Minimum variance stratification of a finite population

This paper considers the combined problem of allocation and stratification in order to minimise the variance of the expansion estimator of a total, taking into account that the population is finite. The proof of necessary minimum variance conditions utilises the Kuhn-Tucker Theorem. Stratified simple random sampling with non-negligible sampling fractions is an important design in sample surveys. We go beyond limiting assumptions that have often been used in the past, such as that the stratification equals the study variable or that the sampling fractions are small. We discuss what difference the sampling fractions will make for stratification. In particular, in many surveys the sampling fraction equals one for some strata. The main theorem of this paper is applied to two populations with different characteristics, one of them being a business population and the other one a small population of 284 Swedish municipalities. We study empirically the sensitivity of deviations from the optimal solution

Feeding back Information on Ineligibility from Sample Surveys to the Frame

It is usually discovered in the data collection phase of a survey that some units in the sample are ineligible even if the frame information has indicated otherwise. For example, in many business surveys a nonnegligible proportion of the sampled units will have ceased trading since the latest update of the frame. This information may be fed back to the frame and used in subsequent surveys, thereby making forthcoming samples more efficient by avoiding sampling nonnegligible units. We investigate what effect on survey estimation the process of feeding back information on ineligibility may have, and derive an expression for the bias that can occur as a result of feeding back. The focus is on estimation of the total using the common expansion estimator. We obtain an estimator that is nearly unbiased in the presence of feed back. This estimator relies on consistent estimates of the number of eligible and ineligible units in the population being available

Estimating the Undercoverage of a Sampling Frame due to Reporting Delays

One of the imperfections of a sampling frame is miscoverage caused by delays in recording real- life events that change the eligibility of population units. For example, new units generally appear on the frame some time after they came into existence and units that have ceased to exist are not removed from the frame immediately. We provide methodology for predicting the undercoverage due to delays in reporting new units. The approach presented here is novel in a business survey context, and is equally applicable to overcoverage due to delays in reporting the closure of units. As a special case, we also predict the number of new-born units per month. The methodology is applied to the principal business register in the UK, maintained by the Office for National Statistics. <br/

Is there a ‘safe area’ where the nonresponserate has only a modest effect on nonresponsebias despite non-ignorable nonresponse?

Rising nonresponse rates in social surveys makes the issue of nonresponse bias highly contentious. Nonresponse may induce bias and increase data collection costs. We study the relationship between response rate and bias, assuming non-ignorable nonresponse and focusing on estimates of totals or means. We show that there is a ‘safe area’ enclosed by the response rate on the one hand and the correlation between the response propensity and the study variable on the other hand; in this area, 1) the response rate does not greatly affect the nonresponse bias and 2) the nonresponse bias is small

On the Stratification of Highly Skewed Populations (No. 1998:3). R&amp;D Report.

This paper considers the combined problem of allocation and stratification in order to minimise the variance of the expansion estimator of a total, taking into account that the population is finite. The proof of necessary minimum variance conditions utilises the Kuhn-Tucker Theorem. Stratified simple random sampling with non-negligible sampling fractions is an important design in sample surveys. We go beyond limiting assumptions that have often been used in the past, such as that the stratification equals the study variable or that the sampling fractions are small. We discuss what difference the sampling fractions will make for stratification. In particular, in many surveys the sampling fraction equals one for some strata. The main theorem of this article is applied to a business population

Formal sensitivity analysis in observational studies

Objective: The positive effect of antidiabetic medication on cognitive decline has been given some support by, among others, Secnik et al (2021) and Secnik et al (2022). However, as they are observational studies, it is not clear whether the effect is causal. Research design and methods: Using the Swedish Dementia Registry and supplementary Swedish registers/databases, we identified 1,873 patients (4,732 observations) with diagnosis of diabetes and Alzheimer’s disease or mixed-pathology dementia who were followed-up at least once after dementia diagnosis. The association of use of metformin with Mini-Mental State Examination scores in patients with diabetes and dementia was studied in two ways. 1) The difference between the last and the first score for each patient was compared with treatment (use of metformin) and subjected to a new sensitivity analysis. 2) The difference between scores for each patient at the points in time when there was a change in use of metformin (either start of use, or discontinuation of use) was studied. Results: There is an association between cognitive decline and use of metformin. However, any conclusion of a causal relationship is tenuous.  Conclusion: The present study offers no basis for causal conclusions, but given the association, further examination of cognitive effects of metformin is warranted