Impact of local mask mandates upon COVID-19 case rates in Oklahoma.

Use of face coverings has been shown to reduce transmission of SARS-CoV-2. Despite encouragements from the CDC and other public health entities, resistance to usage of masks remains, forcing government entities to create mandates to compel use. The state of Oklahoma did not create a state-wide mask mandate, but numerous municipalities within the state did. This study compares case rates in communities with mandates to those without mandates, at the same time and in the same state (thus keeping other mitigation approaches similar). Diagnosed cases of COVID-19 were extracted from the Oklahoma State Department of Health reportable disease database. Daily case rates were established based upon listed city of residence. The daily case rate difference between each locality with a mask mandate were compared to rates for the portions of the state without a mandate. All differences were then set to a d0 point of reference (date of mandate implementation). Piecewise linear regression analysis of the difference in SARS-CoV-2 infection rates between mandated and non-mandated populations before and after adoption of mask mandates was then done. Prior to adopting mask mandates, those municipalities that eventually adopted mandates had higher transmission rates than the rest of the state, with the mean case rate difference per 100,000 people increasing by 0.32 cases per day (slope of difference = 0.32; 95% CI 0.13 to 0.51). For the post-mandate time period, the differences are decreasing (slope of -0.24; 95% CI -0.32 to -0.15). The pre- and post- mandate slopes differed significantly (p<0.001). The change in slope direction (-0.59; 95% CI -0.80 to -0.37) shows a move toward reconvergence in new case diagnoses between the two populations. Compared to rates in communities without mask mandates, transmission rates of SARS-CoV-2 slowed notably in those communities that adopted a mask mandate. This study suggests that government mandates may play a role in reducing transmission of SARS-CoV-2, and other infectious respiratory conditions.

Using the Tukey-Kramer omnibus test in the Hayter-Fisher procedure.

Using Tukey-Kramer versus the ANOVA F-test as the omnibus test of the Hayter-Fisher procedure for comparing all pairs of normally distributed means, when sample sizes are unequal, is investigated. Simulation results suggest that using Tukey-Kramer leads to as much or more any-pairs power compared to using the F-test for certain patterns of mean differences, and equivalent per-pair and all-pairs power for all cases. Furthermore, using Tukey-Kramer results in a consonant test procedure, where there cannot be disagreement between the results of the omnibus test and the subsequent pairwise tests. The results suggest that when sample sizes are unequal, Tukey-Kramer may be preferred over the F-test as the omnibus test for the Hayter-Fisher procedure.

Reformulating the hazard ratio to enhance communication with clinical investigators.

BACKGROUND: Clinical trials with time to event outcomes are often designed utilizing the Cox [1] proportional hazard model with a hazard ratio parameter Delta. PURPOSE: The purpose of this article is to demonstrate that a Cox proportional hazard model with a hazard ratio parameter is equivalent to a Cox proportional hazard model with a parameter equal to the probability that a patient given one treatment will have an event earlier than if the same patient were given a different treatment. This probability will subsequently be referred to as theta. Clinically interesting differences between the treatment arms are easier for researchers to quantify in terms of in situations where they have a difficult time with the hazard ratio, allowing better communication between the statistician and the researcher. METHODS: The problem and its solution are demonstrated mathematically. The utility of the Cox proportional hazard model in terms of theta is illustrated through a Lymphoma clinical trial example. RESULTS: The Cox proportional hazard model with parameter theta is shown to be equivalent to the Cox proportional hazard model with a hazard ratio parameter Delta. A table of typical hazard ratios Delta is presented with their equivalent theta values. In the appendix the mathematical derivations are developed and an unbiased estimate of theta is provided using Gehan's [2] generalization of the Wilcoxon statistic. LIMITATIONS: The equivalence of the Cox proportional hazard model in terms of the probability theta and the hazard ratio Delta is established only for continuous failure times with a single binary covariate. Conditions under which approximate equivalence holds with multiple covariates are discussed in the Appendix. CONCLUSIONS: The probability theta provides a natural parameterization for the Cox proportional hazard model, affords a tool to conceptualize treatment differences, and provides a method to improve communication between statisticians and researchers.