Small-Sample Bias of Point Estimators of the Odds Ratio from Matched Sets

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample bias and mean squared error. In general, these results entail a numerical integration of derivatives of the joint moment generating function of two quadratic forms in normal variables. The computation of these integrals is quite involved. However, we take advantage of the Laplace approximations to the bias and mean squared error, which substantially reduce the computational burden, as they yield relatively simple analytic expressions. We obtain analytic formulae for approximating the effect of filtering on the finite sample bias and mean squared error. We evaluate the adequacy of the approximations by comparison with Monte Carlo simulations, using the Census X-11 filter as a specific example

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Small sample bias reduction of the first-order autoregressive parameter least-squares estimator

IEEE Transactions on Automatic Control ◽

10.1109/tac.1985.1104081 ◽

1985 ◽

Vol 30 (9) ◽

pp. 893-895 ◽

Cited By ~ 1

Author(s):

Z. Nahorski ◽

J. Studzinski

Keyword(s):

Least Squares ◽

Bias Reduction ◽

Small Sample ◽

Least Squares Estimator ◽

First Order ◽

Sample Bias ◽

Autoregressive Parameter

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Analysis of multicenter clinical trials with very low event rates

Trials ◽

10.1186/s13063-020-04801-5 ◽

2020 ◽

Vol 21 (1) ◽

Author(s):

Jiyu Kim ◽

Andrea B. Troxel ◽

Scott D. Halpern ◽

Kevin G. Volpp ◽

Brennan C. Kahan ◽

...

Keyword(s):

Error Rate ◽

Odds Ratio ◽

Type I Error ◽

Event Rate ◽

Small Sample ◽

Type I ◽

Type I Error Rate ◽

Random Intercept ◽

Small Sample Correction ◽

Outcome Event

Abstract Introduction In a five-arm randomized clinical trial (RCT) with stratified randomization across 54 sites, we encountered low primary outcome event proportions, resulting in multiple sites with zero events either overall or in one or more study arms. In this paper, we systematically evaluated different statistical methods of accounting for center in settings with low outcome event proportions. Methods We conducted a simulation study and a reanalysis of a completed RCT to compare five popular methods of estimating an odds ratio for multicenter trials with stratified randomization by center: (i) no center adjustment, (ii) random intercept model, (iii) Mantel–Haenszel model, (iv) generalized estimating equation (GEE) with an exchangeable correlation structure, and (v) GEE with small sample correction (GEE-small sample correction). We varied the number of total participants (200, 500, 1000, 5000), number of centers (5, 50, 100), control group outcome percentage (2%, 5%, 10%), true odds ratio (1, > 1), intra-class correlation coefficient (ICC) (0.025, 0.075), and distribution of participants across the centers (balanced, skewed). Results Mantel–Haenszel methods generally performed poorly in terms of power and bias and led to the exclusion of participants from the analysis because some centers had no events. Failure to account for center in the analysis generally led to lower power and type I error rates than other methods, particularly with ICC = 0.075. GEE had an inflated type I error rate except in some settings with a large number of centers. GEE-small sample correction maintained the type I error rate at the nominal level but suffered from reduced power and convergence issues in some settings when the number of centers was small. Random intercept models generally performed well in most scenarios, except with a low event rate (i.e., 2% scenario) and small total sample size (n ≤ 500), when all methods had issues. Discussion Random intercept models generally performed best across most scenarios. GEE-small sample correction performed well when the number of centers was large. We do not recommend the use of Mantel–Haenszel, GEE, or models that do not account for center. When the expected event rate is low, we suggest that the statistical analysis plan specify an alternative method in the case of non-convergence of the primary method.

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