Monte Carlo conditioning on a sufficient statistic

Lindqvist, Bo Henry; Taraldsen, Gunnar

doi:10.1093/biomet/92.2.451

Cited by 27 publications

(59 citation statements)

References 15 publications

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“…This means that sample means and sample variances of outcome and covariate for each group in each trial, which is computed by using individual outcome and covariate values from each patient drawn from

f ({italicY}_{miss ‐ IPD} | {italicY}_{normalAD}, \overset{true^}{italicξ}, {italicη}^{([], r)})

, must be equivalent to the corresponding sample means and sample variances in Y AD . This difficulty is associated with some issues on the conditional distribution given sufficient statistics (Cheng, ; Engen and Lillegard, ; Lindqvist and Taraldsen, ). Lindqvist and Taraldsen () suggested a general formula in order to calculate the conditional expectation on the basis of this conditional distribution by Monte Carlo approximation.…”

Section: A New Methods Based On Simulated Ipd (Sipd) For Ad Trialsmentioning

confidence: 99%

“…This difficulty is associated with some issues on the conditional distribution given sufficient statistics (Cheng, ; Engen and Lillegard, ; Lindqvist and Taraldsen, ). Lindqvist and Taraldsen () suggested a general formula in order to calculate the conditional expectation on the basis of this conditional distribution by Monte Carlo approximation. We here brief how the sampling technique by Lindqvist and Taraldsen () draws Y miss ‐ IPD from

f ({italicY}_{miss ‐ IPD} | {italicY}_{normalAD}, \overset{true^}{italicξ}, {italicη}^{([], r)})

.…”

Section: A New Methods Based On Simulated Ipd (Sipd) For Ad Trialsmentioning

confidence: 99%

“…Here,

z_{iT}^{[italicr]}

denotes samples from the conditional normal distribution given sample mean

true {\overset{z}{true}}_{italiciT}

and sample variance

s_{z_{i} italicT}^{2}

. A result by Lindqvist and Taraldsen () outlined in Appendix C allows us to achieve this drawing as follows:

{boldz}_{italiciT}^{([], r)} = \{{\overset{true¯}{italicz}}_{iT} + \frac{{italicu}_{italicij} - {\overset{true¯}{italicu}}_{i}}{s_{ui}} {italics}_{{italicz}_{italici} T} : j \in T\}

where { u ij : j ∈ T } denotes n iT random samples from the standard normal distribution. Also,

true {\overset{u}{true}}_{italici}

and

s_{{italicu}_{italici}}^{2}

are a sample mean and a sample variance for them, respectively.…”

Section: A New Methods Based On Simulated Ipd (Sipd) For Ad Trialsmentioning

confidence: 99%

“…Lindqvist and Taraldsen (2005) suggested a general formula in order to calculate the conditional expectation on the basis of this conditional distribution by Monte Carlo approximation. We here brief how the sampling technique by Lindqvist and Taraldsen (2005)…”

Section: 12mentioning

confidence: 99%

“…This means that, for the ith AD trial, we firstly draw z Lindqvist and Taraldsen (2005) outlined in Appendix C allows us to achieve this drawing as follows:…”

Section: 12mentioning

confidence: 99%

See 4 more Smart Citations

Meta‐analysis of a continuous outcome combining individual patient data and aggregate data: a method based on simulated individual patient data

Yamaguchi

Sakamoto

Goto³

et al. 2014

Research Synthesis Methods

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When some trials provide individual patient data (IPD) and the others provide only aggregate data (AD), meta-analysis methods for combining IPD and AD are required. We propose a method that reconstructs the missing IPD for AD trials by a Bayesian sampling procedure and then applies an IPD meta-analysis model to the mixture of simulated IPD and collected IPD. The method is applicable when a treatment effect can be assumed fixed across trials. We focus on situations of a single continuous outcome and covariate and aim to estimate treatment-covariate interactions separated into within-trial and across-trial effect. An illustration with hypertension data which has similar mean covariates across trials indicates that the method substantially reduces mean square error of the pooled within-trial interaction estimate in comparison with existing approaches. A simulation study supposing there exists one IPD trial and nine AD trials suggests that the method has suitable type I error rate and approximately zero bias as long as the available IPD contains at least 10% of total patients, where the average gain in mean square error is up to about 40%. However, the method is currently restricted by the fixed effect assumption, and extension to random effects to allow heterogeneity is required.

