PHLT 8331 Week 3 Hypothesis Statement Paper Example

Hypotheses That Commit: Three Null and Alternative Pairs for a Composite Anticoagulation Registry, Each Naming Its Parameter, Direction and Significance Level Before Any Output Exists

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Walden University

PHLT 8331: Fundamentals of Biostatistics

Instructor Name

Month Day, Year

Hypotheses That Commit: Three Null and Alternative Pairs for a Composite Anticoagulation Registry, Each Naming Its Parameter, Direction and Significance Level Before Any Output Exists

Why Commit in Advance

A hypothesis written after the output is examined can always be made to fit it, and a result that fits a hypothesis designed to fit it shows nothing. This paper writes three pairs of hypotheses for questions the composite anticoagulation registry can answer, each stated in words and symbols, each naming the population parameter it concerns and each fixing the direction of the alternative and the significance level before any test is run. Wasserstein and Lazar (2016) warn that a p-value is neither the chance that a hypothesis holds nor a gauge of how big an effect is, and stating hypotheses clearly in advance is a first step toward interpreting p-values correctly.

Question 1: Did Control Change After Moving to Pharmacist Management?

For patients switched to the pharmacist service, did time in therapeutic range differ between the half year preceding the switch and the half year following it?

The Parameter

The parameter is the mean of the within-patient differences in the source population, written as the population mean difference, mu sub d, with each difference defined as time in range after the move minus time in range before.

The Pair

Null hypothesis: the population mean difference is zero; time in therapeutic range did not change on average. In symbols, mu sub d equals 0.

Alternative hypothesis: the population mean difference is not zero. In symbols, mu sub d does not equal 0.

Direction and Level

The alternative is two-sided. A one-sided alternative, predicting improvement only, might seem natural because pharmacist services have been associated with better control elsewhere (Manzoor et al., 2017). But a decline would also matter to the clinics, and a one-sided test would treat a large decline as no different from no change. The significance level is fixed at .05.

Question 2: Do Pharmacist and Physician Clinics Differ?

Is the mean time in therapeutic range in the most recent six months different between patients at the two clinics with pharmacist management and patients at the clinic with physician management?

The Parameter

The parameter is the difference between two population means, mu sub 1 minus mu sub 2, where mu sub 1 is the mean time in range among patients at pharmacist-managed clinics and mu sub 2 among patients at the physician-managed clinic.

The Pair

Null hypothesis: the two population means are equal; mu sub 1 minus mu sub 2 equals 0.

Alternative hypothesis: the two population means differ; mu sub 1 minus mu sub 2 does not equal 0.

Direction and Level

Two-sided, at .05, for the same reason as the first question. The hypothesis concerns clinics, not management style alone, since the clinics differ in other ways; the paper notes that a difference, if found, could not be attributed to management without further work.

Question 3: Does Good Control Depend on Clinic?

Is the share of well-controlled patients (65% or more of days inside the target INR) unrelated to which clinic they attend?

The Parameter

Here the parameters are the three population proportions with good control, one for each clinic, written p sub A, p sub B and p sub C.

The Pair

Null hypothesis: good control is independent of clinic; the three proportions are equal.

Alternative hypothesis: good control is not independent of clinic; at least one proportion differs from the others.

Direction and Level

A test of independence has no direction; it asks whether any difference exists. The level is .05.

What Failing to Reject Would Mean

For each question, failing to reject the null would not show that the null is true. It would show only that the data were compatible with no difference, within the precision the sample allows. Altman and Bland (1995) make the point that a nonsignificant result is not proof that no effect exists. Each later analysis will report a confidence interval alongside its test, so readers can see the range of differences the data are compatible with, including differences large enough to matter.

Why .05?

The level of .05 follows convention, and convention is a weak reason. It is chosen here because the questions are exploratory and the consequences of a false positive, further study of a pharmacist service, are modest. A decision with larger consequences, such as closing a clinic's physician service, would justify a stricter level or a decision based on effect size and uncertainty rather than a single threshold. Fixing the level now, rather than after seeing the p-value, keeps the choice from being shaped by the result.

What Would Count as Evidence Against Each Null

Stating hypotheses well also means saying in advance what result would lead to rejecting the null. For the first question, a mean difference far enough from zero, relative to its standard error, that a two-sided p-value falls below .05 would count, whether the difference is positive or negative. For the second, the same rule applies to the difference between clinic means. For the third, a chi-square statistic large enough to give p below .05 would count, but it would not say which clinic differs; that would need a follow-up comparison, which should itself be specified now rather than chosen after seeing which clinic looks different. Writing these decision rules down closes off the temptation to reinterpret a borderline result after the fact. It also makes plain that a decision at the .05 level is only one input: each analysis will report an estimate and an interval, and those will carry most of the interpretation. The tests serve the estimates, not the reverse.

Summary

Table 1

The Three Hypothesis Pairs

Note. All hypotheses were recorded before any test was run on the composite registry.

References

Altman, D. G., & Bland, J. M. (1995). Statistics notes: Absence of evidence is not evidence of absence. BMJ, 311(7003), 485. https://doi.org/10.1136/bmj.311.7003.485

Manzoor, B. S., Cheng, W.-H., Lee, J. C., Uppuluri, E. M., & Nutescu, E. A. (2017). Quality of pharmacist-managed anticoagulation therapy in long-term ambulatory settings: A systematic review. Annals of Pharmacotherapy, 51(12), 1122-1137. https://doi.org/10.1177/1060028017721241

Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108