth curve models for MMSE with and without logistic regression models for dropout, GeMS study, Kuopio, Finland, 2004–2007

	Ignorable missingness				Non-ignorable missingness
	Model 1		Model 2		Model 3		Model 4		Model 5
	Est	(SE)	Est	(SE)	Est	(SE)	Est	(SE)	Est	(SE)
Means
Level	24.62	(0.25)	24.61	(0.25)	24.57	(0.25)	24.59	(0.26)	24.59	(0.25)
Slope	−2.99	(0.23)	−2.87	(0.22)	−1.74	(0.27)	−2.66	(0.22)	−1.75	(0.31)
Variances
Level	43.10	(4.08)	42.22	(3.89)	43.06	(3.92)	43.20	(4.05)	42.88	(3.90)
Slope	18.52	(3.28)	18.67	(3.30)	18.16	(3.27)	16.57	(3.30)	17.73	(3.27)
Factor loadings
2004	0*		0*		0*		0*		0*
2005	0.236	(0.05)	0.241	(0.05)	0.329	(0.08)	0.240	(0.06)	0.317	(0.08)
2006	0.692	(0.05)	0.644	(0.05)	0.783	(0.10)	0.716	(0.06)	0.777	(0.11)
2007	1*		1*		1*		1*		1*
Cov (level, slope)	17.24	(2.15)	14.09	(2.01)	5.93	(2.34)	9.42	(1.89)	6.37	(2.51)
	OR	95% CI	OR	95% CI	OR	95% CI	OR	95% CI	OR	95% CI
Missing 2005 ON
MMSE 2004	na		0.93	0.91, 0.96	0.88	0.75, 1.04	na		0.87	0.68, 1.10
MMSE 2005	na		na		1.06	0.89, 1.26	0.94	0.92, 0.97	1.11	0.85, 1.45
Age	na		na		na		na		1.10	1.04, 1.16
Sex	na		na		na		na		0.66	0.37, 1.17
Missing 2006 ON
MMSE 2005	na		0.89	0.87, 0.92	0.32	0.22, 0.47	na		0.33	0.22, 0.51
MMSE 2006	na		na		2.65	1.84, 3.83	0.91	0.89, 0.93	2.64	1.74, 4.01
Age	na		na		na		na		1.16	1.04, 1.29
Sex	na		na		na		na		2.07	0.51, 8.48
Missing 2007 ON
MMSE 2006	na		0.92	0.89, 0.94	0.50	0.29, 0.86	na		0.52	0.28, 0.99
MMSE 2007	na		na		1.91	1.08, 3.40	0.93	0.90, 0.95	1.85	0.93, 3.69
Age	na		na		na		na		1.12	1.03, 1.21
Sex	na		na		na		na		0.46	0.21, 1.02
Number of free parameters	11		17		20		17		26
Log likelihood	−7,827.99		−8,410.61		−8,394.29		−8,477.00		−8,376.91
Scaling correction factor	4.227		2.967		2.888		2.943		2.583

Note:

* Fixed.

Abbreviations: MMSE, Mini-Mental State Examination; Est, estimate; SE, standard error; OR, odds ratio; CI, confidence interval; Cov, covariance; GeMS, Geriatric Multidisciplinary Strategy for the Good Care of the Elderly; na, not applicable; ON, regressed on.

Table 4 Estimation results from latent growth curve models for number of drugs in use with and without logistic regression models for dropout, GeMS study, Kuopio, Finland, 2004–2007

	Ignorable missingness				Non-ignorable missingness
	Model 6		Model 7		Model 8		Model 9		Model 10
	Est	(SE)	Est	(SE)	Est	(SE)	Est	(SE)	Est	(SE)
Means
Level	6.46	(0.14)	6.46	(0.14)	6.41	(0.14)	6.46	(0.14)	6.42	(0.14)
Slope	0.36	(0.04)	0.35	(0.04)	0.32	(0.04)	0.39	(0.04)	0.32	(0.04)
Variances
Level	10.66	(0.67)	10.51	(0.65)	10.45	(0.65)	10.71	(0.65)	10.47	(0.64)
Slope	0.36	(0.07)	0.34	(0.07)	0.38	(0.07)	0.37	(0.07)	0.37	(0.07)
Cov (level, slope)	0*		0*		0*		0*		0*
	OR	95% CI	OR	95% CI	OR	95% CI	OR	95% CI	OR	95% CI
Missing 2005 ON
N of drugs 2004	na		1.07	1.00, 1.14	2.23	1.31, 3.77	na		1.96	1.07, 3.59
N of drugs 2005	na		na		0.39	0.21, 0.74	1.05	0.98, 1.13	0.45	0.21, 0.95
Age	na		na		na		na		1.13	1.06, 1.20
Sex	na		na		na		na		0.78	0.39, 1.54
Missing 2006 ON
N of drugs 2005	na		1.16	1.09, 1.24	1.20	1.00, 1.45	na		1.14	0.98, 1.33
N of drugs 2006	na		na		0.96	0.77, 1.19	1.18	1.10, 1.26	0.99	0.83, 1.18
Age	na		na		na		na		1.14	1.09, 1.20
Sex	na		na		na		na		0.87	0.45, 1.68
Missing 2007 ON
N of drugs 2006	na		1.15	1.08, 1.24	1.03	0.82, 1.28	na		1.09	0.87, 1.38
N of drugs 2007	na		na		1.15	0.91, 1.46	1.19	1.10, 1.29	1.07	0.82, 1.38
Age	na		na		na		na		1.10	1.03, 1.17
Sex	na		na		na		na		0.54	0.28, 1.05
Number of free parameters	10		16		19		16		25
Log likelihood	−6,273.16		−6,849.70		−6,844.12		−6,854.88		−6,817.19
Scaling correction factor	1.709		1.431		1.451		1.418		1.383

Note:

* Fixed.

Abbreviations: Est, estimate; SE, standard error; OR, odds ratio; CI, confidence interval; Cov, covariance; GeMS, Geriatric Multidisciplinary Strategy for the Good Care of the Elderly; N, number; na, not applicable; ON, regressed on.

Table

DATA: FILE IS “path to the data”;

VARIABLE:

NAMES ARE (list of variables);

USEVARIABLES ARE MMSE4 MMSE5 MMSE6 MMSE7 d5-d7;

MISSING ARE ALL (99);

CATEGORICAL ARE d5-d7;

DATA MISSING:

NAMES = MMSE4 MMSE5 MMSE6 MMSE7;

TYPE = SDROPOUT;

BINARY = d5-d7;

ANALYSIS:

ESTIMATOR=MLR;

ALGORITHM = INTEGRATION;

INTEGRATION=MONTECARLO;

MODEL:

i BY MMSE4@1 MMSE5@1 MMSE6@1 MMSE7@1;

s BY MMSE4@0 MMSE5*.236 MMSE6*.692 MMSE7@1;

[MMSE4-MMSE7@0];

[i s];

d5 ON MMSE4 MMSE5;

d6 ON MMSE5 MMSE6;

d7 ON MMSE6 MMSE7;

OUTPUT: TECH1 CINTERVAL;