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f ({italicY}_{miss ‐ IPD} | {italicY}_{normalAD}, \overset{true^}{italicξ}, {italicη}^{([], r)})

Section: A New Methods Based On Simulated Ipd (Sipd) For Ad Trialsmentioning

confidence: 99%

f ({italicY}_{miss ‐ IPD} | {italicY}_{normalAD}, \overset{true^}{italicξ}, {italicη}^{([], r)})

.…”

Section: A New Methods Based On Simulated Ipd (Sipd) For Ad Trialsmentioning

confidence: 99%

“…Here,

z_{iT}^{[italicr]}

denotes samples from the conditional normal distribution given sample mean

true {\overset{z}{true}}_{italiciT}

and sample variance

s_{z_{i} italicT}^{2}

. A result by Lindqvist and Taraldsen () outlined in Appendix C allows us to achieve this drawing as follows:

{boldz}_{italiciT}^{([], r)} = \{{\overset{true¯}{italicz}}_{iT} + \frac{{italicu}_{italicij} - {\overset{true¯}{italicu}}_{i}}{s_{ui}} {italics}_{{italicz}_{italici} T} : j \in T\}

where { u ij : j ∈ T } denotes n iT random samples from the standard normal distribution. Also,

true {\overset{u}{true}}_{italici}

and

s_{{italicu}_{italici}}^{2}

are a sample mean and a sample variance for them, respectively.…”

Section: A New Methods Based On Simulated Ipd (Sipd) For Ad Trialsmentioning

confidence: 99%

Section: 12mentioning

confidence: 99%

“…This means that, for the ith AD trial, we firstly draw z Lindqvist and Taraldsen (2005) outlined in Appendix C allows us to achieve this drawing as follows:…”

Section: 12mentioning

confidence: 99%

See 3 more Smart Citations

Meta‐analysis of a continuous outcome combining individual patient data and aggregate data: a method based on simulated individual patient data

Yamaguchi

Sakamoto

Goto³

et al. 2014

Research Synthesis Methods

View full text Add to dashboard Cite

show abstract

Conditional Inference in Parametric Models

Broniatowski¹,

Caron²

2013

Statistical Models and Methods for Reliability and Survival Analysis

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This paper presents a new approach to conditional inference, based on the simulation of samples conditioned by a statistics of the data. Also an explicit expression for the approximation of the conditional likelihood of long runs of the sample given the observed statistics is provided. It is shown that when the conditioning statistics is sufficient for a given parameter, the approximating density is still invariant with respect to the parameter. A new Rao-Blackwellisation procedure is proposed and simulation shows that Lehmann Scheffé Theorem is valid for this approximation. Conditional inference for exponential families with nuisance parameter is also studied, leading to Monte carlo tests. Finally the estimation of the parameter of interest through conditional likelihood is considered. Comparison with the parametric bootstrap method is discussed.

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Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

Lindqvist

Rannestad

2010

Appl. Stochastic Models Bus. Ind.

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Nonhomogeneous Poisson processes (NHPPs) are often used to model failure data from repairable systems, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for parametric NHPPs. The idea is to use conditional tests given a sufficient statistic under the null hypothesis model. The tests are performed by simulating conditional samples given the sufficient statistic. Algorithms are presented for testing goodness-offit for the power law and the log-linear law NHPP models. It is noted that while exact algorithms for the power law case are well known in the literature, the availability of such algorithms for the log-linear case seems to be less known. A data example, as well as simulations, are considered.

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Monte Carlo conditioning on a sufficient statistic

Cited by 27 publications

References 15 publications

Meta‐analysis of a continuous outcome combining individual patient data and aggregate data: a method based on simulated individual patient data

Meta‐analysis of a continuous outcome combining individual patient data and aggregate data: a method based on simulated individual patient data

Conditional Inference in Parametric Models

Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes

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