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Ton J. Cleophas and Aeilko H. ZwindermanSPSS for Starters and 2nd Levelers10.1007/978-3-319-20600-4_50

50. Monte Carlo Tests for Binary Data (139 Physicians and 55 Patients)

Ton J. Cleophas^{1, 2} and Aeilko H. Zwinderman^2,
3

(1)

Department Medicine, Albert Schweitzer Hospital, Dordrecht, The Netherlands

(2)

European College Pharmaceutical Medicine, Lyon, France

(3)

Department Biostatistics, Academic Medical Center, Amsterdam, The Netherlands

1 General Purpose

Monte Carlo methods allows you to examine complex data more easily than advanced mathematics like integrals and matrix algebra. It uses random numbers from your own study rather than assumed Gaussian curves. Monte Carlo analyses of continuous outcome data are reviewed in the Chap. 27. In this chapter we will review Monte Carlo analyses for paired and unpaired binary data.

2 Schematic Overview of Type of Data File, Paired Data

3 Primary Scientific Question, Paired Data

For paired data McNemar tests is adequate (Chap. 41). Does Monte Carlo analysis of the same data provide better sensitivity of testing.

4 Data Example, Paired Data

In a study of 139 general practitioners the primary scientific question was, is there a significant difference between the numbers of practitioners who give lifestyle advise in the periods before and after postgraduate education.

Lifestyle advise-1	Lifestyle advise-2	Age
,00	,00	89,00
,00	,00	78,00
,00	,00	79,00
,00	,00	76,00
,00	,00	87,00
,00	,00	84,00
,00	,00	84,00
,00	,00	69,00
,00	,00	77,00
,00	,00	79,00

0 = no, 1 = yes

The first 10 physicians of the data file is given above. The entire data file is in extras.springer.com, and is entitled “chapter41pairedbinary”.

5 Analysis: Monte Carlo, Paired Data

For analysis the statistical model Two Related Samples in the module Nonparametric Tests is required.

Command:

Analyze....Nonparametric....Two Related Samples....Test Pairs....Pair 1....Variable 1: enter lifestyleadvise after....Variable 2: enter lifestytleadvise before....mark McNemar....click Exact....click Monte Carlo....set Confidence Intervals: 99 %....set Number of Samples: 10000....click Continue…click OK.

lifestyleadvise before & lifestyleadvise after

Lifestyleadvise before	Lifestyleadvise after
Lifestyleadvise before	,00	1,00
,00	65	28
1,00	12	34

Test Statistics^a,b

			Lifestyle after 1 year – lifestyle
Z			−2,530^c
Asymp. Sig. (2-tailed)			,011
Monte Carlo Sig. (2-tailed)	Sig.		,016
	95 % Confidence Interval	Lower bound	,008
		Upper bound	,024
Monte Carlo Sig. (1-tailed)		Sig.	,010
	95 % Confidence Interval	Lower bound	,004
		Upper bound	,016

^aWilcoxon Signed Ranks Test

^bBased on 1000 sampled tables with starting seed 2000000

^cBased on negative ranks

The above table is in the output. The two sided level of statistical significance is 0,016. This is slightly smaller than the p-value produced by the nonparametric Mc Nemar test (Chap. 41), p = 0,018, and, so, a slightly better fit for the data was obtained by the Monte Carlo method.

6 Schematic Overview of Type of Data File, Unpaired Data

7 Primary Scientific Question, Unpaired Data

For unpaired binary data Pearson chi-square is adequate. Is Monte Carlo testing better sensitive for the analysis of such data.

8 Data Example, Unpaired Data

In 55 patients the effect of the hospital department on the risk of falling out of bed was assessed. The entire data file is in “chapter35unpairedbinary”, and is in extras.springer.com.

Fall out of bed	Department
1 = yes, 0 = no	0 = surgery, 1 = internal medicine
1,00	,00
1,00	,00
1,00	,00
1,00	,00
1,00	,00
1,00	,00
1,00	,00
1,00	,00
1,00	,00
1,00	,00

9 Data Analysis, Monte Carlo, Unpaired Data

For analysis the statistical model Chi-square in the module Nonparametric Tests is required.

Command:

Analyze….Nonparametric tests….Chi-square….Test variable list: enter department and fall out of bed….click “Exact”….Click: Monte Carlo method….set Confidence Interval, e.g., 99 %, and set Numbers of Samples, e.g., 10 000….click Continue….OK.

Test statistics

			Department	Fall out of bed
Chi-Square			4,091^a	,455^a
df			1	1
Asymp.Sig.			,043	,500
Monte Carlo Sig.	Sig.		,064^b	,595^b
	99 % confidence interval	Lower bound	,057	,582
		Upper bound	,070	,608

^a0 cells (,0 %) have expected frequencies less than 5. The minimum expected cell frequency is 27,5

^bBased on 10000 sampled tables with starting seed 926214481

The Monte Carlo analysis provided a larger p -value than did the Pearson chi-square test (Chap. 35) with p-values of respectively 0,064 and 0,021.

10 Conclusion

Monte Carlo methods allow you to examine complex data more easily and more rapidly than advanced mathematics like integrals and matrix algebra. It uses random numbers from your own study. Often, but not always, better p-values are produced.

11 Note

More background, theoretical, and mathematical information of Monte Carlo methods for data analysis is given in Statistics applied to clinical studies 5th edition, Chap. 57, Springer Heidelberg Germany, 2012, from the same authors.

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