Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates

Gail, Mitchell H.; Wieand, Sam; Piantadosi, Steven

doi:10.1093/biomet/71.3.431

Cited by 590 publications

(380 citation statements)

References 11 publications

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“…If estimation of a conditional parameter is desired, adjustment can be made in the two-stage model for specific covariates. Estimation of a fully conditional parameter requires complete knowledge of the covariates, although a conditional odds ratio could be estimated by using mathematical formulations of the attenuation of the population to the conditional odds ratio under assumptions about the direction and strength of the unmeasured covariates [54].…”

Section: Choice Of Target Effect Estimatementioning

confidence: 99%

Identifying the odds ratio estimated by a two‐stage instrumental variable analysis with a logistic regression model

Burgess¹

2013

Statistics in Medicine

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Adjustment for an uncorrelated covariate in a logistic regression changes the true value of an odds ratio for a unit increase in a risk factor. Even when there is no variation due to covariates, the odds ratio for a unit increase in a risk factor also depends on the distribution of the risk factor. An instrumental variable can be used to consistently estimate a causal effect in the presence of arbitrary confounding. With a logistic outcome model, we show that the simple ratio or two-stage instrumental variable estimate is consistent for the odds ratio of an increase in the population distribution of the risk factor equal to the change due to a unit increase in the instrument divided by the average change in the risk factor due to the increase in the instrument. This odds ratio is conditional within strata of the instrumental variable, but marginal across all other covariates, and is averaged across the population distribution of the risk factor. Where the proportion of variance in the risk factor explained by the instrument is small, this is similar to the odds ratio from a randomized controlled trial without adjustment for any covariates, where the intervention corresponds to the effect of a change in the population distribution of the risk factor. This implies that the ratio or two-stage instrumental variable method is not biased, as has been suggested, but estimates a different quantity to the conditional odds ratio from an adjusted multiple regression; a quantity which has arguably more relevance to an epidemiologist or a policy-maker, especially in the context of Mendelian randomization.

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Section: Choice Of Target Effect Estimatementioning

confidence: 99%

Identifying the odds ratio estimated by a two‐stage instrumental variable analysis with a logistic regression model

Burgess¹

2013

Statistics in Medicine

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“…The result that holds generally about heterogeneity is that it leads to a downward biased estimate of duration dependence. Gail et al (1984) showed that the unobserved heterogeneity tends to attenuate the estimated coefficients toward zero. On the other hand, standard errors and test statistics are not biased.…”

Section: Cox Modelmentioning

confidence: 99%

Environmental Determinants of Child Mortality in Kenya

Mutunga¹

2011

Health Inequality and Development

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This paper focuses on the determinants of infant and child mortality in Kenya. It specifically examines how infant and child mortality is related to the household's environmental and socio-economic characteristics, such as mother's education, source of drinking water, sanitation facility, type of cooking fuels and access to electricity. A hazard rate framework is used to analyze the determinants of child mortality. Duration models are easily applicable to the problem of child mortality as this class of models straightforwardly accounts for problems like right-censoring, structural modeling and time varying covariates which traditional econometric techniques cannot handle adequately.A household's environmental and socio-economic characteristics are found to have significant impact on child mortality. Policies aimed at achieving the goal of reduced child mortality should be directed on improving the household's environmental and or socio-economic status if this goal is to be realized.

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“…However, their findings were more qualitative, and do not indicate how "important" the covariates need to be; i.e., how adequate the covariates are in explaining the pairing before regression analysis becomes more effective than a matched pairs analysis. Extensive work on the problem of omitted covariates in general linear models has been done by Gail et al (1984Gail et al ( , 1988, in which the covariates are treated as random variables. Many authors have also examined the pros and cons of matching versus regression adjustment, although their comparisons are restricted to the case when the pairing has been fully modelled by the covariates.…”

Section: Introductionmentioning

confidence: 99%

When Does It Pay to Break the Matches for Analysis of a Matched-Pairs Design?

Lynn¹,

McCulloch²

1992

Biometrics

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SUMMARYTwo methods of analyses are compared to estimate the treatment effect of a comparative study where each treated individual is matched with a single control at the design stage. The usual matched pairs analysis accounts for the pairing directly in its model, whereas regression adjustment ignores the matching but instead models the pairing using a set of covariates. For a normal linear model, the estimated treatment effect from the matched pairs analysis (paired t-test) is more efficient. For a Bernoulli logistic model, matched pairs analysis performs better when the sample size was small, but is inferior to logistic regression for large sample sizes.

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Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates

Cited by 590 publications

References 11 publications

Identifying the odds ratio estimated by a two‐stage instrumental variable analysis with a logistic regression model

Identifying the odds ratio estimated by a two‐stage instrumental variable analysis with a logistic regression model

Environmental Determinants of Child Mortality in Kenya

When Does It Pay to Break the Matches for Analysis of a Matched-Pairs Design?

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