No abstract

Statistical analysis usually treats all observations as equally important. In some circumstances, however, it is appropriate to vary the weight given to different observations. Well known examples are in meta-analysis, where the inverse variance (precision) weight given to each contributing study varies, and in the analysis of clustered data. 1 Differential weighting is also used when different parts of the population are sampled with unequal probabilities of selection. Two examples of intentional unbalanced sampling are:1.Surveys with unequal probabilities of selection-In a national survey of hypertension prevalence, certain groups with relatively rare characteristics (such as people aged ≥65 years) were oversampled to improve the precision of estimates for those groups. 2.Two-phase prevalence studies-In the first phase of a two-phase prevalence study of mental health status, the sampled patients completed a short screening questionnaire. In the second phase, a subsample was selected for a definitive diagnostic test with oversampling of the screen-positive cases to ensure precise estimates for diagnostic prevalence. 3In such cases the ordinary unweighted sample quantities, such as means or proportions, are likely to be biased estimates of their corresponding population quantities. This "selection bias" can be eliminated by performing a weighted estimation, giving each individual's data a weight inversely proportional to their probability of selection. Intuitively, the weighting is used to deflate the weight for those individuals who are oversampled. The weighted analysis can be thought of as creating a study with no differential selection.Inverse probability weighting can also be used when individuals vary in their probability of having missing information. Two contexts where there may be unintentional unbalanced selection are:3.Studies with missing outcome data-In surveys such as that mentioned in example 1, the response rates will be affected by availability or willingness to participate. Likewise in a cohort study of the effect of obesity on hypertension, some individuals are censored due to loss to follow-up (such as emigration) or competing risks (such as death from other causes). 4 In each case the amount of missing information will vary across subgroups. 4.Randomised trials with crossing over from one arm to theother-In a randomised trial 8010 postmenopausal women with early breast cancer were assigned to tamoxifen (n=2459) or letrozole (n=2463) for five years or to sequential treatment with two years of one of these agents followed by three years of the other. There was a selective crossover to letrozole of 619 patients in the tamoxifen arm after significant benefit was reported for letrozole compared with tamoxifen during the study. These 619 women may be artificially censored at the time they crossed over for analysis. 5In these situations, missing outcomes are unlikely to happen at random so that estimates will be biased. While the selection probabilities in examples 1 and 2 are known, the response o...

Penalization is a very general method of stabilizing or regularizing estimates, which has both frequentist and Bayesian rationales. We consider some questions that arise when considering alternative penalties for logistic regression and related models. The most widely programmed penalty appears to be the Firth small-sample bias-reduction method (albeit with small differences among implementations and the results they provide), which corresponds to using the log density of the Jeffreys invariant prior distribution as a penalty function. The latter representation raises some serious contextual objections to the Firth reduction, which also apply to alternative penalties based on t-distributions (including Cauchy priors). Taking simplicity of implementation and interpretation as our chief criteria, we propose that the log-F(1,1) prior provides a better default penalty than other proposals. Penalization based on more general log-F priors is trivial to implement and facilitates mean-squared error reduction and sensitivity analyses of penalty strength by varying the number of prior degrees of freedom. We caution however against penalization of intercepts, which are unduly sensitive to covariate coding and design idiosyncrasies.

Misconceptions about the impact of case-control matching remain common. We discuss several subtle problems associated with matched case-control studies that do not arise or are minor in matched cohort studies: (1) matching, even for non-confounders, can create selection bias; (2) matching distorts dose-response relations between matching variables and the outcome; (3) unbiased estimation requires accounting for the actual matching protocol as well as for any residual confounding effects; (4) for efficiency, identically matched groups should be collapsed; (5) matching may harm precision and power; (6) matched analyses may suffer from sparse-data bias, even when using basic sparse-data methods. These problems support advice to limit case-control matching to a few strong well-measured confounders, which would devolve to no matching if no such confounders are measured. On the positive side, odds ratio modification by matched variables can be assessed in matched case-control studies without further data, and when one knows either the distribution of the matching factors or their relation to the outcome in the source population, one can estimate and study patterns in absolute rates. Throughout, we emphasize distinctions from the more intuitive impacts of cohort matching.

We use causal diagrams to illustrate the consequences of matching and the appropriate handling of matched variables in cohort and case-control studies. The matching process generally forces certain variables to be independent despite their being connected in the causal diagram, a phenomenon known as unfaithfulness. We show how causal diagrams can be used to visualize many previous results about matched studies. Cohort matching can prevent confounding by the matched variables, but censoring or other missing data and further adjustment may necessitate control of matching variables. Case-control matching generally does not prevent confounding by the matched variables, and control of matching variables may be necessary even if those were not confounders initially. Matching on variables that are affected by the exposure and the outcome, or intermediates between the exposure and the outcome, will ordinarily produce irremediable bias.

While most of the existing literatures regarding female athletes' LBP have focused on particular sports with specific low back demands (such as skiing and rowing), many other sports have not been studied very well in this regard. Investigating LBP prevalence and related factors in other types of sports, such as combat sports, badminton and shooting, can help us better understand the prevalence of low back pain and provide us with necessary insight to take effective steps towards its prevention in athletes.

Supplemental use of omega-3 fatty acids decreases depressive symptoms in hemodialysis patients apart from their anti-inflammatory effects.

On base of our results, it can be found that in short term lumbopelvic belt and information in treatment of pregnant women with pelvic girdle pain is superior to exercise plus information or information alone